Artifact 282d127f7ef2f5b49371a0761d026e645f535b833757c9806d5781d1942ffe2c:
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r37/log/reacteqn.rlg
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Sun Aug 18 18:03:24 2002 run on Windows % Examples for the conversion of reaction equations to ordinary % differential equations. % Example taken from Feinberg (Chemical Engineering): species := {A1,A2,A3,A4,A5}; 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} 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 := {}; species := {} reac2ode { A1 + A4 <> 2A1, A1 + A2 <> A3, A3 <> A2 + A5}; new species: a1 new species: a4 new species: a2 new species: a3 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)} on rounded; species := {}; 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)= - 4.24064598853*a1 + 1834.07939004*a1*a4, 2 df(a4,t)=4.24064598853*a1 - 1834.07939004*a1*a4} end; Time for test: 150 ms, plus GC time: 30 ms