Group “Classical and Quantum Dynamical Systems”
Statistical properties of dynamical systems: Probabilistic methods are used to study limit theorems in the case of deterministic and random dynamical systems, in particular the Central Limit Theorem (CLT), the Almost Sure Invariance Principle, large deviations, and the distribution of rare events. The rate of decay of correlations for non-uniformly hyperbolic systems is estimated using new techniques (coupling, renewal). Random systems (by random composition of mappings acting on the same space) and sequential dynamical systems (non-stationary or non-autonomous, where a concatenation of mappings acts on a space) are also studied. We have formulated and developed the theory of extreme values for random and non-autonomous systems, with extensions to networks of coupled mappings.
Fusion plasma physics: We develop reduced fluid and kinetic Hamiltonian models derived from Dirac’s constraint theory to study the fundamental mechanisms of turbulent magnetized plasmas that degrade confinement in tokamak devices. Parasitic instabilities in a hybrid non-Hamiltonian model for the interaction of energetic particles with a thermal plasma are also studied, as well as secondary instabilities following magnetic reconnection. Another part of the research activity concerns the application of stochastic process theory to study the formation of transport barriers in tokamaks.
Biophysics: We focus on fundamental physical processes, in particular resonant electrodynamic forces acting over long distances, which are thought to be responsible for the high efficiency of molecular machinery within living cells and for long-range coherence in biological systems. This activity is pursued both theoretically and experimentally in collaboration with molecular biologists.
Complexity: New methods for measuring the complexity of networks are developed within the framework of Riemannian Information Geometry. Applications to networks of proteomic interactions in cancer cells are currently being developed.
| ASCH | Joachim | Research teacher | +33.4.91.26.95.20 | Contact |
| ASCHBACHER | Walter | Research teacher | +33.4.91.26.95.16 | Contact |
| DAQUIN | Jerome | Research teacher | Contact | |
| EL KETTANI | Perla | Research teacher Unit leader « Systèmes dynamiques classiques et quantiques » | +33.4.91.26.97.93 | Contact |
| FLORIANI | Elena | Research teacher | +33.4.91.26.95.22 | Contact |
| LEBOUAZDA | Yohann | Ph.D. | Contact | |
| LEONCINI | Xavier | Research teacher Team leader « Dynamical Systems: Theory and Applications » | +33.4.91.26.95.38 | Contact |
| PETTINI | Marco | Research teacher | +33.4.91.26.95.49 | Contact |
| ROUVET | Simon | Ph.D. | Contact | |
| VAIENTI | Sandro | Research teacher | +33.4.91.26.95.44 | Contact |
| VITTOT | Michel | Researcher | +33.4.91.26.95.24 | Contact |
Possible role of electrodynamic interactions in long-distance biomolecular recognition
Physical Review E : Statistical, Nonlinear, and Soft Matter Physics [2001-2015], 2015, 91 (5), pp.052710. (10.1103/PhysRevE.91.052710)
Annealed and Quenched Limit Theorems for Random Expanding Dynamical Systems
Probability Theory and Related Fields, 2015, 162 (1), pp.233-274. (10.1007/s00440-014-0571-y)
Special issue on mathematics for the fluid Earth
2015, (10.1088/1751-8113/48/14/140201)
Sampling local properties of attractors via Extreme Value Theory
Chaos, Solitons & Fractals, 2015, Extreme Events and its Applications, 74, pp.55-66. (10.1016/j.chaos.2015.01.016)
On transfer operators and maps with random holes
Nonlinearity, 2015, 28 (3), pp.713. (10.1088/0951-7715/28/3/713)
SPLINE DISCRETE DIFFERENTIAL FORMS AND A NEW FINITE DIFFERENCE DISCRETE HODGE OPERATOR
2014
Vitesse de mélange et théorèmes limites pour les systèmes dynamiques aléatoires et non-autonomes
Mathématiques générales [math.GM]. Université de Toulon, 2014. Français. (NNT : 2014TOUL0005)
Passive Covert Radars using CP-OFDM signals. A new efficient method to extract targets echoes
2014 International Radar Conference (Radar), Oct 2014, Lille, France. pp.1-6, (10.1109/RADAR.2014.7060382)
Higher order Hamiltonian fluid reduction of Vlasov equation
Annals of Physics, 2014, 348, pp.50. (10.1016/j.aop.2014.05.011)
Characterisation of the idiotypic immune network through persistent entropy
European Conference on Complex Systems (ECCS14), Sep 2014, Lucca, Italy. pp.117-128, (10.1007/978-3-319-29228-1_11)
