Related papers: Revisiting the Contact Model with Diffusion Beyond…
The long-time dynamics of the critical contact process which is brought suddenly out of an uncorrelated initial state undergoes ageing in close analogy with quenched magnetic systems. In particular, we show through Monte Carlo simulations…
Model-based reinforcement learning methods often use learning only for the purpose of estimating an approximate dynamics model, offloading the rest of the decision-making work to classical trajectory optimizers. While conceptually simple,…
The earlier times of evolution of a magnetic system contain more information than we can imagine. Capturing correlation matrices G of different time evolutions of a simple testbed spin system, as the Ising model, we analyzed the density of…
The one-dimensional kinetic contact process with parallel update is introduced and studied by Monte Carlo simulations. This process is proposed to describe the plant population replication and epidemic disease spreading among them. The…
Using Monte Carlo simulations, we show that for a certain model of biological evolution, which is driven by non-extremal dynamics, active and absorbing phases are separated by a critical phase. In this phase both the density of active sites…
We investigate the diffusive motion of an overdamped classical particle in a 1D random potential using the mean first-passage time formalism and demonstrate the efficiency of this method in the investigation of the large-time dynamics of…
We study a diffusion approximation for a model of stochastic motion of a particle in one spatial dimension. The velocity of the particle is constant but the direction of the motion undergoes random changes with a Poisson clock. Moreover,…
We study a contact process running in a random environment in $\mathbb {Z}^d$ where sites flip, independently of each other, between blocking and nonblocking states, and the contact process is restricted to live in the space given by…
We propose an interacting particle system to model the evolution of a system of banks with mutual exposures. In this model, a bank defaults when its normalized asset value hits a lower threshold, and its default causes instantaneous losses…
A Non-Markovian generalization of one-dimensional Contact Process (CP) is being introduced in which every particle has an age and will be annihilated at its maximum age $\tau$. There is an absorbing state phase transition which is…
Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed. We trace this consistency to a simple linear effect: the shared Gaussian statistics across…
In the so-called "microscopic" models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a "particle"; the nature of the "interactions" among these particles is determined by the…
In the present paper, we study the relation between criticality and information transmission in the one-dimensional contact process with infection parameter $\lambda .$ To do this we define the {\it sensitivity} of the process to its…
Collisions and contacts of elastic materials are numerically and theoretically investigated. Using a two-dimensional spring-mass model with defect particles under the free boundary condition, we reproduce the Hertzian contact theory at…
We review a recently devised Monte Carlo simulation method for the direct study of quasi-stationary properties of stochastic processes with an absorbing state. The method is used to determine the static correlation function and the…
This paper introduces a modeling framework that is suitable to resolve singularities of impact phenomena encountered in applications. The method involves an exact transformation that turns the continuum, often partial differential equation…
This paper uses dynamical invariants to describe the evolution of collisionless systems subject to time-dependent gravitational forces without resorting to maximum-entropy probabilities. We show that collisionless relaxation can be viewed…
Spreading from a seed is studied by Monte Carlo simulation on a square lattice with two types of sites affecting the rates of birth and death. These systems exhibit a critical transition between survival and extinction. For time- dependent…
We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical…
Stochastic reaction-diffusion models are employed to represent many complex physical, biological, societal, and ecological systems. The macroscopic reaction rates describing the large-scale kinetics in such systems are effective,…