% Template file for an a0 landscape poster.
%-------------------------------------------------------------------------
% Written by Graeme, 2001-03 based on Norman's original microlensing
% poster.
%
% $Id: poster-template-landscape.tex,v 1.1 2001/07/02 17:23:32 norman Exp $
%
% Default mode is landscape, which is what we want, however dvips and
% a0poster do not quite do the right thing, so we end up with text in
% landscape style (wide and short) down a portrait page (narrow and
% long). Printing this onto the a0 printer chops the right hand edge.
% However, 'psnup' can save the day, reorienting the text so that the
% poster prints lengthways down an a0 portrait bounding box.
%
% 'psnup -w85cm -h119cm -f poster_from_dvips.ps poster_in_landscape.ps'
%
%-------------------------------------------------------------------------
% Modified by Ronald Kumon, 06-2002 to incorporate a framebox border,
%   add acknowledgments line at bottom, and change locations of logos
%
% To preview using xdvi:
% 
% $ xdvi -paper 1188x840mm -s 24 -nopostscript poster.dvi
%
% To convert dvi to Postscript:
%
% $ dvips -Ppdf -G0 -o poster.ps poster.dvi
%
% The dvips options are:
% Ppdf: use the PDF printer configuration file
% G0  : shift lower characters to higher position 
%       (splits ligatures when using Times-Roman font)
%
% To convert Postscript to PDF:
%
% $ pstill -c -giptCQ -w 3368 -h 2378 -o poster.pdf poster.ps
% ($ pstill -c -iptCQ -w 3225 -h 2378 -o poster.pdf poster.ps)
%
% Note that the pstill options are
% c:  compression (more c's give more compression; up to four)
% g:  take size from Postscript file
% p:  include all fonts as partial fonts
% i:  include all non-standard fonts
% t:  map graphics transfer functions from PostScript to PDF. 
% C:  use RGB color map
% w:  width in points (1/72 inch) for 1188 mm
% h:  height in points (1/72 inch) for 839 mm
% Q:  take embedded fonts from PSFonts directory, not Postscript file
% Note also that the -w and -h options need to be included else
% some of the Postscript figures may not be displayed (particularly
% those converted using fig2dev), even if the -g option is specified.
% Also, the newest version of pstill (1.55.91) does not deal well with 
% slanted Times Roman font; use italics or the older version (1.55.3). 
%-------------------------------------------------------------------------

%\documentclass[a0]{a0posterslides}
\documentclass[a0,slides]{a0posterslides}
% You might find the 'draft' option to a0 poster useful if you have
% lots of graphics, because they can take some time to process and
% display. (\documentclass[a0,draft]{a0poster})
%
% You might also find the 'slides' option useful.  This will output
% the textblocks on letter-sized pages.  This can be useful for talks
% or for a backup ``mosaic'' style poster (in case the big poster
% is damaged or lost).  *Note*:  The font size in slides mode is 
% different than that in poster mode.
%
% Note that if the ``slides'' option is set, then the conditional
% \ifposter is false.  This conditional is used extensively below
% to be able to generate different output for the poster and slides
% whenever necessary or desired.

% If you want to number equations, set the equation number counter to zero.
%\setcounter{secnumdepth}{0}

% This package gives you coloured text and various other simple
% graphics hacks.  For details, see documentation in 
% in /usr/local/teTeX/texmf/doc/generic/pstricks/*
\usepackage{pstricks}
\newrgbcolor{darkblue}{0.1 0.1 0.5}

% The textpos package is necessary to position textblocks at arbitary 
% places on the page.  Use showboxes option to show outlines of textboxes.
\usepackage[absolute]{textpos}
%\usepackage[absolute,showboxes]{textpos}

% Package to include graphics.  
\usepackage{graphicx}
% Define path for figures
\graphicspath{{/home/kumon/crystal/other/munich/poster/figs/}
{/home/kumon/crystal/other/munich/poster/figsnew/}}

% Wrap text around figures
%\usepackage{wrapfig}

% Use Times font instead of Computer Modern
% Note that without the ``G0'' in the dvips conversion, 
% all character combinations that will normally result in 
% ligatures will have to be hacked to display properly.  For example, 
%     fi --> \mbox{f}\mbox{i}
% Other characters may also fail.  In addition, the Mathtimes font 
% set should really be used for mathematics, but unfortunately they 
% are only proprietary.  (The Computer Modern fonts may still look OK.)
\usepackage{times}

% These colours are tried and tested for titles and headers. Don't
% over use color!
\usepackage[usenames]{color}
\definecolor{DarkBlue}{rgb}{0.1,0.1,0.5}
\definecolor{Black}{rgb}{0.0,0.0,0.0}
\definecolor{Red}{rgb}{0.9,0.0,0.1}
\definecolor{DarkBlue2}{rgb}{0.00,0.08,0.6}
\definecolor{DarkRed2}{rgb}{0.6,0.00,0.08}
\definecolor{DarkGreen2}{rgb}{0.00,0.6,0.08}

% Load shadow box package
%\usepackage{shadow}

% See documentation for a0poster class for the size options here
\let\Textsize\normalsize
\def\RHead#1{\noindent\hbox to \hsize{\hfil{\LARGE\color{DarkBlue} #1}}\bigskip}
\def\LHead#1{\noindent{\LARGE\color{DarkBlue} #1}\bigskip}
\def\CHead#1{\begin{center}\noindent{\LARGE\color{DarkBlue} #1}\end{center}\ifposter{}\else{\vspace{-0.5in}}\fi
}
\def\Subhead#1{\noindent{\large\color{DarkBlue} #1}\bigskip}
\def\Title#1{\noindent{\veryHuge\color{Red} #1}}

% Set up the grid
%
% Note that [40mm,40mm] is the margin round the edge of the page
% it is _not_ the grid size. That is always defined as 
% PAGE_WIDTH/HGRID and PAGE_HEIGHT/VGRID. In this case we use
% 23 x 12. This gives us three columns of width 7 boxes, with a gap of
% width 1 inbetween them. 12 vetrical boxes is a good number to work
% with vertically.
%
% (Note however that texblocks can be positioned fractionally as well,
% so really any convenient grid size can be used.)
%
\TPGrid[40mm,40mm]{54}{42}      % 5 cols of width 10, plus 4 gaps width 1
                                % 3 rows of width 10, plus 2 gaps

% For slide output, redefine the textblock environment
% so that it doesn't do anything but start a new page 
% at the end of the textblock.
\ifposter
  \relax
\else
  \oddsidemargin   0.00 in
  \evensidemargin  0.00 in
  \topmargin       0.00 in
  \headheight      0.00 in
  \headsep         0.00 in
  \textheight     10.00 in
  \footskip        0.00 in
  \textwidth       7.50 in
  \voffset        -0.50 in
  \hoffset        -0.50 in
  \renewenvironment{textblock}[8]
  {\Large
   \setlength{\baselineskip}{0.7\baselineskip}
   \vspace{-2\baselineskip}}
  {\clearpage}
\fi

% Text layout parameters
\parindent=0pt
\parskip=0.5\baselineskip

\begin{document}

% Do not put page numbers at the bottom of the page for poster
% but do so for slides.
\ifposter
  \pagestyle{empty}
\else
  \pagestyle{plain}
\fi

% Declare proper hyphenation
\hyphenation{equi-bi-ax-i-al}
\hyphenation{in-fin-i-tes-i-mal}

\ifposter
%  *** Begin code to draw blue border round poster ***
\psset{linewidth=0.5cm}
% Sets up lengths for frame
\newlength{\frameleft}
\newlength{\frameright}
\newlength{\frametop}
\newlength{\framebottom}
\setlength{\frameleft}{-1cm}
\setlength{\frameright}{\textwidth}
\addtolength{\frameright}{-4\frameleft}
\setlength{\frametop}{1cm}
\setlength{\framebottom}{-\textheight}
\addtolength{\framebottom}{-4\frametop}
% Draws a blue frame
\psframe[linecolor=darkblue,cornersize=absolute,linearc=2]
(\frameleft,\framebottom)(\frameright,\frametop)% need to overlay EOSMLS
%\psline{->}(0cm,0cm)(\textwidth,-\textheight)
%   *** End code to draw border *** 
\fi

% Adjust spacing in long displayed mathematical formulas to tighten them up
\setlength{\abovedisplayskip}{0.75\abovedisplayskip}
\setlength{\belowdisplayskip}{0.75\belowdisplayskip}

% Understanding textblocks is the key to being able to do a poster in
% LaTeX. The first argument gives the block width in grid cells, the
% second gives the positioning on the grid.
%
% You will have to do a lot of previewing to get everything in the 
% right place.
%
\ifposter
\begin{textblock}{54}(00,00)
\begin{center}
\Title{Nonlinear SAW Propagation in Thin-Film Systems with Residual Stress}
\end{center}
\end{textblock}

\begin{textblock}{54}(00,02)
\begin{center}
\LHead{R. E. Kumon}\\
\LHead{\textsl{National Institute of Standards and Technology, 
       Boulder, Colorado, U.S.A.}}
\end{center}
\end{textblock}

% NIST logo on left, Division logo on right
\begin{textblock}{8}(00.5,01)
\includegraphics[height=5cm]{nist2darkblue.eps}
\end{textblock}

\begin{textblock}{8}(48,01)
\includegraphics[height=5cm]{mrd2.eps}
\end{textblock}

\else % for title slide

\Huge 
\ 

\centerline{\textcolor{Red}{Nonlinear SAW Propagation}}
\vspace{0.1in}
\centerline{\textcolor{Red}{in Thin-Film Systems}}
\vspace{0.1in}
\centerline{\textcolor{Red}{with Residual Stress}}
\vspace{0.5in}
\centerline{\textcolor{DarkBlue}{R.~E.~Kumon}}
\vspace{0.2in}
\centerline{\textcolor{DarkBlue}{\textsl{National Institute of}}}
\centerline{\textcolor{DarkBlue}{\textsl{Standards and Technology}}}
\centerline{\textcolor{DarkBlue}{\textsl{Boulder, Colorado, U.S.A.}}}
\vspace{0.1in}
\begin{center}
\includegraphics[width=7cm]{nist2darkblue.eps}
\hspace{2cm}
\includegraphics[width=6cm]{mrd2.eps}
\end{center}
\normalsize
\clearpage
\fi

% Begin 1st row
% [This section has a lot of manual line breaking to prevent 
% hyphenation; this is not necessary in general.  
% You may also use the \raggedright command to do something similar.]
\begin{textblock}{10}(00,05)
\CHead{Introduction}
\begin{itemize}
\item Thin-film deposition processes can create 
\ifposter{}\else{\\}\fi large residual stresses in the film which 
\ifposter{}\else{\\}\fi changes its mechanical properties and 
\ifposter{}\else{\\}\fi therefore its performance in a product. 
\item Residual stress affects the SAW velocity 
\ifposter{}\else{\\}\fi dispersion through 
the acoustoelastic effect, but the changes are often very small.  
\item Finite-amplitude SAWs, which nonlinearly
\ifposter{}\else{\\}\fi generate harmonics as they propagate, 
may be more sensitive to stress because the 
\ifposter{}\else{\\}\fi combined effects of nonlinearity and 
\ifposter{}\else{\\}\fi dispersion are cumulative with distance.
\item Numerical results are presented which 
\ifposter{}\else{\\}\fi compare velocity dispersion, waveform 
\ifposter{}\else{\\}\fi distortion, and harmonic generation for  
\ifposter{}\else{\\}\fi monofrequency SAWs propagating in 
\ifposter{}\else{\\}\fi systems with unstressed and 
compressively stressed Ge \mbox{f}\mbox{i}lms on 
a Si substrate.
\end{itemize}
\end{textblock}

\ifposter{
\begin{textblock}{10}(11,05)
\CHead{Surface Acoustic Waves}
\begin{center}
\includegraphics[bb=75 235 535 560, width=4.0in]{genrayschem5.ps}
\end{center}
\ifposter{}\else{\vspace{-0.5in}}\fi
\begin{itemize}
\item Surface acoustic waves are a type of vibrational wave which occur 
      near the surface of a solid half-space.
\item Almost all the energy of a SAW is localized within a wavelength 
      $\lambda$ of the surface, potentially resulting in large surface 
      amplitudes and nonlinear effects.
%\item Because almost all the energy of a SAW is localized  
%      within a wavelength $\lambda$ of the surface, SAWs can be 
%      good choices for examining near surface mechanical properties.
%\item At high amplitudes, this localization of energy can 
%      give rise to nonlinear effects, as shown in the distorting
%      waveforms below.     
\item Questions:\\
      How do SAWs propagate in stressed thin \mbox{f}\mbox{i}lms?\\
      How big are the linear and nonlinear effects?\\
      Can SAWs evaluate stress in thin \mbox{f}\mbox{i}lms?\\  
\end{itemize}
\end{textblock}}\fi

\begin{textblock}{10}(22,05)
\CHead{SAW Frequency Dispersion}
\begin{center}
\ifposter
\includegraphics[bb=50 500 530 685,width=7in]{sawdisp4.ps}
\else
\includegraphics[bb=50 500 530 685,width=7.5in]{sawdisp4.ps}
\fi
\end{center}
\ifposter{\relax}\else{\vspace{-0.5in}}\fi
\begin{itemize}
\item Without a \mbox{f}\mbox{i}lm, SAWs are nondispersive, i.e., 
      all frequency components travel at the same velocity.
\item With a \mbox{f}\mbox{i}lm of thickness $d$, the lower 
      frequency components ($\lambda\gg d$) travel near the SAW 
      \ifposter{}\else{\\}\fi velocity of the substrate, 
      while the higher \ifposter{}\else{\\}\fi 
      frequency components \ifposter{\\}\fi 
      ($\lambda \leq d$) travel near the SAW velocity of 
      the \mbox{f}\mbox{i}lm.
\item Result of \mbox{f}\mbox{i}lm on SAW:\\ 
      Various frequencies of the waveform 
      disperse relative to one another.  
\end{itemize}
\end{textblock}

\begin{textblock}{10}(33,05)
\CHead{Linear Theory}
Wave equation for the thin \mbox{f}\mbox{i}lm system: %~\cite{pao84}  
\begin{displaymath}
\textcolor{DarkGreen2}{C^{\mathrm{eff}}_{ijkl}}\frac{\partial^2 u_k}{\partial x_j \partial x_l} +
\textcolor{DarkGreen2}{\sigma^{\mathrm{res}}} \frac{\partial^2 u_i}{\partial x^2} =
\textcolor{DarkGreen2}{\rho^{\mathrm{eff}}} \frac{\partial^2 u_i}{\partial t^2}\,,
\end{displaymath}
\vspace{-0.5\baselineskip}
\ifposter{
{\small
\begin{eqnarray*}
\textcolor{DarkGreen2}{C^{\mathrm{eff}}_{ijkl}}  &\textcolor{DarkGreen2}{=}& 
                                                  \textcolor{DarkGreen2}{C_{ijkl}(1-\Delta e^{\mathrm{res}} +
                                                        e_{ii}^{\mathrm{res}}+e_{jj}^{\mathrm{res}} + 
                                                        e_{kk}^{\mathrm{res}}+e_{ll}^{\mathrm{res}})} \\
                                                 &                         &
                                                  \textcolor{DarkGreen2}{+\ C_{ijklmn}e_{mn},}\\
\textcolor{DarkGreen2}{\rho^{\mathrm{eff}}}      &\textcolor{DarkGreen2}{=}& 
                                                  \textcolor{DarkGreen2}{\rho(1-\Delta e^{\mathrm{res}}),}\\
\textcolor{DarkGreen2}{\sigma^{\mathrm{res}}}    &\textcolor{DarkGreen2}{\rightarrow}& 
                                                  \textcolor{DarkGreen2}{\mathrm{equibiaxial~residual~stress},}\\
u_i                     &\rightarrow& \mathrm{SAW~displacement~components}~(i=x,y,z),\\
C_{ijkl(mn)}            &\rightarrow& \mathrm{2nd~and~3rd~order~elastic~constants~(unstressed)},\\
\rho                    &\rightarrow& \mathrm{density~(unstressed)},\\
e^{\mathrm{res}}_{jk}   &\rightarrow& \mathrm{linear~residual~strain~tensor},\\
\Delta e^{\mathrm{res}} &\rightarrow& \mathrm{linear~volume~dilatation~due~to~residual~strain}.\\
\end{eqnarray*}}
\vspace{-3\baselineskip}
}
\else
{\normalsize
\begin{eqnarray*}
\textcolor{DarkGreen2}{C^{\mathrm{eff}}_{ijkl}}  &\textcolor{DarkGreen2}{=}& 
                                                  \textcolor{DarkGreen2}{C_{ijkl}(1-\Delta e^{\mathrm{res}} +
                                                        e_{ii}^{\mathrm{res}}+e_{jj}^{\mathrm{res}} + 
                                                        e_{kk}^{\mathrm{res}}+e_{ll}^{\mathrm{res}})} \\
                                                 &                         &
                                                  \textcolor{DarkGreen2}{+\ C_{ijklmn}e_{mn},}\\
\textcolor{DarkGreen2}{\rho^{\mathrm{eff}}}      &\textcolor{DarkGreen2}{=}& 
                                                  \textcolor{DarkGreen2}{\rho(1-\Delta e^{\mathrm{res}}),}\\
\textcolor{DarkGreen2}{\sigma^{\mathrm{res}}}    &\textcolor{DarkGreen2}{\rightarrow}& 
                                                  \textcolor{DarkGreen2}{\mathrm{equibiaxial~residual~stress},}\\
u_i                     &\rightarrow& \mathrm{SAW~displacement~components}~(i=x,y,z),\\
C_{ijkl(mn)}            &\rightarrow& \mathrm{2nd~and~3rd~order~elastic~constants~(unstressed)},\\
\rho                    &\rightarrow& \mathrm{density~(unstressed)},\\
e^{\mathrm{res}}_{jk}   &\rightarrow& \mathrm{linear~residual~strain~tensor},\\
\Delta e^{\mathrm{res}} &\rightarrow& \mathrm{linear~volume~dilatation~due~to~residual~strain}.\\
\end{eqnarray*}}
\vspace{-3\baselineskip}
}
\fi
\begin{itemize}
\item Assumptions include plane wave propagation and 
      equibiaxial, homogeneous, static stress only in \mbox{f}\mbox{i}lm.
\item Equations are solved for the \textcolor{DarkGreen2}{SAW velocity} $\textcolor{DarkGreen2}{c}$ by a Green's 
      function technique to produce dispersion relations.%\cite{tewary??}
\end{itemize}
\end{textblock}

\begin{textblock}{10}(44,05)
\CHead{Nonlinear Theory}
Frequency domain evolution of a SAW velocity waveform is 
described by the coupled system:%\cite{hamilton99} 
\begin{eqnarray*}
\frac{dv_n}{dx}+\gamma_n v_n=\frac{n^2\omega}{2\rho c^4}
    \sum_{l+m=n}\frac{lm}{|lm|}\textcolor{Red}{S_{lm}}v_lv_m\,,
\end{eqnarray*}
\ifposter
 \vspace{-1.5\baselineskip}
\fi
\ifposter{
{\small
\begin{eqnarray*}
v_n(x)       &\rightarrow& n\mathrm{th~harmonic~amplitude},\\
\gamma_n     &=          & \alpha_n+i\delta_n,\\
\alpha_n     &\rightarrow& \mathrm{attenuation~coefficient~of~}v_n,\\
\delta_n     &\rightarrow& \mathrm{dispersion~coefficient~of~}v_n,\\
\omega       &\rightarrow& \mathrm{fundamental~angular~frequency},\\
\textcolor{Red}{S_{lm}}       &\textcolor{Red}{\rightarrow}& \textcolor{Red}{\mathrm{nonlinearity~matrix}}.
\end{eqnarray*}}
\vspace{-2\baselineskip}
}
\else
{\normalsize
\begin{eqnarray*}
v_n(x)       &\rightarrow& n\mathrm{th~harmonic~amplitude},\\
\gamma_n     &=          & \alpha_n+i\delta_n,\\
\alpha_n     &\rightarrow& \mathrm{attenuation~coefficient~of~}v_n,\\
\delta_n     &\rightarrow& \mathrm{dispersion~coefficient~of~}v_n,\\
\omega       &\rightarrow& \mathrm{fundamental~angular~frequency},\\
\textcolor{Red}{S_{lm}}       &\textcolor{Red}{\rightarrow}& \textcolor{Red}{\mathrm{nonlinearity~matrix}}.
\end{eqnarray*}}
\vspace{-2\baselineskip}
}
\fi
\begin{itemize}
\item Physically, $\textcolor{Red}{S_{lm}}$ describes coupling of the \ifposter{}\else{\\}\fi 
      $l$th and $m$th harmonics to generate the \ifposter{}\else{\\}\fi $n=(l+m)$th harmonic.  
\item A \textcolor{Red}{coe\mbox{f}\mbox{f}icient of nonlinearity} can be 
      de\mbox{f}\mbox{i}ned%\cite{kumon02}
      \begin{displaymath}
      \textcolor{Red}{\beta=4S_{11}/\rho c^2 \,,}
      \end{displaymath}
      which is interpreted physically below.
\end{itemize}
\end{textblock}

% Begin 2nd row
\begin{textblock}{10}(00,17)
\CHead{Dispersion and Nonlinearity}
Consider the following snapshots of evolving waveforms
in the retarded frame (moving at $c_0$):
\ifposter{\relax}\else{\vspace{-0.75in}}\fi
\begin{center}
\includegraphics[width=7.0in]{waveforms2.eps}
\end{center}
\ifposter{\relax}\else{\vspace{-0.5in}}\fi
\begin{itemize}
\item 
Figure (a):\ \ Dispersion, No Nonlinearity\\
Waveforms experience a phase shift in the 
\ifposter{}\else{\\}\fi retarded frame
because they have a different velocity
$c(f)$ relative to $c_0$:
\begin{displaymath}
c(f)=c_0+\textcolor{DarkGreen2}{(dc/df)_0 f} + \cdots \,.
\end{displaymath}
\item 
Figure (b):\ \ Nonlinearity, No Dispersion\\
Parts of the waveforms move at different
\ifposter{}\else{\\}\fi velocities $c(v)$ relative to 
$c_0$ depending on their local particle velocity amplitude $v$:
\begin{displaymath}
c(v)=c_0 + \textcolor{Red}{\beta v} + \cdots \,.
\end{displaymath}
\item 
Relative contributions of dispersion to nonlinearity can 
be characterized by the dimensionless parameter
\begin{displaymath}
\textcolor{DarkBlue}{D}=\frac{\textcolor{DarkGreen2}{(dc/df)_0 f}}
                           {\textcolor{Red}{\beta v}}\,.
\end{displaymath}
\item 
Assume monofrequency source with frequency $f$\,=\,30~MHz 
and peak acoustic particle velocity $v$\,=\,50~m/s 
(peak strain $\epsilon$\,=\,0.01).   With 
$\beta$\,=\,$-$0.12 for the chosen system, these values 
result in a characteristic length scale for nonlinear distortion of 
$x_0$\,=\,20~mm ($X=x/x_0$).
\item 
Thin \mbox{f}\mbox{i}lm assumptions:\\
(1) \mbox{F}\mbox{i}lm only causes dispersion of harmonics.
\ifposter{}\else{\\}\fi  
(2) \mbox{F}\mbox{i}lm does not affect harmonic generation. 
\ifposter{}\else{\\}\fi 
(3) Negligible stress exists in the substrate.
\end{itemize}
\end{textblock}

\ifposter
{\begin{textblock}{32}(11,17)
\CHead{\rule[10pt]{606pt}{3pt}\ Moderate Dispersion ($D$\,=\,0.26)\ \rule[10pt]{606pt}{3pt}}
\end{textblock}}
\fi

\begin{textblock}{10}(11,17)
\ifposter 
  \vspace{2\baselineskip} 
  \includegraphics[bb=55 530 535 650,width=7in]{moddisp3.ps}
\else
  \CHead{Moderate Dispersion ($D$\,=\,0.26)}
  \includegraphics[bb=55 530 535 650,width=7.5in]{moddisp3.ps}
  \vspace{-1.0in}
\fi
\begin{center}
\begin{itemize}
\item Small SAW velocity shift:  $|\Delta c/c| < \;\,$1\,\%.
\item $|D|<$\,1 implies nonlinearity is dominant.
\end{itemize}
\ifposter
  \includegraphics[bb=50 50 555 315,width=7in]{GeSi-stressdiff-high-poster-mod.ps}
\else
  \includegraphics[bb=50 50 555 315,width=7.5in]{GeSi-stressdiff-high-poster-mod.ps}
\fi
\end{center}
\end{textblock}

\begin{textblock}{10}(22,17)
\ifposter
  \vspace{2\baselineskip}
\else
  %\CHead{Waveform Evolution}
  %\CHead{Moderate Dispersion ($D$\,=\,0.26)}
  \textcolor{DarkBlue}{\rule[10pt]{550pt}{3pt}}
  \vspace{-2\baselineskip}  
\fi
\begin{itemize}
\item Waveforms exhibit signi\mbox{f}\mbox{i}cant 
      distortion and harmonic generation with some dispersion.
\end{itemize}
\vspace{-0.75\baselineskip}
\begin{center}
\ifposter
  \includegraphics*[bb=25 270 550 760,width=7in]{Ge-020nm--5.0GPa-Si-_0.0GPa-multpos-color.ps}
\else
  \includegraphics*[bb=25 270 550 760,width=7.5in]{Ge-020nm--5.0GPa-Si-_0.0GPa-multpos-color.ps}
\fi  
\end{center}
\end{textblock}

\begin{textblock}{10}(33,17)
\ifposter
  \vspace{2\baselineskip}
\else
  %\CHead{Harmonic Evolution}
  %\CHead{Moderate Dispersion ($D$\,=\,0.26)}  
  \textcolor{DarkBlue}{\rule[10pt]{550pt}{3pt}}
  \vspace{-2\baselineskip}  
\fi
\begin{itemize}
\item Harmonic magnitudes and phases between the stressed and
      unstressed cases start to differ noticeably for $X >$\,1.5.
\end{itemize}
\begin{center}
\ifposter
  \includegraphics*[bb=55 50 540 450,width=7.6in]{Ge-020nm--5.0GPa-Si-_0.0GPa-propcurv2-color-ann.ps}
\else
  \vspace{-0.5in}
  \includegraphics*[bb=55 50 540 450,width=7.5in]{Ge-020nm--5.0GPa-Si-_0.0GPa-propcurv2-color-ann.ps}
\fi
\end{center}
\end{textblock}

% Begin 3rd row
% (1st column continues from 2nd row)
%\begin{textblock}{10}(0,29)
%\end{textblock}

\ifposter
\begin{textblock}{32}(11,29)
\CHead{\rule[10pt]{631pt}{3pt}\ Strong Dispersion ($D$\,=\,1.30)\ \rule[10pt]{631pt}{3pt}}
\end{textblock}
\fi

\begin{textblock}{10}(11,29)
\ifposter 
  \vspace{2\baselineskip} 
  \includegraphics[bb=55 530 535 650,width=7in]{strongdisp2.ps}
\else
  \CHead{Strong Dispersion ($D$\,=\,1.30)}
  \includegraphics[bb=55 530 535 650,width=7.5in]{strongdisp2.ps}
  \vspace{-1.0in}
\fi
\begin{center}
\begin{itemize}
\item Small SAW velocity shift:  $|\Delta c/c| < \;\,$3\,\%.
\item $|D|>$\,1 implies dispersion is dominant.
\end{itemize}
\ifposter
  \includegraphics[bb=50 50 555 315,width=7in]{GeSi-stressdiff-high-poster-strong.ps}
\else
  \includegraphics[bb=50 50 555 315,width=7.5in]{GeSi-stressdiff-high-poster-strong.ps}  
\fi
\end{center}
\end{textblock}

\begin{textblock}{10}(22,29)
\ifposter
  \vspace{2\baselineskip}
\else
  %\CHead{Waveform Evolution}
  %\CHead{Strong Dispersion ($D$\,=\,1.30)}
  \textcolor{DarkBlue}{\rule[10pt]{550pt}{3pt}}
  \vspace{-2\baselineskip}  
\fi
\begin{itemize}
\item Waveforms exhibit primarily dispersion (180$^\circ$ phase 
      shifts for shown positions) with some distortion.
\end{itemize}
\vspace{-0.75\baselineskip}
\begin{center}
\ifposter
  \includegraphics*[bb=25 270 550 760,width=7in]{Ge-100nm--5.0GPa-Si-_0.0GPa-multpos-color.ps}
\else
  \includegraphics*[bb=25 270 550 760,width=7.5in]{Ge-100nm--5.0GPa-Si-_0.0GPa-multpos-color.ps}  
\fi
\end{center}
\end{textblock}

\begin{textblock}{10}(33,29)
\ifposter
  \vspace{2\baselineskip}
\else
  %\CHead{Harmonic Evolution}
  %\CHead{Strong Dispersion ($D$\,=\,1.30)}
  \textcolor{DarkBlue}{\rule[10pt]{550pt}{3pt}}
  \vspace{-2\baselineskip}  
\fi
\begin{itemize}
\item Harmonic magnitudes exhibit growth and 
      \ifposter{}\else{\\}\fi decay cycles, while the phases show much 
      \ifposter{}\else{\\}\fi variation.
\end{itemize}
\begin{center}
\ifposter
  \includegraphics*[bb=55 35 540 450,width=7.6in]{Ge-100nm--5.0GPa-Si-_0.0GPa-propcurv2-color-ann.ps}
\else
  \vspace{-0.5in}
  \includegraphics*[bb=55 35 540 450,width=7.5in]{Ge-100nm--5.0GPa-Si-_0.0GPa-propcurv2-color-ann.ps}
\fi
\end{center}
\end{textblock}

\begin{textblock}{10}(44,17)
\CHead{Conclusions}
\begin{itemize}
\ifposter
\item Thin~\mbox{f}\mbox{i}lms cause dispersion (phase shifts)
      between frequency components of SAWs.  With 
      \mbox{f}\mbox{i}nite-amplitude SAWs, nonlinearly generated
      harmonics disperse relative to one another causing  
      complicated evolution of waveforms and harmonics. 
\else
\item Thin film causes harmonics to disperse relative to one 
      another, resulting in complicated evolution of 
      waveforms and harmonics. 
\fi  
\item Linear SAWs:  Stress causes small changes 
      in wave velocity (1 to 3\,\%).
\item Nonlinear SAWs:  Moderate dispersion\\
      Stress causes a shift in magnitudes and phases of the harmonics.
      Maximum effects occur at longer propagation distances and 
      higher \ifposter{}\else{\\}\fi harmonics (20 to 60\,\%):
\end{itemize}
\begin{center}
\ifposter
  \includegraphics*[bb=50 288 540 504,width=7in]{Ge-020nm--5.0GPa-Si-_0.0GPa-propdiff-color.ps}
\else
  \vspace{-\baselineskip}
  \includegraphics*[bb=50 288 540 504,width=7.5in]{Ge-020nm--5.0GPa-Si-_0.0GPa-propdiff-color.ps}
\fi
\end{center}
\vspace{-\baselineskip}
\begin{itemize}
\item Nonlinear SAWs:  Strong dispersion\\
      Strong dispersion results in only limited 
      harmonic generation but with spatial  
      oscillations in magnitude.  Stress causes 
      extrema of the harmonic curves to shift around 5\,\% 
      for \ifposter{}\else{\\}\fi every nonlinear length scale traversed:
\end{itemize}
\begin{center}
\ifposter
  \includegraphics*[bb=50 50 545 315,width=7in]{Ge-100nm--5.0GPa-Si-_0.0GPa-extremadiff-color-ann.ps}
\else
\vspace{-1.5\baselineskip}
  \includegraphics*[bb=50 50 545 315,width=7.5in]{Ge-100nm--5.0GPa-Si-_0.0GPa-extremadiff-color-ann.ps}
  \vspace{-2\baselineskip}
\fi
\end{center}
\CHead{Future Work}
\ifposter
      (1) Other \mbox{f}\mbox{i}lm/substrate combinations,
      (2) Broadband sources, (3) Different cuts and directions, 
      (4) Inversion for stress, (5) Effects of applied stress.
\else
      (1) Other \mbox{f}\mbox{i}lm/substrate combinations,\\
      (2) Broadband sources,\\ 
      (3) Different cuts and directions.
\fi
\end{textblock}

\ifposter
\begin{textblock}{54}(00,41.5)
\begin{center}
{\footnotesize Contact information:
Ronald Kumon, 325 Broadway, Mail Stop 853, Boulder, CO\ \ 80305--3328; 
Phone: $+$1 303--497--4205;
Email: \textsl{kumon@boulder.nist.gov}; 
Web: \textsl{http://www.kumonweb.com/ron/}
}
\vspace{-0.75\baselineskip}

{\footnotesize Acknowledgments:  
This work was performed while the author held a National Research
Council Research Associateship Award at NIST.  Thanks also to  
D.~C.~Hurley, V.~Tewary, C.~Flannery, and B.~Yang.}
\end{center}
\end{textblock}

\else

{\Large
 \setlength{\baselineskip}{0.8\baselineskip}
\CHead{Acknowledgments}
This work was performed while the author held a National Research
Council Research Associateship Award at NIST.  
\vspace{-\baselineskip}

Thanks also to 
D.~C.~Hurley, V.~Tewary, C.~Flannery, and B.~Yang for useful discussions.
Poster produced using \LaTeX\ with the ``a0posterslides'' style file.

\CHead{Contact Information}
\begin{center}
Ronald E. Kumon\\
325 Broadway, Mail Stop 853\\
Boulder, CO\ \ 80305--3328\\
Phone: $+$1 303--497--4205\\
Email: \textsl{kumon@boulder.nist.gov}\\
Web: \textsl{http://www.kumonweb.com/ron/}
\end{center}
}
\fi

\end{document}
