2013/04/26 by Alexander Dobrinevski, Pierre Le Doussal, Kay Jörg Wiese · 2 citations
Biochemistry, Genetics and Molecular Biology · Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Barkhausen effect #Barkhausen stability criterion #Earthquake Detection and Analysis #Geomagnetism and Paleomagnetism Studies #Magnetic field #Magnetization #Mathematics #Mechanics #Physics #Power law #Quantum mechanics #Relaxation (psychology) #Statistical physics #Statistics #cond-mat.dis-nn #cond-mat.stat-mech #earthquake and tectonic studies
paper · pdf · doi:10.1103/physreve.88.032106
published as Phys. Rev. E 88, 032106 (2013) · 39 pages, 26 figures
arxiv created 2013/04/26 · openalex publication_date 2013/09/04 · arxiv updated 2013/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study a generalization of the Alessandro-Beatrice-Bertotti-Montorsi (ABBM) model of a particle in a Brownian force landscape, including retardation effects. We show that under monotonous driving the particle moves forward at all times, as it does in absence of retardation (Middleton's theorem). This remarkable property allows us to develop an analytical treatment. The model with an exponentially decaying memory kernel is realized in Barkhausen experiments with eddy-current relaxation and has previously been shown numerically to account for the experimentally observed asymmetry of Barkhausen pulse shapes. We elucidate another qualitatively new feature: the breakup of each avalanche of the standard ABBM model into a cluster of subavalanches, sharply delimited for slow relaxation under quasistatic driving. These conditions are typical for earthquake dynamics. With relaxation and aftershock clustering, the present model includes important ingredients for an effective description of earthquakes. We analyze quantitatively the limits of slow and fast relaxation for stationary driving with velocity v>0. The v-dependent power-law exponent for small velocities, and the critical driving velocity at which the particle velocity never vanishes, are modified. We also analyze nonstationary avalanches following a step in the driving magnetic field. Analytically, we obtain the mean avalanche shape at fixed size, the duration distribution of the first subavalanche, and the time dependence of the mean velocity. We propose to study these observables in experiments, allowing a direct measurement of the shape of the memory kernel and tracing eddy current relaxation in Barkhausen noise.