Asymptotic analysis of mode-coupling theory of active nonlinear microrheology

Journal article (2012)

Authors

M.V. Gnann Max Planck Institute for Mathematics in the Sciences, Universität Konstanz
Th Voigtmann Universität Konstanz, Deutsches Zentrum für Luft- und Raumfahrt (DLR)
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Published Date

23-07-2012

Language

English

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Abstract

We discuss a schematic model of mode-coupling theory for force-driven active nonlinear microrheology, where a single probe particle is pulled by a constant external force through a dense host medium. The model exhibits both a glass transition for the host and a force-induced delocalization transition, where an initially localized probe inside the glassy host attains a nonvanishing steady-state velocity by locally melting the glass. Asymptotic expressions for the transient density correlation functions of the schematic model are derived, valid close to the transition points. There appear several nontrivial time scales relevant for the decay laws of the correlators. For the nonlinear friction coefficient of the probe, the asymptotic expressions cause various regimes of power-law variation with the external force, and two-parameter scaling laws.