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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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% does not look nice, try deleting the line with the fontenc.






\title[Dynamics of Soils and Structures under Uncertainty]
        {Dynamics of Soils and Structures under Uncertainty}


%\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.
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\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} \\ 
Kallol Sett (UB), Konstantinos Karapiperis and Jos{\' e}  Abell }

%\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\\
%  and\\
%  Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley }
  Lawrence Berkeley National Laboratory, Berkeley }
% - 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 CompDyn,  \\ Crete, Greece, May 2015}

\subject{}
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% If you have a file called "university-logo-filename.xxx", where xxx
% is a graphic format that can be processed by latex or pdflatex,
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%\logo{\pgfuseimage{university-logo}}

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\begin{frame}
  \frametitle{Outline}

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  \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.



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\section{Motivation}




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\subsection*{Introduction}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Motivation}

\begin{itemize}



%\vspace*{0.3cm}
  \item Improve seismic design of soil structure systems


\vspace*{1mm}
  \item      {E}arthquake {S}oil {S}tructure {I}nteraction
  ({ESSI}) in time and space, plays a major role in successes and failures



%\vspace*{0.1cm}
\vspace*{1mm}
  \item  Accurate  following  and directing (!) the  flow  of  seismic energy in
  ESSI system to optimize for
    \begin{itemize}
      \item Safety and
      \item Economy
    \end{itemize}


%\vspace*{0.1cm}
\vspace*{1mm}
  \item  Development of  high  fidelity  numerical modeling and simulation tools
  to analyze realistic ESSI behavior: \\
  {Real ESSI} simulator
%   ({\small aka}: {\cyrssDvanaest Stvarno  Lako},
% { Muy F{\'a}cil},
% {Molto  Facile},
% \raisebox{-1.2mm}{\includegraphics[height=5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Chinese.jpeg}},
% \raisebox{-1.2mm}{\includegraphics[height=5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Japanese.jpg}},
% {\greektext{Pragmatik'a E'ukolo}},
% \raisebox{-1.2mm}{\includegraphics[height=5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Farsi.jpg}},
% {Tr{\`e}s Facile},
% {\cyrssDvanaest Vistinski Lesno}
% %{Wirklich Einfach}
% )

\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Predictive Capabilities}
% \frametitle{High Fidelity Modeling of SFS System:
% Verification, Validation and Prediction}

\begin{itemize}


     \item  {{  Verification}  provides  evidence  that  the  model is solved
     correctly.} Mathematics issue.

%\vspace*{0.1cm}
\vspace*{1mm}
     \item  {{  Validation}  provides  evidence  that  the  correct  model is
     solved.} Physics issue.

%\vspace*{0.1cm}
\vspace*{1mm}
   \item {  Prediction under Uncertainty (!)}:  use  of  computational  model
   to  foretell  the  state  of  a  physical  system  under  consideration under
   conditions for which the computational model has not been validated.


\vspace*{1mm}
   \item Modeling and Parametric Uncertainties


\vspace*{1mm}
   \item Predictive capabilities with {low Kolmogorov Complexity}


\vspace*{1mm}
     \item Modeling and simulation goal is to inform, not fit

%
\end{itemize}


\end{frame}






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\subsection*{Uncertainties}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Modeling Uncertainty}

\begin{itemize}



  \item      Simplified  modeling:    Features (important ?)   are neglected (6D
  ground motions, inelasticity)

\vspace*{4mm}
     \item   Modeling   Uncertainty:   unrealistic   and   unnecessary  modeling
     simplifications

\vspace*{4mm}
     \item  Modeling  simplifications   are  justifiable  if  one  or  two  level  higher
     sophistication  model  shows  that  features  being  simplified out are not
     important



\end{itemize}
\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Parametric Uncertainty: Material Stiffness}


%\vspace*{-3mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-7mm}
\includegraphics[width=7.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf}
% \hfill
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
%
\end{center}
\end{figure}

% \vspace*{-1.8cm}
% %\hspace*{-3.3cm}
% \begin{flushright}
% {\tiny
% Transformation  of SPT $N$-value: \\
% 1-D Young's modulus, $E$ \\
% (cf. Phoon and Kulhawy (1999B))\\
% ~}
% \end{flushright}
%
\end{frame}


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Parametric Uncertainty: Material Strength}
% 
% 
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \hspace*{-7mm}
% \includegraphics[width=6.50truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_RawData_and_MeanTrend-Mod.pdf}
% \hspace*{-7mm}
% % \hfill
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_Histogram_PearsonIV-FineTuned-Mod.pdf}
% %
% \end{center}
% \end{figure}
% 
% % \vspace*{-1.8cm}
% % %\hspace*{-3.3cm}
% % \begin{flushright}
% % {\tiny
% % Transformation  of SPT $N$-value: \\
% % 1-D Young's modulus, $E$ \\
% % (cf. Phoon and Kulhawy (1999B))\\
% % ~}
% % \end{flushright}
% % %
% 
% 
% \end{frame}
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Parametric Uncertainty: Material Properties}



\begin{figure}[!hbpt]
\begin{center}
% %
\hspace*{-3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiPdf.pdf}
\hspace*{-3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiCdf.pdf}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuPdf.pdf}
\hspace*{-3mm}
\includegraphics[width=3.0truecm]{/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*{45mm}
\hspace*{-3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiPdf.pdf}
\hspace*{-3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiCdf.pdf}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuPdf.pdf}
\hspace*{-3mm}
\includegraphics[width=3.0truecm]{/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{Realistic ESSI Modeling Uncertainties}


\begin{itemize}


\item   Seismic   Motions:  6D,  inclined,  body  and  surface  waves
(translations, rotations); Incoherency

\vspace*{3mm}
\item    Inelastic    material:    soil,   rock,   concrete,   steel;   Contacts,
foundation--soil, dry, saturated slip--gap; Nonlinear buoyant forces; Isolators,
Dissipators


\vspace*{3mm}
    \item Uncertain loading and material

\vspace*{3mm}
     \item Verification and Validation  $\Rightarrow$  Predictions


% \vspace*{2mm}
%     \item High Fidelity Models $\Rightarrow$ High Performance Computing
% 
% 
% \vspace*{2mm}
%      \item Education
% 



\end{itemize}

\end{frame}

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

%
%





























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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Modeling and Parametric Uncertainty}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Modeling Uncertainty}


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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Real ESSI Models}


\begin{itemize}


\item  Full  seismic  motion  input  (body  and  surface waves) using the Domain
Reduction Method (Bielak et al.)

\vspace*{2mm}
\item Inelastic (saturated or dry) soil/rock

\vspace*{2mm}
\item Inelastic (saturated or dry) contact (foundation --  soil/rock)

\vspace*{2mm}
\item Buoyant (nonlinear) forces

\vspace*{2mm}
\item Inelastic structural modeling (elastic requested?!)

\vspace*{2mm}
\item Verification (extensive) and Validation (in progress)

\end{itemize}

\end{frame}

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


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{6D Free Field Motions}


\vspace*{-2mm}
\begin{center}
%\movie[label=show3,width=8.5cm,poster,autostart,showcontrols,loop]
\hspace*{-7mm}
\movie[label=show3,width=8.8cm,autostart,showcontrols]
  {\includegraphics[width=70mm]{BJicon.png}}{movie_input.mp4}
\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/ESSI_VisIt_movies_Jose_01AApr2015/movie_input.mp4}
%  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
  {\tiny (MP4)}
%
\end{flushleft}


 \end{frame}

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


\vspace*{-2mm}
\begin{center}
\hspace*{-7mm}
\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
  {\includegraphics[width=70mm]{BJicon.png}}{movie_input_closeup.mp4}
\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/ESSI_VisIt_movies_Jose_01AApr2015/movie_input_closeup.mp4}
%  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
  {\tiny (MP4)}
\end{flushleft}
%


 \end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{6D Free Field at Location}


\vspace*{-2mm}
\begin{center}
\hspace*{-7mm}
\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
  {\includegraphics[width=69mm]{BJicon.png}}{movie_ff_3d.mp4}
\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/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
%  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
  {\tiny (MP4)}
\end{flushleft}
%


 \end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{6D Earthquake Soil Structure Interaction}

\vspace*{-2mm}
\begin{center}
\hspace*{-7mm}
\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
  {\includegraphics[width=70mm]{BJicon.png}}
  {movie_npp_3d.mp4}
\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/ESSI_VisIt_movies_Jose_19May2015/movie_npp_3d.mp4}
  {\tiny (MP4)}
\end{flushleft}
%

 \end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{From 6D to 1D?}


\begin{itemize}


\item Assume that a full 6D (3D) motions at the surface are only recorded in one
horizontal direction


\item  From such recorded motions one can develop a vertically propagating shear
wave in 1D

\item  Apply  such  vertically propagating shear wave to the 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{1D Free Field at Location}


\vspace*{-2mm}
\begin{center}
\hspace*{-7mm}
\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
  {\includegraphics[width=70mm]{BJicon.png}}
  {movie_ff_1d.mp4}
\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/ESSI_VisIt_movies_Jose_19May2015/movie_ff_1d.mp4}
  {\tiny (MP4)}
\end{flushleft}
%


 \end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{1D ESSI of NPP}


\vspace*{-2mm}
\begin{center}
\hspace*{-7mm}
\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
  {\includegraphics[width=70mm]{BJicon.png}}
  {movie_npp_1d.mp4}
\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/ESSI_VisIt_movies_Jose_19May2015/movie_npp_1d.mp4}
  {\tiny (MP4)}
\end{flushleft}
%




 \end{frame}

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


\vspace*{-2mm}
\begin{center}
\hspace*{-7mm}
\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
  {\includegraphics[width=69mm]{BJicon.png}}
  {movie_2_npps.mp4}
\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/ESSI_VisIt_movies_Jose_19May2015/movie_2_npps.mp4}
  {\tiny (MP4)}
\end{flushleft}
%



 \end{frame}





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{6D vs 1D: Containment Displacement Response}
% 
% 
% \begin{figure}[!hp]
% \begin{center}
% \hspace*{-13mm}
%  \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/NPP_movies_19May2015/01_displacements_Containment_building_bottom.pdf}
% \hspace*{-6mm}
%  \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/NPP_movies_19May2015/02_displacements_Containment_building_top.pdf}
% \hspace*{-10mm}
% \end{center}
% \end{figure}
% 
% 
% 
% \end{frame}
% 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{6D vs 1D: Containment Acceleration Response}


\begin{figure}[!hp]
\begin{center}
\hspace*{-13mm}
 \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/NPP_movies_19May2015/01_accelerations_Containment_building_bottom.pdf}
\hspace*{-6mm}
 \includegraphics[width=7cm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/NPP_movies_19May2015/02_accelerations_Containment_building_top.pdf}
\hspace*{-10mm}
\end{center}
\end{figure}



\end{frame}




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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Parametric Uncertainty: Probabilistic Inelasticity}
\subsection{Parametric Uncertainty}

 

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

\frametitle{Uncertain Material Parameters and Loads}


\begin{itemize}

  \item Decide on modeling complexity
  
  \vspace*{3mm}
  \item Determine  model/material parameters

  \vspace*{3mm}
  \item  Model/material  parameters are uncertain! 

    \begin{itemize}
    
      \item Measurements
      
      \item Transformation

      \item Spatial variability

    \end {itemize}



\end{itemize}

\end{frame}







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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} 
     =  
     \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*{5mm}
\item Dynamic Finite Elements
%
\begin{equation}
{\bf M} \ddot{\bf u} +
{\bf C} \dot{\bf u} +
{\bf K}^{ep} {\bf u} =
{\bf F}
    \nonumber
\end{equation}


\end{itemize}


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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 
\frametitle{Critique of our Previous Work, PEP and SEPFEM}

\begin{itemize}

\item Constitutive weighted coefficients $N_1$ and $N_2$ do not work well for
stress solution!

\vspace{1mm}
\item  We  suggested   that $\sigma(t)$ be considered a $\delta$-correlated, and
based  on  that  simplified  stiffness  equations.  Both  the assumption and the
resulting equation were not right.


\vspace{1mm}
\item  On  a  SEPFEM  level,  stiffness  needs  update  basis  functions  and KL
coefficients  in  each  step.  We updated   the   eigenvalues  
$\lambda_i$  and kept the same structure (Karhunen-Loeve)  in  the approximation
of  the  stiffness, which is not physical

\vspace{1mm}
\item   Implicitly  assumed    that   the  stiffness remains Gaussian, which is 
not the case


\end{itemize}







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


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 
\frametitle{Gradient Flow Theory of Probabilistic Elasto-Plasticity}


Decomposition of an elastoplastic random process:
% into 
%the following general form:
%
\begin{eqnarray}
\begin{array}{c c c c c}
 \bigg( \displaystyle{\pder[]{t}} - \mathcal{L}_{rev} \bigg) P(\boldsymbol{\sigma},t) &=& 0& \qquad &\text{if } 
 \boldsymbol{\sigma} \in \Omega^{el} 
 \\
 ~
 \\
 \bigg( \displaystyle{\pder[]{t}} - \mathcal{L}_{irr} \bigg) P(\boldsymbol{\sigma},t) &=& 0& \qquad &\text{if } 
 \boldsymbol{\sigma} \in \Omega^{el} \cup \Omega^{pl}
\end{array} 
\nonumber
\end{eqnarray}

%
\begin{itemize}

\item Reversible ($\mathcal{L}_{rev} $) and Irreversible ($\mathcal{L}_{irr} $) operators
%

\vspace*{2mm}
\item Yield PDF is an attractor, similar to plastic corrector

\vspace*{2mm}
\item Ergodicity of the elastic-plastic process can be proven!

\end{itemize}





\end{frame}

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


\begin{frame} 
\frametitle{Gradient Flow Theory of Probabilistic Elasto-Plasticity}

\begin{itemize}

\item 
Elastic, reversible process, Fokker-Planck (forward Kolmogorov) equation
%
\begin{equation}
 \pder[P (\boldsymbol{\sigma},t)]{t} 
  = -\nabla \cdot (\langle \boldsymbol{E} \dot{\boldsymbol{\epsilon}} \rangle P(\boldsymbol{\sigma},t))
  + t ~\text{Var}[\boldsymbol{E}\dot{\boldsymbol{\epsilon}}] \Delta P(\boldsymbol{\sigma},t) 
\nonumber
\end{equation}
%
\begin{equation}
 \mathcal{L}_{rev} = \nabla \cdot (t \,\text{Var}[\boldsymbol{C}\dot{\boldsymbol{\epsilon}}] \nabla - 
 \langle \boldsymbol{C} \dot{\boldsymbol{\epsilon}} \rangle)
\nonumber
\end{equation}

\item 
Plastic, irreversible process,  Fokker-Planck (forward Kolmogorov) equation 
%
\begin{equation}
 \pder[P(\boldsymbol{\sigma},t)]{t} = \nabla \cdot (\nabla \Psi(\boldsymbol{\sigma})
 P(\boldsymbol{\sigma},t)) + D \Delta P(\boldsymbol{\sigma},t)
\nonumber
\end{equation}
%   
\begin{equation}
 \mathcal{L}_{irr} = D \nabla \cdot \bigg(\nabla - \frac{\nabla P_y(\boldsymbol{\sigma})}{P_y(\boldsymbol{\sigma})}\bigg)
\nonumber
\end{equation}
%

\end{itemize}

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 
\frametitle{Gradient Flow Theory of Probabilistic Elasto-Plasticity}

\begin{itemize}

\item Limiting (final) distribution
is  considered  to  be  known 
%(given as a material parameter) and 

\vspace*{2mm}
\item Underlying potential  leading  to  this  distribution is sought

\vspace*{2mm}
\item Transition from uncertain elastic to uncertain plastic response


\vspace*{2mm}
\item Only in a 1D   elastoplastic   problem  does  one  end  up  with  a  stationary
distribution

\vspace*{2mm}
\item In  higher dimensional problems this yield stress distribution is
only   "marginally"  stationary  along  one  or  a  combination  of  the  stress
components.

\end{itemize}


\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 
\frametitle{Probabilistic Elasto-Plasticity: von Mises Surface}


%        An example of a Mises probabilistic yield surface is given in Fig.~\ref{ProbCylinder}.

\begin{figure}[H]
\centering
\vspace*{-5mm}
%\hspace*{-30mm}
 \includegraphics
%  [scale = 0.8, trim = 0.6in 0.4in 0.6in 0.4in, clip=true]
  [width=12cm]
   {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Probabilistic_von_Mises_Surface.jpg}
% \caption{An example of a probabilistic von Mises yield surface.}
 \label{ProbCylinder}
\end{figure}



\end{frame}





% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 
\frametitle{Gradient Theory of Probabilistic Elasto-Plasticity: Numerical Solution}


\begin{itemize}
         
\item  Using  radial  basis  functions  (a  meshless  method)  for solving
Fokker-Planck equations for uncertain elastic-plastic response


\vspace*{6mm}
\item   Details in a talk by Mr. Karapiperis later this afternoon (room 2, MS-6,
17:00-19:00, last talk) 


\end{itemize}
% %


\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 
\frametitle{Gradient Theory of Probabilistic Elasto-Plasticity: 
Verification, Elastic-Perfectly Plastic}
               

%\vspace*{-3mm}
\begin{figure}[H]
\centering
 \includegraphics
% [scale = 0.55, trim = 0.0in 0.0in 0.0in 0.0in, clip=true]
 [width=8cm]
 {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/M+-SD_1D_Perf_Cyclic.pdf}
%  \caption{Combining  the  above  plots to get the evolution of mean $\pm$ std.
% deviation of stress.}
 \label{MSD_12}
\end{figure}


\end{frame}

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

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


\begin{frame}{Stochastic Elastic-Plastic FEM (SEPFEM)}

\begin{itemize}
 \item<1> KL-PC expansion of material random fields (stiffness, etc)
%
% \begin{equation*}
$
\mathbb{D}(\bold{x}, \theta) = \sum_{i=0}^{M} r_{i}(\bold{x}) \Phi_i[\{\xi_r(\theta)\}]
 \label{nonGaussian1}
$
%\end{equation*}

 \item<1> PC expansion of displacement field
%
\begin{eqnarray*}
u(\bold{x},\theta) = \sum_{i=0}^p d_i(\bold{x}) \psi_i[\{\xi_r(\theta)\}]
\label{PC1}
\end{eqnarray*}

\item<1> Stochastic Galerkin

\begin{eqnarray*}
\sum_{n = 1} ^ N K'_{mn} d_{ni} + \sum_{n=1}^N \sum_{j=0}^P d_{nj} \sum_{k=1}^M b_{ijk} K''_{mnk} =
\Phi_{m}\langle\psi_i[\{\xi_r\}]\rangle
\label{Lognormal6}
\end{eqnarray*}

 \end{itemize}


\end{frame}

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

\begin{frame}{SEPFEM Statistical linearization}

Update the FE stiffness in the elastoplastic regime:

\begin{itemize}
 \item  Solve elastoplastic FPE for each integration point
%
\begin{eqnarray*}
 \pder[P^{nl}(\sigma,t)]{t}
 &=& \pder[]{\sigma} \bigg(\bigg\langle D^k (1 - P[\Sigma_y \leq \sigma]) \frac{\Delta
 \epsilon}{\Delta t} \bigg\rangle P\bigg) \nonumber \\
 & & + \pder[^2]{\sigma^2} \bigg( t Var\bigg[ D^k (1 - P[\Sigma_y \leq \sigma]) \frac{\Delta
 \epsilon}{\Delta t} \bigg] P\bigg)
 \label{SEPFEMLinearization1}
\end{eqnarray*}

\item Consider an equivalent linear FPE
%
\begin{eqnarray*}
 \pder[P^{lin}(\sigma,t)]{t}
 &=& N_{(1)}^{eq} \pder[P]{\sigma} + N_{(2)}^{eq} \pder[^2 P]{\sigma^2}
 \label{SEPFEMLinearization2}
\end{eqnarray*}

\item Linearization of the PC coeff. as an optimization problem
%
\begin{equation*}
 \pder[P^{lin}(\sigma,t)]{t}
 = \pder[P^{nl}(\sigma,t)]{t}
\end{equation*}


\end{itemize}

\end{frame}

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

\begin{frame}{Dynamic, Time Domain, SEPFEM}

\begin{itemize}
 \item Gaussian formulation inadequate due to occurrence of "probabilistic softening" modes
 $\Rightarrow$ Need for positive definite kernel

\vspace*{2mm}
 \item Stochastic forcing  (e.g. uncertain earthquake)

\vspace*{2mm}
 \item   Stability   of   time   marching  algorithm  (Newmark, Rosenbrock, Cubic Hermitian )  analyzed  using
 amplification matrix

\vspace*{2mm}
 \item Long-integration error and higher order statistics phase shift
\end{itemize}

%  \begin{figure}[H]
% \centering
%  \includegraphics[scale = 0.4, trim = 0.1in 0.0in 0.0in 0.0in, clip=true]{/home/jeremic/tex/Classes/2015/spring/ECI280A/SEPFEM/odKonstantinosa/figures/Sendai_1Sine_PCk2PCd8.pdf}
%  \label{Sendai_1Sine_PCk2PCd8.pdf}
% \end{figure}
% 


\end{frame}







 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 
\frametitle{Wave Propagation Through Uncertain Soil}

\vspace{-2mm}
 
\begin{figure}[H]
 \centering
 \includegraphics
% [scale = 0.56, trim = 0.0in 0.15in 0.2in 0.16in, clip=true]
 [width=7cm]
 {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_profile.png}
%
%  
\includegraphics
%[scale = 0.56, trim = 0.0in 0.0in 0.0in 0.0in, clip=true]
 [width=1.5cm]
{/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/meshes.png}
% \caption{Simplified profile and properties for the 1-dimensional profile considered.}
 \label{Sendai_profile}
\end{figure}
     


\vspace{-5mm}

 
\begin{figure}[htbp]
\centering
%\hspace{-0.2in}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \includegraphics
% [scale = 0.37, trim = 0.0in 0.0in 0.0in 0.0in,clip=true]
 [width=3.5cm]
 {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/ShearModulusStats.pdf}
\hfill
 \includegraphics
% [scale = 0.37, trim = 0.0in 0.0in 0.0in 0.0in, clip=true]
 [width=3.5cm]
 {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/ShearStrengthStats.pdf}
%\caption{Shear modulus and shear strength statistics in the middle of the soil column.}
\hfill
 \includegraphics
% [scale = 0.62, trim = 0in 0.15in 0in 0.22in, clip=true]
 [width=3.5cm]
 {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV45_BaseInput.pdf}
% \caption{Single sine pulse excitation of the soil column at its base.}
% \label{Sendai_1Sine_PCk2PC2_elastic_COV45_BaseInput}
\end{figure}


\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 
\frametitle{Uncertain Elastic Response at the Surface {\tiny(COV = 120\%)} }
 
 \vspace*{-2mm}
\begin{figure}[H]
 \centering
 \includegraphics
% [scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true]
 [width=9.3cm]
 {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120.pdf}
%  \caption{Mean  $\pm$ std. deviation of the elastic response at the top of the
% soil column for the conservative COV case (COV = 120\%).}
% \label{Sendai_1Sine_PCk2PC2_elastic_COV120}
\end{figure}

\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 
\frametitle{Displacement PDFs at the Surface {\tiny(COV = 120\%)} }

%\vspace*{-20mm} 
%\hspace*{-30mm} 
\begin{figure}[H]
 \centering
 \includegraphics
%[scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true]
 [width=10cm]
 {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120_FullPdf.jpg}
%  \caption{Mean  $\pm$ std. deviation of the elastic response at the top of the
% soil column for the conservative COV case (COV = 120\%).}
% \label{Sendai_1Sine_PCk2PC2_elastic_COV120}
\end{figure}

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 
\frametitle{Displacement CDFs (Fragilities) at the Surface {\tiny(COV = 120\%)}  }
 
 \vspace*{-3mm}
\begin{figure}[H]
 \centering
 \includegraphics
% [scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true]
 [width=11cm]
 {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120_FullCdf.jpg}
%  \caption{Mean  $\pm$ std. deviation of the elastic response at the top of the
% soil column for the conservative COV case (COV = 120\%).}
% \label{Sendai_1Sine_PCk2PC2_elastic_COV120}
\end{figure}

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame} 
\frametitle{Probability of Exceedance, $disp=0.1m$ {\tiny(COV = 120\%)}  }
 
\begin{figure}[H]
 \centering
 \includegraphics
% [scale = 0.62, trim = 0in 0.16in 0in 0.26in, clip=true]
 [width=9cm]
 {/home/jeremic/tex/works/Reports/2015/SEPFEM/figures/Sendai_1Sine_PCk2PC2_elastic_COV120_ProbExc.pdf}
%  \caption{Mean  $\pm$ std. deviation of the elastic response at the top of the
% soil column for the conservative COV case (COV = 120\%).}
% \label{Sendai_1Sine_PCk2PC2_elastic_COV120}
\end{figure}

\end{frame}

% 







% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Summary}


\subsection*{Summary}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
  \frametitle{Concluding Remarks}

  \begin{itemize}

%\vspace*{2mm}
  \item Uncertainty influences results of  numerical predictions 

\vspace*{2mm}
     \item Uncertainty (modeling and parametric)   {must}
     be taken into account



\vspace*{2mm}
     \item Goal is to {predict} and {inform}, not fit

%\vspace*{0.1cm}
\vspace*{2mm}
  \item Philosophy of modeling and simulation system \\
   {\bf Real ESSI} simulator \\ 
%
  ({\small aka: {\cyrssDvanaest Vrlo Prosto},
{ Muy F{\'a}cil},
{Molto  Facile},
\raisebox{-1.2mm}{\includegraphics[height=4mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Chinese.jpeg}},
\raisebox{-1.2mm}{\includegraphics[height=4mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Japanese.jpg}},
{\greektext{Pragmatik'a E'ukolo}},
\raisebox{-1.2mm}{\includegraphics[height=4.5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Hindi.jpg}},
\raisebox{-1.2mm}{\includegraphics[height=4mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Farsi.jpg}},
{Tr{\`e}s Facile},
{\cyrssDvanaest Vistinski Lesno},
{Wirklich Einfach}
})


% \vspace*{0.4cm}
%   \item  Collaborators:
%   Dr.    Budnitz    (LBNL),
%   Mr. Orbovi{\'c} (CNSC),
%   Prof. Pisan{\`o} (TU Delft),
%   Prof.  Sett  (UB),
%   Mr. Watanabe (Shimizu)
%   and
%   UCD students:
%   Mr. Abell,
%   Mr. Karapiperis,
%   Mr. Feng,
%   Mr. Sinha,
%   Mr. Luo
% 
% 
\end{itemize}


\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
  \frametitle{Acknowledgement}

  \begin{itemize}



\vspace*{0.1cm}
  \item  Funding from and collaboration with the US-NRC, US-DOE, US-NSF,   CNSC,
  AREVA NP GmbH, and Shimizu Corp. is greatly appreciated,

\vspace*{4mm}
  \item  Collaborators:
%  Dr.    Budnitz    (LBNL),
  Prof. Kavvas (UCD),
  Prof. Pisan{\`o} (TU Delft),
  Mr. Watanabe (Shimizu),
  Mr. Vlaski (AREVA NP GmbH),
  Mr. Orbovi{\'c} (CNSC)
  and
  UCD students:
  Mr. Abell,
  Mr. Karapiperis,
  Mr. Feng,
  Mr. Sinha,
  Mr. Luo
% 
% 
\end{itemize}


\end{frame}




\end{document}

%
%



