arXiv subjects

Stefano Zapperi

Publications and source records attributed to Stefano Zapperi.

142 records · Page 8Linked to original sources

arXiv1998

Barkhausen noise in soft amorphous magnetic materials under applied stress

We report experimental measurements of Barkhausen noise on Fe_{64}Co_{21}B_{15} amorphous alloy under tensile stress. We interpret the scaling behavior of the noise distributions in terms of the depinning transition of the domain walls. We show that stress induced anisotropy enhance the effect of short-range elastic interactions that dominate over long-range dipolar interactions. The universality class is thus different from the one usually observed in Barkhausen noise measurements and is characterized by the exponents τ= 1.3 and α= 1.5, for the decay of the distributions of jump sizes and durations.

cond-mat.mtrl-sci↗

arXiv1998

Dynamics of a ferromagnetic domain wall: avalanches, depinning transition and the Barkhausen effect

We study the dynamics of a ferromagnetic domain wall driven by an external magnetic field through a disordered medium. The avalanche-like motion of the domain walls between pinned configurations produces a noise known as the Barkhausen effect. We discuss experimental results on soft ferromagnetic materials, with reference to the domain structure and the sample geometry, and report Barkhausen noise measurements on Fe$_{21}$Co$_{64}$B$_{15}$ amorphous alloy. We construct an equation of motion for a flexible domain wall, which displays a depinning transition as the field is increased. The long-range dipolar interactions are shown to set the upper critical dimension to $d_c=3$, which implies that mean-field exponents (with possible logarithmic correction) are expected to describe the Barkhausen effect. We introduce a mean-field infinite-range model and show that it is equivalent to a previously introduced single-degree-of-freedom model, known to reproduce several experimental results. We numerically simulate the equation in $d=3$, confirming the theoretical predictions. We compute the avalanche distributions as a function of the field driving rate and the intensity of the demagnetizing field. The scaling exponents change linearly with the driving rate, while the cutoff of the distribution is determined by the demagnetizing field, in remarkable agreement with experiments.

cond-mat.stat-mech↗

arXiv1998

Dynamically Driven Renormalization Group Applied to Sandpile Models

The general framework for the renormalization group analysis of self-organized critical sandpile models is formulated. The usual real space renormalization scheme for lattice models when applied to nonequilibrium dynamical models must be supplemented by feedback relations coming from the stationarity conditions. On the basis of these ideas the Dynamically Driven Renormalization Group is applied to describe the boundary and bulk critical behavior of sandpile models. A detailed description of the branching nature of sandpile avalanches is given in terms of the generating functions of the underlying branching process.

cond-mat.stat-mech↗

arXiv1998

Mean-field behavior of the sandpile model below the upper critical dimension

We present results of large scale numerical simulations of the Bak, Tang and Wiesenfeld sandpile model. We analyze the critical behavior of the model in Euclidean dimensions $2\leq d\leq 6$. We consider a dissipative generalization of the model and study the avalanche size and duration distributions for different values of the lattice size and dissipation. We find that the scaling exponents in $d=4$ significantly differ from mean-field predictions, thus suggesting an upper critical dimension $d_c\geq 5$. Using the relations among the dissipation rate $ε$ and the finite lattice size $L$, we find that a subset of the exponents displays mean-field values below the upper critical dimensions. This behavior is explained in terms of conservation laws.

cond-mat.stat-mech↗

arXiv1997

Self-organized criticality as an absorbing-state phase transition

We explore the connection between self-organized criticality and phase transitions in models with absorbing states. Sandpile models are found to exhibit criticality only when a pair of relevant parameters - dissipation epsilon and driving field h - are set to their critical values. The critical values of epsilon and h are both equal to zero. The first is due to the absence of saturation (no bound on energy) in the sandpile model, while the second result is common to other absorbing-state transitions. The original definition of the sandpile model places it at the point (epsilon=0, h=0+): it is critical by definition. We argue power-law avalanche distributions are a general feature of models with infinitely many absorbing configurations, when they are subject to slow driving at the critical point. Our assertions are supported by simulations of the sandpile at epsilon=h=0 and fixed energy density (no drive, periodic boundaries), and of the slowly-driven pair contact process. We formulate a field theory for the sandpile model, in which the order parameter is coupled to a conserved energy density, which plays the role of an effective creation rate.

cond-mat.stat-mech↗

arXiv1997

Dynamics of a ferromagnetic domain wall and the Barkhausen effect

We derive an equation of motion for the the dynamics of a ferromagnetic domain wall driven by an external magnetic field through a disordered medium and we study the associated depinning transition. The long-range dipolar interactions set the upper critical dimension to be $d_c=3$, so we suggest that mean-field exponents describe the Barkhausen effect for three-dimensional soft ferromagnetic materials. We analyze the scaling of the Barkhausen jumps as a function of the field driving rate and the intensity of the demagnetizing field, and find results in quantitative agreement with experiments on crystalline and amorphous soft ferromagnetic alloys.

cond-mat.mtrl-sci↗

arXiv1997

How self-organized criticality works: A unified mean-field picture

We present a unified mean-field theory, based on the single site approximation to the master-equation, for stochastic self-organized critical models. In particular, we analyze in detail the properties of sandpile and forest-fire (FF) models. In analogy with other non-equilibrium critical phenomena, we identify the order parameter with the density of ``active'' sites and the control parameters with the driving rates. Depending on the values of the control parameters, the system is shown to reach a subcritical (absorbing) or super-critical (active) stationary state. Criticality is analyzed in terms of the singularities of the zero-field susceptibility. In the limit of vanishing control parameters, the stationary state displays scaling characteristic of self-organized criticality (SOC). We show that this limit corresponds to the breakdown of space-time locality in the dynamical rules of the models. We define a complete set of critical exponents, describing the scaling of order parameter, response functions, susceptibility and correlation length in the subcritical and supercritical states. In the subcritical state, the response of the system to small perturbations takes place in avalanches. We analyze their scaling behavior in relation with branching processes. In sandpile models because of conservation laws, a critical exponents subset displays mean-field values ($ν=1/2$ and $γ= 1$) in any dimensions. We treat bulk and boundary dissipation and introduce a new critical exponent relating dissipation and finite size effects. We present numerical simulations that confirm our results. In the case of the forest-fire model, our approach can distinguish between different regimes (SOC-FF and deterministic FF) studied in the literature and determine the full spectrum of critical exponents.

cond-mat.stat-mech↗

arXiv1996

Order Parameter and Scaling Fields in Self-Organized Criticality

We present a unified dynamical mean-field theory for stochastic self-organized critical models. We use a single site approximation and we include the details of different models by using effective parameters and constraints. We identify the order parameter and the relevant scaling fields in order to describe the critical behavior in terms of usual concepts of non equilibrium lattice models with steady-states. We point out the inconsistencies of previous mean-field approaches, which lead to different predictions. Numerical simulations confirm the validity of our results beyond mean-field theory.

cond-mat.stat-mech↗

arXiv1996

Scaling for the Coalescence of Microfractures before Breakdown

We study the behavior of fracture in disordered systems close to the breakdown point. We simulate numerically both scalar (resistor network) and vectorial (spring network) models with threshold disorder, driven at constant current and stress rate respectively. We analyze the scaling of the susceptibility and the cluster size close to the breakdown. We observe avalanche behavior and clustering of the cracks. We find that the scaling exponents are consistent with those found close to a mean-field spinodal and present analogies between the coalescence of microfractures and the coalescence of droplets in a metastable magnetic system. Finally, we discuss different experimental conditions and some possible theoretical interpretations of the results.

cond-mat.mtrl-sci↗

arXiv1996

Modeling Acoustic Emission in Microfracturing Phenomena

It has been recently observed that synthetic materials subjected to an external elastic stress give rise to scaling phenomena in the acoustic emission signal. Motivated by this experimental finding we develop a mesoscopic model in order to clarify the nature of this phenomenon. We model the synthetic material by an array of resistors with random failure thresholds. The failure of a resistor produces an decrease in the conductivity and a redistribution of the disorder. By increasing the applied voltage the system organizes itself in a stationary state. The acoustic emission signal is associated with the failure events. We find scaling behavior in the amplitude of these events and in the times between different events. The model allows us to study the geometrical and topological properties of the micro-fracturing process that drives the system to the self-organized stationary state.

cond-mat.mtrl-sci↗

arXiv1996

First-Order Transition in the Breakdown of Disordered Media

We study the approach to global breakdown in disordered media driven by increasing external forces. We first analyze the problem by mean-field theory, showing that the failure process can be described as a first-order phase transition, similarly to the case of thermally activated fracture in homogeneous media. Then we quantitatively confirm the predictions of the mean-field theory using numerical simulations of discrete models. Widely distributed avalanches and the corresponding mean-field scaling are explained by the long-range nature of elastic interactions. We discuss the analogy of our results to driven disordered first-order transitions and spinodal nucleation in magnetic systems.

cond-mat.stat-mech↗

arXiv1996

Renormalization of Systems with Non-equilibrium Critical Stationary States

We introduce the general formulation of a renormalization method suitable to study the critical properties of non-equilibrium systems with steady-states: the Dynamically Driven Renormalization Group. We renormalize the time evolution operator by computing the rescaled time transition rate between coarse grained states. The obtained renormalization equations are coupled to a stationarity condition which provides the approximate non-equilibrium statistical weights of steady-state configurations to be used in the calculations. In this way we are able to write recursion relations for the parameters evolution under scale change, from which we can extract numerical values for the critical exponents. This general framework allows the systematic analysis of several models showing self-organized criticality in terms of usual concepts of phase transitions and critical phenomena.

cond-mat.stat-mech↗

arXiv1996

Dynamically Driven Renormalization Group

We present a detailed discussion of a novel dynamical renormalization group scheme: the Dynamically Driven Renormalization Group (DDRG). This is a general renormalization method developed for dynamical systems with non-equilibrium critical steady-state. The method is based on a real space renormalization scheme driven by a dynamical steady-state condition which acts as a feedback on the transformation equations. This approach has been applied to open non-linear systems such as self-organized critical phenomena, and it allows the analytical evaluation of scaling dimensions and critical exponents. Equilibrium models at the critical point can also be considered. The explicit application to some models and the corresponding results are discussed.

cond-mat↗

arXiv1996

Sandpile Model on Sierpinski Gasket Fractal

We investigate the sandpile model on the two--dimensional Sierpinski gasket fractal. We find that the model displays novel critical behavior, and we analyze the distribution functions of avalanche sizes, lifetimes and topplings and calculate the associated critical exponents $τ= 1.51 \pm 0.04$, $α= 1.63 \pm 0.04$ and $μ= 1.36 \pm 0.04$. The avalanche size distribution shows power law behavior modulated by logarithmic oscillations which can be related to the discrete scale invariance of the underlying lattice. Such a distribution can be formally described by introducing a complex scaling exponent $τ^{*} \equiv τ+ i δ$, where the real part $τ$ corresponds to the power law and the imaginary part $δ$ is related to the period of the logarithmic oscillations.

cond-mat↗

arXiv1996

Self-organized branching processes: Avalanche models with dissipation

We explore in the mean-field approximation the robustness with respect to dissipation of self-organized criticality in sandpile models. To this end, we generalize a recently introduced self-organized branching process, and show that the model self-organizes not into a critical state but rather into a subcritical state: when dissipation is present, the dynamical fixed point does not coincide with the critical point. Thus the level of dissipation acts as a relevant parameter in the renormalization-group sense. We study the model numerically and compute analytically the critical exponents for the avalanche size and lifetime distributions and the scaling exponents for the corresponding cutoffs.

cond-mat↗

arXiv1995

Self-Organized Branching Processes: A Mean-Field Theory for Avalanches

We discuss mean-field theories for self-organized criticality and the connection with the general theory of branching processes. We point out that the nature of the self-organization is not addressed properly by the previously proposed mean-field theories. We introduce a new mean-field model that explicitly takes the boundary conditions into account; in this way, the local dynamical rules are coupled to a global equation that drives the control parameter to its critical value. We study the model numerically, and analytically we compute the avalanche distributions.

cond-mat↗