Related papers: The continuous version of the generalized exchange…
A generalized continuous economic model is proposed for random markets. In this model, agents interact by pairs and exchange their money in a random way. A parameter controls the effectiveness of the transactions between the agents. We show…
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 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 construct generalized coherent states (GCS) of a massive accelerated particle. This example is an important step in studying coherent states (CS) for systems with an unbounded motion and a continuous spectrum. First, we represent quantum…
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…
Flocculation is the process whereby particles (i.e., flocs) in suspension reversibly combine and separate. The process is widespread in soft matter and aerosol physics as well as environmental science and engineering. We consider a general…
The "Money Exchange Model" is a type of agent-based simulation model used to study how wealth distribution and inequality evolve through monetary exchanges between individuals. The primary focus of this model is to identify the limiting…
We show the variational convergence of an irreversible Markov jump process describing a finite stochastic particle system to the solution of a countable infinite system of deterministic time-inhomogeneous quadratic differential equations…
We investigate a viscoelastic flow model with a generalized memory, in which a weak-singular component is introduced in the exponential convolution kernel of classical viscoelastic flow equations that remains untreated in the literature. We…
The diffusion model has emerged as a powerful tool for generating atomic structures for materials science. This work calls attention to the deficiency of current particle-based diffusion models, which represent atoms as a point cloud, in…
We compute the growth fluctuations in equilibrium of a wide class of deposition models. These models also serve as general frame to several nearest-neighbor particle jump processes, e.g. the simple exclusion or the zero range process, where…
We have developed a continuum model that explains the complex surface shapes observed in epitaxial regrowth on micron scale gratings. This model describes the dependence of the surface morphology on film thickness and growth temperature in…
We analyze a reaction-diffusion system describing the growth of microbial species in a model of flocculation type that arises in biology. Existence of global classical positive solutions is proved under general growth assumptions, with…
A general theory is developed for the evolution of the cell order (CO) distribution in planar granular systems. Dynamic equations are constructed and solved in closed form for several examples: systems under compression; dilation of very…
We review models of compositional growth, which were introduced to explain the growth statistics of various quantities ranging from firm sizes to GDP. In these models, entities are decomposed into units that grow independently. Thus, the…
Transition rates in continuously driven steady states were derived in [Evans R M L, 2005 J. Phys. A: Math. Gen. 38, 293] by demanding that no information other than the microscopic laws of motion and the macroscopic observables of the…
Growth mixture models (GMMs) incorporate both conventional random effects growth modeling and latent trajectory classes as in finite mixture modeling; therefore, they offer a way to handle the unobserved heterogeneity between subjects in…
In this paper, we propose Continuous Graph Flow, a generative continuous flow based method that aims to model complex distributions of graph-structured data. Once learned, the model can be applied to an arbitrary graph, defining a…
The article discusses a generalization of model of economic growth with constant pace, which takes into account the effects of dynamic memory. Memory means that endogenous or exogenous variable at a given time depends not only on their…
In the theories of generalized modified gravity, the acceleration equation is generally fourth order. So it is hard to analyze the evolution of the Universe. In this paper, we present a class of generalized modified gravity theories which…