kubo_tutorial.xmds

<?xml version="1.0"?>
<!-- $Id -->
<simulation>
  
  <name>kubo_tutorial</name>      <!-- the name of the simulation -->
  
  <author> Paul Cochrane </author>  <!-- the author of the simulation -->
  <description>
    Kubo oscillator example simulation.  This formally represents a
    simple model of an oscillator with a mean frequency omega
    perturbed by a noise term xi(t).
    Adapted from the example given in "Handbook of Stochastic
    Methods", C. W. Gardiner (1997)
  </description>
  
  <!-- Global system parameters and functionality -->
  <prop_dim> t </prop_dim>    <!-- name of main propagation dim -->
  
  <stochastic> yes </stochastic>  <!-- defaults to no -->
  <!-- these three tags only necessary when stochastic is yes -->
  <paths> 1024 </paths>               <!-- no. of paths -->
  <seed> 1 2 </seed>             <!-- seeds for rand no. gen -->
  <noises> 1 </noises>             <!-- no. of noises -->
  
  <use_mpi> no </use_mpi>            <!-- defaults to no -->
  <error_check> yes </error_check>   <!-- defaults to yes -->
  <use_wisdom> yes </use_wisdom>     <!-- defaults to no -->
  <benchmark> yes </benchmark>       <!-- defaults to no -->
  <use_prefs> yes </use_prefs>       <!-- defaults to yes -->
  
  <!-- Global variables for the simulation -->
  <globals>
  <![CDATA[
    double omega = 0;   // mean frequency
    // the word gamma is already used in many maths libraries, hence
    // use gam here.
    double gam = 0.1;   // perturbation strength
    double zo = 1;      // initial value of z
  ]]>
  </globals>
  
  <!-- Field to be integrated over -->
  <field>
    <name> main </name>
    <samples> 1 </samples>       <!-- sample 1st point of dim? -->
    
    <vector>
      <name> main </name>
      <type> complex </type>           <!-- data type of vector -->
      <components> z </components>       <!-- names of components -->
      <fourier_space> no </fourier_space> <!-- defined in k-space? -->
      <![CDATA[
        z = zo;
      ]]>
    </vector>
  </field>
  
  <!-- The sequence of integrations to perform -->
  <sequence>
    <integrate>
      <algorithm> SIEX </algorithm> <!-- RK4EX, RK4IP, SIEX, SIIP -->
      <iterations> 3 </iterations>  <!-- default=3 for SI- algs -->
      <interval> 10 </interval>     <!-- how far in main dim? -->
      <lattice> 1000 </lattice>     <!-- no. points in main dim -->
      <samples> 100 </samples> <!-- no. pts in output moment group -->
      
      <![CDATA[
        dz_dt = i*omega*z + i*sqrt(2.0*gam)*n_1*z;
      ]]>
    </integrate>
  </sequence>
  
  <!-- The output to generate -->
  <output format="ascii">
    <group>
      <sampling>
        <fourier_space> no </fourier_space> <!-- sample in k-space? -->
        <lattice> 100 </lattice>          <!-- no. points to sample -->
        <moments> realz imagz </moments>    <!-- names of moments -->
        <![CDATA[
          realz = real(z);
	  imagz = imag(z);
        ]]>
      </sampling>
    </group>
  </output>
  
</simulation>