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We present numerical evidence for an additional discontinuous transition, upon compression, inside the jammed regime for an asymmetric bidisperse granular packing. This additional transition line separates jammed states with networks of predominantly large particles from jammed networks formed by both large and small particles, and the transition is indicated by a discontinuity in the number of particles contributing to the jammed network. The additional transition line emerges from the curves of jamming transitions and terminates in an end point where the discontinuity vanishes. The additional line is starting at a size ratio around δ=0.22 and grows longer for smaller δ. For δ→0, the additional transition line approaches a limit that can be derived analytically. The observed jamming scenarios are reminiscent of glass-glass transitions found in colloidal glasses.

In contrast to molecular gases, granular gases are characterized by inelastic collisions and require therefore permanent driving to maintain a constant kinetic energy. The kinetic theory of granular gases describes how the average velocity of the particles decreases after the driving is shut off. Moreover, it predicts that the rescaled particle velocity distribution will approach a stationary state with overpopulated high-velocity tails as compared to the Maxwell-Boltzmann distribution. While this fundamental theoretical result was reproduced by numerical simulations, an experimental confirmation is still missing. Using a microgravity experiment that allows the spatially homogeneous excitation of spheres via magnetic fields, we confirm the theoretically predicted exponential decay of the tails of the velocity distribution.

Transport properties of a hard-sphere colloidal fluid are investigated by Brownian dynamics simulations. We implement a novel algorithm for the time-dependent velocity-autocorrelation function (VACF) essentially eliminating the noise of the bare random motion. The measured VACF reveals persistent anti-correlations manifested by a negative algebraic power-law tail t^{-5/2} at all densities. At small packing fractions the simulations fully agree with the analytic low-density prediction, yet the amplitude of the tail becomes dramatically suppressed as the packing fraction is increased. The mode-coupling theory of the glass transition provides a qualitative explanation for the strong variation in terms of the static compressibility as well as the slowing down of the structural relaxation.

Considering a granular fluid of inelastic smooth hard spheres, we discuss the conditions delineating the rheological regimes comprising Newtonian, Bagnoldian, shear thinning, and shear thickening behavior. Developing a kinetic theory, valid at finite shear rates and densities around the glass transition density, we predict the viscosity and Bagnold coefficient at practically relevant values of the control parameters. The determination of full flow curves relating the shear stress σ to the shear rate γ[over ˙] and predictions of the yield stress complete our discussion of granular rheology derived from first principles.

Recent progress on studies of the nanoscale mechanical responses in disordered systems has highlighted a strong degree of heterogeneity in the elastic moduli. In this contribution, using computer simulations, we study the elastic heterogeneities in athermal amorphous solids--composed of isotropic static sphere packings--near the jamming transition. We employ techniques based on linear response methods that are amenable to experimentation. We find that the local elastic moduli are randomly distributed in space and are described by Gaussian probability distributions, thereby lacking any significant spatial correlations, that persist all the way down to the transition point. However, the shear modulus fluctuations grow as the jamming threshold is approached, which is characterized by a new power-law scaling. Through this diverging behavior we are able to identify a characteristic length scale, associated with shear modulus heterogeneities, that distinguishes between bulk and local elastic responses.

We investigate the slow dynamics of a simple glass former whose interaction potential is the sum of a hard core and a square shoulder repulsion. According to mode coupling theory, the competition between the two repulsive length scales gives rise to a complex dynamic scenario: besides the fluid-glass line, the theory predicts a glass-glass line in the temperature-packing fraction plane with two end points. Interestingly, for critical values of the square-shoulder parameters, such end points can be accessed from the liquid phase. We verify, via extensive numerical simulations, the existence of both points through the observation of an unconventional subdiffusive/logarithmic dynamical behavior. Unexpectedly, we also discover that the simultaneous presence of two end points generates special loci in the state diagram along which the dynamics is identical at all length and time scales.

We investigate the dynamics of a driven system of dissipative hard spheres within mode-coupling theory. The dissipation is modeled by normal restitution, and driving is applied to individual particles in the bulk. In such a system, a glass transition is predicted for a finite transition density. With increasing dissipation, the transition shifts to higher densities. Despite the strong driving at high dissipation, the transition persists up to the limit of totally inelastic normal restitution.

Building on mode-coupling-theory calculations, we report a novel scenario for multiple glass transitions in a purely repulsive spherical potential: the square shoulder. The liquid-glass transition lines exhibit both melting by cooling and melting by compression as well as associated diffusion anomalies, similar to the ones observed in water. Differently from all previously investigated models, we find for small shoulder widths a glass-glass line that is disconnected from the liquid phase. Upon increasing the shoulder width such a glass-glass line merges with the liquid-glass transition lines, featuring two distinct end point singularities that give rise to logarithmic decays in the dynamics. We analytically explain these findings by considering the interplay of different repulsive length scales.