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We discuss a microscopic scheme to compute the rigidity of glasses or the plateau modulus of supercooled liquids by twisting replicated liquids. We first summarize the method in the case of harmonic glasses with analytic potentials. Then we discuss how it can be extended to the case of repulsive contact systems : the hard sphere glass and related systems with repulsive contact potentials which enable the jamming transition at zero temperature. For the repulsive contact systems we find entropic rigidity which behaves similarly as the pressure in the low temperature limit: it is proportional to the temperature and tends to diverge approaching the jamming density with increasing volume fraction, which may account for experimental observations of rigidities of repulsive colloids and emulsions.
Some aspects of how sound waves travel through disordered solids are still unclear. Recent work has characterized a feature of disordered solids which seems to influence vibrational excitations at the mesoscales, local elastic heterogeneity. Sound wa
We numerically study the evolution of the vibrational density of states $D(omega)$ of zero-temperature glasses when their kinetic stability is varied over an extremely broad range, ranging from poorly annealed glasses obtained by instantaneous quench
The free energy landscape of mean field marginal glasses is ultrametric. We demonstrate that this feature remains in finite three dimensional systems by finding sets of minima which are nearby in configuration space. By calculating the distance betwe
Active glassy matter has recently emerged as a novel class of non-equilibrium soft matter, combining energy-driven, active particle movement with dense and disordered glass-like behavior. Here we review the state-of-the-art in this field from an expe
It is known by now that amorphous solids at zero temperature do not possess a nonlinear elasticity theory: besides the shear modulus which exists, all the higher order coefficients do not exist in the thermodynamic limit. Here we show that the same p