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\title[ESSI under Uncertainty]
        {Uncertainties in 
        Modelling and Simulation of
        Earthquake Soils Structures Interaction}


%\subtitle
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%{Boris~Jeremi{\'c}}
{Boris Jeremi{\'c}}

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%{ 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 Earthquake Research Institute \\
        University of Tokyo \\
         Tokyo, Japan, January 2016}

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\section{Motivation}




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\subsection{Introduction}



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\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}
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\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  predict  the  state  of SSI system 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: \\
      predict and inform, rather than (force) fit

%
\end{itemize}


\end{frame}






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\subsection{Uncertainties}
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\begin{frame}
 \frametitle{Modeling Uncertainty: Simplified  Models}

\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 and Loads}


\vspace{1cm}
\hspace{-0.5cm}
Example: Elastic 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*{-0.8cm}
%\hspace*{-3.3cm}
\begin{flushleft}
{\tiny
Transformation  of SPT $N$-value: 
1-D Young's modulus, $E$ 
(cf. Phoon and Kulhawy (1999B))
~}
\end{flushleft}

\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}
% \vspace*{1mm}
% \item    Inelastic    material:    soil (dry, saturated),   rock,   concrete,   steel   
% 
% \vspace*{1mm}
% \item Inelastic contact: foundation--soil, dry, saturated, slip--gap
% 
% \vspace*{1mm}
% \item  Nonlinear buoyant forces 
% 
% \vspace*{1mm}
% \item Base Isolators, Dissipators
% 
% \vspace*{1mm}
%     \item Uncertain loading and material
% 
% \vspace*{1mm}
%      \item Verification and Validation  $\Rightarrow$  Predictions
% 
% 
% \end{itemize}
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% 
% 
% 
% 

%
%





























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\section{Modeling and Parametric Uncertainty}


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\subsection{Modeling Uncertainty: Seismic Motions for NPPs}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Modeling and Simulation of Nuclear Power Plants}


\begin{itemize}


\item Nuclear Power Plants (NPPs) design based on a number of simplified assumptions!

\vspace*{1mm}
\item Linear elastic material behavior

\vspace*{1mm}
\item Seismic Motions: $1$D  or $3 \times 1$D, or real 3D (6D)


\vspace*{1mm}
\item   Savings  in  construction  cost  possible with more accurate modeling of
NPPs


\vspace*{1mm}
\item    Improvements in  safety of NPPs also possible, even with higher seismic
motions, as inelastic effects "eat up" (dissipate) seismic energy


\end{itemize}


 \end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Nuclear Power Plants: 6D or 1D Seismic Motions}


\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}


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% 
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Stress Testing NPP SSI Systems}
%  
%  
%  
%  \begin{itemize}
%  
%  \item Excite NPP SSI system with different waves, energies and durations
%  
%  \item Try to "break" the system, shake-out strong and weak links
%  
%  
%  %\vspace*{3mm}
%  %\item 
%  
%  \end{itemize}
%  
%  \vspace*{-2mm}
%  \begin{figure}[!htb]
%  \begin{center}
%  \includegraphics[width=9cm]{/home/jeremic/tex/works/Conferences/2015/CNSC_July/Present/Stress_test_NPP_idea.jpg}
%  \hspace*{-5mm}
%  \end{center}
%  \end{figure}
%  
%  
%  
%  \end{frame}
%  
%  


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
 \frametitle{Synthetic Test Motions}

\begin{itemize}

  \item Develop free field models with sources within
  
  \item Sources are simple, point (mostly), line and surface

  \item Sources will send both P and S waves

  \item Variation in strike and dip 
  
  \item Simulation programs, Real ESSI Simulator and SW4    

\end{itemize}


  
\vspace*{-2mm}
\begin{center}
\hspace*{-7mm}
\movie[label=show3,width=5.0cm,poster,autostart,showcontrols]
  {\includegraphics[width=40mm]{BJicon.png}}{movie_input_closeup.mp4}
 \movie[label=show3,width=5.0cm,poster,autostart,showcontrols]
  {\includegraphics[width=40mm]{BJicon.png}}{movie_ff_3d.mp4}
\end{center}




\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Synthetic Test Motions, 6D vs 1D}

\begin{itemize}

  \item Danger of picking one component of motions for 1D or 3$\times$1D (it is done all the time!)
  
  \item  Excellent  (forced)  fit,  but  not a prediction and information is lost
  (goal is to predict and inform and not (force) fit)


\end{itemize}


  
\vspace*{-2mm}
\begin{center}
\hspace*{-7mm}
 \movie[label=show3,width=5.0cm,poster,autostart,showcontrols]
  {\includegraphics[width=40mm]{BJicon.png}}{movie_ff_3d.mp4}
\movie[label=show3,width=5.0cm,poster,autostart,showcontrols]
  {\includegraphics[width=40mm]{BJicon.png}}{movie_ff_1d.mp4}
\end{center}




\end{frame}





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\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 (1st, 2nd)
\begin{figure}[!hbpt]
\begin{flushright}
  \vspace*{-1cm}
\includegraphics[width=4.0cm]{/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=4.0cm]{/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=4.0cm]{/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=4.0cm]{/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}


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
























%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Local Geology Effects}



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

\begin{frame}
  \frametitle{Layered and Dyke/Sill Models}


\vspace*{5mm}

\begin{itemize}

   \item Uniform soil/rock, to show surface waves
   
\vspace*{1mm}
   \item   Horizontally layered geology (a), to show bending/refraction and more
   surface waves
   
\vspace*{1mm}
   \item  Dyke/Sill  intrusion  within  layered geology (b), to show effects of
   local geology on free field motions


\end{itemize}

\vspace*{-5mm}


\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-5mm}
\includegraphics[width=12.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/models.png}
%
\end{center}
\end{figure}


\end{frame}



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

\begin{frame}
  \frametitle{Variable Sources}


\vspace*{5mm}

\begin{itemize}


   \item Epicenter is  $2500$m away from the location of interest

   \item Source depth $850$m (softer layers) and  $2500$m  (hard rock)
   
   \item Variation: source locations, strike and dip, magnitude, frequencies

   \item Different wave propagation path to the object location
   

\end{itemize}


%\vspace*{-5mm}

\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-5mm}
\includegraphics[width=12.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/geom.png}
%
\end{center}
\end{figure}


\end{frame}



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
%   \frametitle{Layered System, Variable Source Depth}
% 
% \vspace*{2mm}
% 
% \begin{itemize}
% 
%    \item Epicenter is  $2500$m away from the location of interest
% 
%    \item Source depth $850$m (softer layers) and  $2500$m  (hard rock)
%    
%    \item Different wave propagation path to the point of interest
%    
%    \item Surface waves quite pronounced 
% 
% \end{itemize}
% 
% 
% \vspace*{-5mm}
% 
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \hspace*{-5mm}
% %\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_no/bh_x_output_z850_dip45_gaussx4750.png}
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_no/borehole_ux_gauss_x5000.png}
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_no/borehole_uz_gauss_x5000.png}
% %\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_no/bh_x_output_z850_dip45_gaussx5250.png}
% %
% \end{center}
% \end{figure}
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
\begin{frame}
  \frametitle{Layered System , Displacement Traces}



\begin{figure}[!hbpt]
\begin{flushright}
%
\hspace*{-35mm}
  \includegraphics[width=3truecm]{/home/jeremic/tex/works/Conferences/2016/ERI_Tokyo_Jan2016/Present/Layered-model.jpeg}
\end{flushright}
\end{figure}

\vspace*{-1.6cm}
\begin{itemize}

   \item Surface waves
   \item Surface waves not filtered out
   \item Incoherent motions
   
\end{itemize}

\vspace*{-5mm}

\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-10mm}
\includegraphics[width=6.3truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_no/cut_output_z850_dip45_gauss.png}
\includegraphics[width=6.3truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_no/cut_output_z2500_dip45_gauss.png}
%\hspace*{-4mm}
%
\end{center}
\end{figure}

\end{frame}

                  


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Layered System, Variable Source Depth}

%   
% \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}
%   {\includegraphics[width=50mm]{movie_ff_3d_mp4_icon.jpeg}}
% %
% \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}
%   {\includegraphics[width=50mm]{movie_ff_1d_mp4_icon.jpeg}}
% \end{center}
% 

%\vspace*{-2mm}
\begin{center}
\hspace*{-15mm}
%
\movie[label=show3,width=6.0cm,poster,autostart,showcontrols]
  {\includegraphics[width=50mm]{BJicon.png}}{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/movie01.mp4}
%
\movie[label=show3,width=6.0cm,poster,autostart,showcontrols]
  {\includegraphics[width=50mm]{BJicon.png}}{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/movie04.mp4}
\hspace*{-15mm}
%
\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{Dyke/Sill Intrusion, Variable Source Depth}
% 
% \begin{itemize}
% 
%    \item Lower amplitudes than with layered only model!
%    
%    \item Difference in body and surface wave arrivals
%    
%    \item Surface waves present
% 
% \end{itemize}
% 
% 
% 
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \hspace*{-5mm}
% %\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_right/bh_x_output_z850_dip45_gaussx4750.png}
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_right/borehole_ux_gauss_x5000.png}
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_right/borehole_uz_gauss_x5000.png}
% %\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_right/bh_x_output_z850_dip45_gaussx5250.png}
% %
% \end{center}
% \end{figure}
% 
% \end{frame}
% 


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

\begin{frame}
  \frametitle{Dyke/Sill Intrusion, Variable Source Depth}



\begin{figure}[!hbpt]
\begin{flushright}
%
\hspace*{-35mm}
  \includegraphics[width=3truecm]{/home/jeremic/tex/works/Conferences/2016/ERI_Tokyo_Jan2016/Present/Dyke-Sill-model.jpeg}
\end{flushright}
\end{figure}

\vspace*{-1.6cm}
\begin{itemize}

   \item Incoherent motions 
 
   \item Surface waves

   \item Lower amplitudes than with \\
         layered only model!
   
%   \item Difference in body and surface wave arrivals
   
   
   
\end{itemize}
\vspace*{-5mm}



\begin{figure}[!hbpt]
\begin{center}
%
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_right/cut_output_z850_dip45_gauss.png}
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_right/cut_output_z2500_dip45_gauss.png}
%
\end{center}
\end{figure}

\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Dyke/Sill Intrusion, Variable Source Depth}

%   
% \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}
%   {\includegraphics[width=50mm]{movie_ff_3d_mp4_icon.jpeg}}
% %
% \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}
%   {\includegraphics[width=50mm]{movie_ff_1d_mp4_icon.jpeg}}
% \end{center}
% 

%\vspace*{-2mm}
\begin{center}
\hspace*{-15mm}
%
\movie[label=show3,width=6.0cm,poster,autostart,showcontrols]
  {\includegraphics[width=50mm]{BJicon.png}}{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/movie02.mp4}
%
\movie[label=show3,width=6.0cm,poster,autostart,showcontrols]
  {\includegraphics[width=50mm]{BJicon.png}}{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/movie03.mp4}
\hspace*{-15mm}
%
\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{Dyke/Sill as Seismic Energy Sink}

\vspace*{2mm}

\begin{itemize}

   \item  Dyke/Sill (right Fig),  made  of  stiff  rock,  is  an  energy  sink, as well as energy
   reflector

   \item  Variable  wave  lengths behave differently, depending on dyke/sill geometry
   and location
   
   
\end{itemize}

\vspace*{-5mm}


\begin{figure}[!hbpt]
\begin{center}
%
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_no/cut_output_z2500_dip45_gauss.png}
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_right/cut_output_z2500_dip45_gauss.png}
%
\end{center}
\end{figure}

\end{frame}



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

\begin{frame}
  \frametitle{Importance of Realistic Seismic Motion Fields}


\begin{itemize}

   \item   Developed synthetic (!) free field motions need to excite a number of
   (all!) possible responses from a nuclear facility

\vspace*{3mm}
   \item  Knowledge  of  detailed  geology  is  needed,  geometry  and  material
   properties, including inelasticity of shallow layers
   
   
\vspace*{3mm}
   \item  Reduction of modeling uncertainty
   
\vspace*{3mm}
   \item Direct use for Realistic ESSI simulations
   
   


\end{itemize}


\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}












































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


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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
      
  \vspace*{1mm}
      \item Transformation

  \vspace*{1mm}
      \item Spatial variability

    \end {itemize}



\end{itemize}

\end{frame}







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

\frametitle{Uncertainty Propagation through 
Inelastic System}

% 

\begin{itemize}

\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}



\vspace*{5mm}
\item Incremental elastic-plastic 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}

 
  


\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{Real ESSI Simulator System}



%



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

\subsection{Real ESSI Simulator}



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

\begin{frame}
\frametitle{Real ESSI Simulator System}

\begin{itemize}

\item {\bf The Real ESSI-Program} is a 3D, nonlinear, time domain,
parallel finite element program specifically developed for
Hi-Fi modeling  and  simulation  of  Earthquake  Soil/Rock  Structure
Interaction problems for NPPs (infrastructure objects) on ESSI-Computers. \
%The NRC ESSI Program is based on
%a  number of public domain numerical libraries developed at UCD as well as those
%available  on  the  web,  that  are  compiled  and  linked  together to form the
%executable  program (NRC-ESSI-Program). Significant effort is devoted to development
%of  verification  and  validation  procedures,  as  well  as  on  development of
%extensive  documentation.  NRC-ESSI-Program  is  in  public  domain  and is licensed
%through the Lesser GPL.

%\vspace*{0.3cm}
\vspace*{1mm}
\item {\bf The Real ESSI-Computer} is a distributed memory
parallel computer, a cluster of clusters with multiple performance
processors and multiple performance networks.
%Compute  nodes are Shared Memory Parallel
%(SMP)  computers,  that  are  connected,  using  high  speed  network(s), into a
%Distributed Memory Parallel (DMP) computer.

%\vspace*{0.3cm}
\vspace*{1mm}
\item    {\bf        The Real  ESSI-Notes} represent a hypertext
documentation system
(Theory and Formulation, Software and Hardware, Verification and Validation, and
Case  Studies  and  Practical  Examples)
detailing modeling and simulation of ESSI
problems.
%
%the
%NRC-ESSI-Program  code  API (application Programming Interface) and DSLs (Domain
%Specific Language).
%%NRC-ESSI-Notes,    developed  by Boris Jeremic and collaborators, are in public
%domain
%%and  are  licensed  under a Creative Commons Attribution-ShareAlike 3.0 Unported
%%License.
%
%\vspace*{0.3cm}
\end{itemize}

\end{frame}


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

\begin{frame}
\frametitle{Real ESSI Simulator System}


\begin{itemize}


\item Developed with funding from US-DOE, US-NRC, US-NSF and CNSC-CCSN



\vspace*{2mm}
\item  The  Real  ESSI  simulator  system  is  designed based on premise of high
fidelity, high performance, modeling and simulation

\vspace*{2mm}
\item Reduction of modeling uncertainty and propagation of parametric uncertainty

\vspace*{2mm}
\item 
   Real ESSI simulator, also known as 
   {\small{\cyrssDvanaest Vrlo Prosto},
\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_Bengali.pdf}},
{ Muy F{\'a}cil},  
{Molto  Facile},  
\raisebox{-1.2mm}{\includegraphics[height=4.2mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Japanese.jpg}},
{\greektext{Pragmatik'a E'ukolo}},
\raisebox{-1.6mm}{\includegraphics[height=5mm]  {/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Hindi.jpg}},
\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}, 
{\cyrssJedanaest Vistinski Lesno},
{Wirklich Einfach}.

%\raisebox{-1.2mm}{\includegraphics[height=4.5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Chinese.jpeg}},
%{ 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_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},
%\raisebox{-0.80mm}{\includegraphics[height=5.2mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/Real_ESSI_in_different_langauges/Real_ESSI_Arabic.jpg}}.
}


\end{itemize}


\end{frame}


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

\begin{frame}
\frametitle{Real ESSI  Modelling}


\vspace*{4mm}
\begin{figure}[!hbpt]
\begin{center}
\includegraphics[width=3.2cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Theory_Introduction/tex_works_psfigures_loading_stage-increments-iterations.pdf}
%\caption{\label{loading_stages-increments_iterations} }
\end{center}
%\vspace*{-0.5cm}
\end{figure}
%
\end{frame}

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

% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real ESSI Modelling and Simulation Process}
% 
%  \begin{itemize}
% 
% %\vspace*{4mm}
%    \item Mesh development: gmsh (UL), gmESSI, FeConv (Vlaski)
% 
% \vspace*{2mm}
%    \item Model Development: sublime text editor
% 
% \vspace*{2mm}
%    \item Model Simulation:
%      \begin{itemize}
%        \item Domain Specific Language (DSL) for input
%        \item Real ESSI
%        \item output in HDF5 (NCSA...)
%      \end{itemize}
% 
% \vspace*{2mm}
%    \item    Result    Visualization:    VisIt  (LLNL),   visitESSI  plug-in  (all
%    displacements, stress, strain)
% 
%  \end{itemize}
% %
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Source Code Development and Management}
% 
%  \begin{itemize}
% 
% %\vspace*{4mm}
%    \item  Real  ESSI  sources  (finite element, material models, algorithms, DSL
%    interpreter, \&c.) in a private online repository with version control
%  
%  
% \vspace*{4mm}
%    \item Real ESSI dependencies (external libraries: solvers, MPI, BLAS, LAPACK,
%    \&c.)
% 
% 
% % %\vspace*{1mm}
% %    \item   Sequential   performance   optimization  (templates,  global  linking
% %    optimization, pipeline parallel, \&c.)
% % 
% % %\vspace*{1mm}
% %    \item   Parallel  performance  optimization  (Plastic  Domain  Decomposition)
% %    for local clusters as well as large national parallel computers.
% %    
%  \end{itemize}
% %
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real ESSI Developers}
% 
% \begin{itemize}
%          \item UC Davis:
%       Core system architecture (sequential and
%    parallel), finite elements, material models,
%    constitutive  integration,  deterministic  and  stochastic  elastic plastic
%    finite elements 
% 
% \vspace*{2mm}
% 
%         \item  LBNL: Nonlinear/inelastic beam, Nonlinear/inelastic shell (plate
%          and wall, deterministic)
% 
% \vspace*{2mm}
%          \item TU Delft: Material Models (deterministic)
% \end{itemize}
% 
% %
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real ESSI Users}
% 
% 
%      \begin{itemize}
%        \item DOE Project Team:
%           \begin{itemize}
%              \item UC Davis: verification, system modeling, \&c.
% 
%              \item LBNL: verification, validation, validation system design, system modeling)
% 
%              \item UN Reno: validation system design, validation
%           \end{itemize}
%    
% \vspace*{2mm}
%        \item National Labs
% 
% \vspace*{2mm}
%        \item Companies: AREVA, Shimizu Corp., Rizzo and Assoc.
% 
% \vspace*{2mm}
%        \item Universities: TU Delft, NTUA, UCB
% 
%     \end{itemize}
%    
% %
% \end{frame}
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Real ESSI Simulator: Program}


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

\begin{frame}
\frametitle{Real ESSI: Components}


%\vspace*{-3mm}
   \begin{itemize}
%\vspace*{1mm}
     \item Variety of solid, structural and special finite elements
%\vspace*{1mm}
     \item Variety of material models
%\vspace*{1mm}
     \item Variety of static and dynamic solution advancement algorithms
%\vspace*{1mm}
     \item Seismic (realistic) input using DRM 
%\vspace*{1mm}
     \item  High  performance  parallel  computing  for  elastic-plastic FEM and
     multiple  performance  CPUs and networks using Plastic Domain Decomposition
     method
%\vspace*{1mm}
     \item Stochastic Elastic-Plastic Finite Element Method (SEPFEM)
%\vspace*{1mm}
     \item Extensive Verification, working on Validation

   \end{itemize}

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \begin{frame}
% \frametitle{Real ESSI: Material Models}
% 
% %\vspace*{-2mm}
%    \begin{itemize}
%       \item Linear and nonlinear, isotropic and anisotropic  elastic
% \vspace*{3mm}
%        \item  Elastic-Plastic  (von Mises, Drucker Prager, Rounded Mohr-Coulomb,
%               Leon      Parabolic,      Cam-Clay,      SaniSand,     SaniClay,
%               Pisan{\` o}...).  All  elastic-plastic  models can be used as perfectly
%               plastic,  isotropic  hardening/softening  and  kinematic hardening
%               models.
% \vspace*{3mm}
%        \item  Viscous damping solids, Rayleigh and Caughey damping
%    \end{itemize}
% 
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
% \frametitle{Real ESSI: Solution Advancement Algorithms}
% 
%    \begin{itemize}
% %\vspace*{-10mm}
% 
%  \item  Constitutive
%    \begin{itemize}
% %\vspace*{-1mm}
%      \item Explicit, Implicit, Sub-incrementation, Line Search
%    \end{itemize}
% 
% 
%  \item  Nonlinear Static FEM
%    \begin{itemize}
% %\vspace*{-1mm}
%      \item No equilibrium iteration
%      \item Equilibrium Iterations (full Newton, modified N, Initial Stiff.)
%      \item  Hyperspherical  constraint  (arch length, displacement control, load
%      control)
%      \item Line Search
%      \item Convergence criteria: 
%            displacement, load, energy 
%    \end{itemize}
% 
%  \item  Nonlinear Dynamic FEM
%    \begin{itemize}
% %\vspace*{-1mm}
%      \item No equilibrium iteration
%      \item Equilibrium Iterations (full Newton, modified N, Initial Stiff.) 
%      \item Constant or variable time stepping 
%      \item Convergence criteria: displacement, load, energy
%    \end{itemize}
% 
% \end{itemize}
% 
% %\vspace*{-60mm}
% %%\begin{figure}[!hbpt]
% %\begin{flushright}
% %\hspace*{50mm}
% %\includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Theory_Introduction/tex_works_psfigures_loading_stage-increments-iterations.pdf}
% %%\caption{\label{loading_stages-increments_iterations} }
% %\end{flushright}
% %%\vspace*{-0.5cm}
% %%\end{figure}
% 
% 
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
% \frametitle{Real ESSI: Seismic Input}
% 
%    \begin{itemize}
% %\vspace*{-1.5mm}
% 
% \vspace*{4mm}
%  \item    Analytic    input    of  seismic motions (both body (P, S) and surface
%  (Rayleigh,  Love,  etc.,  waves),  including analytic radiation damping using Domain
%  Reduction Method (Bielak et al.)
% 
% \end{itemize}
% %
% %\begin{figure}[!hbpt]
% \begin{center}
% \includegraphics[width=8cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/tex_works_psfigures_DRM_NPP_idea01.pdf}
% %\caption{\label{DRMidea01} Large physical domain with the source of load $P_e(t)$
% %and the local feature (in this case a soil-structure system.}
% \end{center}
% %\end{figure}
% 
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
% \frametitle{Real ESSI Simulator Program: Parallel, HPC}
% 
% \begin{itemize}
% 
% \item High Performance Parallel Computing:
%   both  parallel  and  sequential  version available, however, for high fidelity
%   modeling,    parallel  is really the only option. Parallel Real ESSI Simulator
%   runs  on  clusters  of  PCs  and  on  large supercomputers (Distributed Memory
%   Parallel   machines,   all   top   national  supercomputers).  Plastic  Domain
%   Decomposition   Method   (PDD,   dynamic  computational  load  balancing)  for
%   elastic-plastic  computations  with  multiple  types of finite elements and on
%   variable speed CPUs (and networks)
% %  Parallel  algorithm  uses our
% %  original  Plastic Domain Decomposition method (featuring dynamic computational
% %  load  balancing) that is efficient for elastic-plastic finite element problems
% %  where  elastic-plastic  (slow)  and  elastic (fast) domains change dynamically
% %  during run time.
% 
% 
% \end{itemize}
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
% \frametitle{Real ESSI Simulator Program: Probabilistic/Stochastic}
% %\vspace*{-2mm}
% 
% 
%    \begin{itemize}
% %\vspace*{-2.5mm}
%      \item   Constitutive:   Euler-Lagrange   form   of  Fokker-Planck  (forward
%      Kolmogorov) equation for probabilistic elasto-plasticity (PEP)
% %\vspace*{-1.5mm}
%      \item Spatial: stochastic elastic plastic finite element method (SEPFEM)
%    \end{itemize}
% 
% 
%   Uncertainties  in  material  and  load  are  analytically  taken into account.
%   Resulting  displacements,  stress  and  strain  are  obtained as very accurate
%   (second  order accurate for stress) Probability Density Functions.
%   PEP  and  SEPFEM  are  not  based  on a Monte Carlo method, rather they expand
%   uncertain  input  variables  and  uncertain degrees of freedom (unknowns) into
%   spectral  probabilistic  spaces  and  solve  for  PDFs  of
%   resulting displacement, stress and strain in a single run.
% 
% 
% \end{frame}
% 
% 
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% % 
% % \begin{frame}
% % \frametitle{Real ESSI Simulator Program: Design and Users}
% % 
% % \begin{itemize}
% % 
% % %\vspace*{0.2cm}
% % \item  Based  on  a  Collection  of Useful Libraries  (portable)
% % 
% % \vspace*{0.1cm}
% % \item Library centric software design
% % 
% % \vspace*{0.1cm}
% % \item Sequential (learning) and Parallel (production modeling and simulation)
% % 
% % \vspace*{0.1cm}
% % \item Distributed Memory Parallel (DMP) paradigm, scales well to large supercomputers
% % 
% % 
% % 
% % \vspace*{0.1cm}
% % \item Various public domain licenses (GPL, LGPL, BSD, CC)
% % 
% % %\vspace*{0.3cm}
% % \vspace*{0.1cm}
% % \item Verification (extensive) and Validation (not much)
% % 
% % 
% % \vspace*{0.1cm}
% % \item  Target  users: US-DOE, US-NRC, CNSC, IAEA, Collaborators (AREVA, Shimizu,
% % Rizzo...), others
% % 
% % \vspace*{0.1cm}
% % \item Limited use Expert Modeling and Simulation System, and not a public domain
% % program
% % 
% % 
% % \end{itemize}
% % 
% % \end{frame}
% % 
% % 
% % 
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}[fragile]
% %  \frametitle{ESSI Simulator Computer(s)}
% % 
% %   A distributed memory parallel (DMP) computer
% %    designed for high performance,
% %    parallel finite element simulations
% % 
% %  \begin{itemize}
% % %\vspace*{0.1cm}
% %    \item Multiple performance CPUs \\
% %          and Networks
% % %\vspace*{0.1cm}
% %    \item Most cost-performance \\
% %          effective
% % %\vspace*{0.1cm}
% %    \item Source compatibility with \\
% %          any DMP supercomputer
% % %\vspace*{0.1cm}
% %    \item Current systems:
% %       \begin{itemize}
% %         \item 208CPUs,
% %         \item 40CPUs (8+32)
% %         \item 160CPUs (8x5+2x16+24+64)
% %         \item 32CPUs (multiple machines like this)
% %       \end{itemize}
% % 
% %  \end{itemize}
% % 
% % 
% % \vspace*{-4.5cm}
% % \hspace*{0.5cm}
% % \begin{flushright}
% % \includegraphics[width=4.0cm]{/home/jeremic/public_html/NRC_ESSI_Simulator/NRC_ESSI_Computer/photos/IMG_2607.JPG}
% % %\includegraphics[width=6.0cm]{/home/jeremic/public_html/NRC_ESSI_Simulator/NRC_ESSI_Computer/photos/IMG_2609.JPG}
% % %\includegraphics[width=8.0cm]{/home/jeremic/public_html/NRC_ESSI_Simulator/NRC_ESSI_Computer/photos/IMG_2611.JPG}
% % \end{flushright}
% % 
% % 
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% \subsection{Near Future Plan}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real ESSI: Verification and Validation}
% \begin{itemize}
% %\vspace*{-2mm}
% \item Verification:
%   each element, model, algorithm and procedure has been extensively verified
%   (math  issue) 
% \vspace*{4mm}
% \item Validation: limited 
%   \begin{itemize} 
%     \item Lotung (!), 
% %    \item PRENOLIN (!?)) 
%     \item  UNR tests (!!)
%   \end{itemize} 
% \end{itemize}
% \end{frame}
% 
% 
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% \subsection{Verification and Validation}
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% 
% 
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% 
% 
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% \begin{frame}
%  \frametitle{High Fidelity Predictive Capabilities}
% % \frametitle{High Fidelity Modeling of SFS System:
% % Verification, Validation and Prediction}
% 
% 
% \begin{itemize}
% 
% 
% % \vspace*{0.2cm}
% %    \item {\bf Prediction}:  use  of  computational  model  to foretell the state
% %    of  a  physical  system  under  consideration  under conditions for which the
% %    computational model has not been validated.
% 
% 
% \vspace*{3mm}
%      \item {{Verification} provides evidence that the
%    model is solved correctly.} Mathematics issue.
% 
% \vspace*{3mm}
%      \item {{Validation} provides
%    evidence that the correct model is solved.} Physics issue.
% 
% 
% \vspace*{3mm}
%    \item Goal: predictive capabilities with low information (Kolmogorov) Complexity
% 
% % %% % \vspace*{0.2cm}
% % %   \item {\bf The Finite Element
% % %   Interpreter  \FEI{}} might be one such
% % %   predictive tool (application program)
% 
% \end{itemize}
% 
% \end{frame}
% 
% 
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %  \frametitle{Fundamentals of Verifications and Validation}
% % % \frametitle{High Fidelity Modeling of SFS System:
% % % Verification, Validation and Prediction}
% % 
% %                          
% % \begin{figure}[!h]
% % \vspace*{-0.5cm}
% % \hspace*{-0.5cm}
% % %\begin{center}
% % %{\includegraphics[width=11cm]{/home/jeremic/tex/works/Conferences/2005/OpenSeesWorkshopAugust/DeveloperSymposium/VerifValidFund01.pdf}}
% % {\includegraphics[width=11cm]{/home/jeremic/tex/works/Conferences/2013/NRC_Short_Course_May2013/Present/Present06_figs/VerifValidFund01.pdf}}
% % %\end{center}
% % \end{figure}
% % 
% % 
% % 
% % 
% % 
% % 
% % \end{frame}
% % 
% 
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Verification}
% 
% 
% \begin{itemize}
% \vspace*{1mm}
%    \item    Code    Verification    (code    coverage,  memory leaks and pointer
%    assignment testing, static argument list testing, \&c.)
% 
% \vspace*{1mm}
%    \item  Solution  verification  (finite  elements,  constitutive  integration,
%    material models, algorithms, seismic input, \&c.) based on analytic, closed form solutions 
% 
% \vspace*{1mm}
%    \item Method of manufactured solutions for elasto-plastic verification
% 
% 
% \vspace*{1mm}
%    \item  Parameter bounds (finite elements, material models, algorithms, \&c.)
% 
% \vspace*{1mm}
%    \item Develop error plots for elements, models, algorithms over a range of parameter
% 
% \end{itemize}
% 
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %\subsection{Validation}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Validation}
% 
% \begin{itemize}
% 
%   \item {Traditional Experiments}
%      \begin{itemize}
%        \item Improve the fundamental understanding of physics involved
%        \item Improve the mathematical models for physical phenomena
%        \item Assess component performance
%      \end{itemize}
% 
%  \vspace*{2mm}
%    \item {Validation Experiments}
%      \begin{itemize}
%        \item Model validation experiments
%        \item  Designed  and  executed  to  quantitatively estimate mathematical
%        model's ability to simulate well defined physical behavior
%        \item   The  simulation  tool (Real ESSI Simulator) (conceptual  model,  computational  model,
%        computational solution) is the customer
%        \item  New US-DOE project to validate 
%        inelastic seismic wave propagation and soil-structure interaction
% 
%      \end{itemize}
% 
% 
% 
% 
% \end{itemize}
% 
% 
% 
% 
% \end{frame}
% 
% 
% 

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\section{Summary}


\subsection*{Summary}


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

  \begin{itemize}



%\vspace*{2mm}
  \item    Modeling and simulation of infrastructure object requires high sophistication
  

\vspace*{3mm}
  \item   Uncertainties (modeling  and parametric) influences results 
  
  
\vspace*{3mm}
  \item  Those  uncertainties need to be addressed and propagated to results and
  used in decision making
  

\vspace*{3mm}
     \item Goal is to {predict} and {inform}, and not force fit

\end{itemize}


\end{frame}


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%   \frametitle{Acknowledgement}
% 
%   \begin{itemize}
% 
% 
% 
% \vspace*{2mm}
%   \item  Funding from and collaboration with the US-NRC, US-DOE, US-NSF,   CNSC,
%   AREVA NP GmbH, and Shimizu Corp. is greatly appreciated,
% 
% \vspace*{2mm}
%   \item  Collaborators:
% %  Dr.    Budnitz    (LBNL),
%   Prof. Yang,
%   Dr Cheng, Dr. Jie, Dr. Tafazzoli,
%   Prof. Pisan{\`o},
%   Mr. Watanabe,
%   Mr. Vlaski,
%   Mr. Orbovi{\'c},
%   and
%   UCD students:
%   Mr. Abell,
%   Mr. Karapiperis,
%   Mr. Feng,
%   Mr. Sinha,
%   Mr. Luo,
%   Mr. Lacour,
%   Mr. Yang,
%   Ms. Behbehani
% % 
% % 
% 
% \vspace*{2mm}
%   \item Real ESSI Simulator: 
%   \url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
% 
% \end{itemize}
% 
% 
% \end{frame}
% 
% 


\end{document}

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