Upscaling of dislocation walls in finite domains

We wish to understand the macroscopic plastic behaviour of metals by upscaling the micro-mechanics of dislocations. We consider a highly simplified dislocation network, which allows our microscopic model to be a one dimensional particle system, in which the interactions between the particles (dislocation walls) are singular and non-local. As a first step towards treating realistic geometries, we focus on finite-size effects rather than considering an infinite domain as typically discussed in the literature. We derive effective equations for the dislocation density by means of \Gamma-convergence on the space of probability measures. Our analysis yields a classification of macroscopic models, in which the size of the domain plays a key role

Large-time behavior of solutions to a reaction-diffusion system with distributed microstructure

Abstract We study the large-time behavior of a class of reaction-diffusion systems with constant distributed microstructure arising when modeling diffusion and reaction in structured porous media. The main result of this Note is the following: As t ¿ 8 the macroscopic concentration vanishes, while the microscopic concentrations reach constant concentration profiles independent of the shape of the microstructure. Résumé Comportément en grands temps pour un système de réaction et de diffusion ayant une microstructure distribuée. On étudie le comportement en grands temps pour un système de réaction et de diffusion, dont la microstructure est distribuée uniformement dans l’ éspace. Le résultat principal de cette Note est le suivant : On montre que la concentration macroscopique converge, en grands temps, vers zero et que les concentrations microscopiques devient des constantes indépendentes du choix de la microstructure

Does communication enhance pedestrians transport in the dark?

We study the motion of pedestrians through an obscure tunnel where the lack of visibility hides the exits. Using a lattice model, we explore the effects of communication on the effective transport properties of the crowd of pedestrians. More precisely, we study the effect of two thresholds on the structure of the effective nonlinear diffusion coefficient. One threshold models pedestrians's communication efficiency in the dark, while the other one describes the tunnel capacity. Essentially, we note that if the evacuees show a maximum trust (leading to a fast communication), they tend to quickly find the exit and hence the collective action tends to prevent the occurrence of disasters

Quality utility modelling for multimedia applications for Android mobile devices

With the advances in mobile technologies, smart mobile computing devices have become increasingly affordable and powerful, leading to a significant growth in both the number of advanced mobile users and their bandwidth demands. Moreover multimedia streaming to these high-end mobile devices has become widespread. However, multimedia applications are known to be resource-hungry and in order to cope with this explosion of data traffic, operators have started deploying different, overlapping radio access network technologies. One important challenge in such a heterogeneous wireless environment is to ensure an Always Best Experience to the mobile user, anywhere and anytime. This paper proposes the Quality Utility, a realistic mapping function of the received bandwidth to user satisfaction for multimedia streaming applications. The Quality Utility is mapped to a Google Nexus One Android Mobile device and validated through objective and subjective tests

Modeling Compressible Non-Newtonian Chicken Flow

This paper addresses a few modeling issues relevant for the basic theoretical understanding of the meat flow behavior in simple geometries. We model the meat mixture as a non-Newtonian compressible fluid. Focusing on conceptually easy-to-follow cases like flow in thin molds, or steady incompressible or compressible flow in straight pipes we derive explicit expressions for the velocity and pressure profiles. For the thin moldcase, we formulate a one-dimensional free-boundary problem able to capture the a priori unknown position of the moving meat-air interface. Special attention is payed on the derivation of the free boundary conditions

Fast-reaction asymptotics for a two-scale reaction-diffusion system

We investigate a reaction–diffusion process in a two-phase medium with microscopic length scale ε. The diffusion coefficients in the two phases are highly different (d1/D = ε2) and the reaction constant k is large. First, the homogenisation limit ε → 0 is taken, which leads to a two-scale model. Afterwards, we pass to the fast-reaction limit k → ∞ and obtain a two-scale reaction-diffusion system with a moving boundary traveling within the microstructure