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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=
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