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\title[ESSI under Uncertainty]
{Uncertainties in
Modelling and Simulation of
Earthquake Soils Structures Interaction}
%\subtitle
%{Include Only If Paper Has a Subtitle}
%\author[Author, Another] % (optional, use only with lots of authors)
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%{Boris~Jeremi{\'c}}
{Boris Jeremi{\'c}}
%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
\institute[\pgfuseimage{universitylogo}\hspace*{0.1truecm}\pgfuseimage{lbnllogo}] % (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 Earthquake Research Institute \\
University of Tokyo \\
Tokyo, Japan, January 2016}
\subject{}
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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/Figurefiles/Real_ESSI_in_different_langauges/Real_ESSI_Chinese.jpeg}},
% \raisebox{1.2mm}{\includegraphics[height=5mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/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/Figurefiles/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}
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\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/JGGEGoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01Ed.pdf}
% \hfill
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/YoungModulus_Histogram_Normal_01Ed.pdf}
%
\end{center}
\end{figure}
\vspace*{0.8cm}
%\hspace*{3.3cm}
\begin{flushleft}
{\tiny
Transformation of SPT $N$value:
1D 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/JGGEGoverGmax/figures/ShearStrength_RawData_and_MeanTrendMod.pdf}
% \hspace*{7mm}
% % \hfill
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/ShearStrength_Histogram_PearsonIVFineTunedMod.pdf}
% %
% \end{center}
% \end{figure}
%
% % \vspace*{1.8cm}
% % %\hspace*{3.3cm}
% % \begin{flushright}
% % {\tiny
% % Transformation of SPT $N$value: \\
% % 1D 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: foundationsoil, dry, saturated, slipgap
%
% \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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%
%
%
%
%
%
%
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\section{Modeling and Parametric Uncertainty}
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\subsection{Modeling Uncertainty: Seismic Motions for NPPs}
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\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 soilstructure
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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%
%
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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, shakeout 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}
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\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/Figurefiles/_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/Figurefiles/_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/Figurefiles/_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/Figurefiles/_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/Figurefiles/_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/Figurefiles/_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/Figurefiles/_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/Figurefiles/_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/Layeredmodel.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_50mmesh_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/DykeSillmodel.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_50mmesh_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 elasticplastic 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 (KarhunenLoeve) 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 ElastoPlasticity}
%
%
% 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 elasticplastic process can be proven!
%
% \end{itemize}
%
%
%
%
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% \begin{frame}
% \frametitle{Gradient Flow Theory of Probabilistic ElastoPlasticity}
%
% \begin{itemize}
%
% \item
% Elastic, reversible process, FokkerPlanck (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, FokkerPlanck (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 ElastoPlasticity}
%
% \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 ElastoPlasticity: 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 ElastoPlasticity: Numerical Solution}
%
%
% \begin{itemize}
%
% \item Using radial basis functions (a meshless method) for solving
% FokkerPlanck equations for uncertain elasticplastic response
%
%
% \vspace*{6mm}
% \item Details in a talk by Mr. Karapiperis later this afternoon (room 2, MS6,
% 17:0019:00, last talk)
%
%
% \end{itemize}
% % %
%
%
% \end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Gradient Theory of Probabilistic ElastoPlasticity:
Verification, ElasticPerfectly 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 ElasticPlastic FEM (SEPFEM)}
%
% \begin{itemize}
% \item<1> KLPC 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 Longintegration 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 1dimensional 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 ESSIProgram} is a 3D, nonlinear, time domain,
parallel finite element program specifically developed for
HiFi modeling and simulation of Earthquake Soil/Rock Structure
Interaction problems for NPPs (infrastructure objects) on ESSIComputers. \
%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 (NRCESSIProgram). Significant effort is devoted to development
%of verification and validation procedures, as well as on development of
%extensive documentation. NRCESSIProgram is in public domain and is licensed
%through the Lesser GPL.
%\vspace*{0.3cm}
\vspace*{1mm}
\item {\bf The Real ESSIComputer} 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 ESSINotes} 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
%NRCESSIProgram code API (application Programming Interface) and DSLs (Domain
%Specific Language).
%%NRCESSINotes, developed by Boris Jeremic and collaborators, are in public
%domain
%%and are licensed under a Creative Commons AttributionShareAlike 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 USDOE, USNRC, USNSF and CNSCCCSN
\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/Figurefiles/Real_ESSI_in_different_langauges/Real_ESSI_Chinese.jpeg}},
\raisebox{1.2mm}{\includegraphics[height=4mm] {/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/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/Figurefiles/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/Figurefiles/Real_ESSI_in_different_langauges/Real_ESSI_Hindi.jpg}},
\raisebox{1.2mm}{\includegraphics[height=5mm] {/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/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/Figurefiles/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/Figurefiles/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/Figurefiles/Real_ESSI_in_different_langauges/Real_ESSI_Hindi.jpg}},
%\raisebox{1.2mm}{\includegraphics[height=4mm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/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/Figurefiles/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/Figurefiles/_Chapter_Theory_Introduction/tex_works_psfigures_loading_stageincrementsiterations.pdf}
%\caption{\label{loading_stagesincrements_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 plugin (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 elasticplastic FEM and
multiple performance CPUs and networks using Plastic Domain Decomposition
method
%\vspace*{1mm}
\item Stochastic ElasticPlastic 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 ElasticPlastic (von Mises, Drucker Prager, Rounded MohrCoulomb,
% Leon Parabolic, CamClay, SaniSand, SaniClay,
% Pisan{\` o}...). All elasticplastic 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, Subincrementation, 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/Figurefiles/_Chapter_Theory_Introduction/tex_works_psfigures_loading_stageincrementsiterations.pdf}
% %%\caption{\label{loading_stagesincrements_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/Figurefiles/_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 soilstructure 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
% elasticplastic 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 elasticplastic finite element problems
% % where elasticplastic (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: EulerLagrange form of FokkerPlanck (forward
% Kolmogorov) equation for probabilistic elastoplasticity (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}
%
%
%
%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% % \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: USDOE, USNRC, 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 costperformance \\
% % 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}
% %
% %
% %
% % \end{frame}
% %
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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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% \frametitle{High Fidelity Predictive Capabilities}
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% % \item {\bf Prediction}: use of computational model to foretell the state
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% \item {{Verification} provides evidence that the
% model is solved correctly.} Mathematics issue.
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% \item {{Validation} provides
% evidence that the correct model is solved.} Physics issue.
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% % % \item {\bf The Finite Element
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% % \frametitle{Fundamentals of Verifications and Validation}
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% % %{\includegraphics[width=11cm]{/home/jeremic/tex/works/Conferences/2005/OpenSeesWorkshopAugust/DeveloperSymposium/VerifValidFund01.pdf}}
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% \item Code Verification (code coverage, memory leaks and pointer
% assignment testing, static argument list testing, \&c.)
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% \item Solution verification (finite elements, constitutive integration,
% material models, algorithms, seismic input, \&c.) based on analytic, closed form solutions
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% \item Method of manufactured solutions for elastoplastic verification
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% \item {Traditional Experiments}
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% \item Improve the fundamental understanding of physics involved
% \item Improve the mathematical models for physical phenomena
% \item Assess component performance
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% \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 USDOE project to validate
% inelastic seismic wave propagation and soilstructure interaction
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\section{Summary}
\subsection*{Summary}
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\frametitle{Concluding Remarks}
\begin{itemize}
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\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
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% \frametitle{Acknowledgement}
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% \item Funding from and collaboration with the USNRC, USDOE, USNSF, 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
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% \item Real ESSI Simulator:
% \url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
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