Flux Front Penetration in Disordered Superconductors

Abstract

We investigate flux front penetration in a disordered type-II superconductor by molecular dynamics simulations of interacting vortices and find scaling laws for the front position and the density profile. The scaling can be understood by performing a coarse graining of the system and writing a disordered nonlinear diffusion equation. Integrating numerically the equation, we observe a crossover from flat to fractal front penetration as the system parameters are varied. The value of the fractal dimension indicates that the invasion process is described by gradient percolation.

Deblocking of interacting particle assemblies: from pinning to jamming

“…The presence of disorder (pinning centers) induces substantial effects on the behavior of the system that can be quantified in terms of the front propagation and/or the shape of the density profiles of flux lines. Depending on the boundary conditions, it has been observed that the front is either pinned or simply slowed down [45]. Extensive numerical simulations have also been performed in Refs.…”

“…This is clearly illustrated nowadays by the large variety of studies dealing with front invasion where roughening processes take place such as flow through porous media [16][17][18] or imbibition [19], flame propagation [20,21], deposition processes [14,15], and flux penetration in superconducting materials [32,33,45,46]. From a macroscopic point of view, the development of modeling techniques for the description of these dynamical systems has been generally based on the traditional approach to transport phenomena, where the governing expressions are usually differential equations representing local balances of the quantity of interest (e.g., mass, momentum, flux of superconducting vortices, etc.)…”

“…Extensive numerical simulations have also been performed in Refs. [45,46] to show the compatibility between the MD model with disorder and its coarse-grained representation, Eq. (11).…”

“…To be specific, we consider the situation in which the front penetration takes place in a disordered type II superconductor and the particles are vortices interacting according to Eq. (3) [46,45]. The following BC's correspond to different experimental situations [47,48]:…”

Classes of N-Dimensional Nonlinear Fokker-Planck Equations Associated to Tsallis Entropy

“…These type of phenomena may be found in the motion of particles in porous media [12][13][14][15], the dynamics of surface growth [15], the diffusion of polymer-like breakable micelles [16], the dynamics of interacting vortices in disordered superconductors [17,18], and the motion of overdamped particles through narrow channels [19], among others. An interesting aspect about the Tsallis distribution is that it appears also as a a stable solution of a NLFPE; in its simplest, one-dimensional form, this equation is given by [20][21][22] …”