Limited coagulation-diffusion dynamics in inflating spaces

Jean-Yves Fortin (), Xavier Durang and MooYoung Choi
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Jean-Yves Fortin: Seoul National University
Xavier Durang: University of Seoul
MooYoung Choi: Seoul National University

The European Physical Journal B: Condensed Matter and Complex Systems, 2020, vol. 93, issue 9, 1-12

Abstract: Abstract We consider the one-dimensional coagulation–diffusion problem on a dynamical expanding linear lattice, in which the effect of the coagulation process is balanced by the dilatation of the distance between particles. Distances x(t) follow the general law ẋ (t) ∕ x (t) = α (1 + αt ∕ β) -1 with growth rate α and exponent β, describing both algebraic and exponential (β = ∞) growths. In the space continuous limit, the particle dynamics is known to be subdiffusive, with the diffusive length varying like t1∕2−β for β 1∕2. We interpret and characterize quantitatively this phenomenon as a second order phase transition between an absorbing state and a localized state where particles are not reactive. We furthermore investigate the case when space is discrete and use a generating function method to solve the time differential equation associated with the survival probability. This model is then compared with models of growth on geometrically constrained two-dimensional domains, and with the theory of fractional diffusion in the subdiffusive case. We found in particular a duality relation between the diffusive lengths in the inflating space and the fractional theory. Graphical abstract

Keywords: Statistical; and; Nonlinear; Physics (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1140/epjb/e2020-10058-9

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