Related papers: Attractive n-type contact processes

We show that attractive, translation invariant, one-dimensional spin systems started from the unit step function possess the following basic property. At any time, the entire configuration from a point onward is stochastically decreasing…

Properties of a contact process in continuum for a system of two type particles one type of which is independent are considered. We study dynamics of the first and second order correlation functions, their asymptotics and dependence on…

We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…

Maximal monotonicity is explored as a generalization of the linear theory of passivity, aiming at an algorithmic input/output analysis of physical models. The theory is developed for maximal monotone one-port circuits, formed by the series…

We study stochastic particle systems made up of heterogeneous units. We introduce a general framework suitable to analytically study this kind of systems and apply it to two particular models of interest in economy and epidemiology. We show…

We discuss a simple model of particles hopping in one dimension with attractive interactions. Taking a hydrodynamic limit in which the interaction strength increases with the system size, we observe the formation of multiple clusters of…

We consider a new class of interacting particle systems with a countable number of interacting components. The system represents the time evolution of the membrane potentials of an infinite set of interacting neurons. We prove the existence…

The theory of monotone dynamical systems has been found very useful in the modeling of some gene, protein, and signaling networks. In monotone systems, every net feedback loop is positive. On the other hand, negative feedback loops are…

This thesis uses a quantity that is defined and justified by information theory -- mutual information -- to examine models of condensed matter systems. More precisely, it studies models which are made up out of ferromagnetically interacting…

In this paper we consider an interacting particle system modeled as a system of $N$ stochastic differential equations driven by Brownian motions with a drift term including a confining potential acting on each particle, and an interaction…

Complex (dusty) plasmas allow experimental studies of various physical processes occurring in classical liquids and solids by directly observing individual microparticles. A major problem is that the interaction between microparticles is…

In this paper, plane polynomial systems having a singular point attracting all orbits in positive time are classified up to topological equivalence. This is done by assigning a combinatorial invariant to the system (a so-called "feasible…

We address a fundamental issue in the nonparametric inference for systems of interacting particles: the identifiability of the interaction functions. We prove that the interaction functions are identifiable for a class of first-order…

An infinite system of neutrons interacting by a model pair potential is considered. We investigate a case when this potential is sufficiently strong attractive, so that its scattering length tends to infinity. It appeared, that if the…

Attractors of cooperative dynamical systems are particularly simple; for example, a nontrivial periodic orbit cannot be an attractor. This paper provides characterizations of attractors for the wider class of coherent systems, defined by…

Colloidal particles are not simple rigid particles, in general an isolated particle is a system with many degrees of freedom in its own right, e.g., the counterions around a charged colloidal particle.The behaviour of model colloidal…

In this paper we show that a variety of interacting particle systems with multiple species can be viewed as random walks on Hecke algebras. This class of systems includes the asymmetric simple exclusion process (ASEP), M-exclusion TASEP,…

The coupled dynamics of entangled polymers which span a broad time and length scales govern the unique viscoelastic properties of polymers. To follow chain mobility by numerical simulations from the intermediate Rouse and reptation regimes…

A probabilistic Markov Chain (MC) surrogate model for a two-dimensional system of interacting particles within a square domain having inherent symmetries is developed. Particles are assumed to be circular and identical, colliding with each…

The integrability of one dimensional quantum mechanical many-body problems with general contact interactions is extensively studied. It is shown that besides the pure (repulsive or attractive) $\delta$-function interaction there is another…