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QNMsMorrisThorneWH-2.mw
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QNMsMorrisThorneWH-2.mw
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<?xml version="1.0" encoding="UTF-8"?>
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<Group view="code" labelreference="L2" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"># The Morris-Thorne wormholes : computation of quasi-normal modes from throat to infinity</Text-field>
</Input>
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<Group view="code" labelreference="L3" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">restart: # Matrices assembling for Morris-Thorne wormholes quasi-normal modes computation</Text-field>
</Input>
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<Group view="code" labelreference="L4" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">with(LinearAlgebra):</Text-field>
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<Group view="code" labelreference="L5" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">Digits := 200: # Number of significant digits we compute</Text-field>
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<Group view="code" labelreference="L6" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"># Physical parameters:</Text-field>
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<Group view="code" labelreference="L114" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">L := 0: # angular momentum parameter value</Text-field>
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<Group view="code" labelreference="L8" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">s := 0: # spin parameter value (s = 0, 1, 2)</Text-field>
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<Group view="code" labelreference="L7" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">e := 1 - s^2: # self-explaining</Text-field>
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<Group view="code" labelreference="L14" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"># Numerical parameters:</Text-field>
</Input>
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<Group view="code" labelreference="L15" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">n := 200: # Number of Tchebyshev modes, the matrices will be of size n*n</Text-field>
</Input>
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<Group view="code" labelreference="L19" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"># Definition of final ODE coefficients:</Text-field>
</Input>
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<Group view="code" hide-input="false" labelreference="L21" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">L00 := y -> piecewise(y=-1, -4*L*(L+1)-4*e, y=1, -4*L*(L+1), (y > -1) and (y < 1), -4*L*(L+1) - e*(1 - y)^2):</Text-field>
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<Group view="code" hide-input="false" labelreference="L31" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">L01 := y -> piecewise(y=-1, 8, y=1, 0, (y > -1) and (y < 1), (1 - y)*(3*(1 - y)^2 - 8)):</Text-field>
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<Group view="code" hide-input="false" labelreference="L32" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">L02 := y -> piecewise(y=-1, 0, y=1, 0, (y > -1) and (y < 1), (3 - y)*(1 + y)*(1 - y)^2):</Text-field>
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<Group view="code" hide-input="false" labelreference="L33" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">L10 := y -> piecewise(y=-1, 4, y=1, 0, (y > -1) and (y < 1), 2*(1 - y)):</Text-field>
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<Group view="code" hide-input="false" labelreference="L34" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">L11 := y -> piecewise(y=-1, 0, y=1, 16, (y > -1) and (y < 1), -4*(1 - y)^2 + 16):</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L35" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">L12 := y -> 0:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L36" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">L20 := y -> 4:</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L37" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">L21 := y -> 0:</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L38" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">L22 := y -> 0:</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L23" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">local j: F := y -> simplify(add(a[j]*ChebyshevT(j, y), j=0..n-1)):</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L24" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">M0 := Matrix(n): M1 := Matrix(n): M2 := Matrix(n):</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L39" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"># Assembling the matrices:
for i from 1 to n do
xi := cos((2.0*i-1.0)*Pi/(2.0*n)); # Chebyshev roots collocation points
# xi := -cos(Pi*(i-1)/(n-1)); # [-1, 1] Chebyshev extrema collocation points
expr0 := evalf(L00(xi)*F(xi) + L01(xi)*subs(x=xi, diff(F(x),x)) + L02(xi)*subs(x=xi, diff(F(x),x$2))):
expr1 := evalf(L10(xi)*F(xi) + L11(xi)*subs(x=xi, diff(F(x),x)) + L12(xi)*subs(x=xi, diff(F(x),x$2))):
expr2 := evalf(L20(xi)*F(xi) + L21(xi)*subs(x=xi, diff(F(x),x)) + L22(xi)*subs(x=xi, diff(F(x),x$2))):
for j from 1 to n do
M0[i,j] := coeff(expr0, a[j-1]);
M1[i,j] := coeff(expr1, a[j-1]);
M2[i,j] := coeff(expr2, a[j-1]);
end do:
end do:</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L62" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"># We export the data:</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L40" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">ExportMatrix("../data/M0_200.mat", M0, target=MATLAB, mode=ascii):</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L41" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">ExportMatrix("../data/M1_200.mat", M1, target=MATLAB, mode=ascii):</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L42" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">ExportMatrix("../data/M2_200.mat", M2, target=MATLAB, mode=ascii):</Text-field>
</Input>
</Group></Presentation-Block>
</Worksheet>