Re: Re: From reactions to differential equations
- To: mathgroup at smc.vnet.net
- Subject: [mg93486] Re: [mg93473] Re: From reactions to differential equations
- From: Daniel Lichtblau <danl at wolfram.com>
- Date: Tue, 11 Nov 2008 07:45:31 -0500 (EST)
- References: <gf3mik$emm$1@smc.vnet.net> <200811100830.DAA26365@smc.vnet.net>
janos wrote: > On nov. 8, 10:36, Alexei Boulbitch <Alexei.Boulbi... at iee.lu> wrote: >> Hi,Istvan, >> >> just to add few words to the previous reply. I learned recently from t= > he reply of M.Roellig that using Mathematica you can transform chemical equ= > ations into differential. This makes sense, if you deal with many tens or e= > ven hundreds of reactions. I rule out the evident problem related to stabil= > ity of such a huge system. If one goes this way, he probably have successfu= > lly solved it. >> However, if I understand you right, you asked another question: your prob= > lem is just to translate a certain (not too large) system of chemical react= > ions into differential equations and to analyze them. Right? >> OK, but in this case it is an easy task, provided chemical reactions (lik= > e 2 Subscript[H, 2] + Subscript[O, 2] -> 2 Subscript[H, 2] O) are already e= > stablished. >> "...I would like to understand the method how these reactions are actu= > ally converted to diff.equations..." >> I believe that your problem is not in Mathematica or any other program= > . I doubt that by use of any program one can understand such things. In con= > trast, the rules of translation a chemical reaction into a kinetic equation= > are explained in a number of books. Just in case you missed a good one, ha= > ve a look into >> Segel, L. A. Biological kinetics (eds. Cannings, C., Hoppenstedt, F. C. &= > Segel, L. A.) (Cambridge University Press, Cambridge, 1991). >> I myself learned it first from one of Prigogine=B4s books, such as >> Prigogine, Ilya (1961). Thermodynamics of Irreversible Processes, 2nd Ed,= > New York: Interscience or >> Prigogine, Ilya; Nicolis, G. (1977). Self-Organization in Non-Equilibrium= > Systems. Wiley. ISBN 0471024015. >> There is of coarse, also a lot of other books on this subject. You need t= > o read only few introductory chapters. >> [...] > One solution together with deretministic and stochastic models: > T=F3th, J.: Formal Kinetics with Applications, 6th World Multiconference > on Systemics, Cybernetics and Informatics (July 14-18, 2002, Orlando, > FL, USA), Vol. XI (Computer Science II) (N. Callaos, M. Morgenstern > and B. Sanchez eds.), pp. 573-576. > T=F3th, J.; Rospars, J.-P.: Dynamic modelling of biochemical reactions > with applications to signal transduction: Principles and tools using > Mathematica}, BioSystems, 79 (2005), 33-52. > > Background material: > =C9rdi, P., T=F3th, J.: Mathematical Models of Chemical Reactions. Theory > and Applications of Deterministic and Stochastic Models, Manchester > University Press, Manchester, Princeton University Press, Princeton, > 1989. > > J=E1nos That first is available, in Mathematica notebook form, at http://library.wolfram.com/infocenter/Conferences/4320/ Daniel Lichtblau Wolfram Research
- References:
- Re: From reactions to differential equations
- From: janos <janostothmeister@gmail.com>
- Re: From reactions to differential equations