In this paper, we study a non-local coupled system that arises in the theory of dislocations densities dynamics. Within the framework of viscosity solutions, we prove a long time existence and uniqueness result for the solution of this model. We also propose a convergent numerical scheme and we prove a Crandall-Lions type error estimate between the… (More)
In this paper we study the connection between four models describing dislocation dynamics: a generalized 2D Frenkel-Kontorova model at the atomic level, the Peierls-Nabarro model, the discrete dislocation dynamics and a macroscopic model with dislocation densities. We show how each model can be deduced from the previous one at a smaller scale.
Nowadays, a wide variety of e-learning systems integrate proprietary developed courses. These courses cannot be easily reused and interchanged between various Learning Management Systems (LMS) over the Internet In this paper, an improved WBT Model based on the Learning Technology Systems Architecture (LTSA) standard will be presented. This model includes… (More)
Information and communication systems have several security vulnerabilities. In addition, conventional security software requires tuning effort and may not be able to detect many web attacks. For this reasons, security becomes a worldwide objective to many technological systems including Learning Management Systems (LMSs) such as Moodle. In this work, we… (More)