%%Creator:Adobe Illustrator 9.0, Macintosh 2000 %%Title: Fig8_5_1a.eps %%Date: 7/4/2001 10:50:30 PM %%BoundingBox: 0 0 248 159 %%Coordinates: LL %%StartMarkedPoints %%MarkedPoint:(91,148) : point(0,0) : z %z %%MarkedPoint:(80,76) : point(0,0) : theta %\theta(x,y,a) %%MarkedPoint:(76,36) : point(0,0) : phi %\phi %%MarkedPoint:(132,15) : point(0,0) : Q %Q %%MarkedPoint:(123,73) : point(0,0) : P %P %%MarkedPoint:(211,62) : point(0,0) : y %y %%MarkedPoint:(36,5) : point(0,0) : x %x %%EndMarkedPoints
\begin{xy}
\xyWARMprocessMoEPS{\Fname a}{\grExt}
\xyMarkedImport{\Fname a}
\xyMarkedPos{x}*+!RD{x}
\xyMarkedPos{y}*+!UL{y}
\xyMarkedPos{z}*+!RD{z}
\xyMarkedPos{P}*+!RD{P}
\xyMarkedPos{Q}*+!UR{Q}
\xyMarkedPos{phi}*+!UL{\varphi}
\xyMarkedPos{theta}*+!DR{\theta(x,y,a)}
\end{xy}
%%Creator:Adobe Illustrator 9.0, Macintosh 2000 %%Title: Fig8_5_3.eps %%Date: 7/4/2001 7:1:18 PM %%BoundingBox: 10 11 210 70 %%Coordinates: LL %%StartMarkedPoints %%MarkedPoint:(197,64) : point(0,0) : U %U %%MarkedPoint:(184,38) : point(0,0) : wT %w_0(T) %%MarkedPoint:(172,52) : point(0,0) : h %h %%MarkedPoint:(111,49) : point(0,0) : p1 %p\ne 0 %%MarkedPoint:(130,36) : point(0,0) : p0 %p=0 %%MarkedPoint:(10,11) : point(0,0) : w0 %w_0 %%EndMarkedPoints
\begin{xy}
% \xyShowAllMarkedPoints{}{\Fname}{\grExt}%
\xyWARMprocessMoEPS{\Fname}{\grExt}
\xyMarkedImport{\Fname}
\xyMarkedPos{U}*+!DL{U}
\xyMarkedPos{wT}*+!U!L(.4){w_0(T)}
\xyMarkedPos{h}*++!L{h}
\xyMarkedPos{p1}*++!LD{p\ne 0}
\xyMarkedPos{p0}*+!UR{p=0}
\xyMarkedPos{w0}*+!R{w_0}
\end{xy}
%%Creator:Adobe Illustrator 9.0, Macintosh 2000 %%Title: Fig8_5_2.eps %%Date: 7/6/2001 3:12:4 PM %%BoundingBox: 0 0 259 155 %%Coordinates: LL %%StartMarkedPoints %%MarkedPoint:(233,112) : point(0,0) : phi %\phi %%MarkedPoint:(176,101) : point(0,0) : theta %\theta %%MarkedPoint:(190,90) : point(0,0) : xy %(x,y) %%MarkedPoint:(8,124) : point(0,0) : y %y %%MarkedPoint:(64,60) : point(0,0) : x %x %%EndMarkedPoints
\begin{xy}
% \xyShowAllMarkedPoints{}{\Fname}{\grExt}%
\xyWARMprocessMoEPS{\Fname}{\grExt}
\xyMarkedImport{\Fname}
\xyMarkedPos{phi}*++!L{\varphi}
\xyMarkedPos{theta}*++!DR(.4){\theta}
\xyMarkedPos{x}*+!UL{x}
\xyMarkedPos{y}*++!R{y}
\xyMarkedPos{xy}*++!U!L(.15){(x,y)}
\end{xy}
%%Creator:Adobe Illustrator 9.0, Macintosh 2000 %%Title: Fig8_2_4.eps %%Date: 7/6/2001 3:37:53 PM %%BoundingBox: 0 0 209 72 %%Coordinates: LL %%StartMarkedPoints %%MarkedPoint:(137,35) : point(0,0) : Sigma %\Sigma, surface %%MarkedPoint:(200,13) : point(0,0) : C %C, boundary curve %%MarkedPoint:(184,68) : point(0,0) : n %n, normal vector %%EndMarkedPoints
\begin{xy}
% \xyWARMprocessMo{\Fname}{}
\xyShowAllMarkedPoints{}{\Fname}{\grExt}%
\xyMarkedImport{\Fname}% repeat name else pdfTeX crashes
\xyMarkedPos{Sigma}*+!LU{\Sigma}
\xyMarkedPos{C}*++++!L{C}
\xyMarkedPos{n}*++++!L{\vec{n}}
\end{xy}
%%Creator:Adobe Illustrator 9.0, Macintosh 2000 %%Title: Fig8_2_3.eps %%Date: 7/6/2001 5:26:2 PM %%BoundingBox: 0 0 222 153 %%Coordinates: LL %%StartMarkedPoints %%MarkedPoint:(198,113) : point(0,0) : M %M, manifold %%MarkedPoint:(136,45) : point(0,0) : Ct %C_t, transformed curve %%MarkedPoint:(76,74) : point(0,0) : C %C, curve %%EndMarkedPoints
\begin{xy}
% \xyShowAllMarkedPoints{}{\Fname}{\grExt}%
\xyWARMprocessMoEPS{\Fname}{\grExt}
\xyMarkedImport{\Fname}
\xyMarkedPos{Ct}*+!LU{C_t}
\xyMarkedPos{C}*++!L{C}
\xyMarkedPos{M}*+!LD{M}
\end{xy}
%%Creator:Adobe Illustrator 9.0, Macintosh 2000 %%Title: Fig8_2_2.eps %%Date: 7/6/2001 6:29:58 PM %%BoundingBox: 0 0 155 209 %%Coordinates: LL %%StartMarkedPoints %%MarkedPoint:(143,98) : point(0,0) : pn %force across $S$ is $-p n$ %%MarkedPoint:(152,126) : point(0,0) : n %n, normal vector %%MarkedPoint:(87,192) : point(0,0) : S %S, surface %%EndMarkedPoints
\begin{xy}
% \xyWARMprocessMo{\Fname}{}
\xyShowAllMarkedPoints{}{\Fname}{\grExt}%
\xyMarkedImport{\Fname}% repeat name else pdfTeX crashes
\xyMarkedPos{pn}*++!L\txt{force across $S$\\is $-p\mathbf{n}$}
\xyMarkedPos{n}*++!L{\mathbf{n}}
\xyMarkedPos{S}*+!LD{S}
\end{xy}
%%Creator:Adobe Illustrator 9.0, Macintosh 2000 %%Title: Fig8_2_1.eps %%Date: 7/6/2001 7:16:6 PM %%BoundingBox: 0 0 165 108 %%Coordinates: LL %%StartMarkedPoints %%MarkedPoint:(144,75) : point(0,0) : M %M, manifold %%MarkedPoint:(164,62) : point(0,0) : traj %trajectory of\\fluid particle\\moving through\\$x$ at time $t=t$ %%MarkedPoint:(151,4) : point(0,0) : u %u(\varphi_t(x),t) %%MarkedPoint:(105,22) : point(0,0) : phi %\varphi_t(x) %%MarkedPoint:(38,61) : point(0,0) : x %x %%EndMarkedPoints
\begin{xy}
% \xyWARMprocessMo{\Fname}{}
\xyShowAllMarkedPoints{}{\Fname}{\grExt}%
\xyMarkedImport{\Fname}% repeat name else pdfTeX crashes
\xyMarkedPos{x}*++!D{x}
\xyMarkedPos{phi}*++!D!L(.5){\varphi_t(x)}
\xyMarkedPos{M}*+!LD{M}
\xyMarkedPos{u}*+!UL{u(\varphi_t(x),t)}
\xyMarkedPos{traj}*++!L!U(.5){\parbox{10em}{trajectory of\\fluid particle\\
moving through\\$x$ at time $\mathrm{t}=t$}}
\end{xy}
%%Creator:Adobe Illustrator 9.0, Macintosh 2000 %%Title: Fig8_1_2.eps %%Date: 7/6/2001 7:42:9 PM %%BoundingBox: 0 9 214 94 %%Coordinates: LL %%StartMarkedPoints %%MarkedPoint:(106,90) : point(0,0) : y %y-axis %%MarkedPoint:(208,11) : point(0,0) : x %x-axis %%EndMarkedPoints
\begin{xy}
% \xyShowAllMarkedPoints{}{\Fname}{\grExt}%
\xyWARMprocessMoEPS{\Fname}{\grExt}
\xyMarkedImport{\Fname}
\xyMarkedPos{x}*++!U{x}
\xyMarkedPos{y}*++!L{y}
\end{xy}
Ross Moore 2002-05-08