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Théorie des systèmes complexes/Theory of complex systems
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The theoretical group reflects at a smaller scale the variety of the research topics of SPEC. Its unity is in fact a culture, made of a mixture of statistical physics, critical phenomena and nonlinear physics. During the last decennia, the classical solid state physics has exported some of its methods to many domains in which the matter is more or less regularly organized. Our group has thus gradually become interested in other subjects. Our activity has been split into five main chapters: The header Complex systems gathers various subjects, some of them not necessarily linked to some state of the matter. - A model for the evolution of tropical forests has been built, which belongs to the class of coupled map lattices. - In financial markets, the large fluctuations, responsible for possible crashes but disregarded by the commonly used linear response theories, can be fruitfully described by the methods of statistical physics. - New models have been built for granular assemblies, avalanches and surface flows. - Various applications of cellular automata have been performed. Soft matter and critical phenomena Depending on the solvent selectivity, copolymers can evolve either into branched aggregates or into micelles. In the absence of gravity, supercritical fluids can present an unusual behaviour, such as a fast thermalization despite the infinite diffusion time scale near the critical point. The determination of the universality class of ionic fluids has created a profitable interaction with the liquids group at SPEC. Quantum condensed matter Spin ladders are studied in the context of experiments on superconducting oxydes. Out of equilibrium systems Spin glasses are the most studied such systems, and several directions of investigation have been followed : the slow dynamics and its resemblance with Burgers' turbulence, the aging process, etc. In spatially extended chaotic dynamical systems, there exist many active subjects of research~: pattern formation, unusual collective behaviour, dynamics of localized solutions. Bidimensional models have been built which interpolate between the Ising model and the voter's model. Nonlinear differential equations of physics range from partial differential equations, for which every variable is continuous, to cellular automata, in which they are all discrete. Their analytic study is made in two directions. General methods, all based on Painlevé's ideas, have been developed to test their integrability, in particular a new method to test if a discretization is possibly good or certainly bad. Other, constructive methods have been built and applied to specific equations of interest in various areas of physics, to derive the explicit solutions when they are reachable.

 

Maj : 14/10/2013 (180)

 

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