Error control for the FEM approximation of an upscaled thermo-diffusion system with Smoluchowski interactions

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 transportin 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 em 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

A thermo-diffusion system with Smoluchowski interactions: well-posedness and homogenization

We study the solvability and homogenization of a thermal-diffusion reaction problem posed in a periodically perforated domain. The system describes the motion of populations of hot colloidal particles interacting together via Smoluchowski production terms. The upscaled system, obtained via two-scale convergence techniques, allows the investigation of deposition effects in porous materials in the presence of thermal gradients

Residence time estimates for asymmetric simple exclusion dynamics on stripes

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 stripe. 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 stripe. 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 overall transport mechanism

Multiscale modeling of colloidal dynamics in porous media including aggregation and deposition

We investigate the influence of aggregation and deposition on the colloidal dynamics in a saturated porous medium. On the pore scale, the aggregation of colloids is modeled by the Smoluchowski equation. Essentially, the colloidal mass splits into different size clusters and we treat clusters as different species involved in a diffusion-reaction mechanism. This modeling procedure allows for different material properties to be varied between the different species, specifically the diffusion rate, which changes due to size as described by the Stokes-Einstein relation, and the deposition rate. The periodic homogenization procedure is applied to obtain a macroscopic model. The resulting model is illustrated by numerical computations that capture the colloidal transport with and without aggregation. Keywords: Colloidal transport; Periodic homogenization; Multiscale coefficients; Aggregation; Depositio

Multiscale modeling of colloidal dynamics in porous media : capturing aggregation and deposition effects

We investigate the influence of multiscale aggregation and deposition on the colloidal dynamics in a saturated porous medium. At the pore scale, the aggregation of colloids is modeled by the Smoluchowski equation. Essentially, the colloidal mass is distributed between different size clusters. We treat these clusters as different species involved in a diffusion-advection-reaction mechanism. This modeling procedure allows for different material properties to be varied between the different species, specifically the rates of diffusion, aggregation, deposition as well as the advection velocities. We apply the periodic homogenization procedure to give insight into the effective coefficients of the upscaled model equations. Benefiting from direct access to microstructural information, we capture by means of 2D numerical simulations the effect of aggregation on the deposition rates recovering this way both the blocking and ripening regimes reported in the literature

Lattice model of reduced jamming by a barrier

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.). Particularly, we discover an interesting non--monotonic behavior of the residence time as a function of the barrier length. Besides recovering by means of both the lattice dynamics and mean-field model well-known aspects like faster-is-slower effect and the intermittence of the flow, we propose also a birth-and-death process and a reduced one-dimensional model with variable barrier permeability to capture qualitatively the behavior of the residence time with respect to the parameters. We report our first steps towards the understanding to which extent the presence of obstacles can fluidize pedestrian and biological transport in crowded heterogeneous environments

Cognitive distance, absorptive capacity and group rationality : A simulation study

We report the results of a simulation study in which we explore the joint effect of group absorptive capacity (as the average individual rationality of the group members) and cognitive distance (as the distance between the most rational group member and the rest of the group) on the emergence of collective rationality in groups. We start from empirical results reported in the literature on group rationality as collective group level competence and use data on real-life groups of four and five to validate a mathematical model. We then use this mathematical model to predict group level scores from a variety of possible group configurations (varying both in cognitive distance and average individual rationality). Our results show that both group competence and cognitive distance are necessary conditions for emergent group rationality. Group configurations, in which the groups become more rational than the most rational group member, are groups scoring low on cognitive distance and scoring high on absorptive capacity

Pedestrians moving in the dark : balancing measures and playing games on lattices

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