Related papers: Attractive n-type contact processes
Systems of classical continuous particles in the grand canonical ensemble interacting through purely attractive, yet stable, interactions are defined. By a lattice approximation, FKG ferromagnetic inequalities are shown to hold for such…
The style of mathematical models known to probabilists as Interacting Particle Systems and exemplified by the Voter, Exclusion and Contact processes have found use in many academic disciplines. In many such disciplines the underlying…
An approach to analyse the properties of a particle system is to compare it with different processes to understand when one of them is larger than other ones. The main technique for that is coupling, which may not be easy to construct. We…
We present our recent work on stochastic particle systems on complex networks. As a noninteracting system we first consider the diffusive motion of a random walker on heterogeneous complex networks. We find that the random walker is…
Studying systems where many individual bodies in motion interact with one another is a complex and interesting area. Simple mechanisms that may be determined for biological, chemical, or physical reasons can lead to astonishingly complex…
Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary…
An infinite system of point particles placed in $\mathds{R}^d$ is studied. The particles are of two types; they perform random walks in the course of which those of distinct types repel each other. The interaction of this kind induces an…
We consider a class of multi-layer interacting particle systems and characterize the set of ergodic measures with finite moments. The main technical tool is duality combined with successful coupling.
The duality theory for monotone interacting particle systems was initiated by Gray (1986) and further developed by Sturm and Swart (2018). It contains the better known additive duality as a special case but differs in the sense that the…
Active matter deals with systems whose particles consume energy at the individual level in order to move. To unravel features such as the emergence of collective structures several models have been suggested, such as the on-lattice model of…
Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary…
These lecture notes give an introduction to the theory of interacting particle systems. The main subjects are the construction using generators and graphical representations, the mean field limit, stochastic order, duality, and the relation…
Interaction is so ubiquitous that imaging a world free from it is a difficult fantasy exercise. At the same time, in understanding any complex physical system, our ability of accounting for the mutual interaction of its constituents is…
A discrete time stochastic model for a multiagent system given in terms of a large collection of interacting Markov chains is studied. The evolution of the interacting particles is described through a time inhomogeneous transition…
Using molecular dynamic simulations we study a system of particles interacting through a continuous core-softened potentials consisting of a hard core, a shoulder at closest distances and an attractive well at further distance. We obtain…
We study a system of $N$ interacting particles on $\bf{Z}$. The stochastic dynamics consists of two components: a free motion of each particle (independent random walks) and a pair-wise interaction between particles. The interaction belongs…
Controlling interactions out of thermodynamic equilibrium is crucial for designing addressable and functional self-organizing structures. These active interactions also underpin collective behavior in biological systems. Here we study a…
We study N interacting random walks on the positive integers. Each particle has drift {\delta} towards infinity, a reflection at the origin, and a drift towards particles with lower positions. This inhomogeneous mean field system is shown…
We have studied quasi one-dimensional few-particle systems consisting of one to six ultracold fermionic atoms in two different spin states with attractive interactions. We probe the system by deforming the trapping potential and by…
We numerically studied active Brownian particles with attractive interactions. Contrary to our intuition, the attractive force between particles disrupts the formation of a single cluster observed in motility-induced phase separation,…