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The unjamming transition of granular systems is investigated in a seismic fault model via three dimensional Molecular Dynamics simulations. A two-time force-force correlation function, and a susceptibility related to the system response to pressure changes, allow to characterize the stick-slip dynamics, consisting in large slips and microslips leading to creep motion. The correlation function unveils the micromechanical changes occurring both during microslips and slips. The susceptibility encodes the magnitude of the incoming microslip.PACS numbers: 46.55.+d; 45.70.Ht; 91.30.Px In a number of industrial processes and natural phenomena, such as earthquakes or landslides, disordered solid granular systems start to flow. This solid-to-liquid transition, known as unjamming, occurs either on decreasing the confining pressure P , or increasing the applied shear stress σ. Understanding the properties of this transition is a big challenge due to the absence of an established theoretical framework for granular materials. A proposed analogy with the glass transition [1] of thermal systems has recently triggered the study of the jamming transition via numerical investigations of systems of soft frictionless particles at zero applied shear stress [2], where the only control parameter is the pressure (or the density). As the unjamming transition is approached by decreasing the confining pressure, the vibrational spectrum develops an excess of low frequency modes, known as soft-modes, leading to the identification of a length scale which diverges on unjamming [3]. This length scale is related to the emergence of an increasingly heterogeneous response as the system moves towards the transition [3]. A different approach to the study of the unjamming transition has been followed in a two dimensional numerical study [4] and in a number of experiments [5][6][7][8], where the applied shear stress is controlled via a spring mechanism, as the one in Fig. 1a. A stick-slip motion characterized by a complex slip size statistics [7] is recovered at high confining pressures P and small driving velocities V d . This stick-slip dynamics is altered by the presence of noise [9]. Analogous results have been found at fixed strain rate [10,11].

We investigate a recently introduced seismic fault model where granular particles simulate fault gouge, performing a detailed analysis of the size distribution of slipping events. We show that the model reproduces the Gutenberg-Richter law characterising real seismic occurrence, independently of model parameters. The effect of system size, elastic constant of the external drive, thickness of the gouge, frictional and mechanical properties of the particles are considered. The distribution is also characterised by a bump at large slips, whose characteristic size is solely controlled by the ratio of the drive elastic constant and the system size. Large slips become less probable in the absence of fault gouge and tend to disappear for stiff drives.

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 absence of perturbations, supporting the relevance of acoustic fluidization in earthquake triggering.

We suggest that coarsening dynamics can be described in terms of a generalized random walk, with the dynamics of the growing length L(t) controlled by a drift term, µ(L), and a diffusive one, D(L). We apply this interpretation to the one dimensional Ising model with a ferromagnetic coupling constant decreasing exponentially on the scale R. In the case of non conserved (Glauber) dynamics, both terms are present and their balance depends on the interplay between L(t) and R. In the case of conserved (Kawasaki) dynamics, drift is negligible, but D(L) is strongly dependent on L. The main pre-asymptotic regime displays a speeding of coarsening for Glauber dynamics and a slowdown for Kawasaki dynamics. We reason that a similar behaviour can be found in two dimensions.

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.

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.

Many natural phenomena exhibit power law behaviour in the distribution of event size. This scaling is successfully reproduced by Self Organized Criticality (SOC). On the other hand, temporal occurrence in SOC models has a Poisson-like statistics, i.e. exponential behaviour in the interevent time distribution, in contrast with experimental observations. We present a SOC model with memory: events are nucleated not only as a consequence of the instantaneous value of the local field with respect to the firing threshold, but on the basis of the whole history of the system. The model is able to reproduce the complex behaviour of inter-event time distribution, in excellent agreement with experimental seismic data.After the pioneering work of Bak, Tang and Wiesenfeld [1], Self Organized Criticality (SOC) has been proposed as a successful approach to the understanding of scaling behaviour in many natural phenomena. The term SOC usually refers to a mechanism of slow energy accumulation and fast energy redistribution driving the system toward a critical state. The prototype of SOC systems is the sand-pile model in which particles are randomly added on a two dimensional lattice. When the number of particles σ i in the i-th site exceeds a threshold value σ c , this site is considered unstable and particles are redistributed to nearest neighbor sites. If in any of these sites σ i > σ c , a further redistribution takes place propagating the avalanche. Border sites are dissipatives and discharge particles outside. The system evolves toward a critical state where the distribution of avalanche sizes is a power law obtained without fine tuning: no tunable parameter is present in the model. The simplicity of the mechanism at the basis of SOC has suggested that many physical and biological phenomena characterized by power laws in the size distribution, represent natural realizations of the SOC idea. For instance, SOC has been proposed to model earthquakes [2,3], the evolution of biological systems [4], solar flare occurrence [5], fluctuations in confined plasma [6] snow avalanches [7] and rain fall [8].Moreover, SOC models can be also considered as cellular automata generating stochastic sequences of events. An important quantity showing evidence of time correlations in a sequence is the distribution of time intervals between successive events. Defining ∆t as the time elapsed between the end of an avalanche and the starting of the next one, for the sand-pile model one obtains that ∆t is exponentially distributed [9]. This behaviour reveals the absence of correlations between events typical of a Poissonian process. Conversely the inter-event time distribution N (∆t) of many physical phenomena has a non-exponential shape, as for instance in the case of earthquakes [10], solar flares [9] and confined plasma [11]. The failure in the description of temporal occurrence is generally considered the main restriction for the applicability of SOC ideas to the description of the above phenomena.In this letter we address the problem of introducin...