# LaTeX2HTML 2002 (1.62)
# Associate images original text with physical files.


$key = q/includegraphics[width=hsize]{KraussDensVar-gpl.eps};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="554" HEIGHT="320" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img94.png"
 ALT="\includegraphics[width=\hsize]{KraussDensVar-gpl.eps}">|; 

$key = q/displaystylea(t)=alphacdotleft(V(g(t))-v(t)right),hbox{with}V(g)=v_fcdot(tanh(g+l_c)-tanh(l_c)),;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="502" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img122.png"
 ALT="$\displaystyle a(t) = \alpha \cdot \left( V(g(t)) - v(t) \right) , \hbox{  with  } V(g) = v_f \cdot (\tanh(g+l_c) - \tanh(l_c))  ,$">|; 

$key = q/V'(g);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img135.png"
 ALT="$ V'(g)$">|; 

$key = q/alpha(rho)=c_0^2slashrho;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img131.png"
 ALT="$ \alpha(\rho) = c_0^2/\rho$">|; 

$key = q/varepsilon=1.0,:rho=0.3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img76.png"
 ALT="$ \varepsilon=1.0,\: \rho=0.3 $">|; 

$key = q/displaystylepartial_tv+v,partial_xv=frac{1}{tau}left(V(rho)-vright)+alpha(rho),partial_xrho+nu(rho),partial_x^2v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="346" HEIGHT="49" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img130.png"
 ALT="$\displaystyle \partial_t v + v   \partial_x v = \frac{1}{\tau} \left( V(\rho) - v \right) + \alpha(\rho)   \partial_x \rho + \nu(\rho)   \partial_x^2 v$">|; 

$key = q/displaystylemax{0,v_{rmdes}-varepsilon,a,eta}.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$\displaystyle \max \{ 0 , v_{\rm des} - \varepsilon   a   \eta \} .$">|; 

$key = q/>;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$ &gt;$">|; 

$key = q/g_t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img111.png"
 ALT="$ g_t$">|; 

$key = q/|dVslashdrho|>c_0slashrho;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img133.png"
 ALT="$ \vert dV/d\rho\vert &gt; c_0/\rho$">|; 

$key = q/includegraphics[width=0.32hsize]{rho02eps09-gz.eps};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="162" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img81.png"
 ALT="\includegraphics[width=0.32\hsize]{rho02eps09-gz.eps}">|; 

$key = q/p_{>0}=p_0=0.5;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img116.png"
 ALT="$ p_{&gt;0} = p_0 =
0.5$">|; 

$key = q/downarrow;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img74.png"
 ALT="$ \downarrow$">|; 

$key = q/Deltat;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$ \Delta t$">|; 

$key = q/[0,1];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$ [0,1]$">|; 

$key = q/a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$ a$">|; 

$key = q/{displaymath}p_{rmslow}(v)={cases}p_0=0.5&hbox{if}v_t=0p_{>0}=0.01&hbox{if}v_t>0{cases}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="247" HEIGHT="64" BORDER="0"
 SRC="|."$dir".q|img115.png"
 ALT="\begin{displaymath}
p_{\rm slow}(v) =
\begin{cases}
p_0 = 0.5 &amp; \hbox{if }v_t = 0 \\\\
p_{&gt;0} = 0.01 &amp; \hbox{if } v_t &gt; 0 \\\\
\end{cases}  .
\end{displaymath}">|; 

$key = q/tau;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$ \tau$">|; 

$key = q/displaystylev(t+Deltat);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$\displaystyle v(t+\Delta t)$">|; 

$key = q/V'(rho);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img134.png"
 ALT="$ V'(\rho)$">|; 

$key = q/{rho_ell};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img89.png"
 ALT="$ {\rho_\ell}$">|; 

$key = q/t_{rmrelax};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img84.png"
 ALT="$ t_{\rm relax}$">|; 

$key = q/tilde{v};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$ \tilde{v}$">|; 

$key = q/rho_L=1slashV;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$ \rho_L = 1/V$">|; 

$key = q/includegraphics[width=0.3hsize]{rho075eps18-tif.eps};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="146" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img80.png"
 ALT="\includegraphics[width=0.3\hsize]{rho075eps18-tif.eps}">|; 

$key = q/displaystylev_{t+frac{1}{2}}=min[g_t,v_t+1,v_{max}],;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img110.png"
 ALT="$\displaystyle v_{t+\frac{1}{2}} = \min[ g_t, v_t + 1, v_{max} ] ,$">|; 

$key = q/16.2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$ 16.2$">|; 

$key = q/ellllL;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img104.png"
 ALT="$ \ell \ll L$">|; 

$key = q/displaystylev_{rmsafe};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$\displaystyle v_{\rm safe}$">|; 

$key = q/includegraphics[width=0.3hsize]{rho02eps18-tif.eps};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="146" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img78.png"
 ALT="\includegraphics[width=0.3\hsize]{rho02eps18-tif.eps}">|; 

$key = q/V(g);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img127.png"
 ALT="$ V(g)$">|; 

$key = q/rho_L>rho_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$ \rho_L &gt; \rho_1$">|; 

$key = q/varepsilon=1.0,:rho=0.2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img75.png"
 ALT="$ \varepsilon=1.0,\: \rho=0.2$">|; 

$key = q/{l_c}=1slashrho_{jam}approx7.5~hbox{m};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img109.png"
 ALT="$ {l_c}= 1/\rho_{jam} \approx
7.5&nbsp;\hbox{m}$">|; 

$key = q/rhoapprox0.2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img97.png"
 ALT="$ \rho \approx 0.2$">|; 

$key = q/=;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$ =$">|; 

$key = q/includegraphics[width=hsize]{RhoTemp-fig.eps};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="550" HEIGHT="363" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="\includegraphics[width=\hsize]{RhoTemp-fig.eps}">|; 

$key = q/L;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$ L$">|; 

$key = q/g=tau,tildev;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="$ g =
\tau   \tilde v$">|; 

$key = q/displaystylev_t=left{{array}[c]{ll}max[0,v_{t+frac{1}{2}}-1]&hbox{withprobability}p_{rmslow}(v_t)v_{t+frac{1}{2}}&hbox{else}{array}right.,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="351" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img113.png"
 ALT="$\displaystyle v_t = \left\{ \begin{array}[c]{ll} \max[ 0, v_{t+\frac{1}{2}} - 1...
...} p_{\rm slow}(v_t) \ v_{t+\frac{1}{2}} &amp; \hbox{else } \end{array} \right.  ,$">|; 

$key = q/{ell};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img87.png"
 ALT="$ {\ell}$">|; 

$key = q/includegraphics[width=hsize]{KraussDensVarCont-gpl.eps};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="557" HEIGHT="410" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img95.png"
 ALT="\includegraphics[width=\hsize]{KraussDensVarCont-gpl.eps}">|; 

$key = q/t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="10" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img112.png"
 ALT="$ t$">|; 

$key = q/r_c(rho);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$ r_c(\rho)$">|; 

$key = q/a=0.2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$ a=0.2$">|; 

$key = q/{textrm{Var}({rho_ell})}=0.01;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$ {\textrm {Var}({\rho _\ell })}=0.01$">|; 

$key = q/dVslashdg>alphaslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img126.png"
 ALT="$ dV/dg &gt; \alpha/2$">|; 

$key = q/includegraphics[width=0.7hsize]{KraussNumJamEvol-gpl.eps};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="387" HEIGHT="263" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img86.png"
 ALT="\includegraphics[width=0.7\hsize]{KraussNumJamEvol-gpl.eps}">|; 

$key = q/l_c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img124.png"
 ALT="$ l_c$">|; 

$key = q/includegraphics[width=0.49hsize]{S2SdensVarCont-gpl.eps};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="272" HEIGHT="197" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img121.png"
 ALT="\includegraphics[width=0.49\hsize]{S2SdensVarCont-gpl.eps}">|; 

$key = q/uparrow;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="$ \uparrow$">|; 

$key = q/{ell}=62.5;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$ {\ell }=62.5$">|; 

$key = q/varepsilon=1.0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$ \varepsilon =1.0$">|; 

$key = q/T>T_c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$ T &gt; T_c$">|; 

$key = q/nu(rho)=nu_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img132.png"
 ALT="$ \nu(\rho) = \nu_0$">|; 

$key = q/p>p_c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$ p&gt;p_c$">|; 

$key = q/p_{>0};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$ p_{&gt;0}$">|; 

$key = q/rho_L={N}slash{L};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="$ \rho_L = {N}/ {L}$">|; 

$key = q/Deltat=tau=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="$ \Delta t = \tau = 1$">|; 

$key = q/{l_c};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img108.png"
 ALT="$ {l_c}$">|; 

$key = q/r_c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$ r_c$">|; 

$key = q/Q(rho)=rho,V(rho);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$ Q(\rho) =
\rho   V(\rho)$">|; 

$key = q/{v_{{rmmax}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$ {v_{{\rm max}}}$">|; 

$key = q/includegraphics[width=0.32hsize]{rho03eps10-gz.eps};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="162" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img82.png"
 ALT="\includegraphics[width=0.32\hsize]{rho03eps10-gz.eps}">|; 

$key = q/eta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$ \eta$">|; 

$key = q/rho_1<rho_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$ \rho_1 &lt; \rho_2$">|; 

$key = q/ell=62.5;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img105.png"
 ALT="$ \ell=62.5$">|; 

$key = q/Ltoinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img102.png"
 ALT="$ L \to \infty$">|; 

$key = q/TgeT_c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$ T \ge T_c$">|; 

$key = q/displaystylemin{v(t)+a,Deltat,v_{rmsafe},v_{rmmax}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="198" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$\displaystyle \min \{ v(t) + a   \Delta t, v_{\rm safe} , v_{\rm max} \}$">|; 

$key = q/5.4;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="$ 5.4$">|; 

$key = q/b=0.6;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$ b=0.6$">|; 

$key = q/alpha;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img128.png"
 ALT="$ \alpha$">|; 

$key = q/includegraphics[width=0.7hsize]{gasLiquid-fig.eps};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="387" HEIGHT="181" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="\includegraphics[width=0.7\hsize]{gasLiquid-fig.eps}">|; 

$key = q/rho=0.3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$ \rho =0.3$">|; 

$key = q/rho_L;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$ \rho_L$">|; 

$key = q/varepsilonto0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img107.png"
 ALT="$ \varepsilon \to 0$">|; 

$key = q/varepsilon;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$ \varepsilon $">|; 

$key = q/p_{rmslow}(v);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img114.png"
 ALT="$ p_{\rm slow}(v)$">|; 

$key = q/v_f;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img125.png"
 ALT="$ v_f$">|; 

$key = q/varepsilon=1.8,:rho=0.75;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$ \varepsilon=1.8,\: \rho=0.75 $">|; 

$key = q/1.5;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$ 1.5$">|; 

$key = q/1slash4;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img91.png"
 ALT="$ 1/4$">|; 

$key = q/varepsilonapprox1.7;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img100.png"
 ALT="$ \varepsilon \approx 1.7$">|; 

$key = q/{N};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$ {N}$">|; 

$key = q/1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$ 1$">|; 

$key = q/p_{>0}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img117.png"
 ALT="$ p_{&gt;0} = 0$">|; 

$key = q/{L}=600;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$ {L}=600$">|; 

$key = q/V(rho);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$ V(\rho)$">|; 

$key = q/T;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$ T$">|; 

$key = q/includegraphics[width=0.3hsize]{rho03eps18-tif.eps};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="146" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img79.png"
 ALT="\includegraphics[width=0.3\hsize]{rho03eps18-tif.eps}">|; 

$key = q/barv=(v+tildev)slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$ \bar v = (v + \tilde v)/2$">|; 

$key = q/p_{>0}to0.5;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img118.png"
 ALT="$ p_{&gt;0} \to 0.5$">|; 

$key = q/ellapproxL;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img106.png"
 ALT="$ \ell \approx L$">|; 

$key = q/displaystyletilde{v}(t)+frac{frac{g(t)}{tau}-tildev(t)}{bar{v}(t)slash({b,tau})+1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$\displaystyle \tilde{v} (t) +
\frac{\frac{g(t)}{\tau} - \tilde v(t)}{\bar{v}(t)/({b   \tau}) + 1}$">|; 

$key = q/varepsilon=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img96.png"
 ALT="$ \varepsilon = 1$">|; 

$key = q/81;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$ 81$">|; 

$key = q/rho_1(T_c)=rho_2(T_c);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$ \rho_1(T_c) = \rho_2(T_c)$">|; 

$key = q/7.5;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$ 7.5$">|; 

$key = q/{textrm{Var}({rho_ell})};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img93.png"
 ALT="$ {\textrm{Var}({\rho_\ell})}$">|; 

$key = q/{textrm{Var}({rho_ell})}=0.09;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$ {\textrm {Var}({\rho _\ell })}=0.09$">|; 

$key = q/varepsilon=1.8,:rho=0.3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="$ \varepsilon=1.8,\: \rho=0.3 $">|; 

$key = q/V(.);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img123.png"
 ALT="$ V(.)$">|; 

$key = q/v_{rmsafe};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="$ v_{\rm safe}$">|; 

$key = q/displaystylev_{rmdes};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$\displaystyle v_{\rm des}$">|; 

$key = q/displaystyle{textrm{Var}({rho_ell})}=frac{{ell}}{{L}}sum_{i=1}^{{L}slash{ell}}left({rho_ell}(i)-rho_Lright)^2,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="217" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img90.png"
 ALT="$\displaystyle {\textrm{Var}({\rho_\ell})}= \frac{{\ell}}{{L}} \sum_{i=1}^{{L}/{\ell}} \left({\rho_\ell}(i) - \rho_L\right)^2  ,$">|; 

$key = q/displaystylepartial_trho+partial_x(rho,v)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img129.png"
 ALT="$\displaystyle \partial_t \rho + \partial_x (\rho   v) = 0$">|; 

$key = q/rho_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$ \rho_2$">|; 

$key = q/{L};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img88.png"
 ALT="$ {L}$">|; 

$key = q/rho=0.2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img101.png"
 ALT="$ \rho=0.2$">|; 

$key = q/{v_{{rmmax}}}=3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$ {v_{{\rm max}}}=3$">|; 

$key = q/varepsilon=1.8;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="$ \varepsilon =1.8$">|; 

$key = q/0.8;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img98.png"
 ALT="$ 0.8$">|; 

$key = q/includegraphics[width=hsize]{pt-diag-fig.eps};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="546" HEIGHT="525" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="\includegraphics[width=\hsize]{pt-diag-fig.eps}">|; 

$key = q/displaystyle=;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$\displaystyle =$">|; 

$key = q/includegraphics[width=0.32hsize]{rho075eps10-gz.eps};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="162" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img83.png"
 ALT="\includegraphics[width=0.32\hsize]{rho075eps10-gz.eps}">|; 

$key = q/{v_{{rmmax}}}slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img85.png"
 ALT="$ {v_{{\rm max}}}/ 2$">|; 

$key = q/{L}=1000;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$ {L}=1000$">|; 

$key = q/ell;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img92.png"
 ALT="$ \ell$">|; 

$key = q/p_{>0}=0.5;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img119.png"
 ALT="$ p_{&gt;0} = 0.5$">|; 

$key = q/varepsilon=1.0,:rho=0.75;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img77.png"
 ALT="$ \varepsilon=1.0,\: \rho=0.75$">|; 

$key = q/b;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$ b$">|; 

$key = q/g;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="$ g$">|; 

$key = q/varepsilon=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$ \varepsilon=0$">|; 

$key = q/q;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$ q$">|; 

$key = q/v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$ v$">|; 

$key = q/varepsilon=1.8,:rho=0.2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="$ \varepsilon =1.8,\: \rho=0.2$">|; 

$key = q/22.5;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$ 22.5$">|; 

$key = q/includegraphics[width=0.49hsize]{S2SdensVar-gpl.eps};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="271" HEIGHT="162" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img120.png"
 ALT="\includegraphics[width=0.49\hsize]{S2SdensVar-gpl.eps}">|; 

$key = q/rho;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$ \rho$">|; 

$key = q/T_c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$ T_c$">|; 

$key = q/0.2leqrholeq0.8;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img99.png"
 ALT="$ 0.2 \leq \rho
\leq 0.8$">|; 

$key = q/rho_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$ \rho_1$">|; 

$key = q/elltoinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img103.png"
 ALT="$ \ell \to \infty$">|; 

$key = q/q=rho,v;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$ q = \rho  
v$">|; 

1;

