The Prandtl-Tomlinson model of friction with stochastic driving

We consider the classical PrandtlTomlinson model of a particle moving on a corrugated potential, pulled by a spring. In the usual situation in which pulling acts at constant velocity γ, the model displays an average friction force δ that relates to γ(for small γ) as γ∼ (δ -δc)β, where δc is a critical friction force. The possible values of β are well known in terms of the analytical properties of the corrugated potential. We study here the situation in which the pulling has, in addition to the constant velocity term, a stochastic term of mechanical origin. We analytically show how this term modifies the force-velocity dependence close to the critical force, and give the value of β in terms of the analytical properties of the corrugation potential and the scaling properties of the stochastic driving, encoded in the value of its Hurst exponent.Fil: Jagla, Eduardo Alberto. Comisión Nacional de Energía Atómica; Argentina. Universidad Nacional de Cuyo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Forest-Fire Analogy to Explain the b Value of the Gutenberg-Richter Law for Earthquakes

The Dro¨ssel-Schwabl model of forest fires can be interpreted in a coarse-grained sense as a model for the stress distribution in a single planar fault. Fires in the model are then translated to earthquakes. I show that when a second class of trees that propagate fire only after some finite time is introduced in the model, secondary fires (analogous to aftershocks) are generated, and the statistics of events becomes quantitatively compatible with the Gutenberg-Richter law for earthquakes, with a realistic value of the b exponent. The change in exponent is analytically demonstrated in a simplified percolation scenario. Experimental consequences of the proposed mechanism are indicated.Fil: Jagla, Eduardo Alberto. Comision Nacional de Energia Atomica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina

Critical region of long-range depinning transitions

The depinning transition of elastic interfaces with an elastic interaction kernel decaying as 1/rd+σ is characterized by critical exponents which continuously vary with σ. These exponents are expected to be unique and universal, except in the fully coupled (−d<σ≤0) limit, where they depend on the “smooth” or “cuspy” nature of the microscopic pinning potential. By accurately comparing the depinning transition for cuspy and smooth potentials in a specially devised depinning model, we explain such peculiar limits in terms of the vanishing of the critical region for smooth potentials, as we decrease σ from the short-range (σ≥2) to the fully coupled case. Our results have practical implications for the determination of critical depinning exponents and identification of depinning universality classes in concrete experimental depinning systems with nonlocal elasticity, such as contact lines of liquids and fractures.Fil: Kolton, Alejandro Benedykt. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; ArgentinaFil: Jagla, Eduardo Alberto. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentin

Tensorial description of the plasticity of amorphous composites

We use a continuous mesoscopic model to address the yielding properties of plastic composites, formed by a host material and inclusions with different elastic and/or plastic properties. We investigate the flow properties of the composed material under a uniform externally applied deviatoric stress. We show that due to the heterogeneities induced by the inclusions, a scalar modeling in terms of a single deviatoric strain of the same symmetry as the externally applied deformation gives inaccurate results. A realistic modeling must include all possible shear deformations. Implementing this model in a two-dimensional system, we show that the effect of harder inclusions is very weak to relatively high concentrations. For softer inclusions instead, the effect is much stronger; even a small concentration of inclusions affecting the form of the flow curve and the critical stress. We also present the details of a full three-dimensional simulation scheme and obtain the corresponding results for harder and softer inclusions.Fil: Jagla, Eduardo Alberto. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentin

Aftershock production rate of driven viscoelastic interfaces

We study analytically and by numerical simulations the statistics of the aftershocks generated after large avalanches in models of interface depinning that include viscoelastic relaxation effects. We find in all the analyzed cases that the decay law of aftershocks with time can be understood by considering the typical roughness of the interface and its evolution due to relaxation. In models where there is a single viscoelastic relaxation time there is an exponential decay of the number of aftershocks with time. In models in which viscoelastic relaxation is wave-vector dependent we typically find a power-law dependence of the decay rate that is compatible with the Omori law. The factors that determine the value of the decay exponent are analyzed.Fil: Jagla, Eduardo Alberto. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Spatial and temporal forecasting of large earthquakes in a spring-block model of a fault

We study a recently proposed statistical physics model of earthquake dynamics that includes stress relaxation in the plates as a fundamental ingredient. The model is known to reproduce many realistic features of seismic phenomena, such as: the Gutenberg?Richter law for the event size distribution, the Omori law for aftershocks and an overall velocity-weakening dependence of the average friction force. Here, we analyse the dynamics of the model in detail, in order to investigate to what extent the occurrence of large events in the model can be anticipated. We systematically find that large events occur in fault patches where strain accumulation has exceeded some threshold value. The spatial extent of these patches (which correlate with the magnitude of forthcoming events) can be calculated if the strain state of the system is supposed to be known. In addition, we find that some large events are preceded by well-defined precursor activity. This allows, in a fraction of cases, to complement the forecast of magnitude and spatial location, with a sensible prediction of time of occurrence. Although our work is exclusively limited to the numerical model analysed, we argue that it gives new breath to earthquake forecast techniques that combine the historical analysis of seismic activity with a search of appropriate precursor activity.Fil: Aragón, Luis Enrique. Comision Nacional de Energia Atomica. Centro Atomico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Patagonia Norte; ArgentinaFil: Jagla, Eduardo Alberto. Comision Nacional de Energia Atomica. Centro Atomico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Patagonia Norte; Argentin

Elastic interfaces on disordered substrates: From mean-field depinning to yielding

We consider a model of an elastic manifold driven on a disordered energy landscape, with generalized long range elasticity. Varying the form of the elastic kernel by progressively allowing for the existence of zero modes, the model interpolates smoothly between mean-field depinning and finite dimensional yielding. We find that the critical exponents of the model change smoothly in this process. Also, we show that in all cases the Herschel-Buckley exponent of the flow curve depends on the analytical form of the microscopic pinning potential. Within the present elastoplastic description, all this suggests that yielding in finite dimensions is a mean-field transition.Fil: Ferrero, Ezequiel E.. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología - Nodo Bariloche | Comisión Nacional de Energía Atómica. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología - Nodo Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; ArgentinaFil: Jagla, Eduardo Alberto. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro | Universidad Nacional de Cuyo. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentin

Critical exponents of the yielding transition of amorphous solids

We investigate numerically the yielding transition of a two-dimensional model amorphous solid under external shear. We use a scalar model in terms of values of the total local strain, derived from the full (tensorial) description of the elastic interactions in the system, in which plastic deformations are accounted for by introducing a stochastic "plastic disorder" potential. This scalar model is seen to be equivalent to a collection of Prandtl-Tomlinson particles, which are coupled through an Eshelby quadrupolar kernel. Numerical simulations of this scalar model reveal that the strain rate versus stress curve, close to the critical stress, is of the form γ∼(σ-σc)β. Remarkably, we find that the value of β depends on details of the microscopic plastic potential used, confirming and giving additional support to results previously obtained with the full tensorial model. To rationalize this result, we argue that the Eshelby interaction in the scalar model can be treated to a good approximation in a sort of "dynamical" mean field, which corresponds to a Prandtl-Tomlinson particle that is driven by the applied strain rate in the presence of a stochastic noise generated by all other particles. The dynamics of this Prandtl-Tomlinson particle displays different values of the β exponent depending on the analytical properties of the microscopic potential, thus giving support to the results of the numerical simulations. Moreover, we find that other critical exponents that depend on details of the dynamics show also a dependence with the form of the disorder, while static exponents are independent of the details of the disorder. Finally, we show how our scalar model relates to other elastoplastic models and to the widely used mean-field version known as the Hébraud-Lequeux model.Fil: Fernández Aguirre, I.. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaFil: Jagla, Eduardo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentin

Criticality in elastoplastic models of amorphous solids with stress-dependent yielding rates

We analyze the behavior of different elastoplastic models approaching the yielding transition. We propose two kinds of rules for the local yielding events: Yielding occurs above the local threshold either at a constant rate or with a rate that increases as the square root of the stress excess. We establish a family of "static" universal critical exponents which do not depend on this dynamic detail of the model rules: In particular, the exponents for the avalanche size distribution P(S) ∼ S-τSf(S/Ldf) and the exponents describing the density of sites at the verge of yielding, which we find to be of the form P(x) ≃ P(0) + xθ with P(0) ∼ L-a controlling the extremal statistics. On the other hand, we discuss "dynamical" exponents that are sensitive to the local yielding rule. We find that, apart form the dynamical exponent z controlling the duration of avalanches, also the flowcurve's (inverse) Herschel-Bulkley exponent β ( ∼ (σ-σc)β) enters in this category, and is seen to differ in ½ between the two yielding rate cases. We give analytical support to this numerical observation by calculating the exponent variation in the Hébraud-Lequeux model and finding an identical shift. We further discuss an alternative mean-field approximation to yielding only based on the so-called Hurst exponent of the accumulated mechanical noise signal, which gives good predictions for the exponents extracted from simulations of fully spatial models.Fil: Ferrero, Ezequiel E.. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología - Nodo Bariloche | Comisión Nacional de Energía Atómica. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología - Nodo Bariloche; ArgentinaFil: Jagla, Eduardo Alberto. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro | Universidad Nacional de Cuyo. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro.; Argentin

Thermally rounded depinning of an elastic interface on a washboard potential

The thermal rounding of the depinning transition of an elastic interface sliding on a washboard potential is studied through analytic arguments and very accurate numerical simulations. We confirm the standard view that well below the depinning threshold the average velocity can be calculated considering thermally activated nucleation of defects. However, we find that the straightforward extension of this analysis to near or above the depinning threshold does not fully describe the physics of the thermally assisted motion. In particular, we find that exactly at the depinning point the average velocity does not follow a pure power law of the temperature as naively expected by the analogy with standard phase transitions but presents subtle logarithmic corrections. We explain the physical mechanisms behind these corrections and argue that they are nonpeculiar collective effects which may also apply to the case of interfaces sliding on uncorrelated disordered landscapes.Fil: Kolton, Alejandro Benedykt. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; ArgentinaFil: Jagla, Eduardo Alberto. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentin