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An Ornstein-Uhlenbeck (OU) process can be considered as a continuous time interpolation of the discrete time AR$(1)$ process. Departing from this fact, we analyse in this work the effect of iterating OU treated as a linear operator that…

Statistics Theory · Mathematics 2012-10-02 Argimiro Arratia , Alejandra Cabaña , Enrique M. Cabaña

The transport of independent active Brownian particles within a two-dimensional narrow channel, modeled as an open-wedge, is studied both numerically and theoretically. We show that the active force tends to localize the particles near the…

Statistical Mechanics · Physics 2019-05-01 Lorenzo Caprini , Fabio Cecconi , Umberto Marini Bettolo Marconi

The change of the structure of concentrated colloidal suspensions upon addition of non-adsorbing polymer is studied within a two-component, Ornstein-Zernicke based liquid state approach. The polymers' conformational degrees of freedom are…

Soft Condensed Matter · Physics 2009-10-31 M. Fuchs , K. S. Schweizer

We consider an inertial active Ornstein-Uhlenbeck particle self-propelling in a saw-tooth ratchet potential. Using the Langevin simulation and matrix continued fraction method, the particle transport, steady state diffusion, and coherence…

Soft Condensed Matter · Physics 2022-11-30 M Muhsin , M Sahoo

We report the results of a numerical study of nonequilibrium steady states for a class of Hamiltonian models. In these models of coupled matter-energy transport, particles exchange energy through collisions with pinned-down rotating disks.…

Statistical Mechanics · Physics 2015-05-18 Kevin K. Lin , Lai-Sang Young

In this paper, we analyze the use of the Ornstein-Uhlenbeck process to model dynamical systems subjected to bounded noisy perturbations. In order to discuss the main characteristics of this new approach we consider some basic models in…

Dynamical Systems · Mathematics 2024-01-17 Tomás Caraballo , Renato Colucci , Javier López-de-la-Cruz , Alain Rapaport

Direct Monte Carlo simulations of the Enskog-Boltzmann equation for a spatially uniform system of smooth inelastic spheres are performed. In order to reach a steady state, the particles are assumed to be under the action of an external…

Statistical Mechanics · Physics 2016-08-31 J. M. Montanero , A. Santos

New model equations are derived for dynamics of self-aggregation of finite-size particles. Differences from standard Debye-Huckel and Keller-Segel models are: the mobility of particles depends on the configuration of their neighbors and…

Pattern Formation and Solitons · Physics 2009-11-11 Darryl D. Holm , Vakhtang Putkaradze

An exact description of the statistical motion of active particles in three dimension is presented in the framework of a generalized diffusion equation. Such a generalization contemplates a non-local, in time and space, connecting (memory)…

Statistical Mechanics · Physics 2023-07-20 Francisco J Sevilla

We consider the statistical motion of a convex rigid body in a gas of N smaller (spherical) atoms close to thermodynamic equilibrium. Because the rigid body is much bigger and heavier, it undergoes a lot of collisions leading to small…

Analysis of PDEs · Mathematics 2018-07-04 Thierry Bodineau , Isabelle Gallagher , Laure Saint-Raymond

Actively propelled particles undergoing dissipative collisions are known to develop a state of spatially distributed coherently moving clusters. For densities larger than a characteristic value clusters grow in time and form a stationary…

Soft Condensed Matter · Physics 2013-04-23 Christoph A. Weber , Florian Thüroff , Erwin Frey

A droplet bouncing on a liquid bath can self-propel due to its interaction with the waves it generates. The resulting "walker" is a dynamical association where, at a macroscopic scale, a particle (the droplet) is driven by a pilot-wave…

Soft Condensed Matter · Physics 2013-07-24 Emmanuel Fort , Antonin Eddi , Arezki Boudaoud , Julien Moukhtar , Yves Couder

We simulate by lattice Boltzmann the nonequilibrium steady states of run-and-tumble particles (inspired by a minimal model of bacteria), interacting by far-field hydrodynamics, subject to confinement. Under gravity, hydrodynamic…

Statistical Mechanics · Physics 2010-07-01 R. W. Nash , R. Adhikari , J. Tailleur , M. E. Cates

Active particles in anisotropic, viscoelastic fluids experience competing stresses which guide their trajectories. An aligned suspension of particles can trigger a hydrodynamic bend instability, but the elasticity of the fluid can drive…

Soft Condensed Matter · Physics 2025-06-10 Jingyi Li , Laurel Ohm , Saverio E. Spagnolie

We study interacting active Brownian particles (ABPs) with a space-dependent swim velocity via simulation and theory. We find that, although an equation of state exists, a mechanical equilibrium does not apply to ABPs in activity…

Soft Condensed Matter · Physics 2024-12-13 Adam Wysocki , Anil K. Dasanna , Heiko Rieger

Energetic particles interact with the plasma surrounding them, resonating with certain plasma waves to stabilize them while destabilizing others, and changing the character of the background turbulence in ways that have not been fully…

High Energy Astrophysical Phenomena · Physics 2026-01-27 J. Pratt

Active particles are non-equilibrium entities that uptake energy and convert it into self-propulsion. A dynamically rich class of inertial active particles having features of wave-particle coupling and wave memory are walking/superwalking…

Soft Condensed Matter · Physics 2026-03-03 Rahil N. Valani , David M. Paganin

We consider a particle with a position-dependent mass, moving in a three-dimensional semi-infinite parallelepipedal or cylindrical channel under the influence of some hyperbolic potential. We show that the lack of uniformity in the…

Quantum Physics · Physics 2007-05-23 C. Quesne

We compare theoretical and simulation results for static and dynamic properties for a model of particles interacting via a spherically symmetric repulsive ramp potential. The model displays anomalies similar to those found in liquid water,…

Statistical Mechanics · Physics 2009-11-10 Pradeep Kumar , Sergey V. Buldyrev , Francesco Sciortino , Emanuela Zaccarelli , H. Eugene Stanley

We evidence a Kovacs-like memory effect in a uniformly driven granular gas. A system of inelastic hard particles, in the low density limit, can reach a non-equilibrium steady state when properly forced. By following a certain protocol for…

Statistical Mechanics · Physics 2016-11-17 E. Trizac , A. Prados