A stochastic treatment of reaction and diffusion

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dc.contributor.authorRondoni, Lambertoen
dc.contributor.committeecochairZweifel, Paul F.en
dc.contributor.committeecochairStreater, R.F.en
dc.contributor.committeememberRossi, Johnen
dc.contributor.committeememberBowden, Robert L.en
dc.contributor.committeememberHagedorn, Georgeen
dc.contributor.committeememberHannsgen, Kenneth B.en
dc.contributor.departmentMathematical Physicsen
dc.date.accessioned2014-03-14T21:16:17Zen
dc.date.adate2008-07-28en
dc.date.available2014-03-14T21:16:17Zen
dc.date.issued1991en
dc.date.rdate2008-07-28en
dc.date.sdate2008-07-28en
dc.description.abstractWe develop a theory for the analysis of chemical reactions in "isolated" containers. The main tool for this analysis consists of Boltzmann maps, which are discrete time dynamical systems that describe the time evolution of the normalized concentrations of the chemicals in the reactions. Moreover, the use of these maps allows us to draw conclusions about the continuous dynamical systems that the law of mass action associates with the different reactions. The theorems we prove show that entropy is a strict Liapunov function and that no complex evolution is expected out of the discrete dynamical systems. In fact, we prove convergence to a fixed point for most of the possible cases, and we give solid arguments for the convergence of the remaining ones. The analysis of the continuous systems is more complicated, and fewer results have been proven. However, the conclusions we draw are similar to those relative to the Boltzmann maps. Therefore, we suggest that no chaos is to be found in systems that do not exchange energy nor matter with the outer environment, both for the discrete and for the continuous cases. Such a phenomenon is more likely to occur in "closed" or in "open" reactors. Finally, we argue that the discrete dynamical systems have more physical content than the continuous ones, and that Boltzmann maps may be useful in the analysis of the non chaotic regions of many other kinds of finite dimensional maps.en
dc.description.degreePh. D.en
dc.format.extentvi, 176 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-07282008-134042en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-07282008-134042/en
dc.identifier.urihttp://hdl.handle.net/10919/38840en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1991.R674.pdfen
dc.relation.isformatofOCLC# 24448207en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1991.R674en
dc.subject.lcshDiffusion -- Researchen
dc.subject.lcshStochastic analysis -- Researchen
dc.titleA stochastic treatment of reaction and diffusionen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineMathematical Physicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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