\documentclass[fleqn]{beamer}
%\documentclass[handout]{beamer}
%\usepackage{pgfpages}
%\pgfpagelayout{2 on 1}[letterpaper, border shrink=5mm]

\mode<handout>{\setbeamercolor{background canvas}{bg=black!3}}

\usepackage{epstopdf}


%% Jose Antonio Abell Mena provided this for DSL descriptions
% (used in a file _Chapter_SoftwareHardware_Domain_Specific_Language_English.tex
% This is added for listing FEI DSL
%   since   he   customized   it,   it   needs   to   be   changed   (linked  to
% /usr/share/texmf/tex/latex/misc)
%\usepackage{myListings}
\input{essi_listings_options.tex}


 
\usepackage[absolute,overlay]{textpos}




 
\usepackage{threeparttable}

%\usepackage{MnSymbol}%
% for smileys
\usepackage{wasysym}%
\usepackage{multirow}
% for subfloat figures:
\usepackage{subfig}
\usepackage{tabularx}
%used for truncated section title in headers
\usepackage[breakall]{truncate}
%\usepackage{caption}


\usepackage{ulem}
\usepackage{amsmath}
\usepackage{bm}
\usepackage{IEEEtrantools}
\usepackage{setspace}
\usepackage{scalerel}


      
\usepackage{multimedia}

% for inclusion of other PDF pages, in this case Frank's presentation
\usepackage{pdfpages}

%This is a macro to  convert eps to pdf files on the fly.
% make sure figure syntax uses graphicx syntax NOT epsfig syntax
%from http://mailman.mit.edu/pipermail/macpartners/2005-January/000780.html
%
% \ifx\pdfoutput\undefined
% % we are running LaTeX, not pdflatex
% \usepackage{graphicx}
% \else
% % we are running pdflatex, so convert .pdf files to .pdf
% \usepackage[pdftex]{graphicx}
% \usepackage{epstopdf}
% \fi
% %*****************************************


%% ovo je za cirilicu
\input vuk.def
\newfont{\cyr}{wncyr10 scaled 1000 }
\newfont{\cyb}{wncyb10 scaled 1000 }
\newfont{\cyi}{wncyi10 scaled 1000 }
\newfont{\cysc}{wncysc10 scaled 1000 }
\newfont{\cyss}{wncyss10 scaled 1200 }
\newfont{\romjba}{cmss10 scaled 1000}
\newfont{\cyrjbnaslov}{wncyss10 scaled 1400 }



% % for not showing eq numbers unless eq is references
% \usepackage[fleqn,tbtags]{mathtools}
% \mathtoolsset{
%   showonlyrefs
%   }

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FEI  LOGO definition
\newcommand{\FEI}
{{\sf \uppercase{F}\kern-0.20em\uppercase{E}\kern-0.20em\uppercase{I}}}

% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % % ovo je za cirilicu
% % \input vuk.def
% % %\newfont{\cyr}{wncyr10 scaled 1200}
% % %\newfont{\cyrimena}{wncyb10 scaled 1800}
% % %\newfont{\cyrnaslov}{wncyb10 scaled 2600}
% % %\newfont{\cyrpodnaslov}{wncyr10 scaled 1400}
%
% \newfont{\cyr}{wncyss10 scaled 1200}
% \newfont{\cyrimena}{wncyss10 scaled 2000}
% \newfont{\cyrnaslov}{wncyss10 scaled 2800}
% \newfont{\cyrpodnaslov}{wncyss10 scaled 1400}
%
% \newfont{\cyn}{wncyss10 scaled 2200}
% %% JB sig
% \newfont{\cyrjb}{wncyr10 scaled 600}
% \newcommand{\JB}
% {{\cyrjb \lower0.50ex\hbox{\uppercase{J}}\kern-.58em\hbox{\uppercase{B}}}}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\setbeamertemplate{navigation symbols}{}
\mode<presentation>
{
%  \usetheme{Marburg} % ima naslov i sadrzaj sa desne strane
%  \usetheme{Hannover} % ima naslov i sadrzaj sa leve strane
%  \usetheme{Singapore} % ima sadrzaj i tackice gore
%  \usetheme{Antibes}  % ima sadrzaj gore i kao graf ...
%  \usetheme{Berkeley} % ima sadrzaj desno
%  \usetheme{Berlin} % ima sadrzaj gore i tackice
%  \usetheme{Goettingen} % ima sadrzxaj za desne strane
%  \usetheme{Montpellier} % ima graf sadrzaj gore
%  \usetheme{Warsaw}
%  \usetheme{Warsaw}
  \usetheme{Dresden}
    \usecolortheme[RGB={20,0,128}]{structure}

% or ...

  \setbeamercovered{transparent}


%  \setbeamercovered{transparent}
% or whatever (possibly just delete it)
%  \usecolortheme{albatross} % teget sa svetlim slovima
%  \usecolortheme{beetle} % siva pozadina (vrh plav)
  \usecolortheme{seagull} % sivo
%%%%%%%
%  \usecolortheme{BorisJeremic}
%%%%%%%
%  \usecolortheme{rose}
%   \usefonttheme[onlylarge]{structuresmallcapsserif}
%   \usefonttheme{structuresmallcapsserif}
}

\definecolor{mycolor}{rgb}{0,0.08,0.45}%


\usepackage[greek,english]{babel}


\usepackage{amsmath}
\usepackage{mathrsfs}
\usepackage{amsfonts}

\newcommand{\ud}{{\rm d}}

% % from  https://tex.stackexchange.com/questions/3676/too-many-math-alphabets-error
% % to fix latex problem?
% \newcommand\hmmax{0}
% \newcommand\bmmax{0}


\usepackage{array}



%%%%  HYPERREF  HYPERREF  HYPERREF  HYPERREF  HYPERREF
%%%%  HYPERREF  HYPERREF  HYPERREF  HYPERREF  HYPERREF
\definecolor{webgreen}{rgb}{0, 0.35, 0} % less intense green
\definecolor{webblue}{rgb}{0, 0, 0.50} % less intense blue
\definecolor{webred}{rgb}{0.35, 0, 0} % less intense red
%\usepackage[colorlinks=true,linkcolor=webblue,citecolor=webred,urlcolor=webgreen]{hyperref}


\usepackage{hyperref}
\hypersetup{
  pdfmenubar=true,
  pdftoolbar=true,
  pdfpagemode={None}
             colorlinks=true,
             linkcolor=webblue,
             citecolor=webblue,
             urlcolor=webblue,
}
% \usepackage[pdfauthor={Boris Jeremic},
%             colorlinks=true,
%             linkcolor=webblue,
%             citecolor=webblue,
%             urlcolor=webblue,
%             linktocpage,
%             pdftex]{hyperref}


\usepackage{pause}
% or whatever
%\usepackage{html}
%\usepackage{url}

\usepackage[latin1]{inputenc}
% or whatever
\usepackage{times}
\usepackage[T1]{fontenc}
% Or whatever. Note that the encoding and the font should match. If T1
% does not look nice, try deleting the line with the fontenc.



%      Site Specific Dynamics of Structures: 
%From Seismic Source to 
%the Safety of Occupants and Content


\title[Real-ESSI]
        {Realistic Modeling and Simulation of \\
         Earthquakes, Soil, Structures and their Interaction}


%\subtitle
%{Include Only If Paper Has a Subtitle}

%\author[Author, Another] % (optional, use only with lots of authors)
%{F.~Author\inst{1} \and S.~Another\inst{2}}
% - Give the names in the same order as the appear in the paper.
% - Use the \inst{?} command only if the authors have different
%   affiliation.
\pgfdeclareimage[height=0.2cm]{university-logo}{/home/jeremic/BG/amblemi/ucdavis_logo_blue_sm}
\pgfdeclareimage[height=0.7cm]{lbnl-logo}{/home/jeremic/BG/amblemi/lbnl-logo}


\author[Jeremi{\'c} et al.] % (optional, use only with lots of authors)
%{Boris~Jeremi{\'c}}
{Boris Jeremi{\'c}
}

%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
%\institute[\pgfuseimage{university-logo}\hspace*{0.1truecm}\pgfuseimage{lbnl-logo}] % (optional, but mostly needed)
\institute[\pgfuseimage{university-logo}] % (optional, but mostly needed)
%{ Professor, University of California, Davis\\
{ University of California, Davis
%  \\
%  and\\
%  Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley }
%    Lawrence Berkeley National Laboratory, Berkeley, CA
}
% - Use the \inst command only if there are several affiliations.
% - Keep it simple, no one is interested in your street address.


\date[] % (optional, should be abbreviation of conference name)
{\small Duke University \\
        13th September, 2021}

\subject{}
% This is only inserted into the PDF information catalog. Can be left
% out.



% If you have a file called "university-logo-filename.xxx", where xxx
% is a graphic format that can be processed by latex or pdflatex,
% resp., then you can add a logo as follows:

%\pgfdeclareimage[height=0.2cm]{university-logo}{/home/jeremic/BG/amblemi/ucdavis_logo_gold_lrg}
%\logo{\pgfuseimage{university-logo}}

% \pgfdeclareimage[height=0.5cm]{university-logo}{university-logo-filename}
% \logo{\pgfuseimage{university-logo}}




% Delete this, if you do not want the table of contents to pop up at
% the beginning of each subsection:
% \AtBeginSubsection[]
\setcounter{tocdepth}{3}
 \AtBeginSubsection[]
% \AtBeginSection[]
 {
   \begin{scriptsize}
   \begin{frame}<beamer>
     \frametitle{Outline}
     \tableofcontents[currentsection,currentsubsection]
%    \tableofcontents[currentsection]
   \end{frame}
   \end{scriptsize}
 }


% If you wish to uncover everything in a step-wise fashion, uncomment
% the following command:





\begin{document}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}
  \titlepage
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}
  \frametitle{Outline}

   \begin{scriptsize}
  \tableofcontents
% You might wish to add the option [pausesections]
   \end{scriptsize}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Structuring a talk is a difficult task and the following structure
% may not be suitable. Here are some rules that apply for this
% solution:

% - Exactly two or three sections (other than the summary).
% - At *most* three subsections per section.
% - Talk about 30s to 2min per frame. So there should be between about
%   15 and 30 frames, all told.

% - A conference audience is likely to know very little of what you
%   are going to talk about. So *simplify*!
% - In a 20min talk, getting the main ideas across is hard
%   enough. Leave out details, even if it means being less precise than
%   you think necessary.
% - If you omit details that are vital to the proof/implementation,
%   just say so once. Everybody will be happy with that.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%\subsection{Motivation}
\subsection{\ }



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





 
% 
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Motivation}
%  
%  \begin{itemize}
%  
%  
%  
%   
%  
%  %\vspace*{0.3cm}
%    \item[]  Improve  modeling  and  simulation  for  infrastructure objects
%   
%  
%  % \vspace*{2mm}
%  %  \item[]  Expert numerical modeling and simulation tool
%  % 
%  % \vspace*{1mm}
%  %   \item[]      Use of numerical models to
%  %   analyze statics and dynamics of soil/rock-structure systems
%  % 
%  
%  \vspace*{1mm}
%    \item[]  Reduction  of modeling uncertainty
%  
%  \vspace*{1mm}
%    \item[]  Choice of analysis level of sophistication
%  
%  
%  \vspace*{1mm}
%    \item[] Goal: Predict and Inform rather than fit
%  
%  \vspace*{1mm}
%    \item[] Engineer needs to know!
%  
%  
%  
%  %
%  %  
%  %  
%  %  \vspace*{1mm}
%  %    \item[]  Follow  the  flow, input and dissipation,  of seismic  energy, 
%  
%  % \vspace*{1mm}
%  %   \item[]  
%  % %System  for 
%  %  {\bf Real}istic modeling and simulation of
%  %   {\bf E}arthquakes and/or    
%  %   {\bf S}oils and/or    
%  %   {\bf S}tructures    and    their    
%  %   {\bf I}nteraction:\\
%  %    Real-ESSI 
%  %  \hspace*{5mm} 
%  %   \url{http://real-essi.info/} 
%  % % % %  \hspace*{25mm} 
%  % %     \url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
%  % % %    \href{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}{{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
%  % % %  % \url{http://ms-essi.info/}
%  % % %  
%  % % 
%  
%  
%  
%  
%  \end{itemize}
%  \end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Motivation}

\begin{itemize}



 

%\vspace*{0.3cm}
  \item[]  Improve  modeling  and  simulation  for  infrastructure objects
 

% \vspace*{2mm}
%  \item[]  Expert numerical modeling and simulation tool
% 
% \vspace*{1mm}
%   \item[]      Use of numerical models to
%   analyze statics and dynamics of soil/rock-structure systems
% 

\vspace*{3mm}
  \item[] Modeling sophistication level, epistemic uncertainty

\vspace*{3mm}
  \item[] Parametric, aleatory  uncertainty



\vspace*{3mm}
  \item[] Goal: Predict and Inform 
% rather than (force) fit

\vspace*{3mm}
 \item[]  Expert numerical modeling and simulation tool


\vspace*{3mm}
  \item[] Engineer needs to know!



%
%  
%  
%  \vspace*{1mm}
%    \item[]  Follow  the  flow, input and dissipation,  of seismic  energy, 

%  \vspace*{2mm}
%    \item[]  
%  %System  for 
%   {\bf Real}istic modeling and simulation of
%    {\bf E}arthquakes and/or    
%    {\bf S}oils and/or    
%    {\bf S}tructures    and    their    
%    {\bf I}nteraction:\\
%     Real-ESSI 
%   \hspace*{5mm} 
%    \url{http://real-essi.info/} 
%  % % %  \hspace*{25mm} 
%  %     \url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
%  % %    \href{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}{{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
%  % %  % \url{http://ms-essi.info/}
%  % %  
% 




\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  

%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   \begin{frame}
%    \frametitle{Hypothesis}
%   
%   \begin{itemize}
%   
%   
%   
%   %\vspace*{0.5cm}
%     \item        Interplay    of  the  Earthquake, Soil/Rock and Structure in time
%     domain, plays a major role in successes and failures
%   
%   
%   \vspace*{3mm}
%     \item   Timing  and spatial location of energy dissipation determines location
%     and amount of damage
%   
%   \vspace*{3mm}
%     \item  If timing and spatial location of the energy dissipation
%            can be controlled (directed),
%            we could  optimize soil structure system for
%       \begin{itemize}
%         \item Safety 
%         \item Economy
%       \end{itemize}
%   
%   \end{itemize}
%   \end{frame}
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   
%   
%   
%   
%   
%   
%   
%   
%   
%   
%   
%   
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   \begin{frame}
%    \frametitle{ESSI: Energy Input and Dissipation}
%   
%   \begin{itemize}
%   
%   \vspace*{1mm}
%        \item[] Energy input, dynamic forcing
%   
%   
%   \vspace*{4mm}
%        \item[] Energy dissipation outside SSI domain:
%          \begin{itemize}
%            \item[-] SSI system oscillation radiation
%            \item[-] Reflected wave radiation
%          \end{itemize}
%   
%   
%   \vspace*{1mm}
%        \item[] Energy dissipation/conversion inside SSI domain:
%          \begin{itemize}
%            \item[-] Inelasticity of soil, contact/interface zone, structure, foundation, dissipators
%            \item[-] Viscous coupling,  porous solid-pore fluids, solids/structures-external fluids
%   % %         \item[] potential and kinetic energy
%   %          \item[] potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
%          \end{itemize}                           
%   
%   
%   
%   \vspace*{1mm}
%   %   \item[] Numerical energy dissipation (numerical damping/production and period  errors)
%   %   \item[] Numerical energy dissipation (damping/production)
%      \item[] Numerical, algorithmic energy dissipation/production
%   
%   
%   \end{itemize}
%   
%   %
%   \end{frame}
%   %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   
%   
%   
%   
%   
%   
%   
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   \begin{frame}
%    \frametitle{Prediction under Uncertainty}
%   
%   
%   \begin{itemize}
%   
%   
%   
%   
%   %\vspace*{1mm}
%     \item    \underline{Modeling, Epistemic Uncertainty}, Simplifying assumptions
%       \begin{itemize}
%   
%   \vspace*{2mm}
%         \item[] Low, medium, high  sophistication modeling and simulation
%   
%   \vspace*{2mm}
%         \item[] Choice of sophistication level for confidence in  results
%   
%       \end{itemize}
%   
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   \vspace*{4mm}
%     \item   \underline{Parametric, Aleatory    Uncertainty}, \\
%     \vspace*{2mm}
%      ${M}  \ddot{u_i}  +  {C}  \dot{u_i} + {K}^{ep} {u_i} = {F(t)}$,
%   
%     \begin{itemize}
%   
%   \vspace*{2mm}
%       \item[] Uncertain: mass $M$, viscous damping $C$ and stiffness $K^{ep}$
%   
%   \vspace*{2mm}
%       \item[] Uncertain loads $F(t)$
%   
%   
%   \vspace*{2mm}
%       \item[] Results are PDFs   and   CDFs  for  $\sigma_{ij}$,  $\epsilon_{ij}$,  $u_i$,  $\dot{u}_i$,  $\ddot{u}_i$
%   
%     \end{itemize}
%   
%   
%   
%   
%   \end{itemize}
%   
%   
%   
%   % 
%   % 
%   % %Le doute n'est pas un {\'e}tat bien agr{\'e}able,\\ 
%   %        mais l'assurance est un {\'e}tat ridicule.  (Fran{\c c}ois-Marie Arouet, Voltaire)
%   
%   
%   
%   \end{frame}
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   
%   
%   % 
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   \begin{frame}
%    \frametitle{Goal: Reduction of Modeling Uncertainty}
%   
%   \begin{itemize}
%   
%   
%      \item        Modeling      Uncertainty:   introduced   with   unnecessary and
%      unrealistic modeling simplification
%   
%   \vspace*{2mm}
%     \item  Simplified or inadequate/wrong modeling:  important  features    are
%     omitted. 3C/6C seismic ground motions, inelasticity, etc.
%   
%   \vspace*{2mm}
%        \item  Modeling  simplifications   are  justifiable  if  one, two or higher
%        level sophistication model demonstrates that features being simplified out
%        are not important
%   
%   %
%   %  \vspace*{1mm}
%   %       \item  Use  of  HPC  for  low modeling uncertainty and direct probabilistic
%   %       modeling  and  simulations 
%   %       
%   
%   
%   \end{itemize}
%   \end{frame}
%   
%   
%   
%   
%   
%   %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %  \begin{frame}
%   %   \frametitle{Fully Coupled Formulation, u-p-U}
%   %  
%   %  % 
%   %  %
%   %  \begin{small}
%   %  \begin{eqnarray}
%   %  \hspace*{-13mm}
%   %  \left[ \begin{array}{ccc}
%   %  (M_s)_{KijL} & 0 & 0 \\
%   %   0  & 0 & 0 \\
%   %   0  & 0 & (M_f)_{KijL}
%   %  \end{array} \right]
%   %  \left[ \begin{array}{c}
%   %  \ddot{\overline{u}}_{Lj} \\
%   %  \ddot{\overline{p}}_N \\
%   %  \ddot{\overline{U}}_{Lj}
%   %  \end{array} \right]
%   %  +
%   %  \left[ \begin{array}{ccc}
%   %  (C_1)_{KijL} & 0 & -(C_2)_{KijL} \\
%   %   0  & 0 &   0  \\
%   %  -(C_2)_{LjiK} & 0 & (C_3)_{KijL} \\
%   %  \end{array} \right]
%   %  \left[ \begin{array}{c}
%   %  \dot{\overline{u}}_{Lj} \\
%   %  \dot{\overline{p}}_N \\
%   %  \dot{\overline{U}}_{Lj}
%   %  \end{array} \right]    
%   %  \nonumber
%   %  \\
%   %  + 
%   %  \left[ \begin{array}{ccc}
%   %  (K^{EP})_{KijL} & -(G_1)_{KiM} & 0 \\
%   %  -(G_1)_{LjM}  & -P_{MN} & -(G_2)_{LjM} \\
%   %   0  & -(G_2)_{KiL} & 0
%   %  \end{array} \right]
%   %  \left[ \begin{array}{c}
%   %  \overline{u}_{Lj} \\
%   %  \overline{p}_M \\
%   %  \overline{U}_{Lj}
%   %  \end{array} \right]
%   %  =
%   %  \left[ \begin{array}{c}
%   %  \overline{f}_{Ki}^{solid} \\
%   %  0  \\
%   %  \overline{f}_{Ki}^{fluid}
%   %  \end{array} \right] \nonumber
%   %  %\\
%   %  %\label{68}
%   %  \end{eqnarray}
%   %  \end{small}
%   %  %
%   %  %
%   %  %
%   %  \end{frame}
%   %  %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %  
%   
%   
%   
%   
%   %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %  \begin{frame}
%   %   \frametitle{Fully Coupled Formulation, u-p-U}
%   %  
%   %  % 
%   %  % 
%   %  %
%   %  %
%   %  %
%   %  \begin{eqnarray}
%   %  \hspace*{-10mm} (M_s)_{KijL}&=&\int_{\Omega} H_K^u (1-n) \rho_s \delta_{ij} H_L^u d\Omega
%   %  \hspace*{5mm} (M_f)_{KijL}=\int_{\Omega} H_K^U n \rho_f \delta_{ij} H_L^U d\Omega \nonumber\\
%   %  \hspace*{-10mm} (C_1)_{KijL}&=&\int_{\Omega} H_K^u n^2 k_{ij}^{-1} H_L^u d\Omega 
%   %  \hspace*{5mm} (C_2)_{KijL}=\int_{\Omega} H_K^u n^2 k_{ij}^{-1} H_L^U d\Omega \nonumber\\
%   %  \hspace*{-10mm} (C_3)_{KijL}&=&\int_{\Omega} H_K^U n^2 k_{ij}^{-1} H_L^U d\Omega 
%   %  \hspace*{5mm} (K^{EP})_{KijL}=\int_{\Omega} H_{K,m}^u D_{imjn} H_{L,n}^u d\Omega \nonumber\\
%   %  \hspace*{-10mm} (G_1)_{KiM}&=&\int_{\Omega} H_{K,i}^u (\alpha-n) H_M^p d\Omega
%   %  \hspace*{5mm} (G_2)_{KiM}=\int_{\Omega} n H_{K,i}^U H_M^p d\Omega \nonumber\\
%   %  \hspace*{-10mm} P_{NM}&=&\int_{\Omega} H_N^p \frac{1}{Q} H_M^p d\Omega  \nonumber
%   %  \end{eqnarray}
%   %  %
%   %  %
%   %  %
%   %  %
%   %  %\newpage
%   %  
%   %  %  \begin{eqnarray}
%   %  %  \overline{f}_{Ki}^{solid}&=&(f_1^u)_{Ki}-(f_4^u)_{Ki}+(f_5^u)_{Ki} \nonumber\\
%   %  %  \overline{f}_{Ki}^{fluid}&=&-(f_1^U)_{Ki}+(f_2^U)_{Ki}  \nonumber\\
%   %  %  (f_1^u)_{Ki}&=&\int_{\Gamma_t} H_K^u n_j \sigma_{ij}^{''} d\Gamma \nonumber\\
%   %  %  (f_4^u)_{Ki}&=&\int_{\Gamma_p} H_K^u (\alpha-n) n_i p d\Gamma \nonumber\\
%   %  %  (f_5^u)_{Ki}&=&\int_{\Omega} H_K^u (1-n) \rho_s b_i d\Omega \nonumber\\
%   %  %  (f_1^U)_{Ki}&=&\int_{\Gamma_p} n H_K^U n_i p d\Gamma \nonumber\\
%   %  %  (f_2^U)_{Ki}&=&\int_{\Omega} n H_K^U \rho_f b_i d\Omega
%   %  %  \label{69}
%   %  %  \end{eqnarray}
%   %  %
%   %  
%   %  %
%   %  \end{frame}
%   %  %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %  
%   %  
%   %  
%   
%   % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   % \begin{frame}
%   % 
%   % \frametitle{Energy Dissipation Control Mechanisms}
%   % 
%   % \begin{figure}[!H]
%   % %\hspace*{-10mm}
%   %      \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_plasticity.pdf}
%   %      \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Rayleigh.pdf}
%   %      \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Newmark.pdf}
%   % \end{figure}
%   % 
%   % 
%   % % \hspace*{10mm} Numerical  \hspace*{20mm}  Viscous  \hspace*{20mm} Plasticity 
%   %  \hspace*{10mm} Plasticity \hspace*{20mm}  Viscous  \hspace*{20mm} Numerical
%   % 
%   % 
%   % 
%   % \end{frame}
%   % 
%   % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   
%   %  
%   %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %  \begin{frame}
%   %  
%   %  \frametitle{Energy Dissipation Control}
%   %  
%   %  \begin{figure}[!H]
%   %  %\hspace*{-10mm}
%   %  %     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_a.pdf}
%   %  %     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_b.pdf}
%   %       \includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_g.pdf}
%   %  %     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_e.pdf}
%   %  \end{figure}
%   %  
%   %  
%   %  
%   %  
%   %  \end{frame}
%   %  
%   %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   
%   
%   %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   
%   % 
%   % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   % \begin{frame}
%   %  
%   % \frametitle{Energy Dissipation on Material Level}
%   % 
%   % 
%   % \vspace*{2mm}
%   %  
%   %  Single elastic-plastic element under cyclic shear loading
%   %  
%   % \begin{itemize}
%   % \item[] Difference between plastic work and plastic dissipation
%   % \item[] Plastic work can decrease
%   % \item[] Plastic dissipation always increases
%   % \end{itemize}
%   %  
%   % %\vspace*{-7mm}
%   % \begin{figure}[!hbpt]
%   % \begin{center}
%   % \hspace*{-5mm}
%   % \includegraphics[width=11.0truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Dissipation_Material.png}
%   % \end{center}
%   % \end{figure}
%   %   
%   % \end{frame}
%   % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   % 
%   
%   % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   % \begin{frame}
%   % \frametitle{Liquefaction as Base Isolation, Model}
%   % 
%   % \begin{figure}[!hbpt]
%   % \begin{center}
%   % \includegraphics[width=4.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSI-Site_Response_Analysis/Liquefaction_04.jpg}
%   % \end{center}
%   % \end{figure}
%   % 
%   % \end{frame}
%   % 
%   % 
%   % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   % \begin{frame}
%   % \frametitle{Liquefaction, Wave Propagation}
%   % 
%   % \begin{figure}[!hbpt]
%   % \begin{center}
%   % \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSI-Site_Response_Analysis/Liquefaction_01.jpg}
%   % \end{center}
%   % \end{figure}
%   % 
%   % \end{frame}
%   % 
%   % 
%   % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   % \begin{frame}
%   % \frametitle{Liquefaction, Stress-Strain Response}
%   % 
%   % \begin{figure}[!hbpt]
%   % \begin{center}
%   % \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSI-Site_Response_Analysis/Liquefaction_03.jpg}
%   % \end{center}
%   % \end{figure}
%   % 
%   % \end{frame}
%   % 
%   % 
%   % 
%   % 
%   % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   % 
%   % \begin{frame}
%   % 
%   % \frametitle{Buoyant Force Simulation}
%   % 
%   % \begin{figure}[!H]
%   % \hspace*{-10mm}
%   %      \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/upU_element_type_annotation.pdf}
%   %      \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/bouyant_displacement.pdf}
%   % \end{figure}
%   % 
%   % % -  %
%   % % -  % \begin{tikzpicture}[remember picture,overlay]
%   % % -  %    \node[anchor=south west,inner sep=0pt] at ($(current page.south west)+(7.5cm,2.5cm)$) {
%   % % -  %      \includegraphics[width=0.4\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/bouyant_displacement.pdf}};
%   % % -  % \end{tikzpicture}
%   % % -
%   % % -  %  \vspace{-1.4cm}
%   % %  \begin{itemize}
%   % %   \item \scriptsize Upward structural displacement under buoyant force
%   % %  \end{itemize}
%   % \end{frame}
%   % 
%   % 
%   
%   %
%   
%        
%   % 
%   % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   % 
%   % \begin{frame}
%   %  \frametitle{Solid/Structure-Fluid Interaction, Example}
%   % 
%   % 
%   % 
%   % %\vspace*{-5mm}
%   % \begin{center}
%   % % \hspace*{-15mm}
%   % \movie[label=show3,width=9cm,poster,autostart,showcontrols]
%   % {\includegraphics[width=8.5cm]
%   % {/home/jeremic/tex/works/Conferences/2017/DOE_Project_Review_Meeting_LBNL_09June2017/Present/Solid-Fluid-Interaction.jpg}}
%   % {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Fluid_Solid_interaction/Solid_Fluid_Interaction_NEW.mpeg}
%   % \end{center}
%   % 
%   % 
%   % \begin{flushleft}
%   % \vspace*{-15mm}
%   % \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Fluid_Solid_interaction/Solid_Fluid_Interaction.mp4}
%   % %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%   %   {\tiny (MP4)}
%   % \end{flushleft}
%   % %
%   % 
%   % \end{frame}
%   % 
%   % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   
%   % -
%   % -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   % -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   % -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   % -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   % -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   
%   
%   
%   
%   
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   
%   
%   
















                       

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Numerical Prediction under Uncertainty}


\begin{itemize}




%\vspace*{1mm}
  \item[-]    {Modeling, Epistemic Uncertainty}
    \begin{itemize}

\vspace*{2mm}
      \item[] Modeling simplifications

\vspace*{2mm}
      \item[] Modeling sophistication for confidence in  results 

%
%\vspace*{2mm}
%      \item[] Choice of sophistication level for confidence in  results

    \end{itemize}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\vspace*{4mm}
  \item[-]   {Parametric, Aleatory    Uncertainty}

  \begin{itemize}


\vspace*{2mm}
    \item[]  ${M}  \ddot{u_i}  +  {C}  \dot{u_i} + {K}^{ep} {u_i} = {F(t)}$, 

\vspace*{2mm}
    \item[] Uncertain: mass $M$, viscous damping  $C$ and stiffness $K^{ep}$


\vspace*{2mm}
    \item[] Uncertain  loads, $F(t)$


\vspace*{2mm}
    \item[] Results are PDFs   and   CDFs  for  $\sigma_{ij}$,  $\epsilon_{ij}$,  $u_i$,  $\dot{u}_i$,  $\ddot{u}_i$

  \end{itemize}




\end{itemize}



% 
% 
% %Le doute n'est pas un {\'e}tat bien agr{\'e}able,\\ 
%        mais l'assurance est un {\'e}tat ridicule.  (Fran{\c c}ois-Marie Arouet, Voltaire)



\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Modeling, Epistemic Uncertainty}

\begin{itemize}



  \item[-]  Important (?!)  features are simplified, 1C vs 3C, inelasticity

%\vspace*{4mm}
%     \item   Unrealistic   and   unnecessary  modeling simplifications

\vspace*{1mm}
     \item[-]  Modeling  simplifications   are  justifiable  if  one  or  two 
     level higher sophistication model demonstrates that features being
     simplified out are less or not important



\end{itemize}


% local
%\vspace*{-2mm}
\begin{center}
\hspace*{-7mm}
%\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
\movie[label=show3,width=5.5cm,autostart, showcontrols]
  {\includegraphics[width=50mm]
  {/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_2_npps_mp4_icon.jpeg}}
  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_2_npps.mp4}
%
%\hfill
\hspace*{-5mm}
%
\movie[label=show3,width=6.0cm,autostart,showcontrols]
  {\includegraphics[width=50mm]
  {/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/3D_Nonlinear_Modeling_and_it_Effects/NPP_Plastic_Dissipation_grab.jpg}}
  {/home/jeremic/tex/works/Thesis/HanYang/Files_10Aug2017/NPP_Plastic_Dissipation.mp4}
\hspace*{-7mm}
%\end{flushleft}
%%
\end{center}
% local

% % \vspace*{-5mm}
% \begin{center}
% %\begin{flushleft}
% % \hspace*{-15mm}
% \movie[label=show3,width=5cm,poster,autostart,showcontrols]
% {\includegraphics[width=5cm]
% {/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/3D_Nonlinear_Modeling_and_it_Effects/NPP_Plastic_Dissipation_grab.jpg}}
% {/home/jeremic/tex/works/Thesis/HanYang/Files_10Aug2017/NPP_Plastic_Dissipation.mp4}
% %\end{flushleft}
% %%
% \hfill
% %%
% %\begin{flushright}
% % \hspace*{-15mm}
% \movie[label=show3,width=5cm,poster,autostart,showcontrols]
% {\includegraphics[width=5cm]
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation_screen_grab.jpg}}
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
% %\end{flushright}
% \end{center}
%  



\end{frame}







      
%OVDE

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Modeling Uncertainty, 6C vs 1C Motions}
% 
%      
% % local
% \vspace*{-2mm}
% \begin{center}
% \hspace*{-7mm}
% %\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% \movie[label=show3,width=8.8cm,poster, showcontrols]
%   {\includegraphics[width=92mm]
%   {/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_2_npps_mp4_icon.jpeg}}
%   {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_2_npps.mp4}
% \end{center}
% % local
% %  \vspace*{-2mm}
% %  \begin{center}
% %  \hspace*{-7mm}
% %  \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% %    {\includegraphics[width=90mm]{movie_2_npps_mp4_icon.jpeg}}{movie_2_npps.mp4}
% %  \end{center}
% 
% 
% % online
% \vspace*{-12mm}
% \begin{flushleft}
% %\vspace*{-15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_2_npps.mp4}
%   {\tiny (MP4)}
% \end{flushleft}
% % online
% 
% 
% 
% 
% 
% \end{frame}
% 

    
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Parametric, Aleatory Uncertainty}



\vspace*{2mm}
%\vspace*{-5mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-7mm}
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf}
\hspace*{-3mm}
% \hfill
\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
%
\end{center}
\end{figure}


\vspace*{-5mm}
%\vspace*{-1.8cm}
%\hspace*{-3.3cm}
\begin{flushright}
{\tiny
(cf. Phoon and Kulhawy (1999B))\\
~}
\end{flushright}
%





   

\vspace*{-9mm}
\begin{figure}[!hbpt]
\begin{center}
%
%\hspace*{-7mm}
\includegraphics[width=5.00truecm]{/home/jeremic/tex/works/Thesis/HexiangWang/time_series_motionsn_06ug2019_SMIRT/Acc_realization_200.pdf}
%\hspace*{-3mm}
%\includegraphics[width=2cm]{/home/jeremic/tex/works/Papers/2019/Hexiang/1D_risk/version2/Figures/Acc_time_series_realiztion70.pdf}
%\includegraphics[width=2cm]{/home/jeremic/tex/works/Papers/2019/Hexiang/1D_risk/version2/Figures/Acc_time_series_realiztion100.pdf}
%% \includegraphics[width=0.31\textwidth]{Figures/Acc_time_series_realiztion350.pdf}
%\includegraphics[width=2cm]{/home/jeremic/tex/works/Papers/2019/Hexiang/1D_risk/version2/Figures/Acc_time_series_realiztion367.pdf}
\includegraphics[width=4cm]{/home/jeremic/tex/works/Papers/2019/Hexiang/1D_risk/version2/Figures/SA_GMPE_verification_std_08_no_smooth.pdf}
%
\end{center}
\end{figure}


\vspace*{-7mm}
\begin{flushright}
{\tiny
(cf. Wang et al. (2019))\\
~}
\end{flushright}








\end{frame}









% -- 
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- \begin{frame}
% -- % \frametitle{Sensitivity Analysis}
% --  \frametitle{Engineer Needs to Know!}
% -- 
% -- 
% -- \begin{itemize}
% -- 
% -- 
% -- 
% --   \item[-]    Forward    propagation    of   uncertainty,   full   probabilistic,
% --   nonlinear/inelastic  Earthquake-Soil-Structure-Interaction, ESSI response in
% --   time domain (Jeremic et al 2011, Wang et al 2019)
% -- % %\vspace*{1mm}
% -- %   \item[]      \underline{Sensitivity Analysis} quantifies the relative importance
% -- %   of  input  uncertain  parameters  and their contributions to the probabilistic
% -- %   system response
% -- % 
% -- % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- % \vspace*{4mm}
% -- %   \item[]    \underline{Local sensitivity analysis} focuses on the local impact of
% -- %   input  uncertain  parameters  on model response, quantified by the gradient of
% -- %   system response with respect to the variation of input parameters
% -- % 
% -- 
% -- % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- % \vspace*{4mm}
% -- %   \item[]    \underline{Global sensitivity analysis} studies the
% -- % respective
% -- \vspace*{4mm}
% --   \item[-] Backward propagation, sensitivity analysis, quantifies the relative importance
% --  of  input  uncertain  parameters on the variance of the probabilistic system
% --   response  
% -- (Sobol 2001, Sudret 2008, Jeremic et al 2021)
% -- %Sobol, {\cyss Sobol{p1}} indices (Sobol 2001), Sudret (2008)
% -- % encoding for soft b is {p1}, see
% -- 
% -- 
% -- 
% -- \end{itemize}
% -- 
% -- 
% -- 
% -- \end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



% 




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





      
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Uncertain Inelastic Mechanics}

      
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Stochastic Modeling}
\subsection{Forward Propagation}





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 

\frametitle{Forward Uncertain Inelasticity}

% 

\begin{itemize}



\item[-] Incremental el--pl constitutive equation
%  
    \begin{eqnarray}
    \nonumber
  \Delta \sigma_{ij} 
  = 
%  E^{EP}_{ijkl} 
     E^{EP}_{ijkl} \; \Delta \epsilon_{kl}  
     =  
     \left[
     E^{el}_{ijkl}
       -
       \frac{\displaystyle  E^{el}_{ijmn} m_{mn} n_{pq} E^{el}_{pqkl}}
           {\displaystyle n_{rs} E^{el}_{rstu} m_{tu} - \xi_* h_*}
           \right]
    \Delta \epsilon_{kl}
    \end{eqnarray}

 
  

\vspace*{2mm}
\item[-] Dynamic Finite Elements
%
\begin{equation}
{ M} \ddot{ u_i} +
{ C} \dot{ u_i} +
{ K}^{ep} { u_i} =
{ F(t)}
    \nonumber
\end{equation}


\vspace*{2mm}
\item[-] Material and loads are uncertain



\end{itemize}



\end{frame}














%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 

\frametitle{{Cam Clay  with  Random $G$, $M$ and $p_0$}}


\begin{figure}[!hbpt]
\begin{center}
\hspace*{-15mm}
\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Conferences/2006/KallolsPresentationGaTech/ContourLowOCR_RandomG_RandomM_Randomp0-m.pdf}
%\hspace*{-2mm}
\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Conferences/2006/KallolsPresentationGaTech/ContourHighOCR_RandomG_RandomM-m.pdf}
\hspace*{-15mm}
\end{center}
\end{figure}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\end{frame}
% --  %%%%%%




% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- 
% -- \begin{frame}{Time Domain Stochastic Galerkin Method}
% -- 
% -- 
% -- \vspace*{2mm}
% -- Dynamic Finite Elements 
% -- $
% -- { M} \ddot{ u_i} +
% -- { C} \dot{ u_i} +
% -- { K}^{ep} { u_i} =
% -- { F(t)}$
% -- 
% -- 
% -- \begin{itemize}
% -- \vspace*{2mm}
% -- \item[-] Input random field/process{\normalsize{(non-Gaussian, heterogeneous/ non-stationary)}}:
% --           Multi-dimensional Hermite Polynomial Chaos (PC) with {known coefficients}
% -- %\vspace{0.05in}
% -- \vspace*{2mm}
% -- \item[-] Output response process: Multi-dimensional Hermite PC with {unknown coefficients}
% -- % \vspace{0.05in}
% -- \vspace*{2mm}
% --  \item[-] Galerkin projection: minimize the error to compute unknown coefficients of response process
% -- % %\vspace{0.05in}
% -- % \vspace*{2mm}
% -- %  \item[-] Time integration using Newmark's method
% -- % % : Update coefficients following
% -- % % an elastic-plastic constitutive law at each time step
% --  
% -- \end{itemize}
% -- 
% -- %\scriptsize 
% -- %Note: PC = Polynomial Chaos
% -- 
% -- \end{frame}
% -- 
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- % 
% -- % \begin{frame}{Discretization of Input Random Process/Field $\beta(x,\theta)$}
% -- % \begin{center}
% -- % \includegraphics[scale=0.35]{/home/jeremic/tex/works/Thesis/FangboWang/slides_13Mar2019/Fangbo_slides/figs/PC_KL_explanation.PNG} \\
% -- % \end{center}
% -- % 
% -- % 
% -- % \footnotesize{Note: $\beta(x,\theta)$ is an input random process with any
% -- % marginal distribution,  \\ \hspace{21mm} with any covariance structure;} \\
% -- % \footnotesize{\hspace{8mm} $\gamma(x,\theta)$ is a zero-mean unit-variance Gaussian random process.} \\
% -- % 
% -- % \end{frame}
% -- % 
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- \begin{frame}{Polynomial Chaos Representation}
% -- 
% -- %\scriptsize{
% -- Material random field: \\
% -- %\vspace{-0.3cm}
% -- %\begin{equation*} 
% -- $D(x, \theta)= \sum_{i=1}^{P1} a_i(x) \Psi_i(\left\{\xi_r(\theta)\right\})$      
% -- %\end{equation*}
% -- 
% -- 
% -- \vspace{4mm}
% -- 
% -- Seismic loads/motions random process: \\
% -- %\vspace{-0.3cm}
% -- %\begin{equation*} 
% -- $f_m(t, \theta)=\sum_{j=1}^{P_2} f_{mj}(t) \Psi_j(\{\xi_k(\theta)\})$         
% -- %\end{equation*}
% -- 
% -- \vspace{4mm}
% -- 
% -- Displacement response:  \\
% -- %\vspace{-0.3cm}
% -- %\begin{equation*} 
% -- $u_n(t, \theta)=\sum_{k=1}^{P_3} d_{nk}(t) \Psi_k(\{\xi_l(\theta)\})$         
% -- %\end{equation*}
% -- 
% -- \vspace{3mm}
% -- 
% -- %Acceleration response:
% -- %%\vspace{-0.3cm}
% -- %%\begin{equation*} 
% -- %$\ddot u_n(t, \theta)=\sum_{k=1}^{P_3} \ddot d_{nk}(t) \Psi_k(\{\xi_l(\theta)\})$         
% -- %%\end{equation*}
% -- 
% -- %\vspace{3mm}
% -- \vspace{5mm}
% -- 
% -- where $a_i(x), f_{mj}(t)$ are {known PC coefficients}, while $d_{nk}(t)$
% -- are {unknown PC coefficients}.
% -- %}
% -- 
% -- \end{frame}
% -- 
% -- 
% -- 
% -- 
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Direct Solution for Probabilistic Stiffness and Stress in 1D}
% 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%    BEGGINING PEP    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- 
% -- 
% -- \begin{frame}{Direct Probabilistic Constitutive Solution in 1D}
% -- 
% -- 
% -- % \begin{itemize}
% -- %  
% -- %  \vspace{0.5cm}
% -- % 
% -- % \item<1-> Probabilistic constitutive modeling : \vspace{0.5cm}
% -- 
% -- \begin{itemize}
% -- 
% -- 
% -- \vspace*{4mm}
% -- \item[-]  Zero elastic region elasto-plasticity with stochastic Armstrong-Frederick
% -- kinematic hardening
% -- 
% -- $ \Delta\sigma =\ H_a  \Delta \epsilon  -  c_r \sigma |\Delta \epsilon| ;
% -- \hspace{0.5cm} 
% -- E_t = {d\sigma}/{d\epsilon} = H_a \pm c_r \sigma $
% -- 
% -- \vspace*{4mm}
% -- \item[-] Uncertain: 
% --       init. stiff. $H_a$, 
% --       shear strength $H_a/c_r$, 
% --       strain $\Delta \epsilon$: 
% -- 
% -- $ H_a = \Sigma h_i \Phi_i; \;\;\;  
% --   C_r = \Sigma c_i \Phi_i; \;\;\; 
% --   \Delta\epsilon =  \Sigma \Delta\epsilon_i \Phi_i $
% -- 
% -- 
% -- 
% -- \vspace*{4mm}
% -- \item[-] Resulting stress and stiffness are also uncertain 
% -- 
% -- % - 
% -- % - $ \sum_{l=1}^{P_{\sigma}} \Delta\sigma_i \Phi_i = \sum_{i=1}^{P_h} \sum_{k=1}^{P_e}\ h_i  \Delta \epsilon_k \Phi_i \Phi_k - \sum_{j=1}^{P_g} \sum_{k=1}^{P_e}\sum_{l=1}^{P_{\sigma}} \ c_i \Delta \epsilon_k \sigma_l \Phi_j \Phi_k \Phi_l$
% -- % - 
% -- % - $ \sum_{l=1}^{P_{E_t}} \Delta E_{t_i} \Phi_i = \sum_{i=1}^{P_h}  h_i  \Phi_i \pm \sum_{i=1}^{P_c} \sum_{l=1}^{P_{\sigma}} \ c_i  \sigma_l  \Phi_i \Phi_l$
% -- % - 
% -- 
% -- 
% -- \end{itemize}
% -- 
% -- 
% -- % \vspace{0.5cm}
% -- 
% -- 
% -- 
% -- % \vspace{1cm}
% -- 
% -- %\item<1-> Time integration is done via Newmark algorithm
% -- 
% -- % 
% -- % \end{itemize}
% -- % 
% -- \end{frame}
% -- 
% -- 
% -- % % % % % % % % % % % % % % % %
% -- 
% -- 
% -- 
% -- 
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- \begin{frame}{Direct Probabilistic Stiffness Solution}
% --  
% --  \begin{itemize}
% --   
% -- 
% -- \item[-] Analytic product for all the components, 
% -- 
% -- $ E^{EP}_{ijkl} 
% --      =  
% --      \left[
% --      E^{el}_{ijkl}
% --        -
% --        \frac{\displaystyle  E^{el}_{ijmn} m_{mn} n_{pq} E^{el}_{pqkl}}
% --            {\displaystyle n_{rs} E^{el}_{rstu} m_{tu} - \xi_* h_*}
% --            \right]
% -- $
% -- 
% -- 
% -- 
% -- 
% -- \vspace*{2mm}
% -- \item[-] Stiffness: each Polynomial Chaos component is updated incrementally
% -- % at each Gauss Point via stochastic Galerkin projection
% -- 
% -- 
% -- 
% --   \small{$E_{t_1}^{n+1}  =  \frac{1}{<\Phi_1\Phi_1> }\{\sum_{i=1}^{P_h} \ h_i   <\Phi_i \Phi_1> \pm \sum_{j=1}^{P_c} \sum_{l=1}^{P_{\sigma}} \ c_j  \sigma_l^{n+1} <\Phi_j  \Phi_l \Phi_1>\}$}
% --   \\
% --   . . . 
% -- %  
% -- %
% -- %  $\large{\vdots}$
% -- \\  
% --      \small{$E_{t_P}^{n+1}  =  \frac{1}{<\Phi_1\Phi_P> }\{\sum_{i=1}^{P_h} \ h_i   <\Phi_i \Phi_P> \pm \sum_{j=1}^{P_c} \sum_{l=1}^{P_{\sigma}} \ c_j  \sigma_l^{n+1} <\Phi_j  \Phi_l \Phi_P>\}$}
% --   
% --   
% -- \vspace*{2mm}
% -- \item[-] Total stiffness is : 
% --   
% --   $ E_{t}^{n+1} = \sum_{l=1}^{P_{E}} E_{t_i}^{n+1} \Phi_i $
% -- 
% -- 
% -- 
% -- 
% -- \end{itemize}
% -- 
% -- 
% -- \end{frame}
% -- 
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- 
% -- % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- \begin{frame}{Direct Probabilistic Stress Solution}
% --  
% --  \begin{itemize}
% --   
% --   
% -- 
% -- \item[-] Analytic product, for each stress component, 
% -- 
% -- $ \Delta \sigma_{ij} =  E^{EP}_{ijkl} \; \Delta \epsilon_{kl} $ 
% -- %      =  
% -- %      \left[
% -- %      E^{el}_{ijkl}
% -- %        -
% -- %        \frac{\displaystyle  E^{el}_{ijmn} m_{mn} n_{pq} E^{el}_{pqkl}}
% -- %            {\displaystyle n_{rs} E^{el}_{rstu} m_{tu} - \xi_* h_*}
% -- %            \right]
% -- %     \Delta \epsilon_{kl}
% -- % 
% -- 
% -- 
% -- \vspace*{2mm}
% -- \item[-] Incremental stress: each  Polynomial  Chaos  component  is updated
% -- incrementally 
% -- % via stochastic Galerkin projection
% -- 
% -- 
% --  
% --  
% --   {$\Delta\sigma_1^{n+1}  = \frac{1}{<\Phi_1\Phi_1> }\{\sum_{i=1}^{P_h} \sum_{k=1}^{P_e}\ h_i  \Delta \epsilon_k^n <\Phi_i \Phi_k \Phi_1>- \sum_{j=1}^{P_g} \sum_{k=1}^{P_e}\sum_{l=1}^{P_{\sigma}} \ c_j \Delta \epsilon_k^n \sigma_l^n <\Phi_j \Phi_k \Phi_l \Phi_1>\}$}
% -- \\
% -- . . . 
% -- \\
% -- % ${\vdots}$ 
% -- {$\Delta\sigma_P^{n+1}  = \frac{1}{<\Phi_P\Phi_P> }\{\sum_{i=1}^{P_h} \sum_{k=1}^{P_e}\ h_i  \Delta \epsilon_k^n <\Phi_i \Phi_k \Phi_P>- \sum_{j=1}^{P_g} \sum_{k=1}^{P_e}\sum_{l=1}^{P_{\sigma}} \ c_j \Delta \epsilon_k^n \sigma_l^n <\Phi_j \Phi_k \Phi_l \Phi_P>\}$}
% -- 
% -- 
% -- \vspace*{2mm}
% -- \item[-] Stress  update: 
% -- 
% -- $ \sum_{l=1}^{P_{\sigma}} \sigma_i^{n+1} \Phi_i = \sum_{l=1}^{P_{\sigma}} \sigma_i^{n} \Phi_i + \sum_{l=1}^{P_{\sigma}} \Delta\sigma_i^{n+1} \Phi_i$
% -- 
% -- 
% -- 
% -- \end{itemize}
% -- 
% -- \end{frame}
% -- 
% -- 
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- 
% -- \begin{frame}
% -- \frametitle{Probabilistic Elastic-Plastic Response}
% -- 
% -- 
% -- % % \vspace*{-5mm}
% -- % \begin{center}
% -- % % \hspace*{-15mm}
% -- % \movie[label=show3,width=7cm,poster,autostart,showcontrols]
% -- % {\includegraphics[width=7cm]
% -- % {/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_Plastic_Dissipation_Density.png}}
% -- % %{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_without_Contact_vonMises.mp4}
% -- % {NPP_without_Contact_vonMises.mp4}
% -- % \end{center}
% -- 
% -- %\vspace*{-5mm}
% -- \begin{center}
% -- % \hspace*{-15mm}
% -- \movie[label=show3,width=9cm,poster,autostart,showcontrols]
% -- {\includegraphics[width=9cm]
% -- {/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.png}}
% -- % /home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.pdf
% -- %{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Animations/PEP_Animation.mp4}
% -- {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/PEP_Animation.mp4}
% -- \end{center}
% -- 
% -- 
% --  
% -- 
% -- \begin{flushleft}
% -- \vspace*{-15mm}
% -- \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/PEP_Animation.mp4}
% -- %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
% --   {\tiny (MP4)}
% -- \end{flushleft}
% -- %
% -- 
% -- 
% -- 
% -- 
% -- %
% -- % \includegraphics[width = 12cm]{./img/figure_PEP_25.pdf}
% -- 
% -- 
% -- \end{frame}
% -- 
% -- 
% -- 
% -- 
% -- 
% -- 
% -- 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section[Formulation]{Stochastic Dynamic Finite Element Formulation}
%\subsection[Time domain stochastic Galerkin method]{Time domain stochastic Galerkin method}
%\frame{\tableofcontents[currentsubsection,sectionstyle=show/shaded]}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Stochastic Elastic-Plastic Finite Element Method}



\begin{itemize}

\item[-] Material uncertainty expanded into stochastic shape funcs.
%$E(x,t,\theta) = \sum_{i=0}^{P_d} r_i(x,t) * \Phi_i[\{\xi_1, ..., \xi_m\}]$

\vspace*{1mm}
\item[-] Loading uncertainty expanded into stochastic shape funcs.
%$f(x,t,\theta) = \sum_{i=0}^{P_f} f_i(x,t) * \zeta_i[\{\xi_{m+1}, ..., \xi_f]$

\vspace*{1mm} 
\item[-] Displacement expanded into stochastic shape funcs.
%$u(x,t,\theta) = \sum_{i=0}^{P_u} u_i(x,t) * \Psi_i[\{\xi_1, ..., \xi_m, \xi_{m+1}, ..., \xi_f\}]$

%\item 
%Stochastic system of equation resulting from Galerkin approach (static example):
%
%\item  Time domain integration  using Newmark and/or HHT, in probabilistic spaces



\vspace*{1mm} 
\item[-] Jeremi{\'c} et al. 2011


\end{itemize}


\begin{tiny}
\[
%$
\begin{bmatrix}
    \sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_0> K^{(k)}    & \dots & \sum_{k=0}^{P_d} <\Phi_k \Psi_P \Psi_0> K^{(k)}\\
    \sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_1> K^{(k)}    & \dots & \sum_{k=0}^{P_d} <\Phi_k \Psi_P \Psi_1> K^{(k)}\\  \\
    \vdots & \vdots & \vdots & \vdots\\
    \sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_P> K^{(k)}     & \dots & \sum_{k=0}^{M} <\Phi_k \Psi_P \Psi_P> K^{(k)}
\end{bmatrix}
\begin{bmatrix}
    \Delta u_{10} \\
    \vdots \\
    \Delta u_{N0}\\
    \vdots \\
    \Delta u_{1P_u}\\
    \vdots \\
    \Delta u_{NP_u}
\end{bmatrix}
=
%\]
%\[
\begin{bmatrix}
     \sum_{i=0}^{P_f} f_i  <\Psi_0\zeta_i> \\
    \sum_{i=0}^{P_f} f_i   <\Psi_1\zeta_i> \\
   \sum_{i=0}^{P_f} f_i    <\Psi_2\zeta_i> \\
    \vdots \\
     \sum_{i=0}^{P_f} f_i  <\Psi_{P_u}\zeta_i>\\
\end{bmatrix}
%$
\]
\end{tiny}





\end{frame}





% -- 
% --  
% --  
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  
% --  \begin{frame}
% --  \frametitle{SEPFEM: System Size}
% --  
% --  \begin{itemize}
% --  
% --    \item[-] SEPFEM offers a complete probabilistic solution 
% --  
% --    \item[-]  It is NOT based on Monte Carlo approach
% --  
% --    \item[-]  System of equations grows (!)
% --  
% --  \end{itemize}
% --  
% --  
% --  %   \normalsize{Typical number of terms required for a SEPFEM problem} \vspace{1cm}\\
% --    \scalebox{0.7}{
% --    \begin{tabular}{ c c c c}
% --     \# KL terms material & \# KL terms load & PC order displacement& Total \# terms per DoF\\ \hline
% --     4 & 4 & 10 & 43758 \\  
% --     4 & 4 & 20 & 3 108 105 \\    
% --     4 & 4 & 30 & 48 903 492 \\  
% --     6 & 6 & 10 & 646 646 \\    
% --     6 & 6 & 20 & 225 792 840 \\  
% --     6 & 6 & 30 & 1.1058 $10^{10}$ \\    
% --     8 & 8 & 10 & 5 311 735 \\  
% --     8 & 8 & 20 & 7.3079 $10^{9}$ \\    
% --     8 & 8 & 30 & 9.9149 $10^{11}$\\  
% --     
% --     ...  & ... & ... & ...\\   
% --  %    \hline
% --    \end{tabular}}
% --  
% --  
% --  \end{frame}
% --  
% --  
% --  
% --  
% --  
% --  
% --  









%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



\subsection{Backward Propagation, Sensitivities}
%\subsection{Sobol Sensitivity Analysis}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{ANOVA Representation}




 

%\vspace*{10mm}

Model with $n$ uncertain inputs ($\boldsymbol{x}$) and scalar output $y$:


\vspace*{-6mm}
\begin{equation}
y = f(\boldsymbol{x}) \mbox{;} \ \  \boldsymbol{x} \in I^{n}
\nonumber
\end{equation}

% input parameters $\boldsymbol{x}$ are defined in $n$ dimensional unit
% cube $I^{n}$
%

\vspace*{5mm}
 
The ANalysis Of VAriance representation
% of $f(x)$ 
(Sobol 2001):

\vspace*{-6mm}
\begin{eqnarray*}
f(x_1, ... x_n) = f_0 + \sum_{i=1}^{n} f_i(x_i) + 
\sum_{1\leq i<j\leq n} 
f_{ij}(x_i, x_j) 
+...
%\\
%+ 
f_{1,...n}(x_1,...x_n) 
\nonumber
\label{eq_ANOVA_representation}
\end{eqnarray*}


\end{frame}



% -- 
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  \begin{frame}
% --  \frametitle{Sensitivity Analysis, ANOVA Representation}
% --  
% --  
% --  
% --  
% --  Total of $2^n$ summands
% --  
% --  \vspace*{4mm}
% --  %
% --  Mean value $f_0 = \int_{I^{n}} f(\boldsymbol{x}) d \boldsymbol{x}$ 
% --  %
% --  
% --  \vspace*{4mm}
% --  Integral of each summand 
% --  $\int_{0}^{1} f_{i_1,... i_s}({x_{i_1},... x_{i_s}}) dx_{i_k} = 0 \mbox{;~}
% --   1 \leq k \leq s$ 
% --  %in Equation \ref{eq_ANOVA_representation} over any of its independent variable is zero: 
% --  
% --  %\begin{equation}
% --  %\int_{0}^{1} f_{i_1, ..., i_s}({x_{i_1}, x_{i_2}, ..., x_{i_s}}) \ dx_{i_k} = 0 \ \ \ \mathrm{for} \ \ \ 1 \leq k \leq s 
% --  %\label{eq_summand_integral_zero}
% --  %\end{equation}
% --  % 
% --  % 
% --  % 
% --  
% --  
% --  \vspace*{4mm}
% --  Summands are orthogonal to each other
% --  
% --  \vspace*{-6mm}
% --  %
% --  \begin{eqnarray*}
% --  \int_{I^{n}} f_{i_1,...i_s}({x_{i_1}, x_{i_2},...x_{i_s}}) 
% --  f_{j_1,...j_t}({x_{j_1}, x_{j_2},...x_{j_t}}) d \boldsymbol{x} = 0 
% --  \mbox{;}
% --  %\mathrm{for} \ \ \
% --  \\
% --  \{i_1,...i_s\} \neq \{j_1,...j_t\}  
% --  \nonumber
% --  \label{eq_orthogonal}
% --  \end{eqnarray*}
% --  
% --  
% --  %
% --  
% --  
% --  
% --  \end{frame}
% --  
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  
% --  
% --  
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  \begin{frame}
% --  \frametitle{Sensitivity Analysis, ANOVA Representation}
% --  
% --  ANOVA representation is unique!
% --  % and derived analytically
% --  
% --  \vspace*{5mm}
% --   
% --  Univariate terms: 
% --  %
% --  \begin{eqnarray*}
% --  f_i(x_i) = \int_{I^{n-1}} f(\boldsymbol{x}) \ d\boldsymbol{x}_{\sim i} - f_0 
% --  \end{eqnarray*}
% --  
% --  %$\int_{I^{n-1}} (\cdot) \ d\boldsymbol{x}_{\sim i}$ is integral
% --  %over all dimensions except $x_i$.
% --  %
% --  
% --  \vspace*{5mm}
% --  
% --  
% --  Bivariate terms:
% --  % 
% --  \begin{eqnarray*}
% --  f_{ij}(x_i, x_j) = \int_{I^{n-2}} f(\boldsymbol{x}) \ d\boldsymbol{x}_{\sim [ij]} - f_i(x_i) - f_j(x_j) - f_0 
% --  \end{eqnarray*}
% --  
% --  
% --  
% --  
% --  
% --  
% --  
% --  \end{frame}
% --  
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  \begin{frame}
% --  \frametitle{Sensitivity Analysis, Variance}
% --  
% --  \vspace*{3mm}
% --  
% --  Total variance of the probabilistic model response
% --  $y=f(\boldsymbol{X})$ is
% --  %
% --  \begin{eqnarray*}
% --  D = \mathrm{Var}[f(\boldsymbol{X})] = \int_{I^{n}} f^2(\boldsymbol{x}) \ d\boldsymbol{x} - f_0^2
% --  \end{eqnarray*}
% --  
% --  %Using Equations~\ref{eq_ANOVA_representation} and \ref{eq_orthogonal}, 
% --  Total variance $D$, decomposed 
% --  %
% --  \begin{eqnarray*}
% --  D = \sum_{i=1}^{n} D_i + \sum_{1\leq i <j \leq n} D_{ij} + ... + D_{1,2,...,n} = \sum_{s=1}^{n}\sum_{i_1<...<i_s}D_{i_1...i_s}
% --  \label{eq_variance_decomposition}
% --  \end{eqnarray*}
% --  %
% --  
% --  Variance contribution from individual summand
% --  %
% --  \begin{eqnarray*}
% --  D_{i_1..i_s} = \int_{I^s} f^2_{i_1...i_s}(x_{i_1}, ..., x_{i_s}) \ dx_{i_1}, ...dx_{i_s}, 
% --  \\
% --  1\leq i_1 < ... < i_s \leq n \mbox{;~} s= 1,...n
% --  \end{eqnarray*}
% --  %    
% --  
% --  
% --  \end{frame}
% --  
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Sobol Indices}


\begin{itemize}

\item[-] Sobol' indices $S_{i_1...i_s}$,
fractional contributions from 
random inputs $\{X_{i_1}, ..., X_{i_s}\}$ to the total variance $D$:
$S_{i_1...i_s} = D_{i_1...i_s} / D$
% %The Sobol indices $S_{i_1...i_s}$: 
% %
% \begin{equation*}
% S_{i_1...i_s} = D_{i_1...i_s} / D
% \end{equation*}
% %


\vspace*{2mm}

\item[-] First order indices $S_i$ $\rightarrow$ individual influence of each uncertain input
parameter 
%$X_i$
%

\vspace*{2mm}
\item[-] Higher order indices $S_{i_1...i_s}$ $\rightarrow$ mixed influence from groups
of uncertain input parameters
%



\vspace*{2mm}
\item[-] Total sensitivity indices,
% $S^{\mathrm{total}}_i$
%$\rightarrow$ 
influence of input parameter $X_i$
%
\begin{equation*}
S^{\mathrm{total}}_i = \sum_{\mathscr{S}_i}D_{i_1...i_s} 
\end{equation*}
%
\end{itemize}


\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Sensitivity Analysis}
% 
%        
% The Sobol indices for global sensitivity analysis can be used for
% 
% Ranking of input uncertain parameters $\boldsymbol{X} = [X_1, ..., X_n]$. 
% 
% Neglect of inessential uncertain parameters and high order terms in Equation~\ref{eq_ANOVA_representation}.   
% %
% 
% 
% 
% The total sensitivity indices $S^{\mathrm{total}}_i$ is defined to evaluate the total influence of a certain input parameter $X_i$ as: 
% %
% \begin{equation*}
% S^{\mathrm{total}}_i = \sum_{\mathscr{S}_i}D_{i_1...i_s} 
% \end{equation*}
% %
% 
% set $\mathscr{S}_i$ contains all the indexes involving index $i$ 
% and Sobol' indices set $\{D_{i_1...i_s}\}$ is the
% collection of all partial sensitivity indices that are related to parameter
% $X_i$.
% %
% \begin{equation*}
% \mathscr{S}_i = \{(i_1, ..., i_s): \exists k, 1\leq k \leq s, i_k = i\}
% \label{eq_index_set}
% \end{equation*}
% 
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Sobol Indices and Polynomial Chaos}


PC expansion of response, in ANOVA form (Sudret 2008)


\vspace*{5mm}

Multi-dimensional PC bases $\{\Psi_j(\boldsymbol{\xi})\}$ 
decomposed into products of single dimension PC chaos bases of different orders
%
\begin{equation*}
\Psi_j(\boldsymbol{\xi}) = \prod_{i=1}^{n} \phi_{\alpha_i}(\xi_i) 
\end{equation*}
%
$\phi_{\alpha_i}(\xi_i)$ is the single dimensional, order $\alpha_i$, polynomial function of underlying basic random variable $\xi_i$. 
%

%



 



\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Sobol Sensitivity Analysis}

\vspace*{4mm}            
%ANOVA $\rightarrow$ PC-based Sobol' indices: 
ANOVA $\rightarrow$ Sobol' indices: 
%$S_{i_1...i_s}^{PC}$:
%
$S_{i_1...i_s}^{PC} = \sum_{\boldsymbol{\alpha} \in \mathscr{S}_{{i_1}...i_s}} y^2_{\boldsymbol{\alpha}} \boldsymbol{E} \left[\Psi_{\boldsymbol{\alpha}}^2\right] / D^{PC}$

%  \vspace*{-2mm}            
%  \begin{equation*}
%  S_{i_1...i_s}^{PC} = \sum_{\boldsymbol{\alpha} \in \mathscr{S}_{{i_1},...,i_s}} y^2_{\boldsymbol{\alpha}} \boldsymbol{E} \left[\Psi_{\boldsymbol{\alpha}}^2\right] / D^{PC}
%  \end{equation*}
%  %

    
\vspace*{4mm}            
Total Sobol' indices: $S_{j_1...j_t}^{PC, \mathrm{total}} = \sum_{(i_1, ..., i_s) \in \mathscr{S}_{j_1,...,j_t}} S_{i_1...i_s}^{PC}    $
% % for any group of
% %parameters $\{\xi_{j_1}, ..., \xi_{j_t}\}$ is
% %
% \begin{equation*}
% S_{j_1...j_t}^{PC, \mathrm{total}} = \sum_{(i_1, ..., i_s) \in \mathscr{S}_{j_1,...,j_t}} S_{i_1...i_s}^{PC}   
% \end{equation*}
% %
% where $\mathscr{S}_{j_1,...,j_t} = \{(i_1, ..., i_s): (j_1,...,j_t) \subset (i_1, ..., i_s)\}$

% $\mathscr{S}_{j_1,...,j_t}$ is defined as: 
% %
% \begin{equation}
% \mathscr{S}_{j_1,...,j_t} = \{(i_1, ..., i_s): (j_1,...,j_t) \subset (i_1, ..., i_s)\}
% \end{equation}
% %


\vspace*{4mm}
Using PC representation of probabilistic model response,
Sobol' sensitivity indices are analytic and inexpensive 
%evaluated with very small computational expense. 
%


\end{frame}


% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Sobol Sensitivity Analysis}
% 
% 
% 
% \end{frame}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Sobol Sensitivity Analysis}
% 
% 
% 
% \end{frame}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Sobol Sensitivity Analysis}
% 
% 
% 
% \end{frame}
% 
% 
% 
% 
% 
% 
% 










% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
% \frametitle{SEPFEM: Example in 1D}
% 
% 
% 
% 
% \vspace*{-2mm}
% \begin{center}
% % \hspace*{-15mm}
% \movie[label=show3,width=9cm,poster,autostart,showcontrols]
% {\includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_elastic_900.png}}
% % /home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.pdf
% %{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Animations/SEPFEM_Animation_Elastic.mp4}
% {SEPFEM_Animation_Elastic.mp4}
% \end{center}
% 
% 
% % 
% %  \vspace*{-2mm}
% %  \begin{center}
% %  % \hspace*{-15mm}
% %  \movie[label=show3,width=9cm,poster,autostart,showcontrols]
% %  {\includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_elastic_900.png}}
% %  % /home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.pdf
% %  {/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Animations/SEPFEM_Animation_Elastic.mp4}
% %  \end{center}
% %  
% % \includegraphics[width = 12cm]{./img/figure_elastic_900.pdf}
% 
%  
% 
% \begin{flushleft}
% \vspace*{-15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/SEPFEM_Animation_Elastic.mp4}
% %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%   {\tiny (MP4)}
% \end{flushleft}
% %
% 
% 
% 
% \end{frame}
% 
% 
% 
% 




%  
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
% \frametitle{SEPFEM: Example in 3D}
%  
%  
% 
% %\vspace*{-5mm}
% \begin{center}
% % \hspace*{-15mm}
% \movie[label=show3,width=10cm,poster,autostart,showcontrols]
% {\includegraphics[width=10cm]
% {/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/SFEM_3D.png}}
% % /home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.pdf
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/SFEM_Animation_3D.mp4}
% %{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_27Jun2017/Summer_Slides/Animations/SFEM_Animation_3D.mp4}
% \end{center}
% 
% %  \includegraphics[width = 12cm]{./img/SFEM_3D.pdf}
% 
% \begin{flushleft}
% %\hspace*{-15mm}
% \vspace*{-15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/SFEM_Animation_3D.mp4}
% %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%   {\tiny (MP4)}
% \end{flushleft}
% %
% 
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%































      
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Real-ESSI Simulator}

      
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection*{Real-ESSI Simulator System}
% \subsection{Real ESSI Components}
\subsection{\ }



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 

\frametitle{Real-ESSI Simulator System}

The  Real-ESSI, 
{\underline {\bf Real}}istic  
%{\underline {\bf M}}odeling  and  
%{\underline {\bf S}}imulation  of  
{M}odeling  and  
{S}imulation  of  
{\underline {\bf E}}arthquakes,  
{\underline {\bf S}}oils,
{\underline {\bf S}}tructures  and  their  
{\underline {\bf I}}nteraction  Simulator  is  a  software,  hardware  and
documentation   system   for   time  domain,
linear and  nonlinear,  
elastic and inelastic,  
deterministic  or probabilistic,
3D, 
modeling and simulation of:

    \begin{itemize}
\vspace*{-1mm}
      \item[-] statics and dynamics of soil,
%\vspace*{1mm}
      \item[-]    statics and dynamics of rock,
%\vspace*{1mm}
      \item[-]    statics and dynamics of structures,
%\vspace*{1mm}
      \item[-]    statics of soil-structure systems, and
%\vspace*{1mm}
      \item[-]    dynamics of earthquake-soil-structure system interaction
    \end{itemize}



Used for:
\begin{itemize}
%\vspace*{1mm}
  \item[-] Design, linear elastic, load combinations, dimensioning


%\vspace*{1mm}
  \item[-] Assessment, nonlinear/inelastic, safety margins
\end{itemize}




\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 

\frametitle{Real-ESSI Simulator System}

 
\begin{itemize}


  \item[] Components
    \begin{itemize} 
     \item[-] Real-ESSI Pre (gmsh/gmESSI, X2ESSI) 
     \item[-] Real-ESSI Program (local, remote, cloud)
     \item[-] Real-ESSI Post (Paraview/pvESSI, Python, Matlab)

    \end{itemize} 

\vspace*{1mm}
  \item[] Availability
    \begin{itemize} 
     \item[-] Linux Executables                                           
     \item[-] Amazon Web Services                                          
     \item[-] Docker Container Image
       \begin{itemize} 
      \vspace*{-1mm}
         \item[] Linux 
         \item[] MS-Windows 
         \item[] MacOS 
       \end{itemize} 

    \end{itemize} 
  
  
  
   
   
   
%     \begin{itemize}
% %\vspace*{1mm}
%      \item[-] Educational  Institutions: AWS and Linux Executables, free 
%      \item[-] Government Agencies, National Labs: AWS GovCloud, free
%      \item[-] Professional  Practice: AWS and Linux Executables, commercial
% %\vspace*{1mm}
% %%\vspace*{1mm}
% %      \item Sources available to collaborators
%     \end{itemize}


%  
%  \vspace*{3mm}
%    \item Real-ESSI education and training: theory and applications
%  


\vspace*{1mm}
  \item[] Real-ESSI documentation and program available at  
\url{http://real-essi.us/}    
%\url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
%
%\url{http://real-essi.info/}
%


% \vspace*{2mm}
%   \item
% 


\end{itemize}


\end{frame}




% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Quality Assurance}
% 
% \begin{itemize}
% 
% \item Full verification suit for each element, model, algorithm
% 
% \vspace*{5mm}
% \item Certification process
% 
%  \begin{itemize}
% 
% \vspace*{2mm}
%     \item[-] ASME  NQA-1
%  
% \vspace*{2mm}
%     \item[-] ISO-90003-2014
% 
%  \end{itemize}
% 
% %\vspace*{3mm}
% %\item[] Verification examples given below
% 
% \end{itemize}
% 
% 
% 
% 
% \end{frame}
% 
% %  % 
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Real-ESSI}
%  
%  \begin{itemize}
%  
%  
%  
%  %\vspace*{2mm}
%    \item    A  system  for  time domain, nonlinear/inelastic,  deterministic  or 
%    probabilistic, modeling and simulation of
%  
%      \begin{itemize}
%        \item  statics and dynamics of soil,
%        \item  statics and dynamics of rock,
%        \item  statics and dynamics of structures,
%        \item  statics of soil-structure systems, and
%        \item  dynamics of earthquake-soil-structure system interaction.
%        \end{itemize}
%  
%  
%  \vspace*{1mm}
%    \item Design, linear elastic, load combinations, dimensioning
%  
%  
%  \vspace*{1mm}
%    \item Assessment, nonlinear/inelastic, safety margins
%  
%  
%  
%  %\vspace*{1mm}
%  %  \item  Develops methods and models that inform and predict rather than (force) fit.
%  
%  \vspace*{1mm}
%          \item Collaboration and financial support from the US-DOE, US-NRC,
%          US-NSF, Caltrans, CNSC-CCSN, UN-IAEA, Shimizu, Basler\&Hofmann, etc.
%  
%  
%  
%  \end{itemize}
%   
%  \end{frame}


%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Real-ESSI Modeling Features}
%  
%  \begin{itemize}
%  
%  
%  
%  %\vspace*{2mm}
%    \item[-] Solid elements: dry, (un-)saturated, elastic, inelastic
%  
%  \vspace*{1mm}
%    \item[-] Structural elements: beams, shells, elastic, inelastic 
%  
%  \vspace*{1mm}
%    \item[-] Contact/interface/joint elements: Bonded, Shear/Frictional (EPP, EPH,
%    EPS); Gap/Normal; linear, nonlinear, dry, coupled/saturated,
%  
%  \vspace*{1mm}
%    \item[-] Super element: stiffness and mass matrices
%  
%  \vspace*{1mm}
%    \item[-] Material models: soil, rock, concrete, steel... 
%    
%  \vspace*{1mm}
%    \item[-] Seismic input: 1C and 3C, deterministic or probabilistic
%  
%  \vspace*{1mm}
%    \item[-] Energy dissipation: elastic-plastic, viscous, algorithmic
%  
%  \vspace*{1mm}
%    \item[-] Solid/Structure-Fluid interaction, full coupling, OpenFOAM
%  
%  \vspace*{1mm}
%    \item[-] Intrusive probabilistic inelastic modeling
%  
%  %
%  %\vspace*{1mm}
%  %  \item Modeling features listed at
%  %  \hspace*{5mm}
%  %  \href{http://real-essi.info/}{http://real-essi.info/} 
%  %%  \hspace*{5mm} 
%  %%  and 
%  %%  \hspace*{5mm} 
%  %%  \href{http://real-essi.info/}{http://real-essi.info/}
%  
%  
%  \end{itemize}
%   
%  \end{frame}
%  

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real-ESSI Simulation Features}



%\vspace*{-10mm}

\begin{itemize}

  \item[-] Static loading stages

\vspace*{1mm}
  \item[-] Dynamic loading stages

\vspace*{1mm}
  \item[-] Restart, simulation tree

\vspace*{1mm}
  \item[-] Solution advancement methods/algorithms, \\
        on global and constitutive levels, \\
        with and without enforcing equilibrium


%\vspace*{1mm}
%  \item Load combinations, elastic, for design

\vspace*{1mm}
  \item[-] High Performance Computing
%  clusters, cloud, supercomputers 
    \begin{itemize}
%\vspace*{1mm}
      \item[.] Fine grained, template mataprograms, small matrix library
%\vspace*{1mm}
      \item[.] Coarse grained, distributed memory parallel 
    \end{itemize}


% \vspace*{1mm}
%   \item All  Simulation Features are listed at  
%   \hspace*{5mm}
%   \href{http://real-essi.info/}{http://real-essi.info/} 
% %  \hspace*{5mm} 
% %  and 
% %  \hspace*{5mm} 
% %  \href{http://real-essi.info/}{http://real-essi.info/}



\end{itemize}


 
\vspace*{-60mm}
%\begin{figure}[!hbpt]
\begin{flushright}
\includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Theory_Introduction/tex_works_psfigures_loading_stage-increments-iterations.pdf}
\end{flushright}
%\vspace*{-0.5cm}
%\end{figure}
%




 
\end{frame}



  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Real ESSI Simulator: Domain Specific Language, DSL}
%  
%   \begin{itemize}
%     \item Domain Specific Language (DSL), Yacc \& Lex
%  \vspace*{3mm}
%     \item English like modeling and simulation language
%  \vspace*{3mm}
%     \item Parser and compiler, can define functions, models, etc.
%  \vspace*{3mm}
%     \item Can extend models and methods
%  \vspace*{3mm}
%     \item Requires units!
%   \end{itemize}
%  %
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}[fragile]
%   \frametitle{DSL: English Language Binding Modeling Parser}
%  {\footnotesize
%  \begin{lstlisting}
%  // Defining variables
%  x = 7; // x is double-valued variable with adimenisional units.
%  y = 3.972e+2; // Decimal and scientific notation is supported.
%  // Operations: All standard arithmetic operations (Unites!)
%  a = x + y;  // Addition
%  b = x - y;  // Subtraction
%  c = x*y;  // Product
%  d = x/y;  // Quotient
%  e = y%x;  // Modulus (how many times x fits in y)
%  // Predefined variables. For example, the variable 'm' defines 'meter'.
%  L1 = 1*m;
%  L2 = 40*mm;    // Defines L2 to be 40 millimiters.
%  L3 = 3.14*cm;
%  L4 = 3.14;
%  A5 = 3.14*cm^2;
%  \end{lstlisting}
%  }
%  \end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}[fragile]
%   \frametitle{DSL: English Language Modeling Parser}
%  {\footnotesize
%  \begin{lstlisting}
%  F1 = 10*kN; // Define few forces.
%  F2 = 300*N;
%  F3 = 4*kg*g; // Here g is the predefined acceleration
%               // due to gravity.
%  // Operations are sensitive to units. For example,
%  foo = L1 + F1; // Produces an error because units are
%                 // not compatible. However,
%  L4 = L1 + L2 + L3;  // is OK.
%  // Multiplication (division and modulus) always work
%  // because the result produces a quantity with new units
%  // (except when the adimensional quantity is involved).
%  A = L1*L2;
%  pressure = F1 / A;
%  // All numbers are converted to SI units (kg - m - s)
%  // and internally stored in that system.
%  \end{lstlisting}
%  }
%  \end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{DSL: ESSI Input Language, Basics}
%  
%  
%  \begin{itemize}
%  
%  \item Angle  brackets  \lstinline|<>| denotes  user input
%  
%  \item Expected   unit (dimension)  is  given (example: 
%  \lstinline|<L>|, for length unit)
%  
%  \item Symbol \lstinline|<.>| represents the adimensional quantity.
%  
%  \item Vertical  bar  \lstinline+|+ (``OR'' sign)) is used to separate two or more keyword
%  options,   i.e.   \lstinline+[a|b|c]+   is   used   indicate   keyword   options
%  \lstinline+a+ or \lstinline+b+ or \lstinline+c+.
%  
%  \item The  symbol  \lstinline+|...|+  is  used  to  denote  where several long options
%  exist  and  are  explained elsewhere (an example of this is available below in a
%  material model definitions).
%  
%  \end{itemize}
%  
%  \end{frame}
%  
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{DSL: ESSI Input Language, Units}
%  
%  
%  All    commands  require  unit  consistency.  Base units, SI  or  other (British
%  Imperial)  can be used
%  \begin{itemize}
%    \item  length, symbol  $L$, units [m, in, ft]
%    \item  mass, symbol    $M$, units [kg, lb],
%    \item  time, symbol    $T$, units [s]
%  \end{itemize}
%  
%  Derived units can also be used:
%  
%  \begin{itemize}
%    \item angle, symbol rad (radian), unit [$dimensionless, L/L$]
%    \item force, symbol N (Newton), units [$N, kN, MN, M*L/T^2$],
%    \item stress, symbol Pa (Pascal), units [$Pa, kPa, MPa, N/L^2, M/L/T^2$]
%    \item strain, symbol (no symbol), units [$L/L$]
%    \item mass density, symbol (no symbol), units [$M/L^3$]
%    \item force density, symbol (no symbol), units [$M/L^2/T^2$]
%  \end{itemize}
%  
%  \end{frame}
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{DSL: ESSI Input Language, Loading Stages}
%  
%  
%  Start         a    new    loading    stage  with
%  
%  \lstinline|new loading stage "loading_stage_name";|
%  
%  \vspace*{0.5cm}
%  Example,  starting a new loading stage called {\it "self weight load"}
%  
%  \lstinline|new loading stage "self weight load";|
%  
%  
%  
%  
%  
%  
%  \end{frame}
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  
%  % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}[fragile]
%   \frametitle{DSL: Beam Example, Model}
%  
%  
%  
%  \begin{figure}[!h]
%  \begin{center}
%  \includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Cantilever_Beam.pdf}
%  %\caption{8 node brick element}
%  %\label{fig:8node_command}
%  \end{center}
%  \end{figure}
%  
%  
%  %}
%  \end{frame}
%  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[fragile]
 \frametitle{Real ESSI DSL Example}


\vspace*{-8mm}
\begin{figure}[!h]
\begin{flushright}
\includegraphics[width=4cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Cantilever_Beam.pdf}
%\caption{8 node brick element}
%\label{fig:8node_command}
\end{flushright}
\end{figure}


\vspace*{-4mm}

\begin{lstlisting}
model name "SmallTestModel";
new loading stage "First_static";
// Nodal  Coordinates
add node # 1 at (0*m, 0*m, 0*m) with 6 dofs;
add node # 2 at (0*m, 0*in, 1000*mm) with 6 dofs;
add element # 1 type beam_elastic with
  nodes (1, 2) cross_section=1.0*m^2
  elastic_modulus=1.0e5*KN/m^2
  shear_modulus=2.0e4*KN/m^2
  torsion_Jx=2*0.083*m^4
  bending_Iy=0.083*m^4 bending_Iz=0.083*m^4
  mass_density=2500.0*kg/m^3
  xz_plane_vector = (0, -1, 0)
  joint_1_offset = (0.0*m, 0.0*m, 0.0*m)
  joint_2_offset = (0.0*m, 0.0*m, 0.0*m);
\end{lstlisting}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[fragile]
 \frametitle{Real ESSI DSL Example}


\begin{lstlisting}
fix node No 1 dofs all;
add load # 1 to node # 2 type linear Fy=-9*kN;
define load factor increment 0.01;

define solver UMFPack;

define convergence test
  Norm_Displacement_Increment
  tolerance = 1e-5
  maximum_iterations = 20
  verbose_level = 4;

define algorithm Newton;

simulate 100 steps using static algorithm;

bye;
\end{lstlisting}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Real-ESSI Model Development}
%  
%  \begin{itemize}
%  
%      \item[-] Pre-Processing, model development gmsh/gmESSI
%  
%  \vspace*{1mm}
%      \item[-] Existing model translation, SASSI$\rightarrow$Real-ESSI
%  
%  
%  \vspace*{1mm}
%      \item[-] Self documenting input language
%  
%  \vspace*{1mm}
%      \item[-] Units required for all input variables
%  
%  \vspace*{1mm}
%      \item[-] All variables and constants need to be defined by user
%  
%  
%  
%  \vspace*{1mm}
%      \item[-] Sophistication level of choice
%  
%  %\vspace*{1mm}
%  %     \item[-] Reduce modeling uncertainty
%  
%  \vspace*{1mm}
%      \item[-] Model developed in phases
%  
%  \vspace*{1mm}
%      \item[-] Verify model components
%  
%  
%  \vspace*{1mm}
%      \item[-]  Build confidence in inelastic modeling
%  
%  \end{itemize}
%   
%  \end{frame}
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%    \frametitle{Real-ESSI  Modeling Phases}
%  
%  
%  
%  \begin{figure}[htbp]
%  \begin{center}
%    \includegraphics[width = 2.3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-structure/overview.png}
%  \vspace*{-1mm}
%  \\
%    \includegraphics[width = 0.35cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/free_field_1D/DRM_1D_motion_3D_just_column.jpg}
%  \hspace*{5mm}
%  %  \includegraphics[width = 0.1cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/free_field_1D/DRM1D_Motion3D.png}
%    \includegraphics[width = 2.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/free_field_3D/motion3D_DRM3D_free_field.png}
%  \hspace*{5mm}
%  %  \includegraphics[width = 1cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-foundation/soil_foundation.png}
%  %  \includegraphics[width = 3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-foundation/slice.png}
%    \includegraphics[width = 2.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-foundation/foundation_results.png}
%  %  \includegraphics[width = 3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-structure/overview.png}
%  \\
%  \vspace*{-3mm}
%    \includegraphics[width = 1.0cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/structure-only.png}
%  \hfill
%    \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen1.png}
%  \hfill
%    \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen2.png}
%  \hfill
%    \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen3.png}
%  \hfill
%    \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen4.png}
%  \hfill
%    \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen5.png}
%  \hfill
%    \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen6.png}
%  \hfill
%  %  \includegraphics[width = 1.0cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/imposed_motion/structure-only.png}
%  %\hfill
%    \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/imposed_motion/imposed_motion_results.png}
%  %   \includegraphics[width = 0.1cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-structure/overview.png}
%  \\
%  \vspace*{-1mm}
%    \includegraphics[width = 6cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-structure/DRM3D_motion3D_structure.png}
%  \end{center}
%  \end{figure}
%  
%  
%  
%  \end{frame}
%  
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Real-ESSI Results Post Processing}
%  
%  \begin{itemize}
%  
%  
%        \item All output is saved (stress, strain, displacements, energy...)
%  
%  \vspace*{5mm}
%        \item Time histories, scripts to plot or extract in preferred format
%  
%  \vspace*{5mm}
%        \item 3D visualization, Paraview with pvESSI plugin
%  
%  
%  
%  \end{itemize}
%   
%  \end{frame}
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Real-ESSI Core Functionality}
%  
%  \begin{itemize}
%  
%  
%  
%  %\vspace*{2mm}
%    \item [-] Introduction to inelastic, nonlinear analysis for practicing engineers
%  
%  % 
%  %  % \vspace*{3mm}
%  %    \item Usable models for professional practice
%  %  
%  %  %\vspace*{2mm}
%  %   \item  Core  functionality  needed  for  nonlinear  modeling  in professional
%  %   practice
%  %  % 
%  %  
%  
%  
%  %  %\vspace*{0.3cm}
%  %  %\vspace*{2mm}
%  %    \item Hierarchy of modeling capabilities, 
%  %    
%  %       \begin{itemize}
%  %  
%  %  %\vspace*{1mm}
%  %          \item Linear elastic models, elastic constants, viscous damping
%  %  
%  %  %\vspace*{1mm}
%  %          \item    Nonlinear  models,  core  functionality,  does not require much
%  %          material data however, sensitivity study is advised
%  %    
%  %  %\vspace*{1mm}
%  %          \item High sophistication  nonlinear models, require material data
%  %       
%  %       
%  %       \end{itemize}
%  %  
%  
%  
%  \vspace*{2mm}
%    \item[-]   Use  of prescribed, required (low, medium, high) fidelity numerical
%    models to analyze ESSI behavior
%  
%  
%  \vspace*{2mm}
%    \item[-]  Set of suggested modeling and simulation parameters
%  
%  \vspace*{2mm}
%    \item[-]  Investigate  sensitivity  of  response  to model sophistication
%  
%  \vspace*{2mm}
%    \item[-]  Investigate  sensitivity  of response  to model parameters
%  
%  % 
%  % \vspace*{1mm}
%  %   \item[]  Accurately   follow  the  flow   of  seismic  energy  in  a
%  %   soil structure system
%  % 
%  % \vspace*{1mm}
%  %   \item[]   The  goal is to create methodology and numerical tool that is used to 
%  %   predict and inform and not to fit
%  % 
%  % 
%  % 
%  % %\vspace*{1mm}
%  % %  \item[]   Directing,   in   space   and   time,   seismic  energy  flow  in  the
%  % %  soil structure system
%  % 
%  
%  
%  \end{itemize}
%  \end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Real-ESSI Core Functionality Components}
%  
%  \begin{itemize}
%  
%  
%     \item[-] Structural elements: Truss, Beam, Shell, Super-Element
%  
%  \vspace*{2mm}
%     \item[-] Soil, solids:  elastic, $G/G_{max}$
%          
%  \vspace*{2mm}
%     \item[-] Contacts/interfaces/joints: Bonded, Frictional (EPP, EPH, EPS), Gap
%     open/close
%  
%  
%  \vspace*{2mm}
%     \item[-] Loads: Static, Dynamic (earthquake, 1C or 3$\times$1C), Restart   
%  
%  \vspace*{2mm}
%     \item[-] Simulation: Explicit no-equilibrium, Implicit equilibrium
%  
%  \vspace*{2mm}
%     \item[-] Core Functionality Application programs: APPs
%  % 
%  
%  
%  \end{itemize}
%  
%  
%  \end{frame}
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Real-ESSI Education and Training}
%  
%  \begin{itemize}
%  
%  
%    \item Real-ESSI Eduction 
%      \begin{itemize}
%  \vspace*{1mm}
%        \item[-] Online courses
%  \vspace*{1mm}
%        \item[-] Educational short videos
%  \vspace*{1mm}
%       \item[-] Professional practice 
%  %   \vspace*{1mm}
%  %        \item Developers 
%  \vspace*{1mm}
%       \item[-] Practical examples available in lecture notes, and documentation
%  \vspace*{1mm}
%       \item[-] Documentation, Lecture Notes:
%               (I) Theory and Computational Formulation,
%               (II) Software and Hardware System,
%               (III) Verification and Validation,
%               (IV) Modeling and Simulation Examples,
%               (V) Application to Practical Engineering Problems.
%  
%      \end{itemize}
%  
%  %\vspace{1mm}
%  %  \item Documentation, extensive
%  
%  \vspace{2mm}
%    \item Lecture notes available online through 
%  \url{http://real-essi.info/}    
%    
%  
%  \end{itemize}
%   
%  \end{frame}
%  
%  
%  
%  
%  
%  
%  

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  \subsection{Verification  and Validation}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Verification and Validation}
%  \begin{itemize}
%      
%      
%  
%  
%  
%       \item  {{  Verification:}  provides  evidence  that  the  model is solved
%       correctly.} Mathematics issue.  Well developed 
%       for the Real ESSI Simulator.
%  
%  \vspace*{4mm}
%       \item  {{  Validation:}  provides  evidence  that  the  correct  model is
%       solved.} Physics issue. Work in progress, US-DOE project. 
%          
%  \vspace*{4mm}
%     \item {  Prediction:}  use  of  computational  model
%     to  foretell  the  state  of  a  physical  system  under  consideration under
%     conditions for which the computational model has not been validated.
%    
%  %   \item {  Prediction under Uncertainty}:  use  of  computational  model
%  %   to  predict  the  state  of SSI system under
%  %   conditions for which the computational model has not been validated.
%  % 
%  % 
%  %   
%  % \vspace*{1mm}
%  %    \item  Modeling  and  parametric uncertainties are always present, need to be
%  %    addressed 
%  % 
%  % %\vspace*{1mm}
%  % %   \item Predictive capabilities with {low Kolmogorov Complexity}
%  % %
%  % 
%  % \vspace*{1mm}
%  %      \item Goal: Predict and Inform and rather than (force) Fit
%  % 
%  % 
%  
%  
%  
%  \end{itemize}
%  \end{frame}
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{V \& V Motivation}
%  
%  
%  
%  \begin{itemize}
%  
%  
%  %\vspace*{0.5cm}
%  \item How much can (should) we trust  model implementations (verification)?
%  
%  %\vspace*{0.5cm}
%  \item How much can (should) we trust numerical simulations (validation)?
%  
%  %\vspace*{0.5cm}
%  \item How good are our numerical predictions?
%  
%  %\vspace*{0.5cm}
%  \item    Can      simulation  tools  be used for improving safety and economy?
%  
%  %   \vspace*{2.0truecm}
%     \item  V  \&  V  procedures  are  the  primary means of assessing accuracy in
%     modeling and computational simulations
%  
%  %   \vspace*{1.0truecm}
%     \item  V  \&  V  procedures  are the tools with which we build confidence and
%     credibility in modeling and computational simulations
%  
%  
%  
%  
%  %\vspace*{2.5cm}
%  %\item How do we  use experimental simulations   to improve models
%  
%  
%  
%  
%  \end{itemize}
%  
%  
%  
%  
%  \end{frame}
%  
%  
%  
%     
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % \begin{frame}
%  %  \frametitle{Role of Verification and Validation}
%  % 
%  % 
%  % 
%  % \begin{figure}[!h]
%  % \begin{center}
%  % \hspace*{-2cm}
%  % %{\includegraphics[width=5.0cm]{/home/jeremic/tex/works/Conferences/2012/ASME_V_and_V_symposium/presentetation/RoleVV_NEW_knowledge.pdf}}
%  % {\includegraphics[width=5.0cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/RoleVV_NEW_knowledge.pdf}}
%  % %{\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2011/USNCCM11_Minneapolis/Coupled/Present/VandV_ODEN.jpg}}
%  % {\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/VandV_ODEN.jpg}}
%  % \hspace*{-2cm}
%  % \end{center}
%  % \end{figure}
%  % 
%  % {Oberkampf et al. \hspace*{4cm}  Oden et al.}
%  % %
%  % %\item Models available (some now, some later)
%  % %\vspace*{-2.0cm}
%  % 
%  % %
%  % %\item Models available (some now, some later)
%  % %\vspace*{-2.0cm}
%  % \end{frame}
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  
%  \begin{frame}
%    \frametitle{Fundamentals of Verification and Validation}
%  
%  
%  
%  %--
%  
%  
%  \begin{figure}[!h]
%  % \vspace*{-0.5cm}
%  \hspace*{-8mm}
%  %\begin{center}
%  %{\includegraphics[width=11cm]{/home/jeremic/tex/works/Conferences/2005/OpenSeesWorkshopAugust/DeveloperSymposium/VerifValidFund01.pdf}}
%  {\includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/VerifValidFund01.pdf}}
%  %\end{center}
%  \end{figure}
%  
%  
%  \end{frame}
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Important Sources}
%  
%  
%  
%  \begin{itemize}
%  
%  
%  
%  
%  %\item {\it  Short Course on Verification and Validation in
%  %Computational Mechanics}, by {\sc Dr. William Oberkampf}, Sandia National Laboratories
%  %July 27th, 2003, Albuquerque, New Mexico.
%  
%  \item
%  {\sc W.~L. Oberkampf, T.~G. Trucano, and C. Hirsch.}
%  Verification, validation and predictive capability in computational
%    engineering and physics.
%  In {\em Proceedings of the Foundations for Verification and
%    Validation on the 21st Century Workshop}, pages 1--74, Laurel, Maryland,
%    October 22-23 2002. Johns Hopkins University / Applied Physics Laboratory.
%  %{\href{http://sokocalo.engr.ucdavis.edu/~jeremic/UsefulReadings/Oberkampf-Trucano-Hirsch.pdf}
%  %{PDF available here}}
%  
%  
%  \item
%  {\sc P.~J. Roache.}
%   {\em Verification and Validation in Computational Science and
%    Engineering}.
%  Hermosa publishers, 1998.
%  ISBN 0-913478-08-3.
%  %
%  
%  
%  % \item Material from {\it Verification and Validation in Computational Mechanics}
%  % web site \texttt{http://www.usacm.org/vnvcsm/} at the USACM.
%  
%   \item  William L. Oberkampf and Christopher J. Roy. Verification and Validation
%   in Scientific Computing. Cambridge University Press, 2010.
%  
%  
%  
%  \end{itemize}
%  
%  
%  
%  
%  \end{frame}
%  
%  
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % 
%  % 
%  % 
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Verification}
%  
%  \begin{itemize}
%  
%  \item   Source code management
%  \item   Source code verification
%  
%  \item  Constitutive integration
%  \item   Static and dynamic behavior of single phase solids
%  \item       Static  and dynamic behavior of fully and partially saturated, fully
%  coupled, porous solid-pore fluid problems
%  \item   Static and dynamic behavior of structural elements
%  \item            Static    and    dynamic    behavior    of   special   elements
%  (contacts-interface/gap-frictional/dry-saturated, isolators/dissipators)
%  \item   Static and dynamic FEM solution advancement
%  \item   Seismic wave propagation problems
%  \item FEM Model verification, hierarchy of models
%  %\item   Static and Dynamic Behavior of Soil-Structure-Interaction
%  
%  \end{itemize}
%  
%  \end{frame}
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Constitutive Integration Verification}
%  
%  
%  \begin{itemize}
%  
%    \item Asymptotic regime of convergence
%  
%    \item Richardson extrapolation
%  
%    \item Grid convergence index
%  
%  \end{itemize}
%  
%  
%   \begin{center}
%   \begin{figure}[!htbp]
%  \vspace*{-3mm}
%   \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/asymptotic_regime.pdf}
%   \includegraphics[width=3.5truecm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/asymptotic_nonassociate.pdf}
%  \\
%   \includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/error-map/DPAF_implicitErrMap.pdf}
%   \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/GCI/NonAssociate.pdf}
%  \vspace*{-3mm}
%   \end{figure}
%   \end{center}
%  
%  
%  
%  
%  
%  
%  
%  
%  \end{frame}
%  
%  
%  
%  
%  
%  
%  
%  % 
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % \begin{frame}
%  %  \frametitle{Seismic Energy Input and Dissipation}
%  % 
%  % \begin{itemize}
%  % 
%  % \vspace*{1mm}
%  %      \item[] Seismic energy input, through a closed boundary (DRM)
%  % 
%  % 
%  % \vspace*{4mm}
%  %      \item[] Mechanical dissipation outside SSI domain:
%  %        \begin{itemize}
%  %          \item[] Reflected wave radiation
%  %          \item[] SSI system oscillation radiation
%  %        \end{itemize}
%  % %\vspace*{1mm}
%  %      \item[] Mechanical dissipation/conversion inside SSI domain:
%  %        \begin{itemize}
%  %          \item[] Inelasticity of soil and contact zone
%  %          \item[] Inelasticity/damage of structure and foundation
%  %          \item[] Viscous coupling of fluids and  soils and structure
%  % % %         \item[] potential and kinetic energy
%  % %          \item[] potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
%  %        \end{itemize}                           
%  % 
%  % 
%  % 
%  % %\vspace*{1mm}
%  % %   \item[] Numerical energy dissipation (numerical damping/production and period  errors)
%  % %   \item[] Numerical energy dissipation (damping/production)
%  %    \item[] Numerical energy dissipation/production
%  % 
%  % 
%  % \end{itemize}
%  % 
%  % %
%  % \end{frame}
%  % %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % 
%  
%  
%   
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   
%  \frametitle{Energy Dissipation Verification: \\ Plastic Work $\neq$ Plastic Dissipation}
%   
%  %\begin{itemize}
%  %\item Negative incremental energy dissipation
%  %\item Plastic work is NOT plastic dissipation
%  %\end{itemize}
%   
%  \begin{figure}[!H]
%  \begin{center}
%  \includegraphics[height=4.5cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Negative_Dissipation_Problem.png}
%  \end{center}
%  \end{figure}
%   
%   \vspace*{-2mm}
%  \begin{itemize}
%  
%  \item[] Direct violation of the second law of thermodynamics
%  
%  %\vspace*{3mm}
%  \item[] 600 papers since 1990 (!?!) repeat this error
%  
%  % \vspace*{3mm}
%  % \item[] Important form of energy missing: {Plastic Free Energy}
%  % 
%  % \vspace*{3mm}
%  % \item[] First described by Taylor and Quinney in 1934! 
%  % 
%  % \vspace*{3mm}
%  % \item[] Plastic Work vs. {Plastic Energy Dissipation}
%  
%  
%  %\vspace*{4mm}
%  %\item[] However it seems to be forgotten
%  
%  \end{itemize}
%  
%  
%  \end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % \begin{frame}
%  %  \frametitle{Dynamic Time Stepping Verification}
%  % 
%  % %\footnotesize
%  % Based  on  the  amplification  matrix ${\bf A}$,  to  calculate the analytical solution of
%  % damping ratios and period shift.
%  % 
%  % Example: Hilber-Hughes-Taylor $\alpha=-0.1$
%  % 
%  % \begin{figure}
%  % \hspace*{-5mm}
%  % \includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/dynamic/hht/HHT-alpha-01-xi.jpg}
%  % \includegraphics[width=6cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/dynamic/hht/HHT-alpha-01-period-shift.jpg}
%  % \end{figure}
%  % % HHT Integration $\alpha=-0.2$
%  % % \begin{figure}
%  % % \includegraphics[width=0.36\textwidth]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/dynamic/hht/HHT-alpha-02-xi.jpg}
%  % % \includegraphics[width=0.36\textwidth]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/dynamic/hht/HHT-alpha-02-period-shift.jpg}
%  % % \end{figure}
%  % 
%  % 
%  % \end{frame}
%  % 
%  
%  
%  
%  
%  
%  
%  
%  
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Seismic Input Verification, DRM}
%  % \begin{figure}
%  % % \includegraphics[scale=0.35]{Present06_figs/3DModel.eps}
%  %  \includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/3DModel.eps}
%  % \end{figure}
%  
%  \begin{figure}
%  %\hspace*{-5mm}
%   \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/90m_Northridge_EW.eps}
%  \\
%   \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/90m_Northridge_NS.eps}
%  \\
%   \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/90m_Northridge_UD.eps}
%  \end{figure}
%  
%  
%  
%  
%  % local
%  % local% local
%  % local%\vspace*{-2mm}
%  % local\begin{center}
%  % local\hspace*{-16mm}
%  % local%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
%  % local\movie[label=show3,width=61mm,poster,showcontrols]
%  % local  {\includegraphics[width=60mm]
%  % local  {movie_ff_3d_mp4_icon.jpeg}}
%  % local  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_ff_3d.mp4}
%  % local%\hspace*{-2mm}
%  % local%\hfill
%  % local%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
%  % local\movie[label=show3,width=61mm,poster,showcontrols]
%  % local  {\includegraphics[width=60mm]{movie_ff_1d_mp4_icon.jpeg}}
%  % local  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_ff_1d.mp4}
%  % local\hspace*{-16mm}
%  % local\end{center}
%  % local% local  
%  
%  
%  % online % online
%  % online % online
%  % online % online
%  % online \begin{center}
%  % online \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
%  % online   {\includegraphics[width=50mm]{movie_ff_3d_mp4_icon.jpeg}}
%  % online %
%  % online \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_1d.mp4}
%  % online   {\includegraphics[width=50mm]{movie_ff_1d_mp4_icon.jpeg}}
%  % online \end{center}
%  % online % online
%  % online % online
%  % online % online
%  % online 
%  
%  
%  
%  \end{frame}
%  
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Verification: ANDES Shell}
%  
%   \begin{center}
%  % \includegraphics[width=0.6\textwidth]{./_Jose_Files/fig1_static_tests.pdf}
%  \hspace*{-10mm}
%   \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/fig1_static_tests.pdf}
%  % \includegraphics[width=0.6\textwidth]{./_Jose_Files/fig2_static_tests.pdf}
%   \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/fig2_static_tests.pdf}
%  \hspace*{-10mm}
%  \end{center}
%  
%  \begin{flushleft}
%      \begin{tabular}{|l|l|}
%      \hline
%   $N_{\texttt{subd}}$   &      $u_z$ \\ \hline
%       2 &  96.2118 \\
%       7 & 100.096 \\
%     101 & 100.002 \\
%         &            \\ \hline
%      \end{tabular}
%  \end{flushleft}
%  
%  
%  \vspace*{-30mm}
%  
%   \begin{flushright}
%  % \includegraphics[width=0.9\textwidth]{./_Jose_Files/Test_shell_andes_1_free_vibration_EigenMode1.png}
%  %\hspace*{-10mm}
%   \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/Test_shell_andes_1_free_vibration_EigenMode1.png}
%   \\
%  \vspace*{-8mm}
%   \includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/Test_shell_andes_2_free_vibration_EigenMode1.png}
%  \hspace*{-10mm}
%  \end{flushright}
%  
%  \end{frame}
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  \begin{frame}
%   \frametitle{Verification: Irregular Solids and Poisson's Ratio}
%  
%  
%  % \begin{itemize}
%  %  \item Irregular Mesh
%  %  \item Mesh Refinement
%  % \end{itemize}
%  
%   \begin{figure}
%  %  \hspace*{-25mm}
%  %  \includegraphics[width=5.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/beam_8brick.pdf}
%  % % \hspace*{-25mm}
%  % % \includegraphics[width=5.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/beam_8brick_more_2.pdf}
%   \hspace*{-25mm}
%   \includegraphics[width=6.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/beam_brick27_shape1_vertical.pdf}
%   \hspace*{-35mm}
%   \includegraphics[width=6.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/beam_brick27_shape2_vertical.pdf}
%   \hspace*{-35mm}
%   \includegraphics[width=6.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/beam_brick27_shape3_vertical.pdf}
%   \hspace*{-25mm}
%   \end{figure}
%  
%  
%   \vspace*{-6mm}
%  
%  \begin{figure}
%  \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/irregular_shape.png}
%  \end{figure}
%  
%  % \begin{itemize}
%  %  \item Verification Results of High Poisson's ratios
%  % \end{itemize}
%  
%   \vspace*{-5mm}
%  
%  \begin{figure}
%  \hspace*{-9mm}
%  \includegraphics[width=4.0cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/error27brick_beam_different_poisson_ratio_disp_div100.jpeg}
%  \hspace*{3mm}
%  \includegraphics[width=4.0cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/high_poisson.png}
%  \end{figure}
%  
%  
%  \end{frame}
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Verification of Solid Shell/Plate}
%  
%  
%  \begin{figure}
%  \hspace*{-9mm}
%  \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/circular_plate1.pdf}
%  \hspace*{-5mm}
%  \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/circular_plate3.pdf}
%  \hspace*{-5mm}
%  \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/circular_plate4.pdf}
%  \hspace*{-5mm}
%  \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/circular_plate6.pdf}
%  \hspace*{-9mm}
%  \end{figure}
%  
%  \vspace*{-2mm}
%  
%  \begin{itemize}
%   \item Simply supported and clamped ends
%   \item Timoshenko's analytic solutions 
%  \end{itemize}
%  
%  
%  
%  \vspace*{-3mm}
%  
%  \begin{figure}
%  \hspace*{-2mm}
%  \includegraphics[width=3.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/plate_error_plot.jpeg}
%  \hspace*{3mm}
%  \includegraphics[width=3.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/beam/plate_error_plot_clamped.jpeg}
%  \end{figure}
%  
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Verification of Boussinesq Problem}
%  
%  
%  \begin{figure}
%  \hspace*{-9mm}
%  \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/boussinesq/point_load_on_half_space.png}
%  \hspace*{3mm}
%  \includegraphics[width=2.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/boussinesq/model3Dview.JPG}
%  \end{figure}
%  
%  
%  \vspace*{-3mm}
%  
%  
%  \begin{figure}
%  \hspace*{-9mm}
%  \includegraphics[width=4.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/boussinesq/Boussinesq-8NodeBrick.jpeg}
%  \hspace*{5mm}
%  \includegraphics[width=4.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_18Aug2017/V_V_slides_SMiRT/Figure-files/boussinesq/Boussinesq-27NodeBrick.jpeg}
%  \end{figure}
%  
%  
%  \end{frame}
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Verification for Fully Coupled Problems}
%  
%  
%  \begin{figure}
%  \hspace*{-9mm}
%  \includegraphics[width=8cm]{/home/jeremic/tex/works/Papers/2011/Verification_Coupled_Systems/FIGS/Gajo_comp.pdf}
%  \end{figure}
%  
%  
%  \end{frame}
%  
%  
%  
%   
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Wave Propagation, Mesh Size Effects}
%  \begin{center}
%  \begin{figure}
%   \includegraphics[scale=0.40]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present03_img/Vs1000_8Hz_10m.eps}
%  \end{figure}
%  {\small (Case 1, Vs = 1000 m/s, Cutoff Fq. = 8 Hz, E. Size = 10 m)}
%  \end{center}
%  \end{frame}
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Wave Propagation, Mesh Size Effects}
%  \begin{center}
%  \begin{figure}
%   \includegraphics[scale=0.40]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present03_img/Vs1000_8Hz_20m.eps}
%  \end{figure}
%  {\small (Case 1, Vs = 1000 m/s, Cutoff Fq. = 8 Hz, E. Size = 20 m)}
%  \end{center}
%  \end{frame}
%  
%  %   
%  % 
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % \begin{frame}
%  % \frametitle{Mesh Size Effects Analysis Results}
%  % \begin{center}
%  % \begin{figure}
%  %  \includegraphics[scale=0.40]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present03_img/Vs1000_15Hz_10m.eps}
%  % \end{figure}
%  % {\small (Case 1, Vs = 1000 m/s, Cutoff Fq. = 15 Hz, E. Size = 10 m)}
%  % \end{center}
%  % \end{frame}
%  % 
%  % 
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % \begin{frame}
%  % \frametitle{Mesh Size Effects Analysis Results}
%  % \begin{center}
%  % \begin{figure}
%  %  \includegraphics[scale=0.40]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present03_img/Vs1000_15Hz_20m.eps}
%  % \end{figure}
%  % {\small (Case 1, Vs = 1000 m/s, Cutoff Fq. = 15 Hz, E. Size = 20 m)}
%  % \end{center}
%  % \end{frame}
%  % 
%  % 
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%    \frametitle{V \& V Summary}
%  
%      \begin{itemize}
%         
%        \item  V\&V most important for providing confidence in results
%  
%  \vspace*{3mm}
%        \item Numerical modeling program(s) should not be used without extensive/full V\&V
%  
%  \vspace*{3mm}
%        \item V\&V of FEM models is also essential
%  
%  
%  \vspace*{3mm}
%        \item  Real  ESSI  Simulator has an extensive Verification database, and a
%        smaller Validation database
%  
%  % 
%  %       \item    Education  is  the  key  to successful use of realistic nonlinear
%  %       Earthquake Soil Structure Interaction modeling and simulation
%  % 
%  %     \item     Development     of    the    Real    ESSI    Simulator    system
%  %     \href{http://real-essi.info}{http://real-essi.info}
%  
%  %     \item Importance of using proper models correctly (verification, validation, level of sophistication)
%  % 
%  
%  
%        
%  
%  \end{itemize}
%  
%  
%  
%  \end{frame}
%  %
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %  \begin{frame}
%  %  
%  %  \frametitle{NPP, Inelastic Response, Energy Dissipation}
%  %  
%  %  % Elastoplastic soil with contact elements
%  %  %% Both solid and contact elements dissipate energy
%  %  
%  %  
%  %  % \vspace*{-5mm}
%  %  \begin{center}
%  %  % \hspace*{-15mm}
%  %  \movie[label=show3,width=10cm,poster,autostart,showcontrols]
%  %  {\includegraphics[width=10cm]
%  %  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/NPP_Plastic_Dissipation_grab.jpg}}
%  %  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/NPP_Plastic_Dissipation.mp4}
%  %  \end{center}
%  %  
%  %  
%  %  \begin{flushleft}
%  %  \vspace*{-15mm}
%  %  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animation/NPP_Plastic_Dissipation.mp4}
%  %  %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%  %    {\tiny (MP4)}
%  %  \end{flushleft}
%  %  %
%  %  
%  %  
%  %  
%  %  
%  %  
%  %  % \vspace*{-5mm}
%  %  
%  %  
%  %  
%  %  \end{frame}
%  %  
%  %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %  
%  %   
%  %  
%  %  
%  %  
%  %  
%  %  
%  % 
%  % 
%  % 
%  % 
%  % 
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % 
%  % 
%  % 
%  % 
%  % 
%  % 
%  % 
%  % 
%  % 
%  % 
%  % 
%  % 
%  % 
%  % 
%  % 
%  % 
%  % % -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % % -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \subsection{High Performance Computing}
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}{Course Grained and Fine Grained HPC}
%  
%  
%  \begin{itemize}
%  
%   \vspace*{2mm}
%   \item Hardware Aware Plastic Domain Decomposition (HAPDD) Method
%  
%  
%   \vspace*{2mm}
%   \item Small Tensor Library 
%  
%  \end{itemize}
%  
%  \begin{figure}[!Htbp]
%  \begin{center}
%  \hspace*{-5mm}
%  % \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Exit_Seminar_slides/img_slides_yuan_exit_seminar/1_speedup_analysis.jpg}
%   \includegraphics[width=5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Theory_Parallel_Computing_in_Coputational_Geomechanics/tex_works_Thesis_GuanzhouJie_thesis_Verzija_Februar_Images_Speedup01.pdf}
%  \end{center}
%  \end{figure}
%  
%  
%  
%  
%  
%  \end{frame}
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}{HAPDD}
%  
%  \begin{figure}[!Htbp]
%  \begin{center}
%  \hspace*{-5mm}
%   \includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2019/Hori_and_Watanabe_visit_LBNL_14-15Mar2019/present/HAPDD01.jpg}
%  \end{center}
%  \end{figure}
%  
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %\begin{frame}{HAPDD}
%  %
%  %\begin{figure}[!Htbp]
%  %\begin{center}
%  %\hspace*{-5mm}
%  % \includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2019/Hori_and_Watanabe_visit_LBNL_14-15Mar2019/present/HAPDD02.jpg}
%  %\end{center}
%  %\end{figure}
%  %
%  %
%  %\end{frame}
%  %
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}{Small Tensor Library}
%  
%  \begin{figure}[!Htbp]
%  \begin{center}
%  \hspace*{-5mm}
%   \includegraphics[width=12cm]{/home/jeremic/tex/works/Conferences/2019/Hori_and_Watanabe_visit_LBNL_14-15Mar2019/present/Small_tensor_lib_01.jpg}
%  \end{center}
%  \end{figure}
%  
%  
%  \end{frame}
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  












%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Examples}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Seismic Motions}


%  
%       
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  \begin{frame}
%    \frametitle{Seismic Hazard, World}
%  
%  
%  \vspace*{-3mm}
%  \begin{figure}[!hbpt]
%  \begin{center}
%  %
%  \includegraphics[width=11truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/worldseismap.png}
%  %
%  \end{center}
%  \end{figure}
%  
%  \end{frame}
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Earthquake Ground Motions}
%  
%  
%  
%  \begin{itemize}
%  
%  
%  \vspace*{0.5cm}
%  \item  Real earthquake ground motions
%     \begin{itemize}
%       \item Body, P and S waves
%       \item Surface, Rayleigh and Love waves
%       \item Lack of correlation, incoherent motions
%       \item Inclined waves
%       \item 3D/6D waves
%  %     \item Earthquake energy  dissipation
%  
%     \end{itemize}
%  
%  
%  
%  \vspace*{0.5cm}
%  \item What are the  effects of real earthquake ground motions on soil-structure systems ?!
%  
%  
%  
%  \end{itemize}
%  
%  
%  
%  
%  \end{frame}
%  
%  
%  % \subsection*{Fundamentals}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{T{o}hoku Earthquake, Acc, Disp}
%  
%  
%  \vspace*{-2cm}
%  \begin{figure}[!h]
%  \begin{center}
%  \hspace*{-5cm}
%  {\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Conferences/2011/NRC_Staff_Capacity_Building_25May2011/EW_acc4.jpg}}
%  {\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Conferences/2011/NRC_Staff_Capacity_Building_25May2011/EW_dsp4.jpg}}
%  \hspace*{-5cm}
%  \end{center}
%  \end{figure}
%  \vspace*{-3cm}
%  
%  
%  
%  
%  
%  \end{frame}
%  
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % \begin{frame}
%  % \frametitle{T{o}hoku  Earthquake (DSP)}
%  % 
%  % 
%  % \vspace*{-2cm}
%  % \begin{figure}[!h]
%  % \begin{center}
%  % {\includegraphics[width=7.0cm]{/home/jeremic/tex/works/Conferences/2011/NRC_Staff_Capacity_Building_25May2011/EW_dsp4.jpg}}
%  % \end{center}
%  % \end{figure}
%  % \vspace*{-3cm}
%  % 
%  % 
%  % 
%  % 
%  % 
%  % \end{frame}
%  % 
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{{o}hoku Earthquake, 3D Motions}
%  
%  
%  \vspace*{-2cm}
%  \begin{figure}[!h]
%  \begin{center}
%  {\includegraphics[width=3.0cm]{/home/jeremic/tex/works/Conferences/2011/NRC_Staff_Capacity_Building_25May2011/Tohoku_1Hz-11-locations.jpg}}
%  {\includegraphics[width=6.0cm]{/home/jeremic/tex/works/Conferences/2011/NRC_Staff_Capacity_Building_25May2011/Tohoku_1Hz-21.jpg}}
%  \end{center}
%  \end{figure}
%  \vspace*{-3cm}
%  
%  
%  
%  
%  
%  \end{frame}
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  \begin{frame}
%    \frametitle{1C, 2C, 3C, 6C Seismic Motions}
%  
%  \vspace*{2mm}
%  
%  \begin{itemize}
%  
%     \item  All (most) measured motions are full 3C, 6C
%  
%  \hspace*{5cm}
%  
%     \item What is the effect of neglecting, simplifying out to 1C
%  
%  \hspace*{5cm}
%     \item  One example of an almost 2C motion (LSST07, LSST12)
%  
%  \vspace*{2mm}
%  
%  
%  %
%  %   \item  1D (?): M 6.9 San Pablo, Guatemala EQ, 14Jun2017
%  %
%  \end{itemize}
%  
%  
%  \end{frame}
%  
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  \begin{frame}
%    \frametitle{Lotung, Taiwan ('86) Motions}
%  
%  \vspace*{2mm}
%  
%  \begin{itemize}
%  
%     \item  Example of 2C motion (?), LSST07, LSST12
%  \vspace*{2mm}
%  
%  
%  \begin{figure}[!hbpt]
%  \begin{center}
%  %
%  \hspace*{-10mm}
%  \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Lotung_LSST07_FA25.jpeg}
%  \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Lotung_LSST12_FA25.jpeg}
%  \hspace*{-10mm}
%  %
%  \end{center}
%  \end{figure}
%     
%  
%  %
%  %   \item  1D (?): M 6.9 San Pablo, Guatemala EQ, 14Jun2017
%  %
%  \end{itemize}
%  
%  
%  \end{frame}
%  
%    
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  \begin{frame}
%    \frametitle{San Pablo, Guatemala (2017) Motions}
%  
%  \vspace*{2mm}
%  
%  data from  \url{http://www.strongmotioncenter.org/}
%  
%  %\vspace*{-5mm}
%  
%  
%  \begin{figure}[!hbpt]
%  \begin{center}
%  %
%  \hspace*{-10mm}
%  \includegraphics[width=5.5truecm]{/home/jeremic/oofep/LJUDI/PraveenMalhotra/EQ__01_Guatemala_14Jun2017.jpg}
%  \\
%  \hspace*{-10mm}
%  \includegraphics[width=1.8truecm]{/home/jeremic/oofep/LJUDI/PraveenMalhotra/EQ__02_Guatemala_14Jun2017.jpg}
%  \includegraphics[width=1.6truecm]{/home/jeremic/oofep/LJUDI/PraveenMalhotra/EQ__03_Guatemala_14Jun2017.jpg}
%  \includegraphics[width=1.8truecm]{/home/jeremic/oofep/LJUDI/PraveenMalhotra/EQ__04_Guatemala_14Jun2017.jpg}
%  \includegraphics[width=1.8truecm]{/home/jeremic/oofep/LJUDI/PraveenMalhotra/EQ__05_Guatemala_14Jun2017.jpg}
%  \includegraphics[width=1.8truecm]{/home/jeremic/oofep/LJUDI/PraveenMalhotra/EQ__06_Guatemala_14Jun2017.jpg}
%  \includegraphics[width=1.8truecm]{/home/jeremic/oofep/LJUDI/PraveenMalhotra/EQ__07_Guatemala_14Jun2017.jpg}
%  \hspace*{-10mm}
%  %
%  \end{center}
%  \end{figure}
%  
%  
%  
%  
%  \end{frame}
%  
%  
%  
%  
%  
%  
%  
%  %  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Regional Geophysical  Models}
%  
%  \begin{itemize}
%  
%    \item Free Field seismic motions on regional scale
%  
%  
%  \vspace*{4mm}
%    \item Knowledge of geology (deep and shallow) needed
%  
%  
%  \vspace*{4mm}
%   \item Developed using SW4 and/or Real-ESSI
%  
%  
%  \vspace*{4mm}
%    \item  Collaboration  with LLNL: Dr.~Rodgers, Dr.~Pitarka and Dr.~Petersson
%  
%  
%  
%  
%  \end{itemize}
%   
%  \end{frame}
%  
%  
%   
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Regional Geophysical  Models}
%  
%   \begin{figure}[!htb]
%   \begin{center}
%    \includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/San_Francisco__Regional_Model_BIG.jpg}
%    \includegraphics[width=5.2truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/San_Francisco__Regional_Model.jpg}
%   \end{center}
%  % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
%   \end{figure}
%  
%  Rodgers and Pitarka 
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Regional Geophysical  Models}
%  
%   \begin{figure}[!htb]
%   \begin{center}
%    \includegraphics[width=10truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/USG-Bay_Area_Model_CC_det2_sm.jpg}
%   \end{center}
%  % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
%   \end{figure}
%  
%  USGS
%   
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  
%  
%  %  
%  %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %  \begin{frame}
%  %  \frametitle{Example Regional Model}
%  %  
%  %   \begin{figure}[!htb]
%  %   \begin{center}
%  %    \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/Vs_at_top.jpg}
%  %  %  \includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/Horizontal_Velocity_at_12s.jpg}
%  %    \includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/Peak_Velocity.jpg}
%  %   \end{center}
%  %  % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
%  %   \end{figure}
%  %   
%  %  \end{frame}
%  %  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Example Regional Model (Rodgers)}
%  
%  
%  
%  
%    
%  %\vspace*{5mm}
%  \begin{center}
%  %\hspace*{-5mm}
%  %
%  %\movie[label=show3,width=10.0cm,poster,autostart,showcontrols]
%  \movie[label=show3,width=8.0cm,poster]
%  %\movie[label=show3,width=6.0cm,poster,showcontrols]
%    {\includegraphics[width=80mm]{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_August2017/M6_5_s500_BASIN_STOCHASTIC_mag_SLOW.jpg}}
%       {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_August2017/M6_5_s500_BASIN_STOCHASTIC_mag_SLOW.mpg}
%  \hspace*{-5mm}
%  %
%  \end{center}
%  
%  
%  % online   
%  \vspace*{-5mm}
%  \begin{flushleft}
%  \hspace*{-5mm}
%  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_August2017/M6_5_s500_BASIN_STOCHASTIC_mag_SLOW.mpg}
%    {\tiny (MP4)}
%  %\hspace*{-5mm}
%  \end{flushleft}
%  % online
%  
%  
%  
%  
%  
%  
%  % out 
%  % out %\vspace*{-2mm}
%  % out \begin{center}
%  % out \hspace*{-15mm}
%  % out %
%  % out \movie[label=show3,width=8.0cm,poster,autostart,showcontrols]
%  % out   {\includegraphics[width=60mm]{BJicon.png}}{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/M6.5_s500_BASIN+STOCHASTIC.mag.SLOW.mpg}
%  % out \hspace*{-15mm}
%  % out %
%  % out \end{center}
%  % out 
%  % out 
%  % out \begin{flushleft}
%  % out \vspace*{-15mm}
%  % out \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Rodgers_Free_Field_motions/M6.5_s500_BASIN+STOCHASTIC.mag.SLOW.mpg}
%  % out %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%  % out   {\tiny (MP4)}
%  % out \end{flushleft}
%  % out %
%  % out 
%  
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- \begin{frame}
% -- \frametitle{ESSI: 6C or 1C Seismic Motions}
% -- 
% -- 
% -- \begin{itemize}
% -- 
% -- 
% -- \item Assume that a full 6C (3C) motions at the surface are only recorded in one
% -- horizontal direction
% -- 
% -- 
% -- \item  From such recorded motions one can develop a vertically propagating shear
% -- wave (1C) in 1D
% -- 
% -- \item  Apply  such  vertically propagating shear wave to same soil-structure
% -- system
% -- 
% -- \end{itemize}
% -- 
% -- \vspace*{-3mm}
% -- \begin{figure}[!H]
% -- \begin{center}
% --  \includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2015/CompDyn/Present/6D_to_1D_01.jpg}
% -- \end{center}
% -- \end{figure}
% -- 
% -- 
% -- 
% --  \end{frame}
% -- 
% -- 
% -- 
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- \begin{frame}
% --  \frametitle{Realistic Ground Motions}
% -- 
% -- % \begin{itemize}
% -- %
% -- %  \item[] Free field seismic motion models
% -- %
% -- %\end{itemize}
% -- 
% -- % local
% -- % local
% -- % local
% -- \vspace*{-2mm}
% -- \begin{center}
% -- %\movie[label=show3,width=8.5cm,poster,autostart,showcontrols,loop]
% -- \hspace*{-12mm}
% -- % %\movie[label=show3,width=6.0cm,autostart,showcontrols]
% -- % \movie[label=show3,width=6.0cm,poster]
% -- %   {\includegraphics[width=60mm]{movie_input_mp4_icon.jpeg}}{movie_input.mp4}
% -- % \hspace*{-2mm}
% -- % %\hfill
% -- \hspace*{-5mm}
% -- \movie[label=show3,width=100mm,poster,autostart,showcontrols]
% -- %\movie[label=show3,width=90mm,poster]
% --   {\includegraphics[width=90mm]{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_mp4_icon.jpeg}}
% -- {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input.mp4}
% -- \hspace*{-12mm}
% -- \end{center}
% -- % local
% -- % local
% -- % local
% -- %
% -- 
% -- 
% -- \end{frame}
% -- 



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Realistic Ground Motions}

%\begin{itemize}
%
%  \item[] Sources will send both P and S waves
%
%\end{itemize}

% online
% online  \begin{center}
% online  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input.mp4}
% online    {\includegraphics[width=55mm]{movie_input_mp4_icon.jpeg}}
% online  %
% online  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_closeup.mp4}
% online    {\includegraphics[width=50mm]{movie_input_closeup_mp4_icon.jpeg}}
% online  \end{center}
% online

% local
% local
% local
\vspace*{-2mm}
\begin{center}
%\movie[label=show3,width=8.5cm,poster,autostart,showcontrols,loop]
\hspace*{-12mm}
% %\movie[label=show3,width=6.0cm,autostart,showcontrols]
% \movie[label=show3,width=6.0cm,poster]
%   {\includegraphics[width=60mm]{movie_input_mp4_icon.jpeg}}{movie_input.mp4}
% \hspace*{-2mm}
% %\hfill
% %\hspace*{-7mm}
% %\movie[label=show3,width=5.3cm,poster,autostart,showcontrols]
\movie[label=show3,width=80mm,poster, showcontrols]
  {\includegraphics[width=80mm]{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_closeup.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_closeup.mp4}
\hspace*{-12mm}
\end{center}
% local
% local
% local
%


\end{frame}




% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{1C vs 6C Free Field Motions}



 
\begin{itemize}

  \item[-] One component of motions, 1C from  6C
%  or 3$\times$1D (it is done all the time!)

  \item[-]  Excellent fit
   
  \item[-]  Wrong mechanics
%  (goal is to predict and inform and not (force) fit)


\end{itemize}




% local
%\vspace*{-2mm}
\begin{center}
\hspace*{-16mm}
%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
\movie[label=show3,width=61mm,poster, showcontrols]
  {\includegraphics[width=60mm]{/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_ff_3d_mp4_icon.jpeg}}
  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_ff_3d.mp4}
%\hspace*{-2mm}
%\hfill
%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
\movie[label=show3,width=61mm,poster, showcontrols]
  {\includegraphics[width=60mm]
  {/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_ff_1d_mp4_icon.jpeg}}
  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_ff_1d.mp4}
\hspace*{-16mm}
\end{center}
% local


% online
\vspace*{-6mm}
\begin{center}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
{\tiny (MP4)}
%
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_1d.mp4}
 {\tiny (MP4)}
\end{center}
% online






% out      
% out  % local
% out  %\vspace*{-2mm}
% out  \begin{center}
% out  \hspace*{-16mm}
% out  %\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
% out  \movie[label=show3,width=61mm,poster, showcontrols]
% out    {\includegraphics[width=60mm]{movie_ff_3d_mp4_icon.jpeg}}{movie_ff_3d.mp4}
% out  % \hspace*{-16mm}
% out  % \end{center}
% out  % %  
% out  % %
% out  % %
% out  % \begin{center}
% out  % \hspace*{-16mm}
% out  \movie[label=show3,width=61mm,poster, showcontrols]
% out    {\includegraphics[width=60mm]{movie_ff_1d_mp4_icon.jpeg}}{movie_ff_1d.mp4}
% out  \hspace*{-16mm}
% out  \end{center}
% out  %
% out  
% out  \begin{flushleft}
% out  %\vspace*{-15mm}
% out  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
% out  %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
% out    {\tiny (MP4)}
% out  %
% out  \hspace*{55mm}
% out  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_1d.mp4}
% out  %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
% out    {\tiny (MP4)}
% out  \end{flushleft}
% out  %
% out  
% out  
% out  
% out  % online
% out  % online  \begin{center}
% out  % online  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
% out  % online    {\includegraphics[width=50mm]{movie_ff_3d_mp4_icon.jpeg}}
% out  % online  %
% out  % online  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_1d.mp4}
% out  % online    {\includegraphics[width=50mm]{movie_ff_1d_mp4_icon.jpeg}}
% out  % online  \end{center}
% out  % online
% out  
% out  
% out  
% out  %
% out  
% out  
\end{frame}

% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{6C vs 1C NPP ESSI Response Comparison}

 
% local
\vspace*{-2mm}
\begin{center}
\hspace*{-7mm}
%\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
\movie[label=show3,width=8.8cm,poster, showcontrols]
  {\includegraphics[width=92mm]
  {/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_2_npps_mp4_icon.jpeg}}
  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_2_npps.mp4}
\end{center}
% local
%  \vspace*{-2mm}
%  \begin{center}
%  \hspace*{-7mm}
%  \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
%    {\includegraphics[width=90mm]{movie_2_npps_mp4_icon.jpeg}}{movie_2_npps.mp4}
%  \end{center}


% online
\vspace*{-12mm}
\begin{flushleft}
%\vspace*{-15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_2_npps.mp4}
  {\tiny (MP4)}
\end{flushleft}
% online



% out 
% out  \vspace*{-2mm}
% out  \begin{center}
% out  \hspace*{-7mm}
% out  \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% out    {\includegraphics[width=69mm]{BJicon.png}}
% out    {movie_2_npps.mp4}
% out  \end{center}
% out  
% out  
% out  \begin{flushleft}
% out  \vspace*{-15mm}
% out  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_2_npps.mp4}
% out    {\tiny (MP4)}
% out  \end{flushleft}
% out  %
% out  


 \end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




% -- 
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- \begin{frame}
% -- \frametitle{1C vs 3$\times$1C vs 3C Seismic Motions}
% -- 
% -- 
% -- \begin{itemize}
% -- 
% -- \vspace{2mm}
% --  \item 1C is required by the code
% -- 
% -- \vspace{4mm}
% --  \item 3$\times$1C can be used depending on frequency/wave length of interest, 
% -- 
% -- \vspace{4mm}
% --  \item 3C is more realistic, however it is challenging to define motions in full 3C
% -- 
% -- \end{itemize}
% -- \end{frame}
% -- 
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- 
% -- 
% -- 
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- \begin{frame}
% --  \frametitle{When to  use  3C and/or 3$\times$1C}
% -- 
% -- 
% -- \begin{figure}[!hbpt]
% -- \begin{center}
% -- %
% -- %\includegraphics[width=4.5truecm]{/home/jeremic/tex/works/Papers/2016/3D_vs_3_x_1D_motions/version_04Jan2017/NearFieldESSINPPs/results/3d_vs_1d_6/node_733_acce.pdf}
% -- %\includegraphics[width=4.5truecm]{/home/jeremic/tex/works/Papers/2016/3D_vs_3_x_1D_motions/version_04Jan2017/NearFieldESSINPPs/results/6/node_733_acce.pdf}
% -- % %
% -- % \\
% -- % \includegraphics[width=9.5truecm]{/home/jeremic/tex/works/Papers/2016/3D_vs_3_x_1D_motions/version_04Jan2017/NearFieldESSINPPs/results/3d_vs_1d_6/node_733_fft.pdf}
% -- % \\
% -- \includegraphics[width=11truecm]{/home/jeremic/tex/works/consulting/2017/IAEA/TECDOC/Version_14Mar2017/1Dvs3x1Dvs3D_waves.pdf}
% -- \end{center}
% -- \end{figure}
% -- 
% -- \end{frame}
% -- 
% -- 
% -- 
% -- 





% 

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}

\frametitle{Free Field, Variation in Input Frequency, $\theta = 60^{o}$}

% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy

     
% \vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
%\movie[label=show3,width=10cm,poster,autostart,showcontrols]
\movie[label=show3,width=10cm,poster,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/Free_Field_variation_in_wave_frequency.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/free_field_frequency.mp4}
\end{center}
        
% online   
\vspace*{-12mm}
\begin{flushleft}
\hspace*{-4mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/free_field_frequency.mp4}
  {\tiny (MP4)}
\end{flushleft}
% online  
   

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}

\frametitle{SMR ESSI, Variation in Input Frequency, $\theta = 60^{o}$}

% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy

     
% \vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
%\movie[label=show3,width=10cm,poster,autostart,showcontrols]
\movie[label=show3,width=10cm,poster,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/ESSI_SMR_variation_in_wave_frequency.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/SMR_frequency.mp4}
\end{center}
        
% online   
\vspace*{-12mm}
\begin{flushleft}
\hspace*{-4mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/SMR_frequency.mp4}
  {\tiny (MP4)}
\end{flushleft}
% online  
   

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 



% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - \begin{frame}
% - 
% - %\frametitle{SMR ESSI, Variation in Input Frequency, $\theta = 60^{o}$}
% - \frametitle{SMR ESSI, Variation in Input Frequency, REAL TIME}
% - 
% - % Elastoplastic soil with contact elements
% - %% Both solid and contact elements dissipate energy
% - 
% -      
% - % \vspace*{-5mm}
% - \begin{center}
% - % \hspace*{-15mm}
% - %\movie[label=show3,width=10cm,poster,autostart,showcontrols]
% - \movie[label=show3,width=10cm,poster,showcontrols]
% - {\includegraphics[width=10cm]
% - {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/ESSI_SMR_variation_in_wave_frequency.jpg}}
% - {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR-ESSI_real_time_four_freq.mp4}
% - \end{center}
% -         
% - % online   
% - \vspace*{-12mm}
% - \begin{flushleft}
% - \hspace*{-4mm}
% - \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR-ESSI_real_time_four_freq.mp4}
% -   {\tiny (MP4)}
% - \end{flushleft}
% - % online  
% -    
% - 
% - \end{frame}
% - 
% - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}

%\frametitle{SMR ESSI, Variation in Input Frequency, $\theta = 60^{o}$}
\frametitle{SMR ESSI, 3C vs 3$\times$1C}

% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy

     
% \vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
%\movie[label=show3,width=10cm,poster,autostart,showcontrols]
\movie[label=show3,width=10cm,poster,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/3Dvs1D_deconvolution.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/3Dvs1D_deconvolution.ogv}
\end{center}
        
% online   
\vspace*{-12mm}
\begin{flushleft}
\hspace*{-4mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/3Dvs1D_deconvolution.ogv}
  {\tiny (OGV)}
\end{flushleft}
% online  
   

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


  









%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
% \frametitle{Free Field vs ESSI - Different Frequencies}
% 
% 
% \begin{textblock*}{8cm}(1.0cm,2.5cm) % {block width} (coords) 
%    \scriptsize Acceleration response - Surface center point A
% \end{textblock*}
% \begin{textblock*}{2cm}(0.2cm,4cm) % {block width} (coords) 
%    \tiny X direction
% \end{textblock*}
% \begin{textblock*}{2cm}(0.2cm,6.3cm) % {block width} (coords) 
%    \tiny Z direction
% \end{textblock*}
% \begin{textblock*}{3cm}(2.4cm,7.6cm) % {block width} (coords) 
%    \tiny  (a) $f=1Hz \ \ \theta=60^{o}$
% \end{textblock*}
% \begin{textblock*}{3cm}(5.6cm,7.6cm) % {block width} (coords) 
%    \tiny  (b) $f=5Hz \ \ \theta=60^{o}$
% \end{textblock*}
% \begin{textblock*}{3cm}(8.8cm,7.6cm) % {block width} (coords) 
%    \tiny  (c) $f=10Hz \ \ \theta=60^{o}$
% \end{textblock*}
% 
% \vspace*{-30mm}
%   \begin{figure}[!H]
%     \centering
%      % \begin{flushleft}
%        \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/1Hz_center_ax.pdf}
%        \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/5Hz_center_ax.pdf}
%        \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/10Hz_center_ax.pdf}
%       \\
%        \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/1Hz_center_az.pdf}
%        \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/5Hz_center_az.pdf}
%        \includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/10Hz_center_az.pdf}
%     % \end{flushleft}
%   \end{figure}
% \vspace*{-75mm}
%   \begin{figure}[!H]
%      \begin{flushright}
%      \hspace*{30mm}
%        \includegraphics[width=2.5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/Points_configuration.pdf}
%      \hspace*{-10mm}
%     \end{flushright}
%   \end{figure}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 








% 
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% 
% 
% 
% 
% 
% 
% 
% 
% 
% 
% 
% 
% 
% 
% % -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%












% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Plastic Energy Dissipation}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Energy Input and Dissipation}

\begin{itemize}

\vspace*{1mm}
     \item[] Energy input, static and dynamic forcing


\vspace*{4mm}
     \item[] Energy dissipation outside SSI domain:
       \begin{itemize}
         \item[] SSI system oscillation radiation
         \item[] Reflected wave radiation
       \end{itemize}
%\vspace*{1mm}
     \item[] Energy dissipation/conversion inside SSI domain:
       \begin{itemize}
         \item[] Inelasticity of soil, interfaces, structure, dissipators
         \item[] Viscous coupling with internal/pore and external fluids
% %         \item[] potential and kinetic energy
%          \item[] potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
       \end{itemize}                           



%\vspace*{1mm}
%   \item[] Numerical energy dissipation (numerical damping/production and period  errors)
%   \item[] Numerical energy dissipation (damping/production)
   \item[] Numerical energy dissipation/production


\end{itemize}

%
\end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 
\frametitle{Plastic Energy Dissipation}


\vspace*{2mm}
 
 Single elastic-plastic element under cyclic shear loading
 
\begin{itemize}
\item[] Difference between plastic work and plastic dissipation
%\item[] Plastic work can decrease
%\item[] Plastic dissipation always increases
\end{itemize}
 
%\vspace*{-7mm}
\begin{figure}[!hbpt]
\begin{center}
\hspace*{-5mm}
\includegraphics[width=11.0truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Dissipation_Material.png}
\end{center}
\end{figure}
  
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
% \frametitle{Energy Dissipation Control Mechanisms}
% 
% \begin{figure}[!H]
% %\hspace*{-10mm}
%      \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_plasticity.pdf}
%      \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Rayleigh.pdf}
%      \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Newmark.pdf}
% \end{figure}
% 
% 
% % \hspace*{10mm} Numerical  \hspace*{20mm}  Viscous  \hspace*{20mm} Plasticity 
%  \hspace*{10mm} Plasticity \hspace*{20mm}  Viscous  \hspace*{20mm} Numerical
% 
% 
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}

\frametitle{Energy Dissipation Control}

\begin{figure}[!H]
%\hspace*{-10mm}
%     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_a.pdf}
%     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_b.pdf}
     \includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_g.pdf}
%     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_e.pdf}
\end{figure}




\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



% -- 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Inelastic Modeling of Soil Structure Systems}

\begin{itemize}

%\vspace*{1mm}
     \item[-] Soil, inelastic, elastic-plastic
       \begin{itemize}
         \item[] Dry, single phase
         \item[] Unsaturated, partially saturated
         \item[] Fully saturated
       \end{itemize}


%\vspace*{1mm}
     \item[-] Contact/Interface/Joint, inelastic: dry or saturated
%     , soil/rock -- foundation
%       \begin{itemize}
%         \item[]  Dry,  single  phase,  
           \begin{itemize}
             \item[]  Axial, hard  and  soft, gap open/close
             \item[]  Shear, friction, nonlinear
           \end{itemize}
%         \item[] Saturated, suction/pressure/pumping, buoyant forces
%       \end{itemize}


%\vspace*{1mm}
     \item[-] Structure, inelastic, damage, cracks
       \begin{itemize}
         \item[] Inelastic fiber beam
         \item[] Inelastic layer shell
         \item[] Inelastic 3D solid element
%         \item[] ASR concrete modeling
       \end{itemize}


%%\vspace*{1mm}
%     \item Fluid-Solid interaction (open surface)



\end{itemize}

%
\end{frame}


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
%  \frametitle{NPP Model }
% 
%   \begin{figure}[!h]
%   \begin{center}
%    \includegraphics[width=8.5cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/NPP_With_Shallow_Foundation.pdf}
%   \end{center}
% %  \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
%   \end{figure}
% 
% 
% % \begin{tikzpicture}[remember picture,overlay]
% %     \node[xshift=3.5cm,yshift=-0.6cm] at (current page.center) {\includegraphics[width=0.5\textwidth]{images/Contact_In_Industry}};
% % \end{tikzpicture}
% 
% \end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
%  \frametitle{Structure Model}
% 
%  The nuclear power plant structure comprise of
%  \begin{itemize}
%   \item Auxiliary building, $f^{aux}_{1}= 8Hz$
%   \item Containment/Shield building, $f^{cont}_{1}= 4Hz$
%   \item Concrete raft foundation: $3.5m$ thick
%  \end{itemize}
%   \begin{figure}[!h]
%   \begin{center}
%    \includegraphics[width=0.8\textwidth]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/NPP_Model_Auxiliary_And_Containment_Building.pdf}
%   \end{center}
%   \caption{\label{Fig:NPP_Structure_Model_In_Real_ESSI} Auxiliary and Containment Building }
%   \end{figure}
% 
% \end{frame}
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% -- \begin{frame}
% -- 
% --  \frametitle{Inelastic Soil and Inelastic Contact/Interface/Joint}
% -- 
% --  \begin{itemize}
% --   \item Shear velocity of soil $V_s=500m/s$
% --   \item Undrained shear strength (Dickenson 1994) $V_s [m/s] = 23 (S_u [kPa])^{0.475}$
% --   \item For $V_s=500m/s$ Undrained Strength $S_u=650kPa$ and Young's Modulus of $E=1.3GPa$
% --   \item von Mises, Armstrong Frederick kinematic hardening
% --   ($S_u=650kPa$ at $\gamma=0.01\%$; $h_a = 30MPa$, $c_r = 25$)
% --   \item Soft interface, concrete-soil, gaping and slipping
% --   \end{itemize}
% -- 
% --  \begin{figure}[!h]
% --  \begin{center}
% --   \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Von_Mies_non_Linear_Hardening.pdf}
% --   \includegraphics[width=3.5cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/SoftContact.pdf}
% --  \end{center}
% --   \end{figure}
% -- 
% -- 
% -- \end{frame}
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- 
% -- 


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
%  \frametitle{Acc. Response, Top of Containment Building}
% 
%  \begin{figure}[!h]
%  \begin{center}
% \hspace*{-8mm}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_X.pdf}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_Y.pdf}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_Z.pdf}
% \\
% \hspace*{-8mm}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_X.pdf}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_Y.pdf}
%   \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_Z.pdf}
% % \caption{\label{Fig:Response_of_Top_of_Containment_Building} Seismic Response at Top of Containment Building}
%  \end{center}
% \end{figure}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
%  
%  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}

 \frametitle{Acceleration Traces, Elastic vs Inelastic }


\hspace*{-35mm}
  \begin{figure}[!h]
  \vspace*{-2mm}
  \begin{center}
  \hspace*{-15mm}
   \includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Acceleration_Elastic_Without_Contact_SMIRT_2017.pdf}
  \hspace*{-20mm}
   \includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Acceleration_Inelastic_With_Contact_SMIRT_2017.pdf}
  \hspace*{-25mm}
  \end{center}
 \end{figure}
\hspace*{-35mm}

\hspace*{10mm} Elastic  \hspace*{40mm} Inelastic \hspace*{40mm} 

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}

 
 \frametitle{Displacement Traces, Elastic vs Inelastic}
 
\hspace*{-35mm}
  \begin{figure}[!h]
  \vspace*{-2mm}
  \begin{center}
  \hspace*{-15mm}
   \includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Elastic_Without_Contact_SMIRT_2017.pdf}
  \hspace*{-20mm}
   \includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Inelastic_With_Contact_SMIRT_2017.pdf}
  \hspace*{-25mm}
  \end{center}
 \end{figure}
\hspace*{-35mm}

\hspace*{10mm} Elastic  \hspace*{40mm} Inelastic \hspace*{40mm} 

\end{frame}
 
 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% -- 
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  \begin{frame}
% --  
% --  \frametitle{Elastic and Inelastic Response: Differences}
% --  
% --  % Elastoplastic soil with contact elements
% --  %% Both solid and contact elements dissipate energy
% --  
% --  % \vspace*{-5mm}
% --  \begin{center}
% --  % \hspace*{-15mm}
% --  \movie[label=show3,width=10cm,poster,autostart,showcontrols]
% --  {\includegraphics[width=10cm]
% --  {/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_13Aug2017/NPP_Non_Linear_Effects_Sumeet.jpg}}
% --  {/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_13Aug2017/NPP_Non_Linear_Effects_Sumeet.mp4}
% --  \end{center}
% --  
% --  
% --  
% --  \begin{flushleft}
% --  \vspace*{-15mm}
% --  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_August2017/NPP_Non_Linear_Effects_Sumeet.mp4}
% --  %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
% --    {\tiny (MP4)}
% --  \end{flushleft}
% --  %
% --  
% --  
% --  \end{frame}
% --  
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}

\frametitle{NPP: Energy Dissipation}

% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy

% \vspace*{-5mm}
\begin{center}
% \hspace*{-15mm}
\movie[label=show3,width=10cm,poster,autostart,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/3D_Nonlinear_Modeling_and_it_Effects/NPP_Plastic_Dissipation_grab.jpg}}
{/home/jeremic/tex/works/Thesis/HanYang/Files_10Aug2017/NPP_Plastic_Dissipation.mp4}
\end{center}




\begin{flushleft}
\vspace*{-15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/NPP_Plastic_Dissipation.mp4}
%  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
  {\tiny (MP4)}
\end{flushleft}
%



\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  \begin{frame}
% --   \frametitle{Deeply Embedded Structures}
% --   \begin{columns}[T]
% --    \begin{column}{.5\textwidth}
% --     \vspace{-0.5cm}
% --     \begin{figure}[!H]
% --        \begin{center}
% --          \includegraphics[width=\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/Points_configuration.pdf}
% --       \end{center}
% --     \end{figure}
% --    \end{column}
% --    \begin{column}{.5\textwidth}
% --    \vspace{0.6cm}
% --    \centerline{\scriptsize Location of points}
% --    \vspace{-0.6cm}
% --     \begin{figure}[!H]
% --        \begin{center}
% --          \includegraphics[width=\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/representative_points.pdf}
% --       \end{center}
% --     \end{figure}
% --    \end{column}
% --   \end{columns}
% --  \end{frame}
% --  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  \begin{frame}
% --   \frametitle{SMR: Inelastic ESSI Effects, Top Center}
% --  
% --  
% --  \vspace*{-30mm}
% --  
% --    \begin{figure}[!H]
% --       \begin{flushleft}
% --         \includegraphics[width=3.2cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_point1_ax_time_series.pdf}
% --         \includegraphics[width=3.2cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_point1_ay_time_series.pdf}
% --         \includegraphics[width=3.2cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_point1_az_time_series.pdf}
% --        \\
% --         \includegraphics[width=3.2cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_Point1_ax_fft.pdf}
% --         \includegraphics[width=3.2cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_Point1_ay_fft.pdf}
% --         \includegraphics[width=3.2cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_Point1_az_fft.pdf}
% --      \end{flushleft}
% --    \end{figure}
% --  
% --  
% --  \vspace*{-75mm}
% --  
% --    \begin{figure}[!H]
% --       \begin{flushright}
% --       \hspace*{30mm}
% --         \includegraphics[width=2cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/Points_configuration.pdf}
% --       \hspace*{-10mm}
% --      \end{flushright}
% --    \end{figure}
% --  
% --  
% --  
% --  \end{frame}
% --  
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{SMR: ESSI Effects, Location}
%
%
%
%
%
% \vspace*{-30mm}
%
%   \scriptsize \hspace*{20mm} Point 3 \hspace*{25mm} Point 4   \hspace*{20mm}  Point 5
%   \begin{figure}[!H]
%      \begin{flushleft}
%        \includegraphics[width=3.6cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_point3_ax_time_series.pdf}
%        \includegraphics[width=3.6cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_point4_ax_time_series.pdf}
%        \includegraphics[width=3.6cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_point5_ax_time_series.pdf}
% \\
%        \includegraphics[width=3.6cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_Point3_ax_fft.pdf}
%        \includegraphics[width=3.6cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_Point4_ax_fft.pdf}
%        \includegraphics[width=3.6cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_Point5_ax_fft.pdf}
%     \end{flushleft}
%   \end{figure}
%
%
% \vspace*{-75mm}
%
%   \begin{figure}[!H]
%      \begin{flushright}
%      \hspace*{30mm}
%        \includegraphics[width=2cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/Points_configuration.pdf}
%      \hspace*{-10mm}
%     \end{flushright}
%   \end{figure}
%
%
%
%
%
%
% %
% %
% %
% %   \begin{columns}[T]
% %   \begin{column}{0.8\textwidth}
% %    \vspace{-0.6cm}
% %    \scriptsize \quad \quad \quad \quad Point 3\quad \quad \quad \quad \quad \quad \quad Point 4\quad \quad \quad \quad \quad \quad Point 5
% %    \vspace{-0.3cm}
% %    \begin{figure}[!H]
% %       \begin{center}
% %         \includegraphics[width=0.3\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_point3_ax_time_series.pdf}
% %         \includegraphics[width=0.3\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_point4_ax_time_series.pdf}
% %         \includegraphics[width=0.3\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_point5_ax_time_series.pdf} \\
% %         \includegraphics[width=0.3\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_Point3_ax_fft.pdf}
% %         \includegraphics[width=0.3\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_Point4_ax_fft.pdf}
% %         \includegraphics[width=0.3\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_Point5_ax_fft.pdf}
% %      \end{center}
% %    \end{figure}
% %    \vspace{-0.3cm}
% %    \begin{itemize}
% %     \item Nonlinear effects attenuate along the depth
% %    \end{itemize}
% %   \end{column}
% %   \begin{column}{0.3\textwidth}
% %    \begin{figure}[!H]
% %       \begin{center}
% %         \includegraphics[width=\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/Points_configuration.pdf}
% %      \end{center}
% %    \end{figure}
% %   \end{column}
% %   \end{columns}
%
%
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  \begin{frame}
% --   \frametitle{SMR: ESSI Effects, Material Modeling}
% --   \begin{columns}[T]
% --   \begin{column}{0.6\textwidth}
% --    \scriptsize \quad \quad \quad \quad  \quad Material A\quad \quad \quad \quad \quad \quad \quad Material B
% --    \vspace{-3mm}
% --    \begin{figure}[!H]
% --       \begin{center}
% --         \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_point1_ax_time_series.pdf}
% --         \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/bilinear_point1_ax_time_series.pdf} \\
% --         \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/AF_yuan_Point1_ax_fft.pdf}
% --         \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/bilinear_Point1_ax_fft.pdf}
% --      \end{center}
% --    \end{figure}
% --    \vspace{-0.3cm}
% --    % \begin{itemize}
% --    %  \item
% --    % \end{itemize}
% --   \end{column}
% --   \hspace{-0.3cm}
% --   \begin{column}{0.3\textwidth}
% --   \vspace{-0.35cm}
% --    \begin{figure}[!H]
% --       \begin{center}
% --         \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/ha=30Mpa.png} \\
% --         \tiny \quad Material A: nonlinear, vM - AF\\
% --         \vspace{0.2cm}
% --         \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/material_stress_strain_behavior.pdf} \\
% --         \tiny \quad Material B: Bilinear\\
% --      \end{center}
% --    \end{figure}
% --   \end{column}
% --   \end{columns}
% --  \end{frame}
% --  
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  \begin{frame}
% --   \frametitle{SMR: Accelerations Along Depth}
% --  
% --   \vspace{-0.6cm}
% --  
% --   \begin{columns}[T]
% --  
% --   \hspace{-0.6cm}
% --  
% --   \begin{column}{1.1\textwidth}
% --  
% --    \begin{figure}[!H]
% --       \begin{center}
% --         \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/free_field_acceleration_depth_variation.pdf}\hspace{-0.7cm}
% --         \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/free_field_a_depth_variation_AF.pdf}
% --      \end{center}
% --    \end{figure}
% --  
% --    \vspace{-1.1cm}
% --  
% --    \begin{figure}[!H]
% --       \begin{center}
% --         \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/SMR_acceleration_depth_variation_elastic.pdf}\hspace{-0.7cm}
% --         \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/SMR_acceleration_depth_variation.pdf}
% --      \end{center}
% --    \end{figure}
% --   \end{column}
% --  
% --  
% --   \hspace{-0.7cm}
% --   \begin{column}{0.15\textwidth}
% --   \vspace{1.5cm}
% --   Nonlinear site effects\\
% --   \vspace{2.5cm}
% --   SSI effects
% --   \end{column}
% --   \end{columns}
% --  \end{frame}
% --  
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- \begin{frame}
% -- 
% -- \frametitle{Energy Dissipation for an SMR Model}
% -- 
% -- % Elastoplastic soil with contact elements
% -- %% Both solid and contact elements dissipate energy
% -- 
% -- 
% -- % \vspace*{-5mm}
% -- \begin{center}
% -- % \hspace*{-15mm}
% -- \movie[label=show3,width=10cm,poster,autostart,showcontrols]
% -- {\includegraphics[width=10cm]
% -- {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation_screen_grab.jpg}}
% -- {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
% -- \end{center}
% -- 
% -- 
% -- \begin{flushleft}
% -- \vspace*{-15mm}
% -- \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
% -- %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
% --   {\tiny (MP4)}
% -- \end{flushleft}
% -- %
% -- 
% -- 
% -- 
% -- 
% -- 
% -- % \vspace*{-5mm}
% -- 
% -- 
% -- 
% -- \end{frame}
% -- 
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  \begin{frame}
% --   \frametitle{Depth variation - PGA \& PGD}
% --   \vspace{-0.9cm}
% --    \begin{figure}[!H]
% --       \begin{center}
% --       \hspace*{-10mm}
% --         \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/depth_variation_peak_AH_annotation.pdf}
% --         \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/depth_variation_peak_UH_annotation.pdf}
% --       \hspace*{-5mm}
% --      \end{center}
% --    \end{figure}
% --    \vspace{-0.5cm}
% --    \begin{itemize}
% --     \item \scriptsize The PGA \& PGD of SSI systems are (very) different from free field motions,
% --     \item \scriptsize Material nonlinearity has significant effect on acceleration response.
% --  %   \item \scriptsize Deconvolution methodology for analysis of embedded structure is inaccurate and even dangerous.
% --    \end{itemize}
% --  \end{frame}
% --  
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  
% --  
% --  
% --  
% --  
% --  



   
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
% \frametitle{Energy Dissipation for a SMR}
% 
% % Elastoplastic soil with contact elements
% %% Both solid and contact elements dissipate energy
% 
%      
% % \vspace*{-5mm}
% \begin{center}
% % \hspace*{-15mm}
% %\movie[label=show3,width=9cm,poster,autostart,showcontrols]
% \movie[label=show3,width=10cm,poster,showcontrols]
% {\includegraphics[width=10cm]
% {/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/Nonlinear_Analysis_of_ESSI_for_SMR/SMR_Energy_Dissipation_screen_grab.jpg}}
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mpg}
% %{/home/jeremic/tex/works/Thesis/HanYang/Files_16Aug2017/SMR_Energy_Dissipation.mp4}
% \end{center}
% 
%  
% \begin{flushleft}
% \vspace*{-15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
% %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%   {\tiny (MP4)}
% \end{flushleft}
% %
% 
% 
% 
% 
% \end{frame}
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


















% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Liquefaction as Base Isolation, Model}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=4.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSI-Site_Response_Analysis/Liquefaction_04.jpg}
% \end{center}
% \end{figure}
% 
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Liquefaction, Wave Propagation}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSI-Site_Response_Analysis/Liquefaction_01.jpg}
% \end{center}
% \end{figure}
% 
% \hspace*{40mm} Dry  \hspace*{10mm} Liquefied \hspace*{40mm} 
% 
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Liquefaction, Stress-Strain Response}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSI-Site_Response_Analysis/Liquefaction_03.jpg}
% \end{center}
% \end{figure}
% 
% \hspace*{40mm} Dry  \hspace*{10mm} Liquefied \hspace*{40mm} 
% 
% \end{frame}
% 
% 
% 
% 
% 
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Energy Dissipation for Design}

\begin{figure}[!hbpt]
\begin{center}
\includegraphics[width=10.0truecm]{/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/2D_Frame_Model.pdf}
\end{center}
\end{figure}


\end{frame}






%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Design Alternatives}


% local
%\vspace*{-2mm}
\begin{center}
\hspace*{-16mm}
%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
\movie[label=show3,width=61mm,poster, showcontrols]
  {\includegraphics[width=60mm]{/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Individual_Foundation_screen_grab.jpg}}
  {/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Individual_Foundation.mp4}
%\hspace*{-2mm}
%\hfill
%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
\movie[label=show3,width=61mm,poster, showcontrols]
  {\includegraphics[width=61mm]{/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Continuous_Foundation_screen_grab.jpg}}
  {/home/jeremic/tex/works/Thesis/HanYang/Frame_animations_13Mar2019/Continuous_Foundation.mp4}
\hspace*{-16mm}
\end{center}
% local


% online
\begin{center}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Energy_dissipation_frames/Individual_Foundation.mp4}
{\tiny (MP4)}
%
\hspace*{40mm}
%
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Energy_dissipation_frames/Continuous_Foundation.mp4}
 {\tiny (MP4)}
\end{center}
% online





\end{frame}
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%







% -- 
% -- 
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- \begin{frame}
% -- \frametitle{ASCE-7-21: Buildings and Models, Low Building}
% -- 
% -- %\vspace*{-5mm}
% -- \begin{figure}[!htb]
% -- \begin{center}
% -- \includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/HexiangWang/ATC-144_buildings_results_plots_15Sep2019/steel_frame2.pdf}
% -- \end{center}
% -- \end{figure}
% -- 
% -- \end{frame}
% -- 
% -- % 
% -- % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- % \begin{frame}
% -- % \frametitle{ASCE-7-21: Buildings and Models, Low Building}
% -- % 
% -- % %\vspace*{-5mm}
% -- % \begin{figure}[!htb]
% -- % \begin{center}
% -- % \includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/HexiangWang/ATC-144_buildings_results_plots_15Sep2019/steel_frame_cut.pdf}
% -- % \end{center}
% -- % \end{figure}
% -- % 
% -- % \end{frame}
% -- % 
% -- % 
% -- % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- % \begin{frame}
% -- % \frametitle{ASCE-7-21: Buildings and Models, Low Building}
% -- % 
% -- % %\vspace*{-5mm}
% -- % \begin{figure}[!htb]
% -- % \begin{center}
% -- % \includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/HexiangWang/ATC-144_buildings_results_plots_15Sep2019/steel_frame_cut2.pdf}
% -- % \end{center}
% -- % \end{figure}
% -- % 
% -- % \end{frame}
% -- % 
% -- % 
% -- % 
% -- % 
% -- % 
% -- % 
% -- % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- % \begin{frame}
% -- % \frametitle{ASCE-7-21: Low Building, Eigenmode \#1, $T_1 = 0.69$s}
% -- % 
% -- % %\vspace*{-5mm}
% -- % \begin{figure}[!htb]
% -- % \begin{center}
% -- % \includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/HexiangWang/ATC-144_buildings_results_plots_15Sep2019/Short_building_first_mode_T0_69.pdf}
% -- % %\includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/HexiangWang/ATC-144_buildings_results_plots_15Sep2019/Short_building_second_mode_T0_58.pdf}
% -- % %\includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/HexiangWang/ATC-144_buildings_results_plots_15Sep2019/Short_building_third_mode_T0_51.pdf}
% -- % \end{center}
% -- % \end{figure}
% -- % 
% -- % \end{frame}
% -- % 
% -- % 
% -- % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- % \begin{frame}
% -- % \frametitle{ASCE-7-21: Low Building, Eigenmode \#2, $T_2 = 0.58$s}
% -- % 
% -- % %\vspace*{-5mm}
% -- % \begin{figure}[!htb]
% -- % \begin{center}
% -- % %\includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/HexiangWang/ATC-144_buildings_results_plots_15Sep2019/Short_building_first_mode_T0_69.pdf}
% -- % \includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/HexiangWang/ATC-144_buildings_results_plots_15Sep2019/Short_building_second_mode_T0_58.pdf}
% -- % %\includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/HexiangWang/ATC-144_buildings_results_plots_15Sep2019/Short_building_third_mode_T0_51.pdf}
% -- % \end{center}
% -- % \end{figure}
% -- % 
% -- % \end{frame}
% -- % 
% -- % 
% -- % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- % \begin{frame}
% -- % \frametitle{ASCE-7-21: Low Building, Eigenmodes \#3, $T_3 = 0.51$s}
% -- % 
% -- % %\vspace*{-5mm}
% -- % \begin{figure}[!htb]
% -- % \begin{center}
% -- % %\includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/HexiangWang/ATC-144_buildings_results_plots_15Sep2019/Short_building_first_mode_T0_69.pdf}
% -- % %\includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/HexiangWang/ATC-144_buildings_results_plots_15Sep2019/Short_building_second_mode_T0_58.pdf}
% -- % \includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/HexiangWang/ATC-144_buildings_results_plots_15Sep2019/Short_building_third_mode_T0_51.pdf}
% -- % \end{center}
% -- % \end{figure}
% -- % 
% -- % \end{frame}
% -- % 
% -- % 
% -- % 
% -- % 
% -- % 
% -- % 
% -- % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- % \begin{frame}
% -- % \frametitle{ASCE-7-21: Low Building Response}
% -- % 
% -- % 
% -- % % \vspace*{-5mm}
% -- % \begin{center}
% -- % % \hspace*{-15mm}
% -- % %\movie[label=show3,width=10cm,poster,autostart,showcontrols]
% -- % \movie[label=show3,width=10cm,poster,showcontrols]
% -- % {\includegraphics[width=10cm]
% -- % {/home/jeremic/tex/works/Thesis/HexiangWang/ATC-144_buildings_results_plots_15Sep2019/short_building_response_screen_grab.jpg}}
% -- % {/home/jeremic/tex/works/Thesis/HexiangWang/ATC-144_buildings_results_plots_15Sep2019/short_building_response.mp4}
% -- % \end{center}
% -- %         
% -- % % online  % online   
% -- % % online  \vspace*{-12mm}
% -- % % online  \begin{flushleft}
% -- % % online  \hspace*{-4mm}
% -- % % online  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/free_field_frequency.mp4}
% -- % % online    {\tiny (MP4)}
% -- % % online  \end{flushleft}
% -- % % online  % online  
% -- %    
% -- % 
% -- % 
% -- % 
% -- % \end{frame}
% -- % %\vspace*{10mm}  
% -- % 
% -- %      
% -- % 
% -- % 
% -- % 
% -- 
% -- 
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- \begin{frame}
% -- \frametitle{ASCE-7-21: Low Building Energy Dissipation}
% -- 
% -- 
% -- % \vspace*{-5mm}
% -- \begin{center}
% -- % \hspace*{-15mm}
% -- %\movie[label=show3,width=10cm,poster,autostart,showcontrols]
% -- \movie[label=show3,width=10cm,poster,showcontrols]
% -- {\includegraphics[width=10cm]
% -- {/home/jeremic/tex/works/Thesis/HanYang/ASCE-7-21_low_building_energy_dissipation/ATC_Short_Building_PD.jpg}}
% -- {/home/jeremic/tex/works/Thesis/HanYang/ASCE-7-21_low_building_energy_dissipation/ATC_Short_Building_PD.mp4}
% -- \end{center}
% --         
% -- % online   
% -- \vspace*{-12mm}
% -- \begin{flushleft}
% -- \hspace*{-4mm}
% -- \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Energy_dissipation_frames/ATC_Short_Building_PD.mp4}
% --   {\tiny (MP4)}
% -- \end{flushleft}
% -- % online  
% --    
% -- 
% -- 
% -- 
% -- \end{frame}
% -- %\vspace*{10mm}  
% -- 
% --      
% -- 
% -- 
% -- 
% -- 












  

% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  \begin{frame}
% --  \frametitle{ASCE-7-21: Tall  Building}
% --  
% --  %\vspace*{-5mm}
% --  \begin{figure}[!htb]
% --  \begin{center}
% --  \includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/HexiangWang/ATC-144_buildings_results_plots_15Sep2019/Tall_building_model.pdf}
% --  \end{center}
% --  \end{figure}
% --  
% --  \end{frame}
% --  %\vspace*{10mm}  
% --  
% --  
% --  
% --  
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  \begin{frame}
% --  \frametitle{ASCE-7-21: Buildings and Models, Tall  Building}
% --  
% --  %\vspace*{-5mm}
% --  \begin{figure}[!htb]
% --  \begin{center}
% --  \includegraphics[width=10cm]{/home/jeremic/tex/works/Thesis/HexiangWang/ATC-144_buildings_results_plots_15Sep2019/Tall_building_model_cut.pdf}
% --  \end{center}
% --  \end{figure}
% --  
% --  \end{frame}
% --  %\vspace*{10mm}  
% --  
% --  
% --  
% --  
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  \begin{frame}
% --  \frametitle{ASCE-7-21: Tall  Building Response}
% --  
% --  
% --  % \vspace*{-5mm}
% --  \begin{center}
% --  % \hspace*{-15mm}
% --  %\movie[label=show3,width=10cm,poster,autostart,showcontrols]
% --  \movie[label=show3,width=10cm,poster,showcontrols]
% --  {\includegraphics[width=10cm]
% --  {/home/jeremic/tex/works/Thesis/HexiangWang/ATC-144_buildings_results_plots_15Sep2019/Tall_building_response_screen_grab.jpg}}
% --  {/home/jeremic/tex/works/Thesis/HexiangWang/ATC-144_buildings_results_plots_15Sep2019/Tall_building_response.mp4}
% --  \end{center}
% --          
% --  % online   
% --  \vspace*{-12mm}
% --  \begin{flushleft}
% --  \hspace*{-4mm}
% --  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Energy_dissipation_frames/Tall_building_response.mp4}
% --    {\tiny (MP4)}
% --  \end{flushleft}
% --  % online  
% --  
% --  
% --  
% --  
% --  \end{frame}
% --  %\vspace*{10mm}  

     

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


















 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% -
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%














%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   \subsection{Select Examples}
%   

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Repeat of Simulations}
% 
% \begin{itemize}
% 
% \vspace*{1mm}
%      \item[]
% 
% 
% 
% \end{itemize}
% 
% %
% \end{frame}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Pine Flats Dam, Model}
%  
%  \begin{itemize}
%  
%  %\vspace*{1mm}
%       \item Material properties provided
%       \item Motions applied through DRM, from bottom
%       
%       \item Energy dissipation, Viscous, Numerical, Radiation
%  
%       \item Load cases as provided
%  %     \item 
%  
%  
%  \end{itemize}
%  
%  
%  \vspace*{-5mm}
%  \begin{figure}[!hbpt]
%  \begin{center}
%  %
%  \hspace*{-8mm}
%  \includegraphics[width=12.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Model_Mesh_No_Reservior.pdf}
%  %
%  \end{center}
%  \end{figure}
%  
%  %
%  \end{frame}
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Static, Displacements and \huge{$\sigma_v$}}
%  
%  % \begin{itemize}
%  % %\vspace*{1mm}
%  %      \item Displacements
%  %      \item Vertical stress distribution
%  % \end{itemize}
%  
%  \begin{figure}[!hbpt]
%  \begin{center}
%  %
%  \hspace*{-7mm}
%  \includegraphics[width=12.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Case_A_Vertical_Stress.png}
%  %
%  \end{center}
%  \end{figure}
%  
%  %
%  \end{frame}
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Eigen Analysis, Dry}
%  
%  \begin{itemize}
%  %\vspace*{1mm}
%       \item Eigen frequencies: \\
%   (a) 2.46945~Hz, 
%   (b) 3.82403~Hz, 
%   (c) 4.48795~Hz, \\
%   (d) 5.25455~Hz, 
%   (e) 5.32023~Hz, 
%   (f) 5.60061~Hz, 
%  
%  \end{itemize}
%  
%  %  \begin{table}[!htb]
%  % \centering
%  % \begin{tabular}{c|c}
%  % %\hline
%  % Mode & Natural Frequency (Hz) \\ \hline
%  % 1    & 2.46945                \\ \hline
%  % 2    & 3.82403                \\ \hline
%  % 3    & 4.48795                \\ \hline
%  % 4    & 5.25455                \\ \hline
%  % 5    & 5.32023                \\ \hline
%  % 6    & 5.60061                \\ 
%  % %\hline
%  % \end{tabular}
%  % \end{table}
%  %
%  
%  %
%  \begin{figure}[!htbp]
%  \centering
%  \subfloat[]{\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/mode1.pdf}}
%  \subfloat[]{\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/mode2.pdf}}
%  \subfloat[]{\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/mode3.pdf}}
%  \\
%  \subfloat[]{\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/mode4.pdf}}
%  \subfloat[]{\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/mode5.pdf}}
%  \subfloat[]{\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/mode6.pdf}}
%  %\caption{\label{figure_case_d1_modal_shapes}
%  %Modal shapes: (a) First mode; (b) Second mode; (c) Third mode; (d) Fourth mode; (e) Fifth mode; (f) Sixth mode.}
%  \end{figure}
%  
%  % 
%  % \begin{figure}[!hbpt]
%  % \begin{center}
%  % %
%  % %\hspace*{-5mm}
%  % \includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/}
%  % %
%  % \end{center}
%  % \end{figure}
%  % 
%  %
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Numerical Damping Effects, Elastic
%     {\Large $\ddot{u}_{hor}^{top}$}, 
%     {\Large ${\sigma}_{v}^{heel}$}}
%  
%  %\begin{itemize}
%  %%\vspace*{1mm}
%  %     \item Vertical stress at max tension and max compression
%  %\end{itemize}
%  
%  \begin{figure}[!hbpt]
%  \begin{center}
%  %
%  \hspace*{-5mm}
%  \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Top_Horizontal_Acceleration_IU.pdf}
%  \hfill
%  \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Different_NP_Heel_Vertical_Stress_IU.pdf}
%  \hspace*{-5mm}
%  %\\
%  %\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Max_US.pdf}
%  %\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Min_US.pdf}
%  
%  %
%  \end{center}
%  \end{figure}
%  
%  %
%  \end{frame}
%  
%  
%  
%  
%  
%  %  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%   \frametitle{Numerical Damping Effects, Inelastic 
%     {\Large $\ddot{u}_{hor}^{top}$}, 
%     {\Large ${\sigma}_{v}^{heel}$}}
%  
%  %\begin{itemize}
%  %%\vspace*{1mm}
%  %     \item Vertical stress at max tension and max compression
%  %\end{itemize}
%  
%  \begin{figure}[!hbpt]
%  \begin{center}
%  %
%  \hspace*{-5mm}
%  \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Case_D3_Different_NP_Top_Horizontal_Acceleration_IU.pdf}
%  \hfill
%  \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Case_D3_Different_NP_Heel_Vertical_Stress_IU.pdf}
%  \hspace*{-5mm}
%  %\\
%  %\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Max_US.pdf}
%  %\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Reports/2019/Pine_Flats_Dam_USSD/USSD_Dam_Report_2019/Figures/Dam_Base_Vertical_Stress_Min_US.pdf}
%  
%  %
%  \end{center}
%  \end{figure}
%  
%  %
%  \end{frame}
%  
%  
%  %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %  
%  %  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  \begin{frame}
%   \frametitle{Pine Flat Dam, Dynamic Response with Reservoir}
%  
%  %\vspace*{-5mm}
%  \begin{center}
%  % \hspace*{-15mm}
%  \movie[label=show3,width=9cm,poster,autostart,showcontrols]
%  {\includegraphics[width=8cm]
%  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/soil_fluid_interaction_dam.jpg}}
%  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/soil_fluid_interaction_dam.mp4}
%  \end{center}
%  
%  \begin{flushleft}
%  \vspace*{-15mm}
%  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/soil_fluid_interaction_dam.mp4}
%  %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%    {\tiny (MP4)}
%  \end{flushleft}
%  %
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  \begin{frame}
%   \frametitle{Pine Flat Dam, Hydrodynamic Pressure}
%  
%  %\vspace*{-5mm}
%  \begin{center}
%  % \hspace*{-15mm}
%  \movie[label=show3,width=10cm,poster,autostart,showcontrols]
%  {\includegraphics[width=10.0cm]
%  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/dynamic_pressure.jpg}}
%  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/dynamic_pressure.mp4}
%  \end{center}
%  
%  \begin{flushleft}
%  \vspace*{-15mm}
%  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/dynamic_pressure.mp4}
%  %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%    {\tiny (MP4)}
%  \end{flushleft}
%  %
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  \begin{frame}
%   \frametitle{Pine Flat Dam, Inelastic Interface, Hydrostatic}
%  
%  %\vspace*{-5mm}
%  \begin{center}
%  % \hspace*{-15mm}
%  \movie[label=show3,width=10cm,poster,autostart,showcontrols]
%  {\includegraphics[width=10.0cm]
%  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/Case_D3_Gap_Open_more.jpg}}
%  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/Case_D3_Gap_Open_more.mp4}
%  
%  \end{center}
%  
%  \begin{flushleft}
%  \vspace*{-15mm}
%  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/Case_D3_Gap_Open_more.mp4}
%  %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%    {\tiny (MP4)}
%  \end{flushleft}
%  %
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  \begin{frame}
%   \frametitle{Pine Flat Dam, Inclined Plane Waves}
%  
%  %\vspace*{-5mm}
%  \begin{center}
%  % \hspace*{-15mm}
%  \movie[label=show3,width=10cm,poster,autostart,showcontrols]
%  {\includegraphics[width=10.0cm]
%  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/dynamic_response_inclination.jpg}}
%  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/dynamic_response_inclination.mp4}
%  \end{center}
%  
%  \begin{flushleft}
%  \vspace*{-15mm}
%  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Concrete_Dams/Pine_Flat_Dam/dynamic_response_inclination.mp4}
%  %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%    {\tiny (MP4)}
%  \end{flushleft}
%  %
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  
%  %  
%  %  
%  %  
%  %  
%  %  
%  %  
%  %  
%  %  
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  
%  
%  
%  
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  \begin{frame}
%  
%  \frametitle{Buoyant Force Simulation}
%  
%  \begin{figure}[!H]
%  \hspace*{-20mm}
%       \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/upU_element_type_annotation.pdf}
%       \includegraphics[width=5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/bouyant_displacement.pdf}
%  \hspace*{-20mm}
%  \end{figure}
%  
%  % -  %
%  % -  % \begin{tikzpicture}[remember picture,overlay]
%  % -  %    \node[anchor=south west,inner sep=0pt] at ($(current page.south west)+(7.5cm,2.5cm)$) {
%  % -  %      \includegraphics[width=0.4\textwidth]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/bouyant_displacement.pdf}};
%  % -  % \end{tikzpicture}
%  % -
%  % -  %  \vspace{-1.4cm}
%  %  \begin{itemize}
%  %   \item \scriptsize Upward structural displacement under buoyant force
%  %  \end{itemize}
%  \end{frame}
%  
%  
%  
%  %
%  
%  
%  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  \begin{frame}
%   \frametitle{Solid, Structure-Fluid Interaction, Example}
%  
%  
%  
%  %\vspace*{-5mm}
%  \begin{center}
%  % \hspace*{-15mm}
%  \movie[label=show3,width=9cm,poster,autostart,showcontrols]
%  {\includegraphics[width=8.5cm]
%  {/home/jeremic/tex/works/Conferences/2017/DOE_Project_Review_Meeting_LBNL_09June2017/Present/Solid-Fluid-Interaction.jpg}}
%  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Fluid_Solid_interaction/Solid_Fluid_Interaction_NEW.mpeg}
%  \end{center}
%  
%  
%  \begin{flushleft}
%  \vspace*{-15mm}
%  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Fluid_Solid_interaction/Solid_Fluid_Interaction.mp4}
%  %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%    {\tiny (MP4)}
%  \end{flushleft}
%  %
%  
%  
%  
%  
%  
%  \end{frame}
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Liquefaction as Base Isolation, Model}
%  
%  \begin{figure}[!hbpt]
%  \begin{center}
%  \includegraphics[width=4.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSI-Site_Response_Analysis/Liquefaction_04.jpg}
%  \end{center}
%  \end{figure}
%  
%  \end{frame}
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Liquefaction, Wave Propagation}
%  
%  \begin{figure}[!hbpt]
%  \begin{center}
%  \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSI-Site_Response_Analysis/Liquefaction_01.jpg}
%  \end{center}
%  \end{figure}
%  
%  \end{frame}
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Liquefaction, Stress-Strain Response}
%  
%  \begin{figure}[!hbpt]
%  \begin{center}
%  \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Conferences/2017/Slovenia_IAEA_short_course/present/SSI-Site_Response_Analysis/Liquefaction_03.jpg}
%  \end{center}
%  \end{figure}
%  
%  \end{frame}
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Pile in Liquefiable Soil, Model}
%  
%  \begin{figure}[!hbpt]
%  \begin{center}
%  \includegraphics[width=2.7truecm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Cyclic_Mobility_and_Liquefaction/tex_works_Papers_2008_Pile_in_liquefied_soil_upU_final_FEmesh3D.pdf}
%  \hfill
%  \includegraphics[width=3.5truecm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Cyclic_Mobility_and_Liquefaction/tex_works_Papers_2008_Pile_in_liquefied_soil_upU_final_FEmeshPileBeam.pdf}
%  %\hfill
%  \includegraphics[width=4truecm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Cyclic_Mobility_and_Liquefaction/tex_works_Papers_2008_Pile_in_liquefied_soil_upU_final_SFSIModelSetup_upU_01.pdf}
%  \end{center}
%  \end{figure}
%  
%  
%  \end{frame}
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Pile in Liquefiable Soil, Results}
%  
%  \begin{figure}[!hbpt]
%  \begin{center}
%  \includegraphics[width=6truecm]{/home/jeremic/tex/works/Conferences/2018/Oersted-DONG-Energy/present/Pile_in_liquefied_soil.jpg}
%  \end{center}
%  \end{figure}
%  
%  
%  
%  
%  \end{frame}
%  
%  
%  
%  
%               
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  % -
%  % -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  % -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  
%  
%  
%  
%  
%  


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%






















% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%











%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Sensitivity Analysis}





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% - 
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}

\frametitle{Stochastic Site Response}

\vspace*{5mm}
\begin{itemize}
% \item[-] Three-layered ground with \\
%       uncertain material properties and \\
%       uncertain seismic rock motions

 \item[-] Uncertain material: \\
       uncertain random field, \\
       marginally lognormal \\
       distribution, \\
       exponential correlation \\
       length 10m

\item[-]  Uncertain  seismic \\
          rock motions:  \\
          seismic  scenario \\
           M=7,  R=50km \\
%       Stochastic Fourier amplitude spectra, \\
%       Stochastic Fourier phase derivative

\end{itemize}


\vspace*{-50mm}
\begin{figure}[!hbpt]
\begin{flushright}
\includegraphics[width=5.5cm]{/home/jeremic/tex/works/Conferences/2021/CompDyn_8th_Athens_28-30Jun2021/present/Three-Layer-Model.jpg}
\\
\includegraphics[width=5.5cm]{/home/jeremic/tex/works/Conferences/2021/CompDyn_8th_Athens_28-30Jun2021/present/Input-motions.jpg}
\end{flushright}
\end{figure}

% 
%  \begin{figure}[!hbpt]
%  \begin{center}
%  \includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/structural_uncertainty.pdf}
%  \end{center}
%  \end{figure}
%  
%  
%  \begin{figure}[!hbpt]
%  \begin{center}
%  \includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/probabilsitc_evolution.png}
%  \end{center}
%  \end{figure}
%  
%  
%  
%  \begin{figure}[!hbpt]
%  \begin{center}
%  \includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/seismic_risk_result_framework.png}
%  \end{center}
%  \end{figure}
%  
%  
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}

\frametitle{Stochastic Material Parameters}

%  

\vspace*{5mm}
Lognormal distributed random field with PC Dim. 3 Order 2


\vspace*{-5mm}
\begin{figure}[!hbpt]
\begin{center}
\hspace*{-10mm}
\includegraphics[width=13cm]{/home/jeremic/tex/works/Conferences/2021/CompDyn_8th_Athens_28-30Jun2021/present/Stochastic_material_parameters.jpg}
\end{center}
\end{figure}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}

\frametitle{Stochastic Seismic Motion Development}

\vspace*{5mm}
\begin{itemize}
 \item[-] UCERF3 (Field et al. 2014)
 \item[-] Stochastic motions (Boore 2003) 
 \item[-] Polynomial Chaos Karhunen-Lo{\`e}ve expansion
 \item[-] Probabilistic DRM (Bielak et al. 2003, Wang et al. 2021)
\end{itemize}

\vspace*{-3mm}
\begin{figure}[!hbpt]
\begin{center}
\includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/UCERF3.pdf}
\includegraphics[width=4.0cm]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/SMSIM.pdf}
%\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_exact_dis_correlation_from_dis.pdf}
\end{center}
\end{figure}

% 
%  
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%






% -- 
% -- 
% -- 
% -- 
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- \begin{frame}
% -- 
% -- \frametitle{Stochastic Ground Motion Modeling}
% -- 
% -- \begin{itemize}
% -- 
% -- %\vspace*{1mm}
% -- \item[-] Modeling fundamental characteristics of uncertain ground motions,
% -- Stochastic Fourier amplitude spectra (FAS). and Stochastic Fourier phase spectra
% -- (FPS) and not specific IM
% -- 
% -- \vspace*{1mm}
% -- \item[-]  Mean behavior of stochastic FAS,  $w^2$ source radiation spectrum by
% -- Brune(1970), and Boore(1983, 2003, 2015).
% -- 
% -- \vspace*{1mm}
% -- \item[-] Variability models for stochastic FAS, 
% --  FAS GMPEs by Bora et al. (2015, 2018), Bayless \&
% --  Abrahamson (2019), 
% -- % for marginal median \& variability, 
% -- %Inter-frequency correlation structure by 
% -- Stafford(2017) and Bayless \& Abrahamson (2018).  
% -- 
% -- \vspace*{1mm}
% -- \item[-] Stochastic FPS by phase derivative (Boore,2005), Logistic phase derivative
% -- model by Baglio \& Abrahamson (2017)
% -- 
% -- %\item Upcoming: a major change from \textbf{ $\boldsymbol{Sa(T_0)}$ to FAS} in next five years as envisioned by Abrahamson (2018)
% -- 
% -- \end{itemize}
% -- 
% -- \end{frame}
% -- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -- 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}

\frametitle{Stochastic Seismic Motions}

%  

%Lognormal distributed random field with PC Dim. 3 Order 2



%\vspace*{-50mm}
\begin{figure}[!hbpt]
\begin{center}
\hspace*{-10mm}
\includegraphics[width=12.5cm]{/home/jeremic/tex/works/Conferences/2021/CompDyn_8th_Athens_28-30Jun2021/present/Stochastic_seismic_motions.jpg}
\end{center}
\end{figure}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

         



% --  
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  \begin{frame}
% --  
% --  \frametitle{Stochastic Seismic Motions, Displacement}
% --  
% --  %  
% --  
% --  %\vspace*{-50mm}
% --  \begin{figure}[!hbpt]
% --  \begin{center}
% --  \hspace*{-10mm}
% --  \includegraphics[width=12.5cm]{/home/jeremic/tex/works/Conferences/2021/CompDyn_8th_Athens_28-30Jun2021/present/Stochastic-motions-DISP.jpg}
% --  \end{center}
% --  \end{figure}
% --  
% --  \end{frame}
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  
         
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  \begin{frame}
% --  
% --  \frametitle{Stochastic Seismic Motions, Accelerations}
% --  
% --  %  
% --  
% --  \vspace*{-1mm}
% --  \begin{figure}[!hbpt]
% --  \begin{center}
% --  \hspace*{-10mm}
% --  \includegraphics[width=12.5cm]{/home/jeremic/tex/works/Conferences/2021/CompDyn_8th_Athens_28-30Jun2021/present/Stochastic-motions-ACC.jpg}
% --  \end{center}
% --  \end{figure}
% --  
% --  \end{frame}
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  


% --  
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  \begin{frame}
% --  
% --  \frametitle{Stochastic Site Response}
% --  
% --  %  
% --  
% --  
% --  \vspace*{-3mm}
% --  \begin{figure}[!hbpt]
% --  \begin{center}
% --  \hspace*{-10mm}
% --  \includegraphics[width=12.5cm]{/home/jeremic/tex/works/Conferences/2021/CompDyn_8th_Athens_28-30Jun2021/present/Stochastic-site-response.jpg}
% --  \end{center}
% --  \end{figure}
% --  
% --  
% --  \vspace*{-2mm}
% --  PC dimensions $\xi_1$, - $\xi_3$ are from uncertain soil
% --  
% --  PC dimensions $\xi_4$, - $\xi_{153}$ are from uncertain rock motions
% --  
% --  \end{frame}
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  




% --  
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  \begin{frame}
% --  
% --  \frametitle{Sensitivity of PGA from Uncertain Soil}
% --  
% --  %  
% --  
% --  
% --  \vspace*{10mm}
% --  \begin{itemize}
% --    \item[-] First 10 terms \\
% --          from soil uncertainty
% --  
% --  
% --  
% --    \item[-] Total Sobol     \\
% --          sensitivity index  \\
% --          $S_{1-3}^{PC,total} = 0.51$
% --  
% --  
% --  \end{itemize}
% --  
% --  
% --  
% --  \vspace*{-40mm}
% --  \begin{small}
% --  %\begin{center}
% --  \begin{table}[!htb]
% --  \hspace*{50mm}
% --  \begin{tabular}{l l}
% --  Sobol Index           &  Value  \\ \hline 
% --  $S_{1,123}^{PC}$      &   0,04389  \\
% --  $S_{1,118}^{PC}$      &   0,02605  \\
% --  $S_{1,127}^{PC}$      &   0,02370  \\
% --  $S_{1,100}^{PC}$      &   0,01759  \\
% --  $S_{1,103}^{PC}$      &   0,01700  \\
% --  $S_{1,134}^{PC}$      &   0,01680  \\
% --  $S_{1,141}^{PC}$      &   0,01611  \\
% --  $S_{1,110}^{PC}$      &   0,01358  \\
% --  $S_{1,130}^{PC}$      &   0,01303  \\
% --  $S_{1,132}^{PC}$      &   0,01068 \\
% --  . . .                &   . . .     \\ \hline  
% --      \end{tabular}
% --  \end{table}
% --  %\end{center}
% --  \end{small}
% --  
% --  
% --  
% --  
% --  %
% --  %
% --  %PC dimensions $\xi_1$, - $\xi_3$ are from uncertain soil
% --  %
% --  %PC dimensions $\xi_4$, - $\xi_{153}$ are from uncertain motions
% --  
% --  \end{frame}
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  
% --  
% --  
% --  
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  \begin{frame}
% --  
% --  \frametitle{Sensitivity of  PGA from Uncertain Rock Motions}
% --  
% --  %  
% --  
% --  
% --  \vspace*{10mm}
% --  \begin{itemize}
% --    \item[-] First 10 terms \\
% --          from motions uncertainty
% --  
% --  
% --    \item[-] Total Sobol     \\
% --          sensitivity index \\
% --          $S_{1-153}^{PC,total} = 0.98$
% --  
% --  
% --  \end{itemize}
% --  
% --  
% --  
% --  \vspace*{-40mm}
% --  \begin{small}
% --  %\begin{center}
% --  \begin{table}[!htb]
% --  \hspace*{50mm}
% --  \begin{tabular}{l l}
% --  Sobol Index           &  Value  \\ \hline 
% --  $S_{1,123}^{PC}$      &   0,04389  \\
% --  $S_{137}^{PC}$      &   0,03459  \\
% --  $S_{110}^{PC}$      &   0,03061  \\
% --  $S_{118}^{PC}$      &   0,02698  \\
% --  $S_{1,118}^{PC}$      &   0,02605  \\
% --  $S_{108}^{PC}$      &   0,02482   \\
% --  $S_{141}^{PC}$      &   0,02373  \\
% --  $S_{1,127}^{PC}$      &   0,02370  \\
% --  $S_{1,100}^{PC}$      &   0,01759  \\
% --  $S_{1,103}^{PC}$      &   0,01700  \\
% --  . . .                &   . . .     \\ \hline  
% --      \end{tabular}
% --  \end{table}
% --  %\end{center}
% --  \end{small}
% --  
% --  
% --  
% --  
% --  %
% --  %
% --  %PC dimensions $\xi_1$, - $\xi_3$ are from uncertain soil
% --  %
% --  %PC dimensions $\xi_4$, - $\xi_{153}$ are from uncertain motions
% --  
% --  \end{frame}
% --  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}

\frametitle{Sensitivity Analysis}

%  


%\begin{itemize}
%
%
\vspace*{4mm}
%  \item[-] 
Total variance in PGA, in this case (!), dominated by uncertain ground motions
    \begin{itemize}
\vspace*{4mm}
      \item[] $49$\% from uncertain rock motions at depth
\vspace*{4mm}
      \item[] $2$\% from uncertain soil
\vspace*{4mm}
      \item[] $49$\% from interaction of uncertain rock motions and  uncertain soil 


    \end{itemize}


%  \item 
%\end{itemize}



\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




























% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





\section{Conclusion}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \subsection{\ }





 
%   
%    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%    \begin{frame} 
%    
%    \frametitle{Real-ESSI Simulator System}
%    
%    The  Real-ESSI, Realistic  
%    {\underline {\bf M}}odeling  and  
%    {\underline {\bf S}}imulation  of  
%    {\underline {\bf E}}arthquakes,  
%    {\underline {\bf S}}oils,
%    {\underline {\bf S}}tructures  and  their  
%    {\underline {\bf I}}nteraction.  Simulator  is  a  software,  hardware  and
%    documentation   system   for  high  fidelity,  high  performance,  time  domain,
%    nonlinear/inelastic, deterministic or probabilistic, 3D, finite element modeling
%    and simulation of:
%    
%        \begin{itemize}
%    %\vspace*{1mm}
%          \item statics and dynamics of soil,
%    \vspace*{1mm}
%          \item    statics and dynamics of rock,
%    \vspace*{1mm}
%          \item    statics and dynamics of structures,
%    \vspace*{1mm}
%          \item    statics of soil-structure systems, and
%    \vspace*{1mm}
%          \item    dynamics of earthquake-soil-structure system interaction
%        \end{itemize}
%    
%    
%    \end{frame}
%    
%    

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%






%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Appropriate Quotes}

 
\begin{itemize}


%\vspace*{3mm}
\item[]  Fran{\c c}ois-Marie Arouet,  Voltaire: 
"Le doute n'est pas une condition agr{\'e}able, mais la certitude est absurde."



\vspace*{3mm}
\item[] Max  Planck: 
"A    new    scientific  truth does not triumph by convincing  its opponents and
making  them see the light, but rather because its opponents eventually die, and
a  new  generation  grows  up  that  is familiar with it." 
%(Science advances one funeral at a time)



\vspace*{3mm}
\item[]  Niklaus  Wirth:   
"Software is getting slower more rapidly than hardware becomes faster."

\end{itemize}


\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
  \frametitle{Summary}

  \begin{itemize}

%    \item Importance   of   using  proper  models  correctly  (verification,
%    validation, level of sophistication)
%     
 
%    \item Reduction of modeling uncertainty 
%
\vspace*{1mm}
    \item[-] Numerical modeling to predict and inform
%    , rather than fit

%\vspace*{1mm}
%    \item Change of demand due to inelastic effects

%\vspace*{-1mm}
%      \begin{itemize}
%         \item Reduction of dynamic motions
%         \item Increase in deformations
%      \end{itemize}



%   \vspace*{1mm}
%       \item  Sophisticated inelastic/nonlinear modeling and simulations need to be
%       done carefully and in phases
%   

\vspace*{1mm}
    \item[-] Education and Training is the key !


\vspace*{1mm}
    \item[-]     Collaborators:    Feng,  Yang,  Behbehani,  Lacour, Sinha, 
               Wang, Wang, Pisan{\'o}, Abell, Tafazzoli, Jie, Preisig,
               Tasiopoulou, Watanabe, Luo, Cheng, Yang.
   
   

\vspace*{1mm}
  \item[-]  Funding  from  and  collaboration  with the 
            US-NSF,
            US-DOE,
            US-NRC, 
            US-FEMA/ATC, 
            CNSC-CCSN, 
            CH-ENSI/Basler\&Hofmann,  
            UN-IAEA, and 
            Shimizu Corp. is greatly
            appreciated,


\vspace*{1mm}
  \item[]  
    \url{http://sokocalo.engr.ucdavis.edu/~jeremic}
      

\end{itemize}



\end{frame}
%






\end{document}

%
%
