Centre de Physique Théorique

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Dynamical Systems: Theory and Applications

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, especially the central limit theorem (CLT), the Almost Sure Invariance Principle, the large deviations and the distribution of rare events.
The rate of decay of correlations for non-uniformly hyperbolic systems is estimated through new techniques (coupling, renewal). Random systems (by random composition of maps acting on the same space) and sequential dynamical systems (non-stationary, or non-autonomous, processes where a concatenation of maps act on a space) are also studied. We have formulated and develop the extreme value theory for random and non-autonomous systems and with the extension to coupled map lattices.

Fusion plasma physics : We develop reduced Hamiltonian fluid and kinetic models from Dirac’s constraint theory to investigate fundamental mechanisms of turbulent magnetized plasma that deteriorate the confinement in tokamak devices. Spurious instabilities in non-Hamiltonian hybrid model for interaction of energetic particles with a thermal plasma are also investigated, as well as
secondary instabilities following magnetic reconnection. Another part of the research activity concerns the application of the theory of stochastic processes to study the formation of transport barriers in tokamaks.

Biophysics : We focus on the fundamental physical processes, in particular resonant electrodynamic forces acting at a long distance, which are surmised to be responsible of the high efficiency of the molecular machinery within living cells and long-range coherence in biological systems. This activity is pursued on both theoretical and experimental sides in collaboration with molecular biologists.

Complexity: New methods of measuring networks complexity are developed within the framework of Riemannian Information Geometry. Applications to protein interaction networks in cancer cells are being developed.

Directory of Members

Asch Joachim University faculty
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Aschbacher Walter University faculty
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Bui Olivier PhD candidate
Caby Théophile PhD candidate
ESPANA Andrea PhD candidate
Floriani Elena University faculty
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Gori Matteo Postdoctoral researcher
Lechelon Mathias Postdoctoral researcher
Leoncini Xavier University faculty
Référent pôle de recherche interdisciplinaire et intersectoriel AMU - Energie
Chef de l’équipe « Systèmes dynamiques : théories et applications »
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Maestri Stefano PhD candidate
Pettini Marco University faculty
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Vaienti Sandro University faculty
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Valvo Lorenzo PhD candidate
Vittot Michel Researcher
Chef du Groupe « Systèmes dynamiques classiques et quantiques »
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Wang Tianbo PhD candidate

List of Publications

209 results
Valerio Lucarini, Davide Faranda, Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Holland Mark, Kuna Tobias, Matthew Nicol, Mike Todd, Sandro Vaienti
Extremes and Recurrence in Dynamical Systems
Wiley Interscience, 2016, Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts, 9781118632192
Journal article
Michael Kraus, Emanuele Tassi, Daniela Grasso
Variational integrators for reduced magnetohydrodynamics
Journal of Computational Physics, Elsevier, 2016, ⟨10.1016/j.jcp.2016.05.047⟩
Journal article
Elena Floriani, Ricardo Lima, Ouerdia Ourrad, Lionel Spinelli
Flux through a Markov chain
Chaos, Solitons and Fractals, Elsevier, 2016, 93, pp.136 - 146. ⟨10.1016/j.chaos.2016.10.006⟩
Journal article
Davide Faranda, Jorge Milhazes Freitas, Pierre Guiraud, Sandro Vaienti
Statistical Properties of Random Dynamical Systems with Contracting Direction
Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2016, 49, pp.204001 ⟨10.1088/1751-8113/49/20/204001⟩
Journal article
Emanuele Tassi, Pierre-Louis Sulem, Thierry Passot
Reduced models accounting for parallel magnetic perturbations: gyrofluid and FLR-Landau fluid approaches
Journal of Plasma Physics, Cambridge University Press (CUP), 2016, 82 (6), pp.705820601. ⟨10.1017/S0022377816000921⟩
Conference paper
Shun Ogawa, Benjamin Cambon, Xavier Leoncini, Diego Del Castillo Negrete, Michel Vittot, Guilhem Dif-Pradalier, Xavier Garbet
A study of full particle orbit effects in stochastic magnetic fields
57th Annual Meeting of the APS Division of Plasma Physics, Nov 2015, Savannah, United States
Journal article
C Chandre
Incomplete Dirac reduction of constrained Hamiltonian systems
Annals of Physics, 2015, 361, pp.1. ⟨http://dx.doi.org/10.1016/j.aop.2015.06.011⟩
Journal article
M Perin, Cristel Chandre, P.J. Morrison, E Tassi
Hamiltonian fluid closures of the Vlasov-Ampère equations: from water-bags to N moment models
Physics of Plasmas, American Institute of Physics, 2015, 22, pp.092309
Journal article
Simon Berman, Cristel Chandre, T Uzer
Persistence of Coulomb focusing during ionization in the strong-field regime
Physical Review A, American Physical Society, 2015, 92, pp.023422
Journal article
M Perin, C Chandre, P.J. Morrison, E Tassi
Hamiltonian closures for fluid models with four moments by dimensional analysis
Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2015, 48 (27), pp.275501
209 results