Slow crack propagation through a disordered medium: Critical transition and dissipation

We show that the intermittent and self-similar fluctuations displayed by a slow crack during the propagation in a heterogeneous medium can be quantitatively described by an extension of a classical statistical model for fracture. The model yields the correct dynamical and morphological scaling, and allows to demonstrate that the scale invariance originates from the presence of a non-equilibrium, reversible, critical transition which in the presence of dissipation gives rise to self organized critical behaviour.Comment: 16 pages, 4 figures, to be published on EPL (http://epljournal.edpsciences.org/

Dynamic hysteresis in Finemet thin films

We performed a series of dynamic hysteresis measurements on three series of Finemet films with composition Fe$_{73.5}$Cu$_1$Nb$_3$Si$_13.5$B$_9$, using both the longitudinal magneto-optical Kerr effect (MOKE) and the inductive fluxometric method. The MOKE dynamic hysteresis loops show a more marked variability with the frequency than the inductive ones, while both measurements show a similar dependence on the square root of frequency. We analyze these results in the frame of a simple domain wall depinning model, which accounts for the general behavior of the data.Comment: 3 pages, 3 figure

Is demagnetization an efficient optimization method?

Demagnetization, commonly employed to study ferromagnets, has been proposed as the basis for an optimization tool, a method to find the ground state of a disordered system. Here we present a detailed comparison between the ground state and the demagnetized state in the random field Ising model, combing exact results in $d=1$ and numerical solutions in $d=3$. We show that there are important differences between the two states that persist in the thermodynamic limit and thus conclude that AC demagnetization is not an efficient optimization method.Comment: 2 pages, 1 figur

Investigation of scaling properties of hysteresis in Finemet thin films

We study the behavior of hysteresis loops in Finemet Fe$_{73.5}$Cu$_1$Nb$_3$Si$_{18.5}$B$_4$ thin films by using a fluxometric setup based on a couple of well compensated pickup coils. The presence of scaling laws of the hysteresis area is investigated as a function of the amplitude and frequency of the applied field, considering sample thickness from about 20 nm to 5 $\mu$m. We do not observe any scaling predicted by theoretical models, while dynamic loops show a logarithmic dependence on the frequency.Comment: 2 pages, 2 figure

Preferential attachment in the growth of social networks: the case of Wikipedia

We present an analysis of the statistical properties and growth of the free on-line encyclopedia Wikipedia. By describing topics by vertices and hyperlinks between them as edges, we can represent this encyclopedia as a directed graph. The topological properties of this graph are in close analogy with that of the World Wide Web, despite the very different growth mechanism. In particular we measure a scale--invariant distribution of the in-- and out-- degree and we are able to reproduce these features by means of a simple statistical model. As a major consequence, Wikipedia growth can be described by local rules such as the preferential attachment mechanism, though users can act globally on the network.Comment: 4 pages, 4 figures, revte

Stretched exponential relaxation for growing interfaces in quenched disordered media

We study the relaxation for growing interfaces in quenched disordered media. We use a directed percolation depinning model introduced by Tang and Leschhorn for 1+1-dimensions. We define the two-time autocorrelation function of the interface height C(t',t) and its Fourier transform. These functions depend on the difference of times t-t' for long enough times, this is the steady-state regime. We find a two-step relaxation decay in this regime. The long time tail can be fitted by a stretched exponential relaxation function. The relaxation time is proportional to the characteristic distance of the clusters of pinning cells in the direction parallel to the interface and it diverges as a power law. The two-step relaxation is lost at a given wave length of the Fourier transform, which is proportional to the characteristic distance of the clusters of pinning cells in the direction perpendicular to the interface. The stretched exponential relaxation is caused by the existence of clusters of pinning cells and it is a direct consequence of the quenched noise.Comment: 4 pages and 5 figures. Submitted (5/2002) to Phys. Rev.

Solitons in the noisy Burgers equation

We investigate numerically the coupled diffusion-advective type field equations originating from the canonical phase space approach to the noisy Burgers equation or the equivalent Kardar-Parisi-Zhang equation in one spatial dimension. The equations support stable right hand and left hand solitons and in the low viscosity limit a long-lived soliton pair excitation. We find that two identical pair excitations scatter transparently subject to a size dependent phase shift and that identical solitons scatter on a static soliton transparently without a phase shift. The soliton pair excitation and the scattering configurations are interpreted in terms of growing step and nucleation events in the interface growth profile. In the asymmetrical case the soliton scattering modes are unstable presumably toward multi soliton production and extended diffusive modes, signalling the general non-integrability of the coupled field equations. Finally, we have shown that growing steps perform anomalous random walk with dynamic exponent z=3/2 and that the nucleation of a tip is stochastically suppressed with respect to plateau formation.Comment: 11 pages Revtex file, including 15 postscript-figure

Signature of effective mass in crackling noise asymmetry

Crackling noise is a common feature in many dynamic systems [1-9], the most familiar instance of which is the sound made by a sheet of paper when crumpled into a ball. Although seemingly random, this noise contains fundamental information about the properties of the system in which it occurs. One potential source of such information lies in the asymmetric shape of noise pulses emitted by a diverse range of noisy systems [8-12], but the cause of this asymmetry has lacked explanation [1]. Here we show that the leftward asymmetry observed in the Barkhausen effect [2] - the noise generated by the jerky motion of domain walls as they interact with impurities in a soft magnet - is a direct consequence of a magnetic domain wall's negative effective mass. As well as providing a means of determining domain wall effective mass from a magnet's Barkhausen noise our work suggests an inertial explanation for the origin of avalanche asymmetries in crackling noise phenomena more generally.Comment: 13 pages, 4 figures, to appear in Nature Physic

Barkhausen Noise and Critical Scaling in the Demagnetization Curve

The demagnetization curve, or initial magnetization curve, is studied by examining the embedded Barkhausen noise using the non-equilibrium, zero temperature random-field Ising model. The demagnetization curve is found to reflect the critical point seen as the system's disorder is changed. Critical scaling is found for avalanche sizes and the size and number of spanning avalanches. The critical exponents are derived from those related to the saturation loop and subloops. Finally, the behavior in the presence of long range demagnetizing fields is discussed. Results are presented for simulations of up to one million spins.Comment: 4 pages, 4 figures, submitted to Physical Review Letter

Mean-field limit of systems with multiplicative noise

A detailed study of the mean-field solution of Langevin equations with multiplicative noise is presented. Three different regimes depending on noise-intensity (weak, intermediate, and strong-noise) are identified by performing a self-consistent calculation on a fully connected lattice. The most interesting, strong-noise, regime is shown to be intrinsically unstable with respect to the inclusion of fluctuations, as a Ginzburg criterion shows. On the other hand, the self-consistent approach is shown to be valid only in the thermodynamic limit, while for finite systems the critical behavior is found to be different. In this last case, the self-consistent field itself is broadly distributed rather than taking a well defined mean value; its fluctuations, described by an effective zero-dimensional multiplicative noise equation, govern the critical properties. These findings are obtained analytically for a fully connected graph, and verified numerically both on fully connected graphs and on random regular networks. The results presented here shed some doubt on what is the validity and meaning of a standard mean-field approach in systems with multiplicative noise in finite dimensions, where each site does not see an infinite number of neighbors, but a finite one. The implications of all this on the existence of a finite upper critical dimension for multiplicative noise and Kardar-Parisi-Zhang problems are briefly discussed.Comment: 9 Pages, 8 Figure