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"" 0 "" {TEXT -1 24 "Mixing Rate Calculations" }}{PARA 256 "" 0 "" 
{TEXT -1 37 "mixing4.mws - used to produce Table 2" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 6 "S:=46;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "T:=50;" 
}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Digits:=20;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 6 "a:=10;" }}{PARA 0 "" 0 "" {TEXT -1 31 "a is the length
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0 "" 0 "" {TEXT -1 48 "b is the inverse of the second order coefficien
t" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "n:=100;" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }{TEXT -1 38 "n is the number of terms in the series" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "for t from S to T do print(t);" }}
{PARA 0 "" 0 "" {TEXT -1 44 "t is the time for which we compute the de
cay" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "maxdecay:=0;" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "for x from 9 b
y 0.02 to 9.98 do" }}{PARA 0 "" 0 "" {TEXT -1 77 "x is the starting po
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" 0 "" {TEXT -1 54 "containing the value at which the maximum is achie
ved." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "u:=evalf(b*a/2);" }}{PARA 
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;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "for nn from 1 to n do " }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "dd1:=evalf(exp(-u));" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 17 "dd2:=evalf(Pi^2);" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 53 "dd:=evalf(Pi*nn*(u^2+dd2*nn^2)^(-1)*(1-dd1*(-1)^nn));
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "d1:=evalf(b*a^2);" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 17 "d2:=evalf(b*x/2);" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "d3:=evalf(dd2/d1);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
49 "d4:=2*exp(-(b/4+d3*nn^2)*t+d2)*sin(Pi*x*nn/a)*dd;" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 15 "d:=evalf(d+d4);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 3 "od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "maxdecay:=evalf(max(max
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"" {MPLTEXT 1 0 19 "Tnorm[t]:=maxdecay;" }}{PARA 0 "" 0 "" {TEXT -1 
46 "the line above is the semigroup norm at time t" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 3 "od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 40 "for r from S to T do print(r,Tnorm[r]); \+
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{PARA 0 "" 0 "" {TEXT -1 36 "this prints the quantity of interest" }}
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