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While active matter physics has traditionally focused on particles with overdamped dynamics, recent years have seen an increase of experimental and theoretical work on active systems with inertia. This also leads to an increased need for…

Statistical Mechanics · Physics 2026-02-13 Michael te Vrugt

We perform a coarse-graining analysis of the paradigmatic active matter model, Active Brownian Particles, yielding a continuum description in terms of balance laws for mass, linear and angular momentum, and energy. The derivation of the…

Soft Condensed Matter · Physics 2019-04-30 Jeffrey M. Epstein , Katherine Klymko , Kranthi K. Mandadapu

We derive the hydrodynamic equations of motion for a fluid of active particles described by under- damped Langevin equations that reduce to the Active-Brownian-Particle model, in the overdamped limit. The contraction into the hydrodynamic…

Statistical Mechanics · Physics 2017-06-07 Stefano Steffenoni , Gianmaria Falasco , Klaus Kroy

This paper makes a rigorous case for considering the homogenized continuum derived by the Irving-Kirkwood procedure as a polar medium in which the balances of angular momentum and energy contain contributions due to body couples and couple…

Classical Physics · Physics 2021-06-10 Kranthi K. Mandadapu , B. Emek Abali , Panayiotis Papadopoulos

We present a mesoscopic hydrodynamic description of the dynamics of colloidal suspensions. We consider the system as a gas of Brownian particles suspended in a Newtonian heat bath subjected to stationary non-equilibrium conditions imposed…

Statistical Mechanics · Physics 2009-11-11 S. I. Hernandez , I. Santamaria-Holek , Carlos I. Mendoza , L. F. del Castillo

The classical theory of Brownian dynamics follows from coarse-graining the underlying linearized fluctuating hydrodynamics of the solvent. We extend this procedure to globally non-isothermal conditions, requiring only a local thermal…

Statistical Mechanics · Physics 2016-04-06 G. Falasco , K. Kroy

The force per unit area on the surface of a colloidal particle is a fundamental dynamical quantity in the mechanics and statistical mechanics of colloidal suspensions. Here we compute it in the limit of slow viscous flow for a suspension of…

Soft Condensed Matter · Physics 2018-02-21 Rajesh Singh , R. Adhikari

In the high persistence regime of non-inertial active Brownian particles (ABP), polarization becomes a relevant dynamical field. Based on a recently proposed kinetic description for ABP, we derive Navier-Stokes-like equations for the…

Soft Condensed Matter · Physics 2025-10-21 Martín Pinto-Goldberg , Rodrigo Soto

Active matter describes systems whose constituents convert energy from their surroundings into directed motion, such as bacteria or catalytic colloids. We establish a thermodynamic law for dilute suspensions of interacting active particles…

Statistical Mechanics · Physics 2025-07-22 Lennart Dabelow , Ralf Eichhorn

Active Brownian motion commonly assumes spherical overdamped particles. However, self-propelled particles are often neither symmetric nor overdamped yet underlie random fluctuations from their surroundings. Active Brownian motion has…

Soft Condensed Matter · Physics 2022-10-03 Jonas Mayer Martins , Raphael Wittkowski

Active matter concerns many-body systems comprised of living or self-driven agents that collectively exhibit macroscopic phenomena distinct from conventional passive matter. Using Schwinger-Keldysh effective field theory, we develop a novel…

Soft Condensed Matter · Physics 2025-11-07 Jay Armas , Akash Jain , Ruben Lier

We present a general theory for determining the force (and torque) exerted on a boundary (or body) in active matter. The theory extends the description of passive Brownian colloids to self-propelled active particles and applies for all…

Soft Condensed Matter · Physics 2023-07-19 Wen Yan , John F. Brady

A nonequilibrium fluctuation theorem is established for a colloidal particle driven by an external force within the hydrodynamic theory of Brownian motion, describing hydrodynamic memory effects such as the t^(-3/2) power-law decay of the…

Statistical Mechanics · Physics 2020-06-24 Pierre Gaspard

In the last decade, the study of pressure in active matter has attracted growing attention due to its fundamental relevance to nonequilibrium statistical physics. Active matter systems are composed of particles that consume energy to…

Soft Condensed Matter · Physics 2025-08-14 Guo Yu , Ruiyao Li , Fukang Li , Jiayu Zhang , Xiyue Li , Zequ Chen , Joscha Mecke , Yongxiang Gao

The collective non-equilibrium dynamics of multi-component mixtures of interacting active (self-propelled) and passive (diffusive) particles have garnered great interest in the physics community. However, the mathematical understanding of…

Probability · Mathematics 2025-01-28 Deyue Li

We develop a general hydrodynamic theory describing a system of interacting actively propelling particles of arbitrary shape suspended in a viscous fluid. We model the active part of the particle motion using a slip velocity prescribed on…

Fluid Dynamics · Physics 2019-01-15 Bhargav Rallabandi , Fan Yang , Howard A. Stone

We discuss a minimal generalization of the incompressible Navier-Stokes equations to describe the solvent flow in an active suspension. To account phenomenologically for the presence of an active component driving the ambient fluid flow, we…

Soft Condensed Matter · Physics 2015-04-10 Jonasz Słomka , Jörn Dunkel

The stress of a fluid on a confining wall is given by the mechanical wall forces, independent of the nature of the fluid being passive or active. At thermal equilibrium, an equation of state exists and stress is likewise obtained from…

Soft Condensed Matter · Physics 2024-06-03 Shibananda Das , Gerhard Gompper , Roland G. Winkler

We derive the Hydrodynamics for a system of N active, spherical, underdamped particles, interacting through conservative forces. At the microscopic level, we represent the evolution of the particles in terms of the Kramers equation for the…

Statistical Mechanics · Physics 2022-03-15 Umberto Marini Bettolo Marconi , Andrea Puglisi , Lorenzo Caprini

A general set of fluid equations that allow for energy-conserving momentum transport by gyroscopic motion of fluid elements is obtained. The equations are produced by a class of action principles that yield a large subset of the known fluid…

Plasma Physics · Physics 2015-06-22 M. Lingam , P. J. Morrison
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