Domain-wall dynamics and Barkhausen effect in metallic ferromagnetic materials. I. Theory

Abstract

Article] Domain wall dynamics and Barkhausen effect in metallic ferromagnetic materials. I. TheoryOriginal Citation: Alessandro B.; Beatrice C.; Bertotti G.; Montorsi A. (1990). Domain wall dynamics and Barkhausen effect in metallic ferromagnetic materials. I.

Universal fluctuations and extreme statistics of avalanches near the depinning transition

“…For example, different scaling functions are obtained for the maximum heights of periodic Gaussian interfaces: if the maximum is measured relative to the spatially averaged height, the corresponding EVS is determined by the so-called Airy distribution function [41][42][43][44], whereas measuring the maximum relative to the boundary value leads to the Rayleigh distribution [50,51]. We will discuss the extreme value distribution for an avalanche in a mean field theory of interface depinning known as the Alessandro-BeatriceBertotti-Montorsi (ABBM) model [52] and will show that this avalanche signal can be viewed as a sequence of strongly-correlated, non-identically distributed, nonGaussian variables. The probability distribution function (PDF) of the maximum velocity inside avalanches of fixed duration T follows a universal scaling form P (v m |T ) = (2v m T ) −1/2 F ( 2v m /T ), with a scaling function F (x) that can be derived exactly by a mapping to an equivalent problem of random excursions of Brownian motion in a logarithmic potential.…”

“…However, Eq. (34) can also be obtained from the exact solutions to the untransformed k = 0 Fokker-Planck equation [52] …”

“…The interpretation can be verified by demanding that Eq. (5) predict the correct steady state distribution [52] …”

“…[52]. The model was initially derived to mimic the dynamics of a single domain wall in soft magnets exhibiting Barkhausen noise, but has become a 'standard model' for interface depinning in the presence of longranged forces [1,10,28,53].…”

Record statistics of financial time series and geometric random walks

“…In recent years, there is an increasing interest in the study of record statistics in the context of global warming and climate change [3], occurrence of cyclones and floods [4] and stock markets. In physics, records statistics is useful in understanding the behavior of stochastic motion of a domain wall in metallic ferromagnetic materials [5] and as an alternative indicator of quantum chaos in kicked rotor model [6]. Even as the record breaking events continue to enjoy media attention, there is also an increased research interest in the statistical study of record events [7][8][9][10][11][12].…”