he study of transport and diffusion of Brownian particles in disorder media needs the generation of random potentials with well prescribed statistical properties. Here we present a straightforward method to build a Gaussian potential landscape with an arbitrary spatial correlation with the only requirement of isotropy. The method has the particularity that, although it uses the Fourier space, all its constraints and information are in real space. As practical applications we construct three types of Gaussian disordered correlations: Normal, exponential and power-law. These three cases cover a variety of physical situations.
Lindenberg, K.; Sancho, J M; Khoury, M. J.; Lacasta, A.M Fluctuation and noise letters Vol. 11, num. 01, p. 1240004-01-1240004-09 DOI: 10.1142/S0219477512400093 Data de publicació: 2012-03-31 Article en revista
Particles driven through a periodic potential by an external constant force are known to exhibit a pronounced peak of the diffusion around the critical deterministic force that defines the transition between locked and running states. It has recently been shown both experimentally and numerically that this peak is greatly enhanced if some amount of spatial disorder is superimposed on the periodic potential. Here, we show that this enhancement is a fingerprint of a broad phenomenology that goes well beyond a simple augmentation. For some values of the model parameters, including the characteristic distances associated with the periodic and random components of the potential, the magnitude of the external force, and the temperature, the system can exhibit a rich variety of regimes from normal diffusion to superdiffusion, subdiffusion and even subtransport.
We study initial transient stages in directional solidification by means of a non-variational phase field model with fluctuations. This model applies for the symmetric solidification of dilute binary solutions and does not invoke fluctuation-dissipation theorem to account for the fluctuation statistics. We devote our attention to the transient regime
during which concentration gradients are building up and fluctuations act to destabilize the interface. To this end, we calculate both the temporally dependent growth rate of each mode and the power spectrum of the interface evolving under the effect of fluctuations.
Quantitative agreement is found when comparing the phase-field simulations with