Re: From reactions to differential equations
- To: mathgroup at smc.vnet.net
- Subject: [mg93472] Re: From reactions to differential equations
- From: janos <janostothmeister at gmail.com>
- Date: Mon, 10 Nov 2008 03:30:44 -0500 (EST)
- References: <200811080900.EAA14313@smc.vnet.net> <gf6dsu$k33$1@smc.vnet.net>
On nov. 9, 11:26, "Scot T. Martin" <smar... at deas.harvard.edu> wrote: > This link might also be helpful: > > http://www.mathematica-journal.com/issue/v8i1/features/martin/ > > On Sat, 8 Nov 2008, Alexei Boulbitch wrote: > > Hi, Istvan, > > > just to add few words to the previous reply. I learned recently from th= e = > > reply of M.Roellig that using Mathematica you can transform chemical equa= ti= > ons into differential. This makes sense, if you deal with many tens or ev= en= > hundreds of reactions. I rule out the evident problem related to stabi= lity= > of such a huge system. If one goes this way, he probably have successf= ully= > solved it. > > > However, if I understand you right, you asked another question: your pr= ob= > > lem is just to translate a certain (not too large) system of chemical rea= ct= > ions into differential equations and to analyze them. Right? > > > OK, but in this case it is an easy task, provided chemical reactions (l= ik= > > 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 actua= ll= > > y 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 co= ntra= > st, the rules of translation a chemical reaction into a kinetic equation = ar= > e explained in a number of books. Just in case you missed a good one, hav= e = > 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 E= d,= > > New York: Interscience or> Prigogine, Ilya; Nicolis, G. (1977). Sel= f-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. > > > Even more, I would never trust any program to translate instead of me c= he= > > mical reactions into differential equations. All the physical sense (chem= ic= > al sense, biological sense - cross out those unnecessary) is hidden exact= ly= > in this step. It is here that you make assumptions and formulate your = mode= > l. All the rest is some mathematical analysis which will never give you m= or= > e than you put into your equations during this step. > > > I successfully used Mathematica several times to analyze equations desc= ri= > > bing chemical kinetics. However, if you have more than two-three non-line= ar= > equations describing your system, Mathematica may be not the best choi= ce. = > I have seen at least one other than Mathematica program which was better = de= > signed for this purpose. But moderator informed me that it is not elig= ible= > to give here its name. > > > Finally, I let myself one philosophic comment to the Community. In the = Ma= > > thGroup I often see questions which originated when the author cannot do = so= > mething using Mathematica, but are in fact related to some lack of knowle= dg= > e of the author in Mathematics or in some other discipline. So literally = th= > e answer does not belong to this forum. My attitude is that we should ans= we= > r these questions nevertheless and give hints of where to look for the an= sw= > er. Itself the fact that some question is related to some other field (ra= th= > er than Mathematica) is something to do with Mathematica nevertheless. Ju= st= > due to indication of boundaries. > > > > > Success, Alexei > > >> Hi Istvan, > > >> the reaction kinetic equations only tell you what is changed into what=
- References:
- Re: From reactions to differential equations
- From: Alexei Boulbitch <Alexei.Boulbitch@iee.lu>
- Re: From reactions to differential equations