Related papers: Localisation in a growth model with interaction. A…
We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…
We perform a time-dependent study of the driven dynamics of overdamped particles which are placed in a one-dimensional, piecewise linear random potential. This set-up of spatially quenched disorder then exerts a dichotomous varying random…
Recent work on the structure of social networks and the internet has focussed attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in…
Flocking is ubiquitous in nature and emerges due to short- or long-range alignment interactions among self-propelled agents. Two unfriendly species that antialign or even interact nonreciprocally show more complex collective phenomena,…
Evolving network models under a dynamic growth rule which comprises the addition and deletion of nodes are investigated. By adding a node with a probability $P_a$ or deleting a node with the probability $P_d=1-P_a$ at each time step, where…
We introduce perhaps the simplest models of graph evolution with choice that demonstrate discontinuous percolation transitions and can be analyzed via mathematical evolution equations. These models are local, in the sense that at each step…
Monte Carlo simulations are employed to investigate the surface growth generated by deposition of particles of different sizes on a substrate, in one and two dimensions. The particles have a linear form, and occupy an integer number of…
We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of…
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…
Granular convergence is a property of a granular pack as it is repeatedly sheared in a cyclic, quasistatic fashion, as the packing configuration changes via discrete events. Under suitable conditions the set of microscopic configurations…
The growth of a rough and porous thin surface by deposition of randomly shaped clusters with different sizes over an initially flat linear substrate is simulated, using Monte Carlo technique. Unlike the ordinary Random Deposition, our…
This work presents a technique for particle size generation and placement in arbitrary closed domains. Its main application is the simulation of granular media described by disks. Particle size generation is based on the statistical…
The fundamental solutions of diffusion equation for the local-equilibrium and nonlocal models are considered as the limiting cases of the solution of a problem related to consideration of the Brownian particles random walks. The differences…
A simple model accounting for the ejection of heavy particles from the vortical structures of a turbulent flow is introduced. This model involves a space and time discretization of the dynamics and depends on only two parameters: the…
We study the effect of turbulence on a sedimenting layer of particles by means of direct numerical simulations. A Lagrangian model in which particles are considered as tracers with an additional downward settling velocity is integrated…
We investigate the evolution of a population of non-interacting particles which undergo diffusion and multiplication. Diffusion is assumed to be homogeneous, while multiplication proceeds with different rates reflecting the distribution of…
We solve an one-dimensional stochastic model of interacting particles on a chain. Particles can have branching and coagulation reactions, they can also appear on an empty site and disappear spontaneously. This model which can be viewed as…
In this paper we investigate geometric properties of graphs generated by a preferential attachment random graph model with edge-steps. More precisely, at each time $t\in\mathbb{N}$, with probability $p$ a new vertex is added to the graph (a…
This article formalizes the problem of modeling social networks into an interacting particle system on random geometric graphs. Each vertex of the graph is associated with a geometric position in a latent space describing the unobserved…
We examine the aggregate behavior of one-dimensional random walks in a model known as (one-dimensional) Internal Diffusion Limited Aggregation. In this model, a sequence of $n$ particles perform random walks on the integers, beginning at…