arXiv subjects

Stefano Zapperi

Publications and source records attributed to Stefano Zapperi.

At least 127 records · Page 7Linked to original sources

arXiv2001

Intermittent dislocation flow in viscoplastic deformation

The viscoplastic deformation (creep) of crystalline materials under constant stress involves the motion of a large number of interacting dislocations. Analytical methods and sophisticated `dislocation-dynamics' simulations have proved very effective in the study of dislocation patterning, and have led to macroscopic constitutive laws of plastic deformation. Yet, a statistical analysis of the dynamics of an assembly of interacting dislocations has not hitherto been performed. Here we report acoustic emission measurements on stressed ice single crystals, the results of which indicate that dislocations move in a scale-free intermittent fashion. This result is confirmed by numerical simulations of a model of interacting dislocations that successfully reproduces the main features of the experiment. We find that dislocations generate a slowly evolving configuration landscape which coexists with rapid collective rearrangements. These rearrangements involve a comparatively small fraction of the dislocations and lead to an intermittent behavior of the net plastic response. This basic dynamical picture appears to be a generic feature in the deformation of many other materials. Moreover, it should provide a framework for discussing fundamental aspects of plasticity, that goes beyond standard mean-field approaches that see plastic deformation as a smooth laminar flow.

cond-mat.stat-mech↗

arXiv2001

Complexity in dislocation dynamics: model

We propose a numerical model to study the viscoplastic deformation of ice single crystals. We consider long-range elastic interactions among dislocations, the possibility of mutual annihilation, and a multiplication mechanism representing the activation of Frank-Read sources due to dislocation pinning. The overdamped equations of motion for a collection of dislocations are integrated numerically using different externally applied stresses. Using this approach we analyze the avalanche-like rearrangements of dislocations during the dynamic evolution. We observe a power law distribution of avalanche sizes which we compare with acoustic emission experiments in ice single crystals under creep deformation. We emphasize the connections of our model with non-equilibrium phase transitions and critical phenomena.

cond-mat.stat-mech↗

arXiv2001

Modeling collective dislocation dynamics in ice single crystals

We propose a model to study the plasticity of ice single crystals by numerical simulations. The model includes the long-range character of the interaction among dislocations, as well as the possibility of mutual annihilation of these line defects characterized by its Burgers vector. A multiplication mechanism representing the activation of Frank-Read sources due to dislocation pinning is also introduced in the model. With our approach we are able to probe the dislocation patterns, which result from the dislocation dynamics. Furthermore, our results exhibit features characteristic of driven dynamic critical phenomena such as scaling behavior, and avalanche dynamics. Some of these results account for the experimental findings reported for ice single crystals under creep deformation, like the power-law distributions of the acoustic emission intensity observed sistematically in experiments.

cond-mat.stat-mech↗

arXiv2001

Flux front penetration in disordered superconductors

We investigate flux front penetration in a disordered type II superconductor by molecular dynamics (MD) simulations of interacting vortices and find scaling laws for the front position and the density profile. The scaling can be understood performing a coarse graining of the system and writing a disordered non-linear diffusion equation. Integrating numerically the equation, we observe a crossover from flat to fractal front penetration as the system parameters are varied. The value of the fractal dimension indicates that the invasion process is described by gradient percolation.

cond-mat.supr-con↗

arXiv2001

Critical behavior of a one-dimensional fixed-energy stochastic sandpile

We study a one-dimensional fixed-energy version (that is, with no input or loss of particles), of Manna's stochastic sandpile model. The system has a continuous transition to an absorbing state at a critical value $ζ_c$ of the particle density. Critical exponents are obtained from extensive simulations, which treat both stationary and transient properties. In contrast with other one-dimensional sandpiles, the model appears to exhibit finite-size scaling, though anomalies exist in the scaling of relaxation times and in the approach to the stationary state. The latter appear to depend strongly on the nature of the initial configuration. The critical exponents differ from those expected at a linear interface depinning transition in a medium with point disorder, and from those of directed percolation.

cond-mat.stat-mech↗

arXiv2000

Sandpiles and absorbing-state phase transitions: recent results and open problems

We review some recent results on the relations between sandpiles and a class of absorbing state phase transitions. We use the concept of fixed energy sandpiles (FES), in which external driving and dissipation are absent. FES are shown to exhibit an absorbing state transition with critical properties coinciding with those of the corresponding sandpile model. We propose a set of Langevin equations capturing the relevant features of this transition. These equations characterize the universality class of systems with an infinite number of absorbing states and a static conserved field coupled to the order parameter. Different models in this class are identified, and strong evidence is presented showing that the Manna sandpile, as well as some other stochastic sandpiles, belong in this universality class. Finally some open problems and questions are discussed.

cond-mat↗

arXiv2000

Depinning of a dislocation: the influence of long-range interactions

The theory of the depinning transition of elastic manifolds in random media provides a framework for the statistical dynamics of dislocation systems at yield. We consider the case of a single flexible dislocation gliding through a random stress field generated by a distribution of immobile dislocations threading through its glide plane. The immobile dislocations are arranged in a "restrictedly random" manner and provide an effective stress field whose statistical properties can be calculated explicitly. We write an equation of motion for the dislocation and compute the associated depinning force, which may be identified with the yield stress. Numerical simulations of a discretized version of the equation confirm these results and allow us to investigate the critical dynamics of the pinning-depinning transition.

cond-mat.mtrl-sci↗

arXiv2000

Paths to Self-Organized Criticality

We present a pedagogical introduction to self-organized criticality (SOC), unraveling its connections with nonequilibrium phase transitions. There are several paths from a conventional critical point to SOC. They begin with an absorbing-state phase transition (directed percolation is a familiar example), and impose supervision or driving on the system; two commonly used methods are extremal dynamics, and driving at a rate approaching zero. We illustrate this in sandpiles, where SOC is a consequence of slow driving in a system exhibiting an absorbing-state phase transition with a conserved density. Other paths to SOC, in driven interfaces, the Bak-Sneppen model, and self-organized directed percolation, are also examined. We review the status of experimental realizations of SOC in light of these observations.

cond-mat.stat-mech↗

arXiv2000

Damage in Fiber Bundle Models

We introduce a continuous damage fiber bundle model that gives rise to macroscopic plasticity and compare its behavior with that of dry fiber bundles. Several interesting constitutive behaviors are found in this model depending on the value of the damage parameter and on the form of the disorder distribution. In addition, we compare the behavior of global load transfer models with local load transfer models and study in detail the damage evolution before failure. We emphasize the analogies between our results and spinodal nucleation in first-order phase transitions.

cond-mat.stat-mech↗

arXiv2000

Planar cracks in the fuse model

We simulate the propagation of a planar crack in a quasi-two dimensional fuse model, confining the crack between two horizontal plates. We investigate the effect on the roughness of microcrack nucleation ahead of the main crack and study the structure of the damage zone. The two dimensional geometry introduces a characteristic length in the problem, limiting the crack roughness. The damage ahead of the crack does not appear to change the scaling properties of the model, which are well described by gradient percolation.

cond-mat.stat-mech↗

arXiv2000

Absorbing-state phase transitions in fixed-energy sandpiles

We study sandpile models as closed systems, with conserved energy density $ζ$ playing the role of an external parameter. The critical energy density, $ζ_c$, marks a nonequilibrium phase transition between active and absorbing states. Several fixed-energy sandpiles are studied in extensive simulations of stationary and transient properties, as well as the dynamics of roughening in an interface-height representation. Our primary goal is to identify the universality classes of such models, in hopes of assessing the validity of two recently proposed approaches to sandpiles: a phenomenological continuum Langevin description with absorbing states, and a mapping to driven interface dynamics in random media. Our results strongly suggest that there are at least three distinct universality classes for sandpiles.

cond-mat.stat-mech↗

arXiv2000

Scaling exponents for Barkhausen avalanches in polycrystals and amorphous ferromagnets

We investigate the scaling properties of the Barkhausen effect, recording the noise in several soft ferromagnetic materials: polycrystals with different grain sizes and amorphous alloys. We measure the Barkhausen avalanche distributions and determine the scaling exponents. In the limit of vanishing external field rate, we can group the samples in two distinct classes, characterized by exponents τ= 1.50 \pm 0.05 or τ= 1.27 \pm 0.03, for the avalanche size distributions. We interpret these results in terms of the depinning transition of domain walls and obtain an expression relating the cutoff of the distributions to the demagnetizing factor which is in quantitative agreement with experiments.

cond-mat.mtrl-sci↗

arXiv1999

Effect of impact energy on the shape of granular heaps

We study experimentally the shape of a granular heap formed pouring a granular material into a vertical Hele-Shaw cell and analyze the effect of the grain impact energy. We propose a continuous model for the steady profile of the heap that explicitly considers energy dissipation of flowing grains through inelastic collisions. We solve the model analytically and analyze the resulting height profile as a function of several parameters, such as the restitution coefficient of the grains and their impact energies. We find good agreement between theory and experiments.

cond-mat.soft↗

arXiv1999

Avalanche and spreading exponents in systems with absorbing states

We present generic scaling laws relating spreading critical exponents and avalanche exponents (in the sense of self-organized criticality) in general systems with absorbing states. Using these scaling laws we present a collection of the state-of-the-art exponents for directed percolation, dynamical percolation and other universality classes. This collection of results should help to elucidate the connections of self-organized criticality and systems with absorbing states. In particular, some non-universality in avalanche exponents is predicted for systems with many absorbing states.

cond-mat.stat-mech↗

arXiv1999

Avalanches in Breakdown and Fracture Processes

We investigate the breakdown of disordered networks under the action of an increasing external---mechanical or electrical---force. We perform a mean-field analysis and estimate scaling exponents for the approach to the instability. By simulating two-dimensional models of electric breakdown and fracture we observe that the breakdown is preceded by avalanche events. The avalanches can be described by scaling laws, and the estimated values of the exponents are consistent with those found in mean-field theory. The breakdown point is characterized by a discontinuity in the macroscopic properties of the material, such as conductivity or elasticity, indicative of a first order transition. The scaling laws suggest an analogy with the behavior expected in spinodal nucleation.

cond-mat.stat-mech↗

arXiv1998

Critical exponents in stochastic sandpile models

We present large scale simulations of a stochastic sandpile model in two dimensions. We use moments analysis to evaluate critical exponents and finite size scaling method to consistently test the obtained results. The general picture resulting from our analysis allows us to characterize the large scale behavior of the present model with great accuracy.

cond-mat.stat-mech↗

arXiv1998

Driving, conservation and absorbing states in sandpiles

We use a phenomenological field theory, reflecting the symmetries and conservation laws of sandpiles, to compare the driven dissipative sandpile, widely studied in the context of self-organized criticality, with the corresponding fixed-energy model. The latter displays an absorbing-state phase transition with upper critical dimension $d_c=4$. We show that the driven model exhibits a fundamentally different approach to the critical point, and compute a subset of critical exponents. We present numerical simulations in support of our theoretical predictions.

cond-mat.stat-mech↗

arXiv1998

Universality in sandpiles

We perform extensive numerical simulations of different versions of the sandpile model. We find that previous claims about universality classes are unfounded, since the method previously employed to analyze the data suffered a systematic bias. We identify the correct scaling behavior and conclude that sandpiles with stochastic and deterministic toppling rules belong to the same universality class.

cond-mat.stat-mech↗