Overdamped 2D Brownian motion for self-propelled and nonholonomic particlesReport as inadecuate

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* Corresponding author 1 E-MOTION - Geometry and Probability for Motion and Action Inria Grenoble - Rhône-Alpes, LIG - Laboratoire d-Informatique de Grenoble

Abstract : This paper provides a complete analytical solution to the Brownianmotion of a self-propelled particle that moves in two spatial dimensions in theoverdamped limit by satisfying kinematic constraints. The analytical expression ofany-order moment of the probability distribution is obtained by a direct integration ofthe Langevin equation. Each moment is expressed as a multiple integral of the activemotion performed by the particle. This allows obtaining any order moment for anyactive motion, i.e., when the particle is propelled by arbitrary time-dependent forceand torque. For the special case when the ratio between the force and the torqueis constant, the multiple integrals can be easily analytically solved and expressed asthe real or the imaginary part of suitable analytic functions. As an application ofthe derived analytical results, the paper investigates the di usivity of the consideredBrownian motion for constant and for arbitrary time-dependent force and torque.

Author: Agostino Martinelli -

Source: https://hal.archives-ouvertes.fr/


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