|
|
|
| e-Pub |
Previous | 
Home
Section: Application Domains
Physics
Our applications to physics concern:
Non-equilibrium statistical physics
Describing, understanding, predicting and controlling the complex physical phenomena occurring in classical or quantum dynamical systems with a large or infinite number of degrees of freedom are important issues for equilibrium and non-equilibrium statistical mechanics and remain an important challenge for mathematical physics. Some of the typical questions are the following. How does a collective dynamics emerge from the interactions of individual entities? How to compute transport coefficients in terms of microscopic quantities and more generally, what is the role of the local (microscopic) dynamics on global transport properties? What are the system ergodic properties and how are asymptotic states, if they exist, approached? What are the dynamical mechanisms for approach to equilibrium in such systems?
Cold atoms
A typical problem we are concerned with is the effect of interactions (modeled by a nonlinearity in the evolution equation) on the localization properties of quantum kicked rotors, experimentally realized in cold-atom experiments.
Laser propagation
We are interested in variants of the NonLinear Schrödinger Equation (NLSE), which govern the evolution of optical fibers, and in particular photonic crystal fibers (PCF). These are key to information and communication technology, and form an unmatchable platform to explore complex nonlinear phenomena.
Maxwell equations
A posteriori error estimators developed for the Maxwell equations are very useful tools for practical computations. They are implemented in the software "Carmel-3D" (see the softwares section). This numerical code is used in order to study some original applications, like electrical machines or specific actuators. It is also devoted to nondestructive control by the use of Foucault currents, to the simulation of devices using magnetic fluids or of induced currents in human bodies.