krebs.xmds

XMDS is a code generator that integrates equations. You write them down in human readable form in a

<?xml version="1.0"?>
<simulation>
  
<!-- $Id: krebs.xmds,v 1.1 2004/06/22 10:18:18 paultcochrane Exp $ -->

<!--  Copyright (C) 2000-2004                                           -->
<!--                                                                    -->
<!--  Code contributed by Greg Collecutt, Joseph Hope and Paul Cochrane -->
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<!--  This file is part of xmds.                                        -->
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<!--  This program is free software; you can redistribute it and/or     -->
<!--  modify it under the terms of the GNU General Public License       -->
<!--  as published by the Free Software Foundation; either version 2    -->
<!--  of the License, or (at your option) any later version.            -->
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<!--  This program is distributed in the hope that it will be useful,   -->
<!--  but WITHOUT ANY WARRANTY; without even the implied warranty of    -->
<!--  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the     -->
<!--  GNU General Public License for more details.                      -->
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<!--  Foundation, Inc., 59 Temple Place - Suite 330, Boston,            -->
<!--  MA  02111-1307, USA.                                              -->

  <name> krebs </name>      <!-- the name of the simulation -->
  
  <author> Paul Cochrane </author>  <!-- the author of the simulation -->
  <description>
    <!-- a description of what the simulation is supposed to do -->
    Simulation of a simplification of the Krebs cycle of biochemical
    reactions. 
    Adapted for xmds from "Mathematica computer programs for physical
    chemistry", William H. Cropper, Springer Verlag (1998)
    This is a cyclic reaction scheme with the following reactions:
      A + R -> B + S
          B -> C
      R + C -> S + D
          D -> A
    with this reaction included which produces R at a constant rate
    from a reactant P whose concentration is large enough to be nearly
    constant.
          P -> R
    The overall reaction is 
          R -> S
    With equations:
      d[A]_dt = k4[D] - k1[A][R]
      d[B]_dt = k1[A][R] - k2[B]
      d[C]_dt = k2[B] - k3[C][R]
      d[D]_dt = k3[C][R] - k4[D]
      d[R]_dt = k5 - k1[A][R] - k3[C][R]
  </description>
  
  <!-- Global system parameters and functionality -->
  <prop_dim> t </prop_dim>    <!-- name of main propagation dim -->
  
  <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[
    // rate constants (in L/mol/s)
    const double k1 = 1.0;
    const double k2 = 0.1;
    const double k3 = 1.0;
    const double k4 = 0.1;
    const double k5 = 0.001;
    // initial concentrations (in mol/L)
    const double Ao = 0.1;
    const double Bo = 0.0;
    const double Co = 0.0;
    const double Do = 0.0;
    const double Ro = 0.0;
  ]]>
  </globals>
  
  <!-- Field to be integrated over -->
  <field>
    <name> main </name>
    <samples> 1 </samples>       <!-- sample 1st point of dim? -->
    
    <vector>
      <name> main </name>
      <type> double </type>           <!-- data type of vector -->
      <components> A B C D R </components>       <!-- names of components -->
      <![CDATA[
        A = Ao;
	B = Bo;
	C = Co;
	D = Do;
	R = Ro;
      ]]>
    </vector>
  </field>
  
  <!-- The sequence of integrations to perform -->
  <sequence>
    <integrate>
      <algorithm> RK4IP </algorithm> <!-- RK4EX, RK4IP, SIEX, SIIP -->
      <interval> 250 </interval>   <!-- how far in main dim? -->
      <lattice> 100000 </lattice>     <!-- no. points in main dim -->
      <samples> 1000 </samples> <!-- no. pts in output moment group -->
      <![CDATA[
        dA_dt = k4*D - k1*A*R;
	dB_dt = k1*A*R - k2*B;
	dC_dt = k2*B - k3*C*R;
	dD_dt = k3*C*R - k4*D;
	dR_dt = k5 - k1*A*R - k3*C*R;
      ]]>
    </integrate>
  </sequence>
  
  <!-- The output to generate -->
  <output format="ascii">
    <group>
      <sampling>
        <moments> Aout Bout Cout Dout Rout </moments>           <!-- names of moments -->
        <![CDATA[
          Aout = A;
	  Bout = B;
	  Cout = C;
	  Dout = D;
	  Rout = R;
        ]]>
      </sampling>
    </group>
  </output>
  
</simulation>