Liquid to supercooled-liquid crossover from a Boltzmann transport approach to escape and diffusion

We develop a model describing the motion of a non-Brownian particle in a periodic potential, which we then use to predict the temperature dependence of the diffusivity of a glass-former. In the model, the velocity of the particle is drawn for the equilibrium distribution at rate 1/t _c, where t _c is the intercollision time in the relaxation time approximation. Solutions within a Boltzmann transport approach show that the diffusivity crossovers from a low-t _c regime in which the particle at most crosses a single barrier in between two successive collisions, to a high-t _c regime in which the particle may cross several barriers. We then use our model to predict the temperature dependence of the diffusion coefficient of a system of harmonic-spheres, whose energy landscape has features resembling those of the potential considered in our model. We successfully recover a crossover in the temperature dependence of the diffusion coefficient observed through numerical dynamics simulations, as well as the relationship of the diffusivity on the temperature in the high-temperature limit.

Induced and endogenous acoustic oscillations in granular faults

The frictional properties of disordered systems are affected by external perturbations. These perturbations usually weaken the system by reducing the macroscopic friction coefficient. This friction reduction is of particular interest in the case of disordered systems composed of granular particles confined between two plates, as this is a simple model of seismic fault. Indeed, in the geophysical context frictional weakening could explain the unexpected weakness of some faults, as well as earthquake remote triggering. In this manuscript, we review recent results concerning the response of confined granular systems to external perturbations, considering the different mechanisms by which the perturbation could weaken a system, the relevance of the frictional reduction to earthquakes, as well as discussing the intriguing scenario whereby the weakening is not monotonic in the perturbation frequency, so that a re-entrant transition is observed, as the system first enters a fluidized state and then returns to a frictional state.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.

Controlled Viscosity in Dense Granular Materials

We experimentally investigate the fluidization of a granular material subject to mechanical vibrations by monitoring the angular velocity of a vane suspended in the medium and driven by an external motor. On increasing the frequency, we observe a reentrant transition, as a jammed system first enters a fluidized state, where the vane rotates with high constant velocity, and then returns to a frictional state, where the vane velocity is much lower. While the fluidization frequency is material independent, the viscosity recovery frequency shows a clear dependence on the material that we rationalize by relating this frequency to the balance between dissipative and inertial forces in the system. Molecular dynamics simulations well reproduce the experimental data, confirming the suggested theoretical picture.

Synchronized oscillations and acoustic fluidization in confined granular materials

According to the acoustic fluidization hypothesis, elastic waves at a characteristic frequency form inside seismic faults even in the absence of an external perturbation. These waves are able to generate a normal stress which contrasts the confining pressure and promotes failure. Here, we study the mechanisms responsible for this wave activation via numerical simulations of a granular fault model. We observe the particles belonging to the percolating backbone, which sustains the stress, to perform synchronized oscillations over ellipticlike trajectories in the fault plane. These oscillations occur at the characteristic frequency of acoustic fluidization. As the applied shear stress increases, these oscillations become perpendicular to the fault plane just before the system fails, opposing the confining pressure, consistently with the acoustic fluidization scenario. The same change of orientation can be induced by external perturbations at the acoustic fluidization frequency.

Dynamic Weakening by Acoustic Fluidization during Stick-Slip Motion

The unexpected weakness of some faults has been attributed to the emergence of acoustic waves that promote failure by reducing the confining pressure through a mechanism known as acoustic fluidization, also proposed to explain earthquake remote triggering. Here we validate this mechanism via the numerical investigation of a granular fault model system. We find that the stick-slip dynamics is affected only by perturbations applied at a characteristic frequency corresponding to oscillations normal to the fault, leading to gradual dynamical weakening as failure is approaching. Acoustic waves at the same frequency spontaneously emerge at the onset of failure in the absence of perturbations, supporting the relevance of acoustic fluidization in earthquake triggering.

Dynamics and instantaneous normal modes in a liquid with density anomalies

We investigate the relation between the dynamical features of a supercooled liquid and those of its potential energy landscape, focusing on a model liquid with density anomalies. We consider, at fixed temperature, pairs of state points with different density but the same diffusion constant and find that surprisingly they have identical dynamical features at all length and time scales. This is shown by the collapse of their mean square displacements and of their self-intermediate scattering functions at different wavevectors. We then investigate how the features of the energy landscape change with density and establish that state points with equal diffusion constant have different landscapes. In particular, we find a correlation between the fraction of instantaneous normal modes connecting different energy minima and the diffusion constant, but unlike in other systems these two quantities are not in one-to-one correspondence with each other, showing that additional landscape features must be relevant in determining the diffusion constant.

Solid-on-solid single-block dynamics under mechanical vibration

The suppression of friction between sliding objects, modulated or enhanced by mechanical vibrations, is well established. However, the precise conditions of occurrence of these phenomena are not well understood. Here we address these questions focusing on a simple spring-block model, which is relevant to investigate friction both at the atomistic as well as the macroscopic scale. This allows us to investigate the influence on friction of the properties of the external drive, of the geometry of the surfaces over which the block moves, and of the confining force. Via numerical simulations and a theoretical study of the equations of motion, we identify the conditions under which friction is suppressed and/or recovered, and we evidence the critical role played by surface modulations and by the properties of the confining force.

Shear- and vibration-induced order-disorder transitions in granular media

By molecular dynamics simulations we investigate the order-disorder transitions induced in granular media by an applied drive combining vibrations and shear. As the steady state is attained, the pack is found in disordered configurations for comparatively high intensities of the drive; conversely, ordering and packing fractions exceeding the random close packing are found when vibrations and shear are weak. As forcing amplitudes get smaller, we find diverging time scales in the dynamics, as the system enters a jamming region. Under this perspective, our picture supports the intuition that externally applied forcing has, in driven granular media, a role similar to temperature in thermal systems.

Phenomenology and theory of horizontally oscillated granular mixtures

We overview the physics of a granular mixture subject to horizontal oscillations, recently investigated via experiments and molecular dynamics simulations. First we discuss the rich phenomenology exhibited by this system, which encompasses both segregation and dynamical instabilities. Then we show that the phenomenology can be explained via an effective interaction approach, by which the driven, non-thermal, granular mixture in mapped into a monodispersed thermal system of particles interacting via an effective potential. After determining the effective interaction we discuss its microscopic origin and investigate how it induces the observed phenomenology. Finally, as much as in thermal fluids, from the effective interaction we derive a Cahn-Hilliard dynamics equation, which appears to capture the essential characteristics of the dynamics of the granular mixture.

Optimizing on-ramp entries to exploit the capacity of a road

In this paper, we perform simulations of an extended Nagel-Schreckenberg model for one-lane and two-lane roads. We consider the presence of many entry ramps, placed in different locations, and we determine how the flux of cars of each entry ramp must be controlled in order to better exploit the capacity of the road. Our results are of relevance for the optimization of daily traffic, and set rules for the design of evacuation plans of urban conglomerations exposed to natural hazards, such as volcanoes.

Size segregation in granular media induced by phase transition

In order to study analytically the nature of the size segregation in granular mixtures, we introduce a mean field theory in the framework of a statistical mechanics approach, based on Edwards' original ideas. For simplicity we apply the theory to a lattice model for a hard sphere binary mixture under gravity, and we find a new purely thermodynamic mechanism that gives rise to the size segregation phenomenon. By varying the number of small grains and the mass ratio, we find a crossover from the Brazil nut to the reverse Brazil nut effect, which becomes a true phase transition when the number of small grains is larger then a critical value. We suggest that this transition is induced by the effective attraction between large grains due to the presence of small ones (depletion force). Finally the theoretical results are confirmed by numerical simulations of the 3d system under taps.

Monodisperse model suitable to study the glass transition

We study the properties of a monodisperse lattice glass model with a simple geometrical interpretation, which reproduces many features of glass forming liquids, such as the cage effect, vanishing diffusivity, and the presence of two time scales in relaxation functions. The model has a crystalline ground state at high density, but has no tendency to crystallize when quenched, even at extremely low cooling rates, which makes it suitable for the study of the glass transition. We study the model in mean field on random regular graphs, finding a scenario analogous to p-spin models.

Lattice glass model with no tendency to crystallize

We study a lattice model with two-body interactions that reproduces in three dimensions many features of structural glasses, such as cage effect and vanishing diffusivity. While having a crystalline state at low temperatures, it does not crystallize when quenched, even at the slowest cooling rate used, which makes it suitable to study the glass transition. We study the model on the Bethe lattice as well, and find a scenario typical of p-spin models, as in the Biroli-Mézard model.