RESUMO
In many complex systems a continuous input of energy over time can be suddenly relaxed in the form of avalanches. Conventional avalanche models disregard the possibility of internal dynamical effects in the interavalanche periods, and thus miss basic features observed in some real systems. We address this issue by studying a model with viscoelastic relaxation, showing how coherent oscillations of the stress field can emerge spontaneously. Remarkably, these oscillations generate avalanche patterns that are similar to those observed in seismic phenomena.
RESUMO
We study the probability distribution function (PDF) of the position of a Lévy flight of index 0 < α < 2 in the presence of an absorbing wall at the origin. The solution of the associated fractional Fokker-Planck equation can be constructed using a perturbation scheme around the Brownian solution (corresponding to α = 2) as an expansion in ε = 2-α. We obtain an explicit analytical solution, exact at the first order in ε, which allows us to conjecture the precise asymptotic behavior of this PDF, including the first subleading corrections, for any α. Careful numerical simulations, as well as an exact computation for α = 1, confirm our conjecture.
Assuntos
Algoritmos , Difusão , Modelos Estatísticos , Simulação por ComputadorRESUMO
We study, using exact numerical simulations, the statistics of the longest excursion l(max)(t) up to time t for the fractional Brownian motion with Hurst exponent 0