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DY: Fachverband Dynamik und Statistische Physik

DY 41: Statistical Physics: General

DY 41.3: Vortrag

Donnerstag, 21. März 2024, 10:00–10:15, BH-N 128

Stochastically driven motion under nonlinear, Coulomb-tanh friction — a basic representation of the consequences of shear thinning — Theo Lequy¹ and •Andreas M. Menzel² — ¹Eidgenössische Technische Hochschule Zürich, Rämistrasse 101, 8092 Zürich, Switzerland — ²Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany

Nonlinear friction is abundant in nearly all kinds of scenarios of relative motion. We here consider the stochastically driven dynamics of an object that is subject to the so-called Coulomb-tanh friction force [1]. This force increases linearly with speed at small magnitudes of the velocity and levels off at a constant value at large speeds. In this way, it interpolates between linear and solid (dry, Coulomb) friction. Under such conditions, in the case of one-dimensional motion, we find that the velocity spectrum can be found by formally linking the mathematical description to a Schrödinger equation including a Pöschl-Teller potential. Thus, an analytical approach is possible. We consider the velocity and displacement statistics of individual objects and find intermediate non-Gaussian tails in the spatial distribution function that are pushed outward over time. Both limits of linear and solid (dry, Coulomb) friction are well reproduced. For instance, our description should apply to the case of an object driven on a vibrated substrate covered by a layer of shear-thinning material that leads to the mentioned nonlinear friction.
[1] Theo Lequy, Andreas M. Menzel (submitted).

Keywords: nonlinear friction; stochastic motion; shear thinning; velocity statistics; displacement statistics