相关论文: Mathematical Theory of Exchange-driven Growth

The exchange-driven growth (EDG) model describes the evolution of clusters through the exchange of single monomers between pairs of interacting clusters. The dynamics of this process are primarily influenced by the interaction kernel…

Exchange-driven growth (EDG) is a process in which pairs of clusters interact by exchanging single unit with a rate given by a kernel $K(j,k)$. Despite EDG model's common use in the applied sciences, its rigorous mathematical treatment is…

The exchange-driven growth model describes a process in which pairs of clusters interact through the exchange of single monomers. The rate of exchange is given by an interaction kernel $K$ which depends on the size of the two interacting…

We study the self-similar behavior of the exchange-driven growth model, which describes a process in which pairs of clusters, consisting of an integer number of monomers, interact through the exchange of a single monomer. The rate of…

The continuous generalized exchange-driven growth model (CGEDG) is a coagulation-fragmentation equation that describes the evolution of the macroscopic cluster size distribution induced by a microscopic dynamic of binary exchanges of masses…

We derive the exchange-driven growth (EDG) equations as the mean-field limit of interacting particle systems on the complete graph. Extending previous work, we consider symmetric exchange kernels $c(k, l) = c(l, k)$ satisfying super-linear…

We study a class of growth processes in which clusters evolve via exchange of particles. We show that depending on the rate of exchange there are three possibilities: I) Growth: Clusters grow indefinitely; II) Gelation: All mass is…

The exchange-driven growth model describes the mean field kinetics of a population of composite particles (clusters) subject to pairwise exchange interactions. Exchange in this context means that upon interaction of two clusters, one loses…

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…

We investigate a system of interacting clusters evolving through mass exchange and supplemented by input of small clusters. Three possibilities depending on the rate of exchange generically occur when input is homogeneous: continuous…

The discrete collisional breakage equation, which captures the dynamics of cluster growth when clusters encounter binary collisions with possible matter transfer, is discussed in this article. The existence of global mass-conserving…

The continuous generalized exchange-driven growth model (CGEDG) is a system of integro-differential equations describing the evolution of cluster mass under mass exchange. The rate of exchange depends on the masses of the clusters involved…

We give a comprehensive rate equation description for the irreversible growth of aggregates by migration from small to large aggregates. For a homogeneous rate K(i;j) at which monomers migrate from aggregates of size i to those of size j,…

In this article, we discuss the continuous version of the generalized exchange-driven growth model which is a variant of the coagulation model in which a smaller size particle is detached from a bigger one and merges with another particle.…

We study a nonlinear kinetic model of mass exchange between interacting grains. The transition rates follow the Arrhenius equation with an activation energy that depends on the grain mass. We show that the activation parameter can be…

In this paper we introduce and discuss kinetic equations for the evolution of the probability distribution of the number of particles in a population subject to binary interactions. The microscopic binary law of interaction is assumed to be…

We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…

Competitive balance model has been proposed as an extension to the balance model to address the conflict of interests in signed networks arXiv:2001.04664 . In this model two different paradigms compete with each other due to the competitive…

We introduce and analyse a mathematical model describing the dynamics of particles generated by charge-exchange interactions. The model extends the well-established exchange-driven growth model, previously studied in several works, by…

We present a proof of the monotonic entropy growth for a nonlinear discrete-time model of a random market. This model, based on binary collisions, also may be viewed as a particular case of Ulam's redistribution of energy problem. We…