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We consider an extension of the zero-range process to the case where the hop rate depends on the state of both departure and arrival sites. We recover the misanthrope and the target process as special cases for which the probability of the…
In a view for a simple model where natural selection at the individual level is confronted to selection effects at the group level, we consider some individual-based models of some large population subdivided into a large number of groups.…
We propose a new dynamic stochastic blockmodel that focuses on the analysis of interaction lengths in networks. The model does not rely on a discretization of the time dimension and may be used to analyze networks that evolve continuously…
Three-dimensional molecular dynamics simulations of dissipative particles (~ 10^6) are carried out for studying the clustering kinetics of granular media during cooling. The inter-connected high particle density regions are identified,…
The one-dimensional contact process is analyzed by a cluster approximation. In this approach, the hierarchy of rate equations for the densities of finite length empty intervals are truncated under the assumption that adjacent intervals are…
Recent experiments with self-phoretic particles at low concentrations show a pronounced dynamic clustering [I. Theurkauff \emph{et al.}, Phys.\ Rev.\ Lett.\ \textbf{108}, 268303 (2012)]. We model this situation by taking into account the…
We study the equilibrium behavior of one-dimensional granular clusters and one-particle granular gases for a variety of velocity dependent coefficients of restitution $r$. We obtain equations describing of the long time behavior for the…
Active matter systems provide fascinating examples of pattern formation and collective motility without counterparts in equilibrium systems. Here, we employ Brownian dynamics simulations to study the collective motion and self-organization…
In fully-dynamic consistent clustering, we are given a finite metric space $(M,d)$, and a set $F\subseteq M$ of possible locations for opening centers. Data points arrive and depart, and the goal is to maintain an approximately optimal…
We simulate the dynamics of fractal star clusters, in order to investigate the evolution of substructure in recently formed clusters. The velocity dispersion is found to be the key parameter determining the survival of substructure. In…
We study the dynamics and clustering of dust particles with inertia in shock-dominated compressible turbulence using the two-dimensional, stochastically forced Burgers equation. At small Stokes numbers, shock trapping leads to extreme…
Understanding how stick-slip dynamics manifests in diverse physical conditions is a crucial topic in tribology. Although it has been extensively studied in simple frictional configurations, the characterization of stick-slip behavior in…
The notion of `adhesion' has been advanced for the phenomenon of stabilization of large-scale structure emerging from gravitational instability of a cold medium. Recently, the physical origin of adhesion has been identified: a systematic…
The stochastic scenario of relaxation in the complex systems is presented. It is based on a general probabilistic formalism of limit theorems. The nonexponential relaxation is shown to result from the asymptotic self-similar properties in…
We present a simplified dynamical model of the ``Bullet'' system of two colliding clusters. The model constrains the masses of the system by requiring that the orbits of the main and sub components satisfy the cosmological initial…
Contact between fluctuating, fluid-lubricated soft surfaces is prevalent in engineering and biological systems, a process starting with adhesive contact, which can give rise to complex coarsening dynamics. One representation of such a…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
We consider one-dimensional systems of self-gravitating sticky particles with random initial data and describe the process of aggregation in terms of the largest cluster size L_n at any fixed time prior to the critical time. The asymptotic…
Mixed positive and negative feedback loops are often found in biological systems which support oscillations. In this work we consider a prototype of such systems, which has been recently found at the core of many genetic circuits showing…
We compare the slow dynamics of irreversible gels, colloidal gels, glasses and spin glasses by analyzing the behavior of the so called non-linear dynamical susceptibility, a quantity usually introduced to quantitatively characterize the…