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R. Sasportes

Publications and source records attributed to R. Sasportes.

4 recordsLinked to original sources
arXiv2025

The discrete generalized exchange-driven system

We study a discrete model for generalized exchange-driven growth in which the particle exchanged between two clusters is not limited to be of size one. This set of models include as special cases the usual exchange-driven growth system and the coagulation-fragmentation system with binary fragmentation. Under reasonable general condition on the rate coefficients we establish the existence of admissible solutions, meaning solutions that are obtained as appropriate limit of solutions to a finite-dimensional truncation of the infinite-dimensional ODE. For these solutions we prove that, in the class of models we call isolated both the total number of particles and the total mass are conserved, whereas in those models we can non-isolated only the mass is conserved. Additionally, under more restrictive growth conditions for the rate equations we obtain uniqueness of solutions to the initial value problems.

math.CA↗
arXiv2018

Point island dynamics under fixed rate deposition

In this paper we consider the dynamics of point islands during submonolayer deposition, in which the fragmentation of subcritical size islands is allowed. To understand asymptotics of solutions, we use methods of centre manifold theory, and for globalisation, we employ results from the theories of compartmental systems and of asymptotically autonomous dynamical systems. We also compare our results with those obtained by making the quasi-steady state assumption.

math.CA↗
arXiv2013

The Redner - Ben-Avraham - Kahng cluster system

We consider a coagulation model first introduced by Redner, Ben-Avraham and Krapivsky in [Redner, Ben-Avraham, Kahng: Kinetics of 'cluster eating', J. Phys. A: Math. Gen., 20 (1987), 1231-1238], the main feature of which is that the reaction between a j-cluster and a k-cluster results in the creation of a |j-k|-cluster, and not, as in Smoluchowski's model, of a (j+k)-cluster. In this paper we prove existence and uniqueness of solutions under reasonably general conditions on the coagulation coefficients, and we also establish differenciability properties and continuous dependence of solutions. Some interesting invariance properties are also proved. Finally, we study the long-time behaviour of solutions, and also present a preliminary analysis of their scaling behaviour.

math.CA↗