Artifact 4d20ddf97a3f53b22b0d93693f84ce26adbae7042c087fb2bec00b98d06a17f9:
- Executable file
r38/packages/misc/reacteqn.txt
— part of check-in
[f2fda60abd]
at
2011-09-02 18:13:33
on branch master
— Some historical releases purely for archival purposes
git-svn-id: https://svn.code.sf.net/p/reduce-algebra/code/trunk/historical@1375 2bfe0521-f11c-4a00-b80e-6202646ff360 (user: arthurcnorman@users.sourceforge.net, size: 5590) [annotate] [blame] [check-ins using] [more...]
REDUCE Support for Reaction Equation Systems Herbert Melenk Konrad-Zuse-Zentrum Berlin January 1991 The REDUCE package REACTEQN allows one to transform chemical reaction systems into ordinary differential equation systems (ode) corresponding to the laws of pure mass action. A single reaction equation is an expression of the form <n1><s1> + <n2><s2> + ... -> <n3><s3> + <n4><s4> + ... or <n1><s1> + <n2><s2> + ... <> <n3><s3> + <n4><s4> + ... where the <si> are arbitrary names of species (REDUCE symbols) and the <ni> are positive integer numbers. The number 1 can be omitted. The connector -> describes a one way reaction, while <> describes a forward and backward reaction. A reaction system is a list of reaction equations, each of them optionally followed by one or two expressions for the rate constants. A rate constant can a number, a symbol or an arbitrary REDUCE expression. If a rate constant is missing, an automatic constant of the form RATE(n) (where n is an integer counter) is generated. For double reactions the first constant is used for the forward direction, the second one for the backward direction. The names of the species are collected in a list bound to the REDUCE variable SPECIES. This list is automatically filled during the processing of a reaction system. The species enter in an order corresponding to their appearance in the reaction system and the resulting ode's will be ordered in the same manner. If a list of species is preassigned to the variable SPECIES either explicitly or from previous operations, the given order will be maintained and will dominate the formatting process. So the ordering of the result can be easily influenced by the user. Syntax: reac2ode { <reaction> [,<rate> [,<rate>]] [,<reaction> [,<rate> [,<rate>]]] .... }; where two rates are applicable only for <> reactions. Result is a system of explicit ordinary differential equations with polynomial righthand sides. As side effect the following variables are set: lists: rates: list of the rates in the system species: list of the species in the system matrices: inputmat: matrix of the input coefficients outputmat: matrix of the output coefficients In the matrices the row number corresponds to the input reaction number, while the column number corresponds to the species index. Note: if the rates are numerical values, it will be in most cases appropriate to select a REDUCE evaluation mode for floating point numbers. That is REDUCE 3.3: on float,numval; REDUCE 3.4: on rounded; Inputmat and outputmat can be used for linear algebra type investigations of the reaction system. The classical reaction matrix is the difference of these matrices; however, the two matrices contain more information than their differences because the appearance of a species on both sides is not reflected by the reaction matrix. EXAMPLES: % Example taken from Feinberg (Chemical Engineering): species := {A1,A2,A3,A4,A5}; reac2ode { A1 + A4 <> 2A1, rho, beta, A1 + A2 <> A3, gamma, epsilon, A3 <> A2 + A5, theta, mue}; 2 {DF(A1,T)=RHO*A1*A4 - BETA*A1 - GAMMA*A1*A2 + EPSILON*A3, DF(A2,T)= - GAMMA*A1*A2 + EPSILON*A3 + THETA*A3 - MUE*A2*A5, DF(A3,T)=GAMMA*A1*A2 - EPSILON*A3 - THETA*A3 + MUE*A2*A5, 2 DF(A4,T)= - RHO*A1*A4 + BETA*A1 , DF(A5,T)=THETA*A3 - MUE*A2*A5} % the corresponding matrices: inputmat; [1 0 0 1 0] [ ] [1 1 0 0 0] [ ] [0 0 1 0 0] outputmat; [2 0 0 0 0] [ ] [0 0 1 0 0] [ ] [0 1 0 0 1] % computation of the classical reaction matrix as difference % of output and input matrix: reactmat := outputmat-inputmat; [1 0 0 -1 0] [ ] REACTMAT := [-1 -1 1 0 0] [ ] [0 1 -1 0 1] % Example with automatic generation of rate constants % and automatic extraction of species species := {}; reac2ode { A1 + A4 <> 2A1, A1 + A2 <> A3, a3 <> A2 + A5}; new species: A1 new species: A4 new species: A3 new species: A2 new species: A5 2 {DF(A1,T)= - A1 *RATE(2) + A1*A4*RATE(1) - A1*A2*RATE(3) + A3*RATE(4), 2 DF(A4,T)=A1 *RATE(2) - A1*A4*RATE(1), DF(A2,T)= - A1*A2*RATE(3) - A2*A5*RATE(6) + A3*RATE(5) + A3*RATE(4), DF(A3,T)=A1*A2*RATE(3) + A2*A5*RATE(6) - A3*RATE(5) - A3*RATE(4), DF(A5,T)= - A2*A5*RATE(6) + A3*RATE(5)} % Example with rates computed from numerical expressions species := {}; reac2ode { A1 + A4 <> 2A1, 17.3* 22.4^1.5, 0.04* 22.4^1.5 }; new species: A1 new species: A4 2 {DF(A1,T)= - 4.24065*A1 + 1834.08*A1*A4, 2 DF(A4,T)=4.24065*A1 - 1834.08*A1*A4} Herbert Melenk Konrad-Zuse-Zentrum fuer Informationstechnik Heilbronner Str 10 D 1000 Berlin 31 Germany Phone: (49) 30 89604 195 FAX: (49) 30 89604 125 E-mail: melenk@zib.de