36,119 research outputs found
Active Brownian particles with velocity-alignment and active fluctuations
We consider a model of active Brownian particles with velocity-alignment in
two spatial dimensions with passive and active fluctuations. Hereby, active
fluctuations refers to purely non-equilibrium stochastic forces correlated with
the heading of an individual active particle. In the simplest case studied
here, they are assumed as independent stochastic forces parallel (speed noise)
and perpendicular (angular noise) to the velocity of the particle. On the other
hand, passive fluctuations are defined by a noise vector independent of the
direction of motion of a particle, and may account for example for thermal
fluctuations.
We derive a macroscopic description of the active Brownian particle gas with
velocity-alignment interaction. Hereby, we start from the individual based
description in terms of stochastic differential equations (Langevin equations)
and derive equations of motion for the coarse grained kinetic variables
(density, velocity and temperature) via a moment expansion of the corresponding
probability density function.
We focus here in particular on the different impact of active and passive
fluctuations on the onset of collective motion and show how active fluctuations
in the active Brownian dynamics can change the phase-transition behaviour of
the system. In particular, we show that active angular fluctuation lead to an
earlier breakdown of collective motion and to emergence of a new bistable
regime in the mean-field case.Comment: 5 figures, 22 pages, submitted to New Journal of Physic
A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales
In this work it is shown how the immersed boundary method of (Peskin2002) for
modeling flexible structures immersed in a fluid can be extended to include
thermal fluctuations. A stochastic numerical method is proposed which deals
with stiffness in the system of equations by handling systematically the
statistical contributions of the fastest dynamics of the fluid and immersed
structures over long time steps. An important feature of the numerical method
is that time steps can be taken in which the degrees of freedom of the fluid
are completely underresolved, partially resolved, or fully resolved while
retaining a good level of accuracy. Error estimates in each of these regimes
are given for the method. A number of theoretical and numerical checks are
furthermore performed to assess its physical fidelity. For a conservative
force, the method is found to simulate particles with the correct Boltzmann
equilibrium statistics. It is shown in three dimensions that the diffusion of
immersed particles simulated with the method has the correct scaling in the
physical parameters. The method is also shown to reproduce a well-known
hydrodynamic effect of a Brownian particle in which the velocity
autocorrelation function exhibits an algebraic tau^(-3/2) decay for long times.
A few preliminary results are presented for more complex systems which
demonstrate some potential application areas of the method.Comment: 52 pages, 11 figures, published in journal of computational physic
Levy--Brownian motion on finite intervals: Mean first passage time analysis
We present the analysis of the first passage time problem on a finite
interval for the generalized Wiener process that is driven by L\'evy stable
noises. The complexity of the first passage time statistics (mean first passage
time, cumulative first passage time distribution) is elucidated together with a
discussion of the proper setup of corresponding boundary conditions that
correctly yield the statistics of first passages for these non-Gaussian noises.
The validity of the method is tested numerically and compared against
analytical formulae when the stability index approaches 2, recovering
in this limit the standard results for the Fokker-Planck dynamics driven by
Gaussian white noise.Comment: 9 pages, 13 figure
- …