Global continuous solutions to diagonalizable hyperbolic systems with large and monotone data

In this paper, we study diagonalizable hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and nondecreasing initial data. Moreover, we show in particular cases some uniqueness results. We also remark that these results cover the case of systems which are hyperbolic but not strictly hyperbolic. Physically, this kind of diagonalizable hyperbolic systems appears naturally in the modelling of the dynamics of dislocation densities

Short time existence and uniqueness in Hölder spaces for the 2D dynamics of dislocation densities

In this paper, we study the model of Groma and Balogh describing the dynamics of dislocation densities. This is a two-dimensional model where the dislocation densities satisfy a system of two transport equations. The velocity vector field is the shear stress in the material solving the equations of elasticity. This shear stress can be related to Riesz transforms of the dislocation densities. Basing on some commutator estimates type, we show thatthis model has a unique local-in-time solution corresponding to any initial datum in the space $C^r(\R^2)\cap L^p(\R^2)$ for $r>1$ and $

Derivation and study of dynamical models of dislocation densities

In this paper, starting from the microscopic dynamics of isolated dislocations, we explain how to derive formally mean field models for the dynamics of dislocation densities. Essentially these models are tranport equations, coupled with the equations of elasticity. Rigorous results of existence of solutions are presented for some of these models and the main ideas of the proofs are given

A convergent scheme for a non-local coupled system modelling dislocations densities dynamics

International audienceIn 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 continuous solution and the numerical one. As far as we know, this is the first error estimate of Crandall-Lions type for Hamilton-Jacobi systems. We also provide some numerical simulations

Diagonal hyperbolic systems with large and monotone data Part I: Global continuous solutions

In this paper, we study diagonal hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and non-decreasing initial data. We remark that these results cover the case of systems which are hyperbolic but not strictly hyperbolic. Physically, this kind of diagonal hyperbolic systems appears naturally in the modelling of the dynamics of dislocation densities

NEUROCOMPUTING AND INTERFACING DIGITAL TASTING SYSTEM: RESEARCH, DESIGN, AND EVALUATION

The continuous evolution in computing and interfacing has been extended to develop multi-sensory experiences in many domains such as neurological, auditory, vision, and haptic domains. So far, only a few remarkable system approaches have been approved to be serving the taste sensation digitally. Although taste sensation is linked to the brain, there is a lack of optimal neurocomputing digital taste sensation systems. Our study provides a new neurocomputing method to digitally stimulate the sense of taste by electrical stimulation on the human tongue. We aim to link chemical stimulation and electrical stimulation in order to design an electronic interface for inducing taste digitally. The design proposes a module that is responsible for electric and stimulation to produce different taste sensations. In addition, the taste is delivered through the tongue interface by silver electrodes, coupled with a control system responsible for generating specific stimulation parameters based on user inputs selected on his mobile. A spoon for implementing the taste interface is issued in order to provide a user-friendly tool as a solution for various problems. Experimental results showed that the new model and design of the digital taste system works well and testing results showed clearly that 90% of the tested members were able to distinguish the taste. Among the taste categories, the initial results recommended that sourness and saltiness are the most probable sensations that would be induced. Besides the Biomedical importance of the new taste system for people suffering from taste problems, (no sense of taste, bad taste in the mouth, diminished sense of taste, distorted sense of taste) and for people having diabetes and hypertension, this technology shows the possibility and could be considered for sharing tastes in social networking and adapting it in virtual reality, gaming and other domains, also the sensation of tastes could be improved by involving others senses such as olfactory and sounds and increasing the population of tested members