Self-sustained reaction fronts in a disordered medium subject to an external flow display self-affine roughening, pinning, and depinning transitions. We measure spatial and temporal fluctuations of the front in 1+1 dimensions, controlled by a single parameter, the mean flow velocity. Three distinct universality classes are observed, consistent with the Kardar-Parisi-Zhang (KPZ) class for fast advancing or receding fronts, the quenched KPZ class (positive-qKPZ) when the mean flow approximately cancels the reaction rate, and the negative-qKPZ class for slowly receding fronts. Both qKPZ classes exhibit distinct depinning transitions, in agreement with the theory.
Quasi-static strain-controlled measurements of stress vs strain curves in macroscopic amorphous solids result in a nonlinear looking curve that ends up either in mechanical collapse or in a steadystate with fluctuations around a mean stress that remains constant with increasing strain. It is therefore very tempting to fit a nonlinear expansion of the stress in powers of the strain. We argue here that at low temperatures the meaning of such an expansion needs to be reconsidered. We point out the enormous difference between quenched and annealed averages of the stress vs. strain curves, and propose that a useful description of the mechanical response is given by a stress (or strain) dependent shear modulus for which a theoretical evaluation exists. The elastic response is piece-wise linear rather than nonlinear.
Brownian motion in a granular gas in a homogeneous cooling state is studied theoretically and by means of molecular dynamics. We use the simplest first-principle model for the impact-velocity dependent restitution coefficient, as it follows for the model of viscoelastic spheres. We reveal that for a wide range of initial conditions the ratio of granular temperatures of Brownian and bath particles demonstrates complicated non-monotonous behavior, which results in transition between different regimes of Brownian dynamics: It starts from the ballistic motion, switches later to superballistic one and turns at still later times into subdiffusion; eventually normal diffusion is achieved. Our theory agrees very well with the MD results, although extreme computational costs prevented to detect the final diffusion regime. Qualitatively, the reported intermediate diffusion regimes are generic for granular gases with any realistic dependence of the restitution coefficient on the impact velocity.
We perform large-scale event-driven Molecular dynamics (MD) simulations for granular gases of particles interacting with the impact-velocity dependent restitution coefficient ε(vimp). We use ε(vimp) as it follows from the simplest first-principle collision model of viscoelastic spheres. Both cases of force-free and uniformly heated gases are studied. We formulate a simplified model of an effective constant restitution coefficient ε eff , which depends on a current granular temperature and compute ε eff , using the kinetic theory. We develop a theory of the velocity distribution function for driven gases of viscoelastic particles and analyze evolution of granular temperature and of the Sonine coefficients, which characterize the form of the velocity distribution function. We observe that for not large dissipation the simulation results are in an excellent agreement with the theory for both, homogeneous cooling state and uniformly heated gases. At the same time a noticeable discrepancy between the theory and MD results for the Sonine coefficients is detected for large dissipation. We analyze the accuracy of the simplified model, based on the effective restitution coefficient ε eff and conclude that this model can accurately describe granular temperature. It provides also an acceptable accuracy for the velocity distribution function for small dissipation, but fails when dissipation is large.
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