arXiv subjects

E. A. Jagla

Publications and source records attributed to E. A. Jagla.

At least 37 records · Page 2Linked to original sources

arXiv2017

Scaling theory of thermal rounding phenomena in depinning and related transitions

We present a scaling theory for the effect of thermal fluctuations on the characteristics of the depinning transition, and also in the closely related directed percolation model. Thermal effects act as a sort of external field that produces a rounding of the sharp transition occurring at zero temperature. The theory allows to predict the value of the thermal rounding exponent that quantifies the rounding effect. It also gives insight into the spatial and temporal correlations between thermally activated events, which are highly non-trivial.

cond-mat.stat-mech↗

arXiv2015

Avalanches in Tip-Driven Interfaces in Random Media

We analyse by numerical simulations and scaling arguments the avalanche statistics of 1-dimensional elastic interfaces in random media driven at a single point. Both global and local avalanche sizes are power-law distributed, with universal exponents given by the depinning roughness exponent $ζ$ and the interface dimension $d$, and distinct from their values in the uniformly driven case. A crossover appears between uniformly driven behaviour for small avalanches, and point driven behaviour for large avalanches. The scale of the crossover is controlled by the ratio between the stiffness of the pulling spring and the elasticity of the interface; it is visible both in the global and local avalanche-size distributions, as in the average spatial avalanche shape. Our results are relevant to model experiments involving locally driven elastic manifolds at low temperatures, such as magnetic domain walls or vortex lines in superconductors.

cond-mat.dis-nn↗

arXiv2015

Observation of the two way shape memory effect in an atomistic model of martensitic transformation

We study a system of classical particles in two dimensions interacting through an isotropic pair potential that displays a martensitic phase transition between a triangular and a rhomboidal structure upon the change of a single parameter. Previously it was shown that this potential is able to reproduce the shape memory effect and super-elasticity, among other well known features of the phenomenology of martensites. Here we extend those previous studies and describe the development of the more subtle two-way shape memory effect. We show that in a poly-crystalline sample, the effect can be associated to the existence of retained martensite within the austenite phase. We also study the case of a single crystal sample where the effect is associated to particular orientations of the dislocations, either induced by training or by an ad hoc construction of a starting sample.

cond-mat.mtrl-sci↗

arXiv2015

Frictional dynamics of viscoelastic solids driven on a rough surface

We study the effect of viscoelastic dynamics on the frictional properties of a (mean field) spring-block system pulled on a rough surface by an external drive. When the drive moves at constant velocity V, two dynamical regimes are observed: at fast driving, above a critical threshold Vc, the system slides at the drive velocity and displays a friction force with velocity weakening. Below Vc the steady sliding becomes unstable and a stick-slip regime sets in. In the slide-hold-slide driving protocol, a peak of the friction force appears after the hold time and its amplitude increases with the hold duration. These observations are consistent with the frictional force encoded phenomenologically in the rate-and-state equations. Our model gives a microscopical basis for such macroscopic description.

cond-mat.stat-mech↗

arXiv2015

Viscoelastic Effects in Avalanche Dynamics: A Key to Earthquake Statistics

In many complex systems a continuous input of energy over time can be suddenly relaxed in the form of avalanches. Conventional avalanche models disregard the possibility of internal dynamical effects in the inter-avalanche periods, and thus miss basic features observed in some real systems. We address this issue by studying a model with viscoelastic relaxation, showing how coherent oscillations of the stress field can emerge spontaneously. Remarkably, these oscillations generate avalanche patterns that are similar to those observed in seismic phenomena.

cond-mat.stat-mech↗

arXiv2015

Avalanche size distributions in mean field plastic yielding models

I discuss the size distribution ${\cal N}(S)$ of avalanches occurring at the yielding transition of mean field (i.e., Hebraud-Lequeux) models of amorphous solids. The size distribution follows a power law dependence of the form: ${\cal N}(S)\sim S^{-τ}$. However (contrary to what is found in its depinning counterpart) the value of $τ$ depends on details of the dynamic protocol used. For random triggering of avalanches I recover the $τ=3/2$ exponent typical of mean field models, which in particular is valid for the depinning case. However, for the physically relevant case of external loading through a quasistatic increase of applied strain, a smaller exponent (close to 1) is obtained. This result is rationalized by mapping the problem to an effective random walk in the presence of a moving absorbing boundary.

cond-mat.stat-mech↗

arXiv2014

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, compatible with the Omori law. The factors that determine the value of the decay exponent are analyzed.

cond-mat.stat-mech↗

arXiv2013

Creep dynamics of viscoelastic interfaces

The movement of a purely elastic interface driven on a disordered energy potential is characterized by a depinning transition: when the pulling force S is larger than some critical value S_1 the system is in a flowing regime and moves at a finite velocity. If S < S_1 the interface remains pinned and its velocity is zero. We show that for a one-dimensional interface, the inclusion of viscoelastic relaxation produces the appearance of an intervening regime between the pinned and the flowing phases in a well defined stress interval S_0 S_0 the creep velocity vanishes in an universal way that is governed by a directed percolation process. As S --> S_1 the creep velocity increases as a power law due to the increase of the typical size of the avalanches. The present observations may serve to improve the understanding of fatigue failure mechanisms.

cond-mat.stat-mech↗

arXiv2013

A forest-fire analogy to explain the b-value of the Gutenberg-Richter law for earthquakes

The Drossel-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.

cond-mat.stat-mech↗

arXiv2012

Tuning spreading and avalanche-size exponents in directed percolation with modified activation probabilities

We consider the directed percolation process as a prototype of systems displaying a nonequilibrium phase transition into an absorbing state. The model is in a critical state when the activation probability is adjusted at some precise value p_c. Criticality is lost as soon as the probability to activate sites at the first attempt, p1, is changed. We show here that criticality can be restored by "compensating" the change in p1 by an appropriate change of the second time activation probability p2 in the opposite direction. At compensation, we observe that the bulk exponents of the process coincide with those of the normal directed percolation process. However, the spreading exponents are changed, and take values that depend continuously on the pair (p1, p2). We interpret this situation by acknowledging that the model with modified initial probabilities has an infinite number of absorbing states.

cond-mat.stat-mech↗

arXiv2012

Velocity weakening and possibility of aftershocks in nanofriction experiments

We study the frictional behavior of small contacts as those realized in the atomic force microscope and other experimental setups, in the framework of generalized Prandtl-Tomlinson models. Particular attention is paid to mechanisms that generate velocity weakening, namely a decreasing average friction force with the relative sliding velocity.The mechanisms studied model the possibility of viscous relaxation, or aging effects in the contact. It is found that, in addition to producing velocity weakening, these mechanisms can also produce aftershocks at sufficiently low sliding velocities. This provides a remarkable analogy at the microscale, of friction properties at the macroscale, where aftershocks and velocity weakening are two fundamental features of seismic phenomena.

cond-mat.mes-hall↗

arXiv2012

Seismic cycles, size of the largest events, and the avalanche size distribution in a model of seismicity

We address several questions on the behavior of a numerical model recently introduced to study seismic phenomena, that includes relaxation in the plates as a key ingredient. We make an analysis of the scaling of the largest events with system size, and show that when parameters are appropriately interpreted, the typical size of the largest events scale as the system size, without the necessity to tune any parameter. Secondly, we show that the temporal activity in the model is inherently non-stationary, and obtain from here justification and support for the concept of a "seismic cycle" in the temporal evolution of seismic activity. Finally, we ask for the reasons that make the model display a realistic value of the decaying exponent $b$ in the Gutenberg-Richter law for the avalanche size distribution. We explain why relaxation induces a systematic increase of $b$ from its value $b\simeq 0.4$ observed in the absence of relaxation. However, we have not been able to justify the actual robustness of the model in displaying a consistent $b$ value around the experimentally observed value $b\simeq 1$.

cond-mat.stat-mech↗

arXiv2010

Creep rupture of materials: insights from a fiber bundle model with relaxation

I adapted a model recently introduced in the context of seismic phenomena, to study creep rupture of materials. It consists of linear elastic fibers that interact in an equal load sharing scheme, complemented with a local viscoelastic relaxation mechanism. The model correctly describes the three stages of the creep process, namely an initial Andrade regime of creep relaxation, an intermediate regime of rather constant creep rate, and a tertiary regime of accelerated creep towards final failure of the sample. In the tertiary regime creep rate follows the experimentally observed one over time-to-failure dependence. The time of minimum strain rate is systematically observed to be about 60-65 % of the time to failure, in accordance with experimental observations. In addition, burst size statistics of breaking events display a -3/2 power law for events close to the time of failure, and a steeper decay for the all-time distribution. Statistics of interevent times shows a tendency of the events to cluster temporarily. This behavior should be observable in acoustic emission experiments.

cond-mat.mtrl-sci↗

arXiv2010

Realistic spatial and temporal earthquake distributions in a modified Olami-Feder-Christiensen model

We propose and study a modified version of the Olami-Feder-Christiensen model of seismicity, that includes a mechanism of structural relaxation. We obtain realistic features of seismicity that are not obtained with the original version, mainly: aftershocks that obey the Omori law and cluster spatially around the slip surface of the main shock, and averaged frictional properties qualitatively similar to those observed in rock friction, in particular the velocity weakening effect.

cond-mat.stat-mech↗

arXiv2010

Delayed dynamic triggering of earthquakes: Evidences from a statistical model of seismicity

I study a recently proposed statistical model of earthquake dynamics that incorporates aging as a fundamental ingredient. The model is known to generate earthquake sequences that quantitatively reproduce the spatial and temporal clustering of events observed in actual seismic patterns. The aim of the present work is to investigate if this model can give support to the empirical evidence that earthquakes can be triggered by transient small perturbations, particularly by the passing of seismic waves originated in events occurring in far geographical locations. The effect of seismic waves is incorporated into the model by assuming that they produce instantaneous small modifications in the dynamical state of the system at the time they are applied. This change in the dynamical state has two main effects. On one side, it induces earthquakes that occur right at the application of the perturbation. These are called immediate events. On the other side, after the application of the perturbation there is a delayed effect: the seismic activity increases abruptly after the perturbation, then falls down below the level of background activity, and eventually recovers to the background value. The time scale of these variations depends on the internal dynamics of the system, and is totally independent of the duration of the perturbation. The number of delayed events in excess of the background activity is typically observed to be around a factor of twenty larger than the number of immediate events. The origin of the enhanced activity period following the perturbation is associated to the existence of aging relaxation, and it does not occur if relaxation is absent. These findings give support to the experimental evidence that earthquake can be remotely triggered by small transient perturbations as those produced by seismic waves.

cond-mat.stat-mech↗

arXiv2010

Shear band dynamics from a mesoscopic modeling of plasticity

The ubiquitous appearance of regions of localized deformation (shear bands) in different kinds of disordered materials under shear is studied in the context of a mesoscopic model of plasticity. The model may or may not include relaxational (aging) effects. In the absence of relaxational effects the model displays a monotonously increasing dependence of stress on strain-rate, and stationary shear bands do not occur. However, in start up experiments transient (although long lived) shear bands occur, that widen without bound in time. I investigate this transient effect in detail, reproducing and explaining a t^1/2 law for the thickness increase of the shear band that has been obtained in atomistic numerical simulations. Relaxation produces a negative sloped region in the stress vs. strain-rate curve that stabilizes the formation of shear bands of a well defined width, which is a function of strain-rate. Simulations at very low strain-rates reveal a non-trivial stick-slip dynamics of very thin shear bands that has relevance in the study of seismic phenomena. In addition, other non-stationary processes, such as stop-and-go, or strain-rate inversion situations display a phenomenology that matches very well the results of recent experimental studies.

cond-mat.soft↗

arXiv2010

Towards a modeling of the time dependence of contact area between solid bodies

I present a simple model of the time dependence of the contact area between solid bodies, assuming either a totally uncorrelated surface topography, or a self affine surface roughness. The existence of relaxation effects (that I incorporate using a recently proposed model) produces the time increase of the contact area $A(t)$ towards an asymptotic value that can be much smaller than the nominal contact area. For an uncorrelated surface topography, the time evolution of $A(t)$ is numerically found to be well fitted by expressions of the form [$A(\infty)-A(t)]\sim (t+t_0)^{-q}$, where the exponent $q$ depends on the normal load $F_N$ as $q\sim F_N^β$, with $β$ close to 0.5. In particular, when the contact area is much lower than the nominal area I obtain $A(t)/A(0) \sim 1+C\ln(t/t_0+1)$, i.e., a logarithmic time increase of the contact area, in accordance with experimental observations. The logarithmic increase for low loads is also obtained analytically in this case. For the more realistic case of self affine surfaces, the results are qualitatively similar.

cond-mat.stat-mech↗

arXiv2009

Classical isotropic two body potentials generating martensitic transformations

An isotropic interaction potential for classical particles is devised in such a way that the crystalline ground state of the system changes discontinuously when some parameter of the potential is varied. Using this potential we model martensitic transformations, and are able to study in detail the processes that are usually associated with it: shape memory effect, superelasticity, as well as many details concerning the dynamics of the transformation, particularly the characteristics of the martensitic texture obtained as a function of parameters affecting the transformation rate. Here we introduce the interaction potentials and present some basic results about the transformation it describes, for the particular case of two dimensional triangular-rombohedral and triangular-square transformation.

cond-mat.stat-mech↗