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{SECT 0 {EXCHG {PARA 258 "" 0 "" {TEXT 257 60 "Simulation of wave pack
et propagation in a dispersive medium" }{TEXT 258 2 "\n\n" }{TEXT -1 
21 "Instructions for use:" }}{PARA 264 "" 0 "" {TEXT -1 431 "Start wit
h cursor at the first line of red text in the file.  Keep pressing the
 enter key, waiting for the computer to finish the computation each ti
me.  In order to run the animation, select the graph, then click on th
e \"play button\" on the tool bar (looks like a triangle pointing to t
he right).  If you change some function or parameter, you only need to
 re-run the \"execution groups\" below that point where you made the c
hange." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 21 "restart:\nwith(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 45 "g(k) := exp(-50*(k-1)^2);\nplot(g(k), k=0..4);" }}{PARA 13 "" 
0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 259 33 "Initial k-spectru
m of wave packet" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "wp := 1
0; c := 3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "wk := (k) -> \+
wp*(1+c^2*k^2/(2*wp^2)): plot(wk(k),k=0..3);" }}{PARA 13 "" 0 "" 
{TEXT -1 0 "" }}{PARA 259 "" 0 "" {TEXT 260 19 "Dispersion relation" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "y := (x,t) -> Re(int(g(k)*
exp(I*(k*x-wk(k)*t)), k=-infinity..infinity));" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 38 "plot(y(x,0),x=-50..350,numpoints=250);" }}
{PARA 13 "" 0 "" {TEXT -1 0 "" }}{PARA 260 "" 0 "" {TEXT 261 30 "Snaps
hot of wave packet at t=0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
40 "plot(y(x,280),x=-50..350,numpoints=250);" }}{PARA 13 "" 0 "" 
{TEXT -1 0 "" }}{PARA 261 "" 0 "" {TEXT 262 98 "Snapshot of wave packe
t at t=280 (notice the \"chirp\": shorter wavelength at leading edge o
f pulse)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "animate(y(x,t),
x=-50..350,t=0..450,numpoints=250,frames=150);" }{TEXT -1 0 "" }}
{PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 256 44 "Wave
 packet propagation in dispersive medium" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{MARK "9" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
{PAGENUMBERS 0 1 2 33 1 1 }