Non-steady relaxation and critical exponents at the depinning transition via large scale GPU simulations
Ezequiel Ferrero, Centro Atómico Bariloche – CONICET
We study the non-steady relaxation of a driven one-dimensional elastic interface at the depinning transition by extensive numerical simulations concurrently implemented on graphics processing units (GPUs). We compute the time-dependent velocity and roughness as the interface relaxes from a given initial configuration at the thermodynamic critical force. We extract critical exponents from the Short Time Dynamics behavior of the system. Above the first, non-universal microscopic time-regime, we find a non-trivial long crossover towards the non-steady macroscopic critical regime, where it is accurate to fit. Our study may explain numerical discrepancies (as large as 30% for the velocity exponent $\beta$) found in the literature.
In addition, if time permits, I would like to briefly mention other implementations we have been developing for simulations in GPUs, including Monte Carlo dynamics of classical spin systems and Langevin dynamics for a $\Phi^4$ model.