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This paper introduces stochastic processes that describe the evolution of systems of particles in which particles immigrate according to a Poisson measure and split according to a self-similar fragmentation. Criteria for existence and…

Probability · Mathematics 2007-05-23 Benedicte Haas

We derive the fully time-dependent solution to a run-and-tumble model for a particle which has tumbling restricted to the boundaries of a one-dimensional interval. This is achieved through a field-theoretic perturbative framework by…

Statistical Mechanics · Physics 2025-08-06 Connor Roberts , Gunnar Pruessner

The existence of stationary radial solutions to a partial differential equation arising in the theory of epitaxial growth is studied. Our results depend on the size of a parameter that plays the role of the velocity at which mass is…

Classical Analysis and ODEs · Mathematics 2015-06-17 Carlos Escudero , Robert Hakl , Ireneo Peral , Pedro J. Torres

In this paper, we construct under general assumptions the stochastic dynamics of an interacting particle system in a bounded domain $\Omega$ with sticky boundary. Under appropriate conditions on the interaction the constructed process…

Probability · Mathematics 2015-08-12 Robert Voßhall

We propose an open-boundary molecular dynamics method in which an atomistic system is in contact with an infinite particle reservoir at constant temperature, volume and chemical potential. In practice, following the Hamiltonian adaptive…

Statistical Mechanics · Physics 2020-06-24 Maziar Heidari , Kurt Kremer , Ramin Golestanian , Raffaello Potestio , Robinson Cortes-Huerto

We study semi-infinite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction…

Probability · Mathematics 2024-12-20 Mikhail Menshikov , Serguei Popov , Andrew Wade

We study statistical properties of a one dimensional infinite system of coalescing particles. Each particle moves with constant velocity $\pm v$ towards its closest neighbor and merges with it upon collision. We propose a mean-field theory…

Statistical Mechanics · Physics 2015-06-25 S. Ispolatov , P. L. Krapivsky

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,…

Functional Analysis · Mathematics 2022-04-21 Adam Bobrowski , Tomasz Komorowski

We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under…

Probability · Mathematics 2021-07-21 Watthanan Jatuviriyapornchai , Stefan Grosskinsky

We investigate a diffusive motion of a system of interacting Brownian particles in quasi-one-dimensional micropores. In particular, we consider a semi-infinite 1D geometry with a partially absorbing boundary and the hard-core inter-particle…

Statistical Mechanics · Physics 2012-03-06 Artem Ryabov , Petr Chvosta

We consider an interacting particle system on the one dimensional lattice $\bf Z$ modeling combustion. The process depends on two integer parameters $2\le a<M<\infty$. Particles move independently as continuous time simple symmetric random…

Probability · Mathematics 2016-09-07 Francis Comets , Jeremy Quastel , Alejandro F. Ramirez

We study finite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which…

Probability · Mathematics 2024-05-07 Vadim Malyshev , Mikhail Menshikov , Serguei Popov , Andrew Wade

Boundary-catalytic branching processes describe a broad class of natural phenomena where the population of diffusing particles grows due to their spontaneous binary branching (e.g., division, fission or splitting) on a catalytic boundary…

Statistical Mechanics · Physics 2026-03-05 Denis S. Grebenkov , Yilin Ye

We consider an infinite system of coupled stochastic differential equations (SDE) describing dynamics of the following infinite particle system. Each partricle is characterised by its position $x\in \mathbb{R}^{d}$ and internal parameter…

Functional Analysis · Mathematics 2025-02-21 Georgy Chargaziya , Alexei Daletskii

We consider a model system of persistent random walkers that can jam, pass through each other or jump apart (recoil) on contact. In a continuum limit, where particle motion between stochastic changes in direction becomes deterministic, we…

Statistical Mechanics · Physics 2023-05-03 Matthew J Metson , Martin R Evans , Richard A Blythe

We study a system of branching Brownian motions on $\mathbb R$ with annihilation: at each branching time a new particle is created and the leftmost one is deleted. In [7] it has been studied the case of strictly local creations (the new…

Probability · Mathematics 2017-11-27 A. De Masi , P. A. Ferrari , E. Presutti , N. Soprano-Loto

We study a general class of interacting particle systems over a countable state space $V$ where on each site $x \in V$ the particle mass $\eta(x) \geq 0$ follows a stochastic differential equation. We construct the corresponding Markovian…

Probability · Mathematics 2023-08-16 Viktor Bezborodov , Luca Di Persio , Martin Friesen , Peter Kuchling

We consider systems of n particles that move with constant velocity between collisions. Their total momentum but not necessarily their kinetic energy is preserved at collisions. As there are no further constraints, these systems are…

Mathematical Physics · Physics 2024-11-07 Andreas Knauf , Manuel Quaschner

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…

Probability · Mathematics 2007-05-23 Matteo Ortisi

An active Brownian particle is a minimal model for a self-propelled colloid in a dissipative environment. Experiments and simulations show that, in the presence of boundaries and obstacles, active Brownian particle systems approach…

Soft Condensed Matter · Physics 2024-01-17 Caleb G. Wagner , Michael F. Hagan , Aparna Baskaran