Related Experiment Video
Updated: Aug 24, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
Stationary motion of active Brownian particles
1Department of Biomedical Engineering, Zhejiang University, 310027 Hangzhou, China. zjudeng@yahoo.com.cn
Abstract:
The stationary motion of active Brownian particles is studied by using the stochastic averaging method for quasi-integrable Hamiltonian systems. First the stochastic averaging method for quasi-integrable Hamiltonian systems is briefly introduced. Then the stationary solution of the dynamic equations governing an active Brown particle in plane with the Rayleigh velocity-dependent friction model subject to Gaussian white noise excitations is obtained by using the stochastic averaging method. The solution is validated by comparison with the result from Monte Carlo simulation. Finally, two more stationary solutions of the dynamic equations governing active Brownian particle with the Schienbein-Gruler and Erdmann velocity-dependent friction models, respectively, subject to Gaussian white noise excitations are also given.
Related Concept Videos
Planar Rigid-Body Motion
Planar motion is typically divided into three distinct categories. The first is rectilinear translation, demonstrated by a subway train that moves along...
Motion Of A Charged Particle In A Magnetic Field
Simple Harmonic Motion and Uniform Circular Motion
There is an easy way to produce simple harmonic motion by using uniform circular motion. For instance, consider a ball attached to a uniformly rotating...
Equilibrium Conditions for a Particle
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
First Law: Particles in Two-dimensional Equilibrium
Newton's first law tells us about the...
First Law: Particles in One-dimensional Equilibrium

