lorenz.xmds

<?xml version="1.0"?>
<!-- Example simulation: lorenz -->

<!-- Adapted from the example in "Numerical methods for physics"-->
<!-- by Alejandro L. Garcia, pg 78-->

<!-- Try the simulation for different values of xo, yo and zo -->
<!-- e.g.: xo = 1, yo = 1, zo = 20 -->

<!-- Note: this simulation can be run as a shell/Perl/Python script by -->
<!-- changing the values of xo, yo and zo using the command line arguments -->

<simulation>

  <!-- General information about the simulation -->
  <name>lorenz</name>
  <author>Paul Cochrane</author>
  <description>
    Lorenz attractor example simulation.  Adapted from the example in
    "Numerical methods for physics" by Alejandro L. Garcia, page 78 (1st ed.).
  </description>

  <!-- Global system parameters and functionality -->
  <prop_dim>t</prop_dim>

  <!-- Global variables for the simulation -->
  <globals>
    <![CDATA[
    const double sigma = 10.0;
    const double b = 8.0/3.0;
    const double r = 28.0;
    const double xo = 1.0;     // initial conditions
    const double yo = 1.0;     // initial conditions
    const double zo = 20.0;    // initial conditions
    ]]>
  </globals>

  <!-- Field to be integrated over -->
  <field>
    <samples>1</samples>
    <vector>
      <name>main</name>
      <type>double</type>
      <components>x y z</components>
      <![CDATA[
        x = xo;
        y = yo;
	z = zo;
      ]]>
    </vector>
  </field>

  <!-- The sequence of integrations to perform -->
  <sequence>
    <integrate>
      <algorithm>RK4EX</algorithm>
      <interval>10.0</interval>
      <lattice>10000</lattice>
      <samples>200</samples>
      <![CDATA[
        dx_dt = sigma*(y - x);
        dy_dt = r*x - y - x*z;
	dz_dt = x*y - b*z;
      ]]>
    </integrate>
  </sequence>

  <!-- The output to generate -->
  <output>
    <filename>lorenz.xsil</filename>
    <group>
      <sampling>
        <moments>xOut yOut zOut</moments>
          xOut = x;
	  yOut = y;
	  zOut = z;
      </sampling>
    </group>
  </output>

</simulation>