Regensburg 2016 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 45: Brownian Motion and Transport

DY 45.1: Vortrag

Mittwoch, 9. März 2016, 16:30–16:45, H46

Velocity and displacement statistics under nonlinear friction showing bounded particle speed — •Andreas M. Menzel — Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany

Often, models on the stochastic motion of colloidal particles in a surrounding fluid assume linear "viscous" friction. This case can be solved analytically for free Brownian motion of non-interacting particles.

A prominent example of nonlinear friction is given by "dry" friction of the Coulomb type. In this case, the friction always shows the same magnitude as soon as the particle is in motion. Stochastic models using this type of friction were broadly analyzed over the past few years using different technical tools.

In the present contribution, we introduce a different type of nonlinear friction. It increases linearly with the velocity at low particle speed; it increases more than linearly at higher speeds; finally, it diverges at a certain maximum particle speed. Both, velocity and displacement statistics, are evaluated under stochastic motion in one dimension using the Fokker-Planck approach. For a specific value of the maximum particle speed, significant analytical progress can be made, revealing a formal connection to the Schrödinger equation for an infinite square-well potential. The mean-squared displacement is found to still increase linearly in time, while higher-order moments signal non-Gaussian displacement statistics. Using elements from quantum-mechanical perturbation theory, the influence of an additional drift force is included. Our description should apply for the stochastic motion in shear-thickening environments, possibly starch suspensions.