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Résumé |
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. Furthermore, there has been recently many attempts to
relate the important corpus of known results for such ‘passive' amorphous materials, and
their counterparts in active matter such as confluent biological tissues. One strong
motivation is that the interplay between activity and structural disorder might in turn be
related to biological functionalities.
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 rigorous
analogies, at the mean-field level, between different families driven disordered systems,
such as sheared granular materials and active matter.
[1] "Out-of-equilibrium dynamical equations of infinite-dimensional particle systems I.
The isotropic case",
E. Agoritsas, T. Maimbourg and F. Zamponi, J. Phys. A: Math. and Theor. 52, 144002 (2019).
[2] "Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. II.
The anisotropic case under shear strain",
E. Agoritsas, T. Maimbourg and F. Zamponi, J. Phys. A: Math. and Theor. 52, 334001 (2019).
[3] "A direct link between active matter and sheared granular systems »,
P. Morse*, S. Roy*, E. Agoritsas*, E. Stanifer, E. I. Corwin, and M. L. Manning, PNAS 118,
e2019909118 (2021).
[4] "Mean-field dynamics of infinite-dimensional particle systems: global shear versus
random local forcing »,
E. Agoritsas, J. Stat. Mech. 2021, 033501 (2021) |
