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% %% 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}
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\usepackage[absolute,overlay]{textpos}




 
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% for inclusion of other PDF pages, in this case Frank's presentation
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%from http://mailman.mit.edu/pipermail/macpartners/2005-January/000780.html
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% \fi
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%  \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}
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%  \usecolortheme{beetle} % siva pozadina (vrh plav)
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%%%%%%%
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%%%%%%%
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}

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\usepackage[greek,english]{babel}



\usepackage{amsmath}
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%%%%  HYPERREF  HYPERREF  HYPERREF  HYPERREF  HYPERREF
%%%%  HYPERREF  HYPERREF  HYPERREF  HYPERREF  HYPERREF
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%             colorlinks=true,
%             linkcolor=webblue,
%             citecolor=webblue,
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%             linktocpage,
%             pdftex]{hyperref}


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\usepackage[latin1]{inputenc}
% or whatever
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\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]
        { Modeling and Simulation of \\
         Earthquake Soil Structure 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)
%{ Professor, University of California, Davis\\
{ University of California, Davis, CA\\
%  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 Shijiazhuang Tiedao University \\
         Shijiazhuang, July 2019}

\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}}




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\begin{document}

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

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\begin{frame}
  \frametitle{Outline}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% 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}



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





 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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 modeling and simulation of
  Earthquakes and/or    Soils and/or    Structures    and    their    Interaction:\\
   Real-ESSI, 
  \raisebox{-1.2mm}{\includegraphics[height=5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Chinese.jpeg}}
%  \\
%  \vspace*{1mm}
% % %  \hspace*{25mm} 
% %     \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{Prediction under Uncertainty}


\begin{itemize}




%\vspace*{1mm}
  \item    \underline{Modeling 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    Uncertainty},  ${M}  \ddot{u_i}  +  {C}  \dot{u_i} + {K}^{ep} {u_i} = {F(t)}$,

  \begin{itemize}

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


\vspace*{2mm}
    \item[] Propagation  of uncertainty in  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 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 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,poster,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,poster,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 Uncertainty: Soil Stiffness and Strength}


\vspace*{2mm}
%\vspace*{-3mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-7mm}
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf}
\hspace*{-3mm}
% \hfill
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
%
\end{center}
\end{figure}

\vspace*{-5mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-7mm}
\includegraphics[width=5.00truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_RawData_and_MeanTrend-Mod.pdf}
\hspace*{-3mm}
% \hfill
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_Histogram_PearsonIV-FineTuned-Mod.pdf}
%
\end{center}
\end{figure}

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


\end{frame}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Parametric Uncertainty: Material Properties}
% 
%           
% 
% \vspace*{5mm}
% \begin{figure}[!hbpt]
% \begin{center}
% % %
% \hspace*{-3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiPdf.pdf}
% \hspace*{-3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiCdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuPdf.pdf}
% \hspace*{-3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuCdf.pdf}
% \\
% %\vspace*{-2mm}
% \hspace*{-2.5cm} \mbox{\tiny Field $\phi$} \hspace*{3.5cm} \mbox{\tiny Field $c_u$}
% \\
% \vspace*{10mm}
% \hspace*{-3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiPdf.pdf}
% \hspace*{-3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiCdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuPdf.pdf}
% \hspace*{-3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuCdf.pdf}
% \\
% %\vspace*{-8mm}
% \hspace*{-2.5cm} \mbox{\tiny Lab $\phi$} \hspace*{3.5cm} \mbox{\tiny Lab $c_u$}
% \end{center}
% \end{figure}
% 
% 
% 
% \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 with pore fluids, 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, algorithmic energy dissipation/production


\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}
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




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% \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
% 
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% \end{frame}
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\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}

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

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

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



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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,  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}



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

    \end{itemize} 

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



\vspace*{1mm}
  \item Real-ESSI Short Courses, online, worldwide



\vspace*{1mm}
  \item 
% System description and documentation at  
    \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 elements, dry, coupled/saturated, 

\vspace*{1mm}
  \item[-] Super element, stiffness and mass matrices

\vspace*{1mm}
  \item[-] Material models, soil, concrete, steel... 
  
\vspace*{1mm}
  \item[-] Seismic input, 1C and 3C, deterministic or probabilistic

\vspace*{1mm}
  \item[-] Energy dissipation calculations

\vspace*{1mm}
  \item[-] Solid/Structure -- Fluid interaction, full coupling

\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*{2mm}
  \item[-] Dynamic loading stages

\vspace*{2mm}
  \item[-] Restart, simulation tree

\vspace*{2mm}
  \item[-] Solution advancement methods/algorithms, \\
        on global and constitutive levels, \\
        with and without enforcing equilibrium


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

\vspace*{2mm}
  \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 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[-] Choose level of sophistication

\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

% OVDE dodaj primere vizualizacije


\end{itemize}
 
\end{frame}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real-ESSI Verification}
% 
% \begin{itemize}
% 
% 
%   \item Implementation  verification
% 
% \vspace*{2mm}
%   \item Solution verification for each component
%     \begin{itemize}
%        \item Finite elements
%        \item Constitutive algorithms
%        \item Solution advancement, static and dynamic 
% 
%     \end{itemize}
% 
% 
% \vspace*{2mm}
%   \item Error quantification for ranges of modeling parameters
% 
% \vspace*{2mm}
%   \item Automatic verification, a 13 hour process on multiple CPUs
% 
% 
% 
% \end{itemize}
%  
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real-ESSI Validation}
% 
% %OVDE
% \begin{itemize}
% 
%   \item Validation partially done, need for high quality data
% 
% \vspace*{1mm}
%   \item Validation, UNR soil box tests in the near future
%     \begin{itemize}
% 
% %\vspace*{1mm}
%       \item Soil testing, range of strains, confinements, stress paths
%       
% %\vspace*{1mm}
%       \item Contact testing,  axial, shear, soil-concrete, formed, poured
% 
% %\vspace*{1mm}
%       \item Wave propagation through soil, equivalent elastic and inelastic, 
%       1C and 2C, dilatancy influence
% 
% %\vspace*{1mm}
%             \item Inelastic structural behavior for beams, walls, plates, shells, use of
%             already published high quality test data
% 
% %\vspace*{1mm}
%       \item ESSI tests for a complete simplified SSI systems
% 
%     \end{itemize}
% 
% 
% \end{itemize}
%  
% 
% \begin{figure}[!htbp]
% \begin{flushleft}
% \includegraphics[width=2cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/soilbox_model_gmsh.png}
% \hspace*{1mm}
% \includegraphics[width=1.2cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mesh_detail.pdf}
% \end{flushleft}
% \end{figure}
% 
% 
% 
% \vspace*{-30mm}
% \begin{figure}[!htbp]
% \begin{flushright}
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode1_side.pdf} 
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode2_side.pdf} 
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode3_side.pdf} 
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode4_side.pdf} 
% \\
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode5_side.pdf} 
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode6_side.pdf} 
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode7_side.pdf} 
% \includegraphics[width=1.6cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode8_side.pdf} 
% % \includegraphics[width=1cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode9_side.pdf} 
% % \includegraphics[width=1cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode10_side.pdf}
% % \includegraphics[width=1cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode11_side.pdf}
% % \includegraphics[width=1cm]{/home/jeremic/tex/works/Thesis/FangboWang/UNR_soil_box_model/_all_files_UNR_box_report_Sep2018/Fangbo_figs/mode12_side.pdf}
% \end{flushright}
% \end{figure}
% 
% 
% 
% \end{frame}
% 


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\begin{frame}
\frametitle{Real-ESSI Training and Education}

\begin{itemize}


  \item Short Courses: 
    \begin{itemize}
\vspace*{1mm}
      \item[-] Online short course, Fall 2019
%\vspace*{1mm}
%     \item[-] Professional practice 
% %   \vspace*{1mm}
%        \item Developers 
\vspace*{1mm}
     \item[-] Examples available in lecture notes, and documentation
%\vspace*{1mm}
%      \item[-] Real-ESSI Simulator system, with examples on Amazon Web Services 
%      (AWS)

    \end{itemize}

%\vspace{1mm}
%  \item Documentation, extensive

\vspace{2mm}
  \item Full lecture notes (2600+ pages) available online
 \url{http://sokocalo.engr.ucdavis.edu/~jeremic/}


%\vspace{2mm}
%  \item Up to date information on Real-ESSI at: 
%  \\ \vspace*{2mm}
%  \hspace*{5mm} 
%    \url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
%%  
%%
%%\href{http://real-essi.info/}{http://real-essi.info/}
%%

\end{itemize}
 
\end{frame}

% OVDE  OVDE  OVDE   


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\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}
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\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: Bonded, Frictional, 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}









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%  
%  \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}
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\subsection{Stochastic Modeling}





% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Uncertainties are inevitable in predicting behaviors of structures during future earthquakes}
%\vspace{0.5cm}
% 
% \begin{tabular}{c  c}
% \begin{minipage}{0.45\textwidth}
% %
% \hspace{-1cm} {\color{blue} Soils are spatially non-uniform}
% \begin{itemize}
% 
% \footnotesize
% \item Spatial non-uniformity is a function of soil formation process.
% \vspace*{0.1cm}
% \item Spatial non-uniformity is usually 'uncertain', due to limited data! 
% \vspace*{0.1cm}
% \item Soil parameters are ideally described as non-Gaussian random fields 
% \end{itemize}
% 
% \end{minipage} &
% %
% \hspace*{0.75truecm} 
% \begin{minipage}{0.50\textwidth}
% 
% \begin{figure}
% \includegraphics[height=5.45cm]{Fangbo_figs/TypicalSoilVariability.jpg} 
% \end{figure}
% \vspace*{-0.5truecm}
% \centering
% \scriptsize Schematic profile of a soil deposit \\
% \hspace*{0.1cm} {\tiny(Terzaghi, Peck and Mesri, 1996)}
% \end{minipage}
% \end{tabular}
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Uncertainties are inevitable in predicting behaviors of structures during future earthquakes}
% 
% \begin{columns}
% 
% \column{0.5\textwidth}
% 
% {\color{blue} Bedrock motion is also uncertain}
% \begin{itemize}
% \small
% \item Factors lead to uncertainty: 
% \begin{itemize}
% \item Mechanism of source
% \item Source parameters
% \item Earthquake propagation path
% \item ...
% \end{itemize}
% 
% \item Bedrock motion is ideally described as a non-stationary random process
% \end{itemize}
% \vspace{0.5cm}
% 
% 
% \column{0.5\textwidth}
% \includegraphics[scale=0.2]{Fangbo_figs/Three_stages_of_ground_mtion_Jie_Li.pdf} \\
% \vspace{-0.6cm}
% \begin{flushright}
% \scriptsize{Three stages explicitly indicate the non-stationarity of seismic wave}
% \end{flushright}
% \centering
% \vspace{-0.3cm}
% \hspace{0.5cm} \tiny(Li and Chen, 2009)
% 
% 
% \end{columns}
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
% \frametitle{Uncertainties are inevitable in predicting behaviors of structures during future earthquakes}
% \vspace{0.2cm}
% {\color{blue}{Design frameworks can account for uncertainties:}}
% \footnotesize
% \begin{itemize}
% \item ASD $\rightarrow$ a single factor of safety
% \item LRFD $\rightarrow$ load and resistance factors
% \item Performance-based design (PBD):
% \end{itemize}
% 
% \vspace{-0.4cm}
% \begin{figure}
% \includegraphics[scale=0.3]{Fangbo_figs/Performance_design_framework.jpg} 
% \vspace{-0.3cm}
% \caption{ \scriptsize{Schematic of PBD framework} {\tiny(Moehle and Deierlein, 2004)} }
% \end{figure}
% 
% \end{frame}
% 
% 
% \begin{frame}[t]
% \frametitle{Uncertainties are inevitable in predicting behaviors of structures during future earthquakes}
% 
% {\footnotesize \color{blue}{However, numerical simulations -- which are used to feed design framework -- still remain exclusively deterministic:}}
% \vspace{-0.2cm}
% \begin{columns}
% \column{0.5\textwidth}
% \minipage[c][0.6\textheight][s]{\columnwidth}
% \begin{figure}
%   \includegraphics[width=0.8\textwidth, angle=90]{Fangbo_figs/SSI_model_deterministic}
%   \tiny{\linespread{1.0} Schematic of a Soil-Foundation-Structure system subjected to earthquake}
% \end{figure}
% 
% \endminipage
% 
% \column{0.5\textwidth}
% \footnotesize
% 
% \begin{itemize}
% \item Although high-fidelity models that reduce modeling uncertainty are increasingly being used
% \item Uncertainties in model parameters are ignored:
%  \begin{itemize}
%      \scriptsize
%      \item Material parameters
%      \item Forcing function
%  \end{itemize}
%  \item Resulting in negation of the effects of nonlinear stochastic dynamics
% \end{itemize}
% 
% \end{columns}
% 
% \end{frame}
% 
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% \begin{frame}{Effects of nonlinear stochastic dynamics must be captured for accurate prediction}
% 
% \begin{columns}
% 
% \column{0.4\textwidth}
% \scriptsize
% 
% %\begin{center}
% %traditional SSI model \\
% %+ \\
% %uncertain soil deposit \\
% %+ \\
% %uncertain bedrock motion \\
% %$\Downarrow$ \\
% %stochastic SSI model
% %\end{center}
% Dynamic interaction of:
% \vspace{0.3cm}
% \begin{itemize}
% \item Non-Gaussian characteristics and spatial correlation of material parameters
% \item Temporal correlation of the forcing function
% \item Probabilistic evolution of material parameters as materials plastify
% \end{itemize}
% 
% \column{0.60\textwidth}
% \vspace{-1cm}
% %  \hspace{-0.9cm}
% \begin{figure}
%   \begin{flushleft}
%   \includegraphics[width=0.7\textwidth, angle=90]{Fangbo_figs/SSI_model_stochastic}
%   \end{flushleft}
%   \caption{\scriptsize Schematic illustration of a stochastic soil-foundation-structure system.}
% \end{figure}
% 
% \end{columns}
% 
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %\begin{frame}{Governing equations of solid mechanics}
% %\footnotesize
% %{
% %\begin{itemize}
% % \item Equilibrium equation: 
% %   \begin{flushleft}
% %     \begin{equation*}
% %        \frac{\partial \sigma_{ij}}{\partial x_j}+ {\color{blue}{b_j}} = \rho u_i
% %     \end{equation*}
% %   \end{flushleft}
% % \item Strain compatibility equation: 
% %     \begin{equation*}
% %        \epsilon_{ij} = \frac{1}{2} \left( \frac{\partial u_{i}}{\partial x_j}+ \frac{\partial u_{j}}{\partial x_i} \right)
% %     \end{equation*}
% % \item Constitutive equation:   
% %           \begin{equation*}
% %       \dot{\sigma}_{ij} = {\color{blue}{D_{ijkl}}} \dot{\epsilon}_{kl}
% %     \end{equation*}
% %\end{itemize}
% %}
% %\vspace{0.5cm}
% %\centering Input uncertainties (${\color{blue}{D_{ijkl}}}$, ${\color{blue}{b_j}}$) $\rightarrow$ stochastic PDE
% %\end{frame}
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Existing Simulation Methods for Stochastic PDEs}

\begin{itemize}

\item Analytical, stochastic differential equation approach: difficult to solve with complex random coefficients

\vspace*{3mm}
\item Monte Carlo method : Computationally expensive

\vspace*{3mm}
\item Perturbation approach: Small variation with respect to mean, closure problem

\vspace*{3mm}
\item Stochastic collocation method: Global error minimization

\vspace*{3mm}
\item Stochastic Galerkin method: Local error minimization
%    \begin{itemize}
%         \item \color{blue}{ \footnotesize Previous studies$\rightarrow$ Uncertain static loading, linear elastic material.}
%         \item \color{blue}{ \footnotesize My research$\rightarrow$ Uncertain dynamic loading, nonlinear material.}
%    \end{itemize}
\end{itemize}

\end{frame}




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\begin{frame} 

\frametitle{Uncertainty Propagation through 
Inelastic System}

% 

\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 load parameters are uncertain



\end{itemize}



\end{frame}






 
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\begin{frame} 

\frametitle{Probabilistic Elastic-Plastic Response}


\begin{figure}[!hbpt]
\begin{center}
%\includegraphics[width=8cm]{/home/jeremic/tex/works/Papers/2007/ProbabilisticYielding/figures/vonMises_G_and_cu_very_uncertain/Contour_PDF-edited.pdf}
\includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2012/DOE-LLNL-workshop-27-28-Feb-2012/ProbabilisticYielding_vonMises_G_and_cu_very_uncertain_Contour_PDF-edited.pdf}
\end{center}
\end{figure}

\end{frame}



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\begin{frame}
\frametitle{Probabilistic Elastic-Plastic Modeling}


% % \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}

%
% \includegraphics[width = 12cm]{./img/figure_PEP_25.pdf}


\end{frame}











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% \begin{frame} 
% 
% \frametitle{Previous Work}
% 
%  
% 
% \begin{itemize}
% 
% \item 
% Linear algebraic or differential equations:
% 
%      \begin{itemize}
%         \item Variable Transf. Method (Montgomery and Runger 2003)
%         \item Cumulant Expansion Method (Gardiner 2004)
%      \end{itemize}
% 
% \item 
% Nonlinear differential equations:
%      
%       \begin{itemize}
% 
%       \item  Monte  Carlo Simulation (Schueller 1997, De Lima et al 2001, Mellah
%       et al. 2000, Griffiths et al. 2005...) \\ $\rightarrow$ can be accurate, very costly
% 
%       \item  Perturbation  Method  (Anders and Hori 2000, Kleiber and Hien 1992,
%       Matthies  et  al. 1997) \\ $\rightarrow$ first and second order Taylor series
%       expansion  about mean - limited to problems with small C.O.V. and inherits
%       "closure problem"
% 
%       \item SFEM (Matthies et al,  2004, 2005, 2014...)
% 
% 
%       \end{itemize}
% 
% % 
% %  \item 
% %  Monte Carlo method: accurate, very costly
% %  
% %  \item 
% %  Perturbation method: 
% 
% \end{itemize}
% 
% 
%  
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \end{frame}
% 
% 


% 
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% \begin{frame} \frametitle{{3D FPK Equation}}
% 
% \begin{footnotesize}
% 
% \begin{eqnarray}
% \nonumber
% \lefteqn{\displaystyle \frac{\partial P(\sigma_{ij}(x_t,t), t)}{\partial t} = \displaystyle \frac{\partial}{\partial \sigma_{mn}} 
% \left[ \left\{\left< \vphantom{\int_{0}^{t}} \eta_{mn}(\sigma_{mn}(x_t,t), D_{mnrs}(x_t), \epsilon_{rs}(x_t,t))\right> \right. \right.} \\
% \nonumber
% &+& \left. \left. \int_{0}^{t} d\tau Cov_0 \left[\displaystyle \frac{\partial \eta_{mn}(\sigma_{mn}(x_t,t), D_{mnrs}(x_t), 
% \epsilon_{rs}(x_t,t))} {\partial \sigma_{ab}}; \right.  \right. \right. \\
% \nonumber
% & & \left. \left. \left. \eta_{ab} (\sigma_{ab}(x_{t-\tau}, t-\tau), D_{abcd}(x_{t-\tau}), \epsilon_{cd}(x_{t-\tau}, t-\tau) 
% \vphantom{\int_{0}^{t}} \right] \right \} P(\sigma_{ij}(x_t,t),t) \right] \\
% \nonumber
% &+& \displaystyle \frac{\partial^2}{\partial \sigma_{mn} \partial \sigma_{ab}} \left[ \left\{ \int_{0}^{t} d\tau Cov_0 \left[ 
% \vphantom{\int_{0}^{t}} \eta_{mn}(\sigma_{mn}(x_t,t), D_{mnrs}(x_t), \epsilon_{rs}(x_t,t)); \right. \right. \right. \\
% \nonumber
% & & \left. \left. \left. \eta_{ab} (\sigma_{ab}(x_{t-\tau}, t-\tau), D_{abcd}(x_{t-\tau}), \epsilon_{cd}(x_{t-\tau}, t-\tau)) 
% \vphantom{\int_{0}^{t}} \right] \vphantom{\int_{0}^{t}} \right\} P(\sigma_{ij}(x_t,t),t) \right]
% \end{eqnarray}
% 
%  
% \end{footnotesize}
% 
% 
% 
% %-- \begin{itemize}
% %-- 
% %-- 
% %-- 
% %-- \item 6 equations
% %-- 
% %-- \item Complete description of 3-D probabilistic stress-strain response
% %-- 
% %-- \end{itemize}
% %-- 
% %--  
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \end{frame}
% 
% 
% 



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
% 
% \frametitle{FPK Equation}
% 
%  
% 
% \begin{itemize}
% 
% \item Advection-diffusion equation 
% %
% \begin{equation}                
% \nonumber
% \frac{\partial P(\sigma,t)}{\partial t} = -\frac{\partial}{\partial \sigma}\left[N_{(1)}P(\sigma,t)-\frac{\partial}{\partial \sigma}
% \left\{N_{(2)} P(\sigma,t)\right\} \right]
% \end{equation}
% 
% %
% 
% \item Complete probabilistic description of response 
% 
% 
% \item Solution PDF is second-order exact to covariance of time (exact mean and variance)
% 
% 
% \item It is deterministic equation in probability density space
% 
% \item It is linear PDE in probability density space 
% $\rightarrow$ simplifies the numerical solution process
% 
% %\vspace*{0.2truecm}
% 
% \end{itemize}
% 
% % 
% % \vspace*{0.5cm}
% % {%
% % \begin{beamercolorbox}{section in head/foot}
% % \usebeamerfont{framesubtitle}\tiny{B. Jeremi\'{c}, K. Sett, and M. L. Kavvas, "Probabilistic
% % Elasto--Plasticity: Formulation in 1--D", \textit{Acta Geotechnica}, Vol. 2, No. 3, 2007, In press (published
% % online in the \textit{Online First} section)}
% % %\vskip2pt\insertnavigation{\paperwidth}\vskip2pt
% % \end{beamercolorbox}%
% % }
% 
% 
% 
% \end{frame}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
% 
% 
% 
% \frametitle{Template Solution of FPK Equation}
% 
%  
% 
% \begin{itemize}
% 
% 
% 
% 
% \item FPK diffusion--advection equation is applicable to any material model $\rightarrow$ 
% only the coefficients $N_{(1)}$ and $N_{(2)}$ are different for different material models
% % %
% % %
% % %
% % %\begin{normalsize}
% % \begin{equation}                
% % \nonumber
% % \frac{\partial P(\sigma,t)}{\partial t} = -\frac{\partial}{\partial \sigma}\left[N_{(1)}P(\sigma,t)-\frac{\partial}{\partial \sigma}
% % \left\{N_{(2)} P(\sigma,t)\right\} \right]
% % %\nonumber
% %  = -\frac{\partial \zeta}{\partial \sigma}
% % \end{equation}
% % %\end{normalsize}
% 
% %
% 
% \item Initial condition 
% 
% \begin{itemize}
% 
% \item Deterministic $\rightarrow$ Dirac delta function $\rightarrow$ $ P(\sigma,0)=\delta(\sigma) $
% 
% \item Random $\rightarrow$ Any given distribution
% 
% \end{itemize}
% 
% \item Boundary condition: Reflecting BC $\rightarrow$ conserves probability mass
% $\zeta(\sigma,t)|_{At \ Boundaries}=0$
% 
% \item Solve using finite differences and/or finite elements
% 
% 
% \item  However  (!!)  it  is a stress solution and probabilistic stiffness is an
% approximation!
% 
% \end{itemize}
% 
%  
% \end{frame}
% 
% 
% 
% 
% 
% 
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Direct Solution for Probabilistic Stiffness and Stress in 1D}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%    BEGGINING PEP    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% \begin{frame}{Direct Probabilistic Constitutive Modeling in 1D}
% 
% 
% % \begin{itemize}
% %  
% %  \vspace{0.5cm}
% % 
% % \item<1-> Probabilistic constitutive modeling : \vspace{0.5cm}
% 
% \begin{itemize}
% 
% 
% \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*{2mm}
% \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*{2mm}
% \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}{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]
% $
% 
% 
% 
% 
% \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{$E_{t_P}^{n+1}  =  \frac{1}{<\Phi_1\Phi_P> }\{\sum_{i=1}^{P_h} \ h_i   <\Phi_i \Phi_P> \pm \sum_{j=1}^{P_c} \sum_{l=1}^{P_{\sigma}} \ c_j  \sigma_l^{n+1} <\Phi_j  \Phi_l \Phi_P>\}$}
%   
%   
% \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}{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*{1mm}
% \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*{1mm}
% \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}
% 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\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}{Time Domain Stochastic Galerkin Method}

\begin{itemize}
\item Input random field/process{\normalsize{(non-Gaussian, heterogeneous/ non-stationary)}}
 \begin{itemize}
 \item[] Multi-dimensional Hermite Polynomial Chaos (PC) with {known coefficients}
 \end{itemize}
\vspace{0.05in}
\item Output response process
 \begin{itemize}
 \item[] Multi-dimensional Hermite PC with {unknown coefficients}
 \end{itemize}
 \vspace{0.05in}
 \item Galerkin projection: minimize the error to compute unknown coefficients of response process
\vspace{0.05in}
 \item Time integration using Newmark's method
  \begin{itemize}
   \item[] Update coefficients following an elastic-plastic constitutive law at each time step
  \end{itemize}
 
\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{3mm}

Motion 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{3mm}

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{3mm}

where $a_i(x), f_{mj}(t)$ are {known PC coefficients}, while $d_{nk}(t)$
are {unknown PC coefficients}.
%}

\end{frame}












 



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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


\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 solution (single step) 
% 
%   \item  It is NOT based on Monte Carlo approach
% 
%   \item  System of equations does grow (!)
% 
% \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}
% 
% 
% 
% 
% 







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


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

\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}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/SEPFEM_Animation_Elastic.mp4}
\end{center}

% \includegraphics[width = 12cm]{./img/figure_elastic_900.pdf}




\end{frame}

































%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{High Performance Computing}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Course 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}
\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{Modeling and Simulation Examples}



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




% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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{6C Free Field Motions (closeup)}
% 
% 
%   
% %\vspace*{-2mm}
% \begin{center}
% \movie[label=show3,width=80mm,poster,showcontrols]
% {\includegraphics[width=80mm]{/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_input_closeup_mp4_icon.jpeg}}
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_closeup.mp4}
% \end{center}
% 
% \begin{flushleft}
% \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}
%   {\tiny (MP4)}
% \end{flushleft}
% % local
% % local
% %
% 
% 
% % out 
% % out  
% % out  \vspace*{-2mm}
% % out  \begin{center}
% % out  \hspace*{-7mm}
% % out  \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% % out    {\includegraphics[width=70mm]{BJicon.png}}{movie_input_closeup.mp4}
% % out  \end{center}
% % 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_01AApr2015/movie_input_closeup.mp4}
% % out  %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
% % out    {\tiny (MP4)}
% % out  \end{flushleft}
% % out  %
% % out  
% 
%  \end{frame}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{1C vs 6C Free Field Motions}
% 
% 
% 
%  
% \begin{itemize}
% 
%   \item One component of motions (1D) from  3D
% %  or 3$\times$1D (it is done all the time!)
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% % \frametitle{1D vs 3$\times$1D vs 3D Seismic Motions}
% % 
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% % \begin{itemize}
% % 
% % \vspace{2mm}
% %  \item 1D is required by the code
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% %  \item 3$\times$1D can be used depending on frequency/wave length of interest, 
% % 
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% % %\includegraphics[width=4.5truecm]{/home/jeremic/tex/works/Papers/2016/3D_vs_3_x_1D_motions/version_04Jan2017/NearFieldESSINPPs/results/3d_vs_1d_6/node_733_acce.pdf}
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% % % %
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% % % \includegraphics[width=9.5truecm]{/home/jeremic/tex/works/Papers/2016/3D_vs_3_x_1D_motions/version_04Jan2017/NearFieldESSINPPs/results/3d_vs_1d_6/node_733_fft.pdf}
% % % \\
% % \includegraphics[width=11truecm]{/home/jeremic/tex/works/consulting/2017/IAEA/TECDOC/Version_14Mar2017/1Dvs3x1Dvs3D_waves.pdf}
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% %  \frametitle{1D vs 3D, Bottom Control Point}
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% % \includegraphics[width=5truecm]{/home/jeremic/tex/works/Thesis/HexiangWang/3Dvs1D_29Nov2017/images/XY_plane_acc_637.jpg}
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% % \end{center}
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% %  \frametitle{Free Field 3D vs 1D Convolution From Base Point}
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% % \includegraphics[width=3.4truecm]{/home/jeremic/tex/works/Thesis/HexiangWang/3Dvs1D_29Nov2017/images/motion_compare_surface_ax.pdf}
% % \includegraphics[width=3.4truecm]{/home/jeremic/tex/works/Thesis/HexiangWang/3Dvs1D_29Nov2017/images/motion_compare_surface_ay.pdf}
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% % 
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% % \begin{frame}
% %  \frametitle{3D vs 3$\times$1D vs 1D, Top of SMR}
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% % \includegraphics[width=3.4truecm]{/home/jeremic/tex/works/Thesis/HexiangWang/3Dvs1D_29Nov2017/images/point1Ax.pdf}
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\begin{frame}
\frametitle{Seismic Motions}


%\vspace*{-10mm}  

\begin{itemize}

\item Variation in  inclination, frequency, energy, duration...

\item Deterministic and Probabilistic

\item Stress test the soil-structure system

\end{itemize}


\vspace*{10mm}  



%\vspace*{-4mm}  
\begin{figure}[!htb]
\begin{flushleft}
\hspace*{-5mm}
\includegraphics[width=5cm]{/home/jeremic/tex/works/Conferences/2018/BestPSHANI/Presentation/stress_test_Best_SHANI_May2018.jpg}
\end{flushleft}
\end{figure}


% 
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% \begin{figure}[!htb]
% \begin{flushright}
% \includegraphics[width=4cm]{/home/jeremic/tex/works/Conferences/2015/CNSC_July/Present/Stress_test_NPP_idea.jpg}
% \hspace*{-5mm}
% \end{flushright}
% \end{figure}


\hspace*{10mm}  
\vspace*{-35mm}  
\begin{figure}[!htb]
\begin{flushright}
\includegraphics[width=6cm]{/home/jeremic/tex/works/consulting/2017/IAEA/TECDOC/Version_14Mar2017/1Dvs3x1Dvs3D_waves.pdf}
\hspace*{-5mm}
\end{flushright}
\end{figure}




\end{frame}






%   

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

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

     
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{\includegraphics[width=10cm]
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% online   
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\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}
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\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]
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{/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}
        
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\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}
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%\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}
        
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\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}
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% 


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\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)}
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% online  
   

\end{frame}

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


	 
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\begin{frame}
  \frametitle{3C, 6C Seismic Motions}

\vspace*{2mm}

\begin{itemize}

   \item  All (most) measured motions are full 3C, 6C

   \item  One example of an almost 2C motion (LSST07, LSST12)
\vspace*{2mm}


\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-5mm}
\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*{-5mm}
%
\end{center}
\end{figure}
   

%
%   \item  1D (?): M 6.9 San Pablo, Guatemala EQ, 14Jun2017
%
\end{itemize}


\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}
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% %
% %\movie[label=show3,width=10.0cm,poster,autostart,showcontrols]
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%   {\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}
% 
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% % online   
% \vspace*{-5mm}
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% \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}
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\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}


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\begin{frame}
\frametitle{6C Free Field Motions (closeup)}


  
%\vspace*{-2mm}
\begin{center}
\movie[label=show3,width=80mm,poster,showcontrols]
{\includegraphics[width=80mm]{/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_input_closeup_mp4_icon.jpeg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_small_model_April2015/movie_input_closeup.mp4}
\end{center}

\begin{flushleft}
\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}
  {\tiny (MP4)}
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% local
% local
%


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 \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
%  (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
\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}
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%  
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{1D vs 3$\times$1C vs 3C Seismic Motions}
% 
% 
% \begin{itemize}
% 
% \vspace{2mm}
%  \item 1D is required by the code
% 
% \vspace{4mm}
%  \item 3$\times$1D can be used depending on frequency/wave length of interest, 
% 
% \vspace{4mm}
%  \item 3C is more realistic, however it is challenging to define motions in full 3C
% 
% \end{itemize}
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{When to  use  3C and/or 3$\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}
% 
% 
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
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% online



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\begin{frame}
\frametitle{Stress Testing SSI Systems}



\begin{itemize}

\item Excite SSI system with a suite of  seismic motions

\item  Waves: P, SV, SH, Surface (Rayleigh, Love, etc.)
   
\item Variation in inclination, frequency, energy and duration

\item Try to "break" the system, shake-out strong and weak links

\end{itemize}

\vspace*{-4mm}  
\begin{figure}[!htb]
\begin{center}
\hspace*{-5mm}
\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2018/BestPSHANI/Presentation/stress_test_Best_SHANI_May2018.jpg}
\end{center}
\end{figure}

 
\vspace*{-5mm}  
\begin{figure}[!htb]
\begin{center}
\hspace*{-5mm}  
%\includegraphics[width=4cm]{/home/jeremic/tex/works/consulting/2017/IAEA/TECDOC/Version_14Mar2017/1Dvs3x1Dvs3D_waves_02.pdf}
\includegraphics[width=7.5cm]{/home/jeremic/tex/works/Conferences/2018/WCCM2018/Present/1Dvs3x1Dvs3D_waves_03.pdf}
\hspace*{4mm}
\includegraphics[width=3.6cm]{/home/jeremic/tex/works/Conferences/2018/WCCM2018/Present/1Dvs3x1Dvs3D_waves_02.pdf}
\hspace*{-5mm}
\end{center}
\end{figure}


\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Stress Test Source Signals}

\begin{itemize}


%   \item Gauss 
% \begin{figure}[!hbpt]
% \begin{flushright}
%   \vspace*{-0.5cm}
% \includegraphics[width=7.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/gauss.png}
% \end{flushright}
% \end{figure}

  \item Ricker 
\begin{figure}[!hbpt]
\begin{flushright}
  \vspace*{-1cm}
\includegraphics[width=4.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ricker2nd.pdf}
\includegraphics[width=4.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ricker2nd_FFT.pdf}
  \hspace*{-0.7cm}
\end{flushright}
\end{figure}
    
  \item Ormsby   
\begin{figure}[!hbpt]
\begin{flushright}
  \vspace*{-1cm}
\includegraphics[width=4.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ormsby.pdf}
\includegraphics[width=4.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ormsby_FFT.pdf}
  \hspace*{-0.7cm}
\end{flushright}
\end{figure}

\end{itemize}

% \begin{figure}[!hbpt]
% \begin{center}
% %
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/gauss.png}
% %
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ricker2nd.pdf}
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ricker2nd_FFT.pdf}
% %
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ormsby.pdf}
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ormsby_FFT.pdf}
% %
% \end{center}
% \end{figure}


\end{frame}


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%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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}
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%      \hspace*{30mm}
%        \includegraphics[width=2.5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/Points_configuration.pdf}
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\subsection{Plastic Energy Dissipation}



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\begin{frame}
 \frametitle{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 zone, structure, foundation, dissipators
         \item[] Viscous coupling with internal/pore fluids, 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}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


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\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}

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\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, inelastic, soil/rock -- foundation
       \begin{itemize}
         \item[]  Dry,  single  phase,  
           \begin{itemize}
             \item[]  Normal, hard  and  soft, gap open/close
             \item[]  Friction, nonlinear
           \end{itemize}
         \item[] Fully saturated, suction, excess pressure, buoyant force
       \end{itemize}


%\vspace*{1mm}
     \item Structure, inelastic, damage, cracks
       \begin{itemize}
         \item[] Nonlinear/inelastic 1D reinforced concrete fiber beam
         \item[] Nonlinear/inelastic 3D reinforced concrete solid element
         \item[] Alcali Silica Reaction 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}

 \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 contact (concrete-soil), gaping and nonlinear shear
  \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{Energy Dissipation in a Large-Scale 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/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}

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\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}

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






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\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 % 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 {\tiny (MP4)}
% 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  {\tiny (MP4)}
% online \end{center}
% online % online





\end{frame}






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\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}

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\subsection{Uncertain Inelasticity}
%\section[1-D stochastic structural dynamic analysis]{1-D stochastic structural dynamic analysis}
%\frame{\tableofcontents[currentsubsection,sectionstyle=show/shaded]}








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\begin{frame} 
\frametitle{Uncertain Model Description}

\begin{textblock}{15}(0.3, 3.4)
\includegraphics[width=0.70\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/example_illustration.png}
\end{textblock}


\begin{textblock}{15}(1.2, 11.6)
\scriptsize
\begin{itemize}
\item Fault 1: San Gregorio fault 
\item Fault 2: Calaveras fault
\item Uncertainty: Segmentation, \\ slip rate, rupture geometry, etc.
\end{itemize} 
\end{textblock}


\begin{textblock}{15}(7.2, 11.7)
\scriptsize
\begin{itemize}
\item $Vs_{30}=620m/s$
\item $m=100kips/g$
\item $\overline{k} = 168kip/in$
\end{itemize}
\end{textblock}

\begin{textblock}{15}(9.7, 6.5)
\scriptsize
\[Cov_k  = 
\begin{bmatrix}
1.0 & 0.6 & 0.3 & 0.2\\
0.6 & 1.0 & 0.5 & 0.2\\
0.3 & 0.5 & 1.0 & 0.7\\
0.2 & 0.2 & 0.7 & 1.0
\end{bmatrix}
\]
\end{textblock}

\end{frame}
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\begin{frame}
\frametitle{Seismic Source Characterization}

\begin{textblock}{15}(0.3, 3.4)
\includegraphics[width=0.65\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/SSC_legend.pdf}
\end{textblock}

\begin{textblock}{15}(6.5, 12.1)
\scriptsize
\begin{itemize}
\item 371 total seismic scenarios 
\item $M \ 5 \sim 5.5$ and $6.5 \sim 7.0$
\item $R_{jb} \ 20km \sim 40km$
\end{itemize}
\end{textblock}

\begin{textblock}{15}(11.7, 3.3)
\includegraphics[width=0.22\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/Acc_time_series100.pdf}\\
\includegraphics[width=0.22\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/Acc_time_series343.pdf}\\
\includegraphics[width=0.22\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/Acc_time_series439.pdf}
\end{textblock}
\end{frame}
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\begin{frame} 
\frametitle{Stochastic Ground  Representation}

{\begin{textblock}{15}(-0.1, 3.62)
\scriptsize
\includegraphics[width=0.3\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_mean_acc_from_acc.pdf}

\quad \quad Acc. marginal mean
\end{textblock}

\begin{textblock}{15}(3.7, 3.62)
\scriptsize
\includegraphics[width=0.3\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_var_acc_from_acc.pdf}

\quad \quad Acc. marginal S.D. 
\end{textblock}

\begin{textblock}{15}(7.6, 3.8)
\scriptsize
\includegraphics[width=0.3\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_exact_acc_correlation_from_acc.pdf}

\quad \quad \quad Acc. realization Cov.
\end{textblock}

\begin{textblock}{15}(11.8, 3.9)
\scriptsize
\includegraphics[width=0.3\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_simulated_acc_correlation_from_acc.pdf}

\quad \quad Acc. synthesized Cov.
\end{textblock}}

\begin{textblock}{15}(-0.1, 9.3)
\scriptsize
\includegraphics[width=0.31\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_mean_dis_from_dis.pdf}
\end{textblock}

\begin{textblock}{15}(0.9, 13.75)
\scriptsize
Dis. marginal mean
\end{textblock}

\begin{textblock}{15}(4.2, 9.4)
\scriptsize
\includegraphics[width=0.3\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_var_dis_from_dis.pdf}
\end{textblock}

\begin{textblock}{15}(5.1, 13.75)
\scriptsize
Dis. marginal S.D. 
\end{textblock}

\begin{textblock}{15}(8.2, 9.5)
\scriptsize
\includegraphics[width=0.27\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_exact_dis_correlation_from_dis.pdf}

\quad \quad Dis. realization Cov.
\end{textblock}

\begin{textblock}{15}(12.2, 9.6)
\scriptsize
\includegraphics[width=0.27\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/KL_simulated_dis_correlation_from_dis.pdf}

\quad Dis. synthesized Cov.
\end{textblock}
\end{frame}
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\begin{frame} 

\frametitle{Probabilistic Dynamic Response}

\begin{textblock}{15}(2.9, 4)
\scriptsize
\includegraphics[width=0.65\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/Probabilistic_Response_Node_1_new.pdf}
\end{textblock}

\begin{textblock}{15}(4.8, 3.8)
\scriptsize Probabilistic response of top floor from SFEM
\end{textblock}
\end{frame}
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% \begin{frame} 
% 
% \frametitle{Probabilistic Dynamic Response}
% 
% \begin{textblock}{15}(0.9, 4.4)
% \scriptsize
% \includegraphics[width=0.55\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/probability_evolution.jpg}
% \includegraphics[width=0.43\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/Contour_PDF_evolution_top_floor_deformation.pdf}
% \end{textblock}
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% \scriptsize Probabilistic density of displacements evolution of top floor
% \end{textblock}
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\begin{frame} 

\frametitle{Maximum Inter-story Drift Ratio (MIDR)}

% \begin{textblock}{15}(0.7, 4.8)
% \scriptsize
% \includegraphics[width=0.55\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/PDF_evolution.png}
% \end{textblock}
% 
\vspace*{-5mm}
\begin{figure}[htb]
\begin{center}
\includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/MIDR_distribution.pdf}
\end{center}
\end{figure}

\end{frame}
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\begin{frame} 

\frametitle{Seismic Risk Analysis}

\begin{textblock}{15}(0.7, 4.8)
\scriptsize
\includegraphics[width=0.45\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/combined_risk_curve.pdf}
\end{textblock}

\begin{textblock}{15}(7.9, 4.8)
\scriptsize
\includegraphics[width=0.48\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/risk_deaggregation_MIDR1.pdf}
\end{textblock}

\begin{textblock}{15}(0.9, 11.9)
\begin{itemize}
\item[] \scriptsize $\lambda(MIDR >1 \%) = 9.7 \times 10^{-3}$
\item[] \scriptsize $\lambda(MIDR >2 \%) = 1.7 \times 10^{-3}$
\item[] \scriptsize $\lambda(MIDR >4 \%) = 5.9 \times 10^{-5}$
\end{itemize}
\end{textblock}

\begin{textblock}{15}(9.3, 12.5)
\scriptsize Risk de-aggregation for $\lambda(MIDR >1 \%)$
\end{textblock}

\end{frame}
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% \begin{frame} 
% 
% \frametitle{Sensitivity Study}
% 
% \begin{textblock}{15}(1.7, 3.0)
% \scriptsize
% \includegraphics[width=0.42\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/risk_curve_different_stressdrop.pdf}
% \end{textblock}
% 
% \begin{textblock}{15}(9.1, 3.0)
% \scriptsize
% \includegraphics[width=0.42\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/risk_curve_different_kappa.pdf}
% \end{textblock}
% 
% 
% \begin{textblock}{15}(1.7, 8.7)
% \scriptsize
% \includegraphics[width=0.42\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/median_FAS_stressdrop_comparison.pdf}
% \end{textblock}
% 
% \begin{textblock}{15}(9.1, 8.7)
% \scriptsize
% \includegraphics[width=0.42\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/median_FAS_kappa_comparison1.pdf}
% \end{textblock}
% 
% \begin{textblock}{15}(7.9, 8.7)
% \scriptsize Site $\kappa_0$:
% \end{textblock}
% 
% \begin{textblock}{15}(0.3, 8.7)
% \scriptsize Source $\Delta \sigma$:
% \end{textblock}
% 
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% \begin{frame} 
% \frametitle{Sensitivity Study}
% 
% \begin{textblock}{15}(1.3, 4.2)
% Fundamental frequency $f$ increases from 1.6Hz to 8Hz:
% \end{textblock}
% 
% \begin{textblock}{15}(4.7, 5)
% \scriptsize
% \includegraphics[width=0.55\linewidth]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/risk_curve_different_kappa_highfrequency.pdf}
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\begin{frame} 
\frametitle{Seismic Risk, Uncertain Material}


\begin{figure}[htb]
\begin{center}
\includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2019/CompDyn/present/pic/seismic_risk_compare.pdf}
\end{center}
\end{figure}


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\section{Conclusion}



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    \subsection{Real-ESSI Simulator System}





 

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\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{Real-ESSI Simulator System}

 
\begin{itemize}


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

    \end{itemize} 

\vspace*{1mm}
  \item Real-ESSI System availability:                   
    \begin{itemize}
%\vspace*{1mm}
     \item Educational  Institutions: Amazon Web Services (AWS), free 
     \item Government Agencies, National Labs: AWS GovCloud
     \item Professional  Practice: AWS, commercial
%\vspace*{1mm}
%%\vspace*{1mm}
%      \item Sources available to collaborators
    \end{itemize}



%\vspace*{1mm}
%\item Quality Management System, ASME-NQA-1, ISO9003-2018, Certification in progress


\vspace*{1mm}
  \item Real-ESSI Short Courses (online, this Fall)



\vspace*{1mm}
  \item System description and documentation at  
    \url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
%
%\url{http://real-essi.info/}
%


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


\end{itemize}


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%\subsection*{Summary}


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\begin{frame} 

\frametitle{Science Quotes}

\begin{itemize}


\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  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  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,  Sinha,  Wang, Wang,
   Pisan{\'o}, Abell, Tafazzoli, Jie, Preisig, Tasiopoulou, Watanabe, Luo, 
   Cheng, Yang...
   
   

\vspace*{1mm}
  \item  Funding  from  and  collaboration  with  the US-DOE, US-NRC, US-NSF, 
  CNSC-CCSN, UN-IAEA, and Shimizu Corp. is greatly appreciated,


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

\end{itemize}



\end{frame}
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\end{document}

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