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<?xml version="1.0" encoding="UTF-8"?>
<simulation xmds-version="2">
<name>diffusion_arguments</name>
<author>Andy Ferris</author>
<description>
Simple one-dimensional diffusion with a pointless second dimension thrown in for fun.
Uses arguments and argument preprocessing. Essentially the simulation "looks" the
same for any given "size", as the interval/etc is scaled to fit the interesting region.
The user may use width_scale, time_scale and ratio to zoom out and in...
</description>
<features>
<benchmark />
<bing />
<fftw plan="exhaustive" />
<validation kind="run-time"/>
<globals>
<![CDATA[
real minx;
real maxx;
real miny;
real maxy;
real width;
real time_interval;
]]>
</globals>
<arguments>
<argument name="size" type="real" default_value="20.0"/>
<argument name="ratio" type="real" default_value="0.1"/>
<argument name="width_factor" type="real" default_value="1.0"/>
<argument name="time_factor" type="real" default_value="1.0"/>
<![CDATA[
minx = -0.5*size;
maxx = 0.5*size;
miny = -0.5*size*ratio;
maxy = 0.5*size*ratio;
width = 0.5*sqrt(0.5)*size*ratio*width_factor; // half the simulation size
// The time intersting stuff happens scales as width^2
time_interval = 20.0 * width*width * time_factor;
]]>
</arguments>
</features>
<geometry>
<propagation_dimension> t </propagation_dimension>
<transverse_dimensions>
<dimension name="x" lattice="32" domain="(minx, maxx)" />
<dimension name="y" lattice="128" domain="(miny, maxy)" />
</transverse_dimensions>
</geometry>
<vector name="main" initial_basis="x y" type="complex">
<components>
phi
</components>
<initialisation>
<![CDATA[
phi = exp(-y*y/(2*width*width));
]]>
</initialisation>
</vector>
<sequence>
<!-- This is an interesting simulation because using IP operators means there is NO error due to the algorithm (though there may be numerical error) -->
<integrate algorithm="RK4" interval="time_interval" steps="24">
<samples>24</samples>
<operators>
<operator kind="ip" basis="x ky">
<operator_names>L</operator_names>
<![CDATA[
L = -0.02*ky*ky;
]]>
</operator>
<integration_vectors>main</integration_vectors>
<![CDATA[
dphi_dt = L[phi];
]]>
</operators>
</integrate>
</sequence>
<output>
<sampling_group basis="x(0) y" initial_sample="yes">
<moments>dens</moments>
<dependencies>main</dependencies>
<![CDATA[
dens = mod2(phi);
]]>
</sampling_group>
</output>
</simulation>
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