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<?xml version="1.0" encoding="UTF-8"?>
<simulation xmds-version="2">
<testing>
<input_xsil_file name="bessel_cosine_groundstate_breakpoint_expected.xsil" />
<xsil_file name="bessel_cosine_evolution.xsil" expected="bessel_cosine_evolution_expected.xsil" absolute_tolerance="1e10" relative_tolerance="8e-5" />
</testing>
<name>bessel_cosine_evolution</name>
<author>Graham Dennis</author>
<description>
Evolve the 3D ground state of a Rubidium BEC in a harmonic magnetic trap assuming
cylindrical symmetry about the z axis and reflection symmetry about z=0.
This permits us to use the cylindrical bessel functions to expand the solution transverse
to z and a cosine series to expand the solution along z.
This testcase tests using both Fourier transforms and Matrix transforms in a single simulation.
</description>
<features>
<auto_vectorise />
<benchmark />
<bing />
<globals>
<![CDATA[
const real omegaz = 2*M_PI*20;
const real omegarho = 2*M_PI*200;
const real hbar = 1.05457148e-34;
const real M = 1.409539200000000e-25;
const real g = 9.8;
const real scatteringLength = 5.57e-9;
const real Uint = 4.0*M_PI*hbar*hbar*scatteringLength/M;
const complex miUint_hbar = -i*Uint/hbar;
const real Nparticles = 5.0e5;
/* offset constants */
const real EnergyOffset = pow(15.0*Nparticles*Uint*omegaz*omegarho*omegarho/(8*M_PI), 2.0/5.0)
* pow(M/2.0, 3.0/5.0);
]]>
</globals>
</features>
<geometry>
<propagation_dimension> t </propagation_dimension>
<transverse_dimensions>
<dimension name="z" lattice="32" domain="(0.0, 1.0e-4)" transform="dct" volume_prefactor="2.0" />
<dimension name="r" lattice="32" domain="(0.0, 1.0e-5)" transform="bessel" volume_prefactor="2.0*M_PI"/>
</transverse_dimensions>
</geometry>
<vector name="potential" type="complex">
<components>
V1
</components>
<initialisation>
<![CDATA[
real Vtrap = 0.5*M*(omegarho*omegarho*r*r + omegaz*omegaz*z*z);
V1 = -i/hbar*(Vtrap - EnergyOffset);
]]>
</initialisation>
</vector>
<vector name="wavefunction" type="complex">
<components>
phi
</components>
<initialisation kind="hdf5">
<filename>bessel_cosine_groundstate_breakpoint_expected.h5</filename>
</initialisation>
</vector>
<sequence>
<integrate algorithm="ARK45" tolerance="1e-6" interval="1e-3">
<samples>10</samples>
<operators>
<operator kind="ip" constant="yes" type="imaginary">
<operator_names>T</operator_names>
<![CDATA[
T = -i*0.5*hbar/M*(kr*kr + kz*kz);
]]>
</operator>
<integration_vectors>wavefunction</integration_vectors>
<dependencies>potential</dependencies>
<![CDATA[
dphi_dt = T[phi] + (V1 + miUint_hbar*mod2(phi))*phi;
]]>
</operators>
</integrate>
</sequence>
<output format="hdf5">
<sampling_group basis="r z" initial_sample="no">
<moments>dens</moments>
<dependencies>wavefunction</dependencies>
<![CDATA[
dens = mod2(phi);
]]>
</sampling_group>
</output>
</simulation>
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