Mean-field dynamics of particle systems: global shear versus random local forcing

27.10.2020 16:00 – 17:00

Amorphous materials are ubiquitous around us: emulsions as mayonnaise, foams, sandpiles or biological tissues are all structurally disordered, and this has key implications for their response to an external deformation. Nevertheless, theoretical descriptions of such ‘driven' amorphous materials remain challenging, despite of decades of extensive analytical and computational studies. The difficulties pertain to the interplay of competing sources of stochasticity, and to the resulting out-of-equilibrium nature of these systems. A standard model for amorphous materials, which allows to focus on the key role of their structural (positional) disorder, is provided by dense many-body systems of pairwise interacting particles. In infinite dimension, these systems even provide exact analytical benchmarks for quasistatic features of amorphous materials, such as their response under quasistatic shear.

Here I will discuss recent results on the exact mean-field dynamics of these many-body systems, that we have derived in the limit of infinite spatial dimension, for different driving protocols. We were in particular able to establish a direct equivalence between a global forcing (external shear) and a random local forcing (reminiscent of active matter), upon a simple rescaling of the control parameter (the accumulated strain). In this framework, global shear is thus simply a special case of a much broader family of local forcing, that can be explored by tuning its spatial correlations. Our predictions were moreover found to be in remarkably good agreement with two-dimensional numerical simulations. These results hint at a unifying framework for establishing rigourous analogies, at the mean-field level, between different families driven disordered systems, such as sheared granular materials and active matter.

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Bâtiment: Ecole de Physique

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