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Kinetic model of mass exchange with dynamic Arrhenius transition rates

Christopoulos Dionysios, Muradova Aliki

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Extent15 pagesen
TitleKinetic model of mass exchange with dynamic Arrhenius transition ratesen
CreatorChristopoulos Dionysiosen
CreatorΧριστοπουλος Διονυσιοςel
CreatorMuradova Alikien
CreatorMuradova Alikiel
Content SummaryWe study a nonlinear kinetic model of mass exchange between interacting grains. The transition rates follow the Arrhenius equation with an activation energy that depends dynamically on the grain mass. We show that the activation parameter can be absorbed in the initial conditions for the grain masses, and that the total mass is conserved. We obtain numerical solutions of the coupled, nonlinear, ordinary differential equations of mass exchange for the two-grain system, and we compare them with approximate theoretical solutions in specific neighborhoods of the phase space. Using phase plane methods, we determine that the system exhibits regimes of diffusive and growth-decay (reverse diffusion) kinetics. The equilibrium states are determined by the mass equipartition and separation nullcline curves. If the transfer rates are perturbed by white noise, numerical simulations show that the system maintains the diffusive and growth-decay regimes; however, the noise can reverse the sign of equilibrium mass difference. Finally, we present theoretical analysis and numerical simulations of a system with many interacting grains. Diffusive and growth-decay regimes are established as well, but the approach to equilibrium is considerably slower. Potential applications of the mass exchange model involve coarse-graining during sintering and wealth exchange in econophysics.en
Type of ItemPeer-Reviewed Journal Publicationen
Type of ItemΔημοσίευση σε Περιοδικό με Κριτέςel
Date of Item2018-10-19-
Date of Publication2016-
SubjectGrain growthen
SubjectKinetic modelen
SubjectNon-equilibrium processen
SubjectReverse diffusionen
Bibliographic CitationD. T. Hristopulos and A. Muradova, "Kinetic model of mass exchange with dynamic Arrhenius transition rates," Physica A Stat. Mech. Appl., vol. 444, pp. 95-109, Feb. 2016. doi: 10.1016/j.physa.2015.10.007en