Related papers: The discrete generalized exchange-driven system
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.…
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 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 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…
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…
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…
Exchange-driven growth is a process in which pairs of clusters interact and exchange a single unit of mass. The rate of exchange is given by an interaction kernel $K(j,k)$ which depends on the masses of the two interacting clusters. In this…
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…
In this paper we study the discrete coagulation--fragmentation models with growth, decay and sedimentation. We demonstrate the existence and uniqueness of classical global solutions provided the linear processes are sufficiently strong.…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under…
We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such…
In exchange processes clusters composed of elementary building blocks, monomers, undergo binary exchange in which a monomer is transferred from one cluster to another. In assortative exchange only clusters with comparable masses participate…
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 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…
Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model…
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 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…
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 investigate a discrete model consisting of self-propelled particles that obey simple interaction rules. We show that this model can self-organize and exhibit coherent localized solutions in one- and in two-dimensions.In one-dimension,…