The target of our study is to approximate numerically and, in some particular physically relevant cases, also analytically, the residence time of particles undergoing an asymmetric simple exclusion dynamics on a vertical strip. The source of asymmetry is twofold: (i) the choice of boundary conditions (different reservoir levels) and (ii) the strong anisotropy from a nonlinear drift with prescribed directionality. We focus on the effect of the choice of anisotropy in the flux on the asymptotic behavior of the residence time with respect to the length of the strip. The topic is relevant for situations occurring in pedestrian flows or biological transport in crowded environments, where lateral displacements of the particles occur predominantly affecting therefore in an essentially way the efficiency of the ENMC thanks Kerry Landman (Melbourne), Roberto Fernández (Utrecht), and Lorenzo Bertini (Roma) for very stimulating discussions and useful references. cms-serw001.tex -1 agosto 2018 22:05 arXiv:1411.5490v2 [nlin.CG] 9 Feb 2015 overall transport mechanism.

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We study an asymmetric simple exclusion process in a strip in the presence of a solid impenetrable barrier. We focus on the effect of the barrier on the residence time of the particles, namely, the typical time needed by the particles to cross the whole strip. We explore the conditions for reduced jamming when varying the environment (different drifts, reservoir densities, horizontal diffusion walks, etc.). In particular, we discover an interesting nonmonotonic behavior of the residence time as a function of the barrier length. Besides recovering by means of both the lattice dynamics and the mean-field model well-known aspects like the faster-is-slower effect and the intermittence of the flow, we propose also a birth-and-death process and a reduced one-dimensional (1D) model with variable barrier permeability to capture the behavior of the residence time with respect to the parameters.

We analyze a coupled system of evolution equations that describes the effect of thermal gradients on the motion and deposition of N populations of colloidal species diffusing and interacting together through Smoluchowski production terms. This class of systems is particularly useful in studying drug delivery, contaminant transport in complex media, as well as heat shocks thorough permeable media. The particularity lies in the modeling of the nonlinear and nonlocal coupling between diffusion and thermal conduction. We investigate the semidiscrete as well as the fully discrete a priori error analysis of the finite elements approximation of the weak solution to a thermo-diffusion reaction system posed in a macroscopic domain. The mathematical techniques include energy-like estimates and compactness arguments.

We present two conceptually new modeling approaches aimed at describing the motion of pedestrians in obscured corridors:(i) a Becker-Döring-type dynamics and (ii) a probabilistic cellular automaton model. In both models the group formation is affected by a threshold. The pedestrians are supposed to have very limited knowledge about their current position and their neighborhood; they can form groups up to a certain size and they can leave them. Their main goal is to find the exit of the corridor.Although being of mathematically different character, the discussion of both models shows that it seems to be a disadvantage for the individual to adhere to larger groups.We illustrate this effect numerically by solving both model systems. Finally we list some of our main open questions and conjectures.