On large deviation regimes for random media models

The focus of this article is on the different behavior of large deviations of random subadditive functionals above the mean versus large deviations below the mean in two random media models. We consider the point-to-point first passage percolation time $a_n$ on $\mathbb{Z}^d$ and a last passage percolation time $Z_n$. For these functionals, we have $\lim_{n\to\infty}\frac{a_n}{n}=\nu$ and $\lim_{n\to\infty}\frac{Z_n}{n}=\mu$. Typically, the large deviations for such functionals exhibits a strong asymmetry, large deviations above the limiting value are radically different from large deviations below this quantity. We develop robust techniques to quantify and explain the differences.Comment: Published in at http://dx.doi.org/10.1214/08-AAP535 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Suspension flow: do particles act as mixers?

Recently, Roht et al. [J. Contam. Hydrol. 145, 10-16 (2013)] observed that the presence of suspended non-Brownian macroscopic particles decreased the dispersivity of a passive solute, for a pressure-driven flow in a narrow parallel-plates channel at low Reynolds number. This result contradicts the idea that the streamline distortion caused by the random diffusive motion of the particles increases the dispersion and mixing of the solute. Therefore, to estimate the influence of this motion on the dispersivity of the solute, and investigate the origin of the reported decrease, we experimentally studied the probability density functions (pdf) of the particle velocities, and spatio-temporal correlations, in the same experimental configuration. We observed that, as the mean suspension velocity exceeds a critical value, the pdf of the streamwise velocities of the particles markedly changes from a symmetric distribution to an asymmetric one strongly skewed to high velocities and with a peak of most probable velocity close to the maximum velocity. The latter observations and the analysis of suspension microstructure indicate that the observed decrease in the dispersivity of the solute is due to particle migration to the mid-plane of the channel, and consequent flattening of the velocity profile. Moreover, we estimated the contribution of particle diffusive motion to the solute dispersivity to be three orders of magnitude smaller than the reported decrease, and thus negligible. Solute dispersion is then much more affected by how particles modify the flow velocity profile across the channel, than by their diffusive random motion