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Mechanical deformation of amorphous solids can be described as consisting of an elastic part in which the stress increases linearly with strain, up to a yield point at which the solid either fractures or starts deforming plastically. It is well established, however, that the apparent linearity of stress with strain is actually a proxy for a much more complex behavior, with a microscopic plasticity that is reflected in diverging nonlinear elastic coefficients. Very generally, the complex structure of the energy landscape is expected to induce a singular response to small perturbations. In the athermal quasistatic regime, this response manifests itself in the form of a scale free plastic activity. The distribution of the corresponding avalanches should reflect, according to theoretical mean field calculations (Franz and Spigler, Phys. Rev. E., 2017, 95, 022139), the geometry of phase space in the vicinity of a typical local minimum. In this work, we characterize this distribution for simple models of glass forming systems, and we find that its scaling is compatible with the mean field predictions for systems above the jamming transition. These systems exhibit marginal stability, and scaling relations that hold in the stationary state are examined and confirmed in the elastic regime. By studying the respective influence of system size and age, we suggest that marginal stability is systematic in the thermodynamic limit.
We show that the low-frequency regime of the density of states of structural glass formers is crucially sensitive to the stress-ensemble from which the configurations are sampled. Specifically, in two dimensions, an exactly isotropic ensemble with ze
Sound attenuation in low temperature amorphous solids originates from their disordered structure. However, its detailed mechanism is still being debated. Here we analyze sound attenuation starting directly from the microscopic equations of motion. We
The mechanical response of naturally abundant amorphous solids such as gels, jammed grains, and biological tissues are not described by the conventional paradigm of broken symmetry that defines crystalline elasticity. In contrast, the response of suc
We show that the distribution of elements $H$ in the Hessian matrices associated with amorphous materials exhibit singularities $P(H) sim {lvert H rvert}^{gamma}$ with an exponent $gamma < 0$, as $lvert H rvert to 0$. We exploit the rotational invari
The holographic principle has proven successful in linking seemingly unrelated problems in physics; a famous example is the gauge-gravity duality. Recently, intriguing correspondences between the physics of soft matter and gravity are emerging, inclu