# Compositional evolution with mass transfer in closed systems

## Repositori DSpace/Manakin

 dc.contributor Universitat de Girona. Departament d'Informàtica i Matemàtica Aplicada dc.contributor.author Jarauta Bragulat, Eusebio dc.contributor.author Egozcue, Juan José dc.contributor.editor Daunis i Estadella, Josep dc.contributor.editor Martín Fernández, Josep Antoni dc.date.issued 2008-05-29 dc.identifier.citation Jarauta Bragulat, E.; Egozcue, J.J. 'Compositional evolution with mass transfer in closed systems' a CODAWORK’08. Girona: La Universitat, 2008 [consulta: 13 maig 2008]. Necessita Adobe Acrobat. Disponible a Internet a: http://hdl.handle.net/10256/725 dc.identifier.uri http://hdl.handle.net/10256/725 dc.description.abstract Evolution of compositions in time, space, temperature or other covariates is frequent in practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of the sample, thus producing a transfer of mass from some components to other ones, but preserving the total mass present in the system. This evolution is traditionally modelled as a system of ordinary di erential equations of the mass of each component. However, this kind of evolution can be decomposed into a compositional change, expressed in terms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despite of some subcompositions behaving linearly. The goal is to study the characteristics of such simplicial systems of di erential equa- tions such as linearity and stability. This is performed extracting the compositional dif ferential equations from the mass equations. Then, simplicial derivatives are expressed in coordinates of the simplex, thus reducing the problem to the standard theory of systems of di erential equations, including stability. The characterisation of stability of these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and the associated behaviour of the orbits are the main tools. For a three component system, these orbits can be plotted both in coordinates of the simplex or in a ternary diagram. A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is a radioactive decay dc.description.sponsorship Geologische Vereinigung; Institut d’Estadística de Catalunya; International Association for Mathematical Geology; Càtedra Lluís Santaló d’Aplicacions de la Matemàtica; Generalitat de Catalunya, Departament d’Innovació, Universitats i Recerca; Ministerio de Educación y Ciencia; Ingenio 2010. dc.format.mimetype application/pdf dc.language.iso eng dc.publisher Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada dc.rights Tots els drets reservats dc.subject Models geomètrics dc.subject Equacions diferencials dc.title Compositional evolution with mass transfer in closed systems dc.type info:eu-repo/semantics/conferenceObject
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