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Non-linear dynamic

Grant number: 07/54000-0
Support type:Research Projects - Thematic Grants
Duration: December 01, 2007 - July 31, 2012
Field of knowledge:Physical Sciences and Mathematics - Physics
Cooperation agreement: CNRS
Principal Investigator:Iberê Luiz Caldas
Grantee:Iberê Luiz Caldas
Principal investigator abroad: Sadruddin Benkadda
Institution abroad: Université de Provence, France
Home Institution: Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Co-Principal Investigators:Jose Carlos Sartorelli
Associated grant(s):10/02220-0 - Plasma turbulence control, AV.EXT
08/58588-5 - Philip James Morrison | University of Texas at Austin - Estados Unidos, AV.EXT
Associated scholarship(s):10/00740-6 - Transport in Nontwist Hamiltonian systems, BP.DR
11/12438-5 - Information theory and Biological Neural Networks, BP.IC
10/04638-1 - Real-time pattern dependent drug application protocols applied to central pattern generators: effects of serotonin (5-HT) and glutamate in the stomatogastric nervous system of Callinectes sapidus, BP.MS
+ associated scholarships 10/02138-1 - Chaotic transport in magnetized plasmas, BP.PD
08/06529-5 - Electrocommunication in weakly electric fish from the Gymnotus carapo species - an application of information theory, BP.DR
09/02149-6 - Efect of low power laser applied to the crustacean stomatogastric nervous system, BP.IC
08/00054-5 - The interaction of three waves and electrostatic turbulence in tokamaks, BP.PD - associated scholarships

Abstract

ln this proposal we describe our experimental and theoretical research plans in nonlinear dynamics applied to hamiltonian and dissipative systems, turbulence and biological systems. Hamiltonian chaos and turbulence will be studied by applying the theory of nonlinear hamiltonian dynamical systems to investigate several problems in the magnetic confinement of plasma. The main restriction to the application of the magnetic confinement of plasma is the unexpected loss of particles that leave the plasma. Several recent experiments confirmed that this anomalous transport of particles depends on the configurations of the electric and magnetic fields in the edge of the plasma. We intend to investigate the effect of these configurations on this transport. The electric field equilibrium is changed by the modification of its radial profile in the edge of the plasma, as already experimentally observed in some tokamaks. The magnetic field is modified by resonant external electric currents, as the ones given by a magnetic limiter or a divertor. We will also investigate the origin of the turbulence of the drift waves in tokamaks. ln particular, the appearance of spatial and temporal chaotic waves will be analyzed as consequence of dominant waves, as well as the experimental control of this kind of turbulence. ln several experiments with dissipative systems we will address basic properties of classical chaos theory that can be experimentally verified by studying the behavior of chaotic systems of interest in applied physics, engineering and medicine. The dynamical properties are identified in the parameter space, where we can represent common properties of the attractors and the bifurcations between these attractors. Some methods of control are analyzed, considering both ideal systems (with infinite power) as well as non ideal (with finite powers). Systems described by either differential equations or analytical maps will be considered. The main chaotic systems to be investigated are: electromechanical devices, electric circuits, particle advection in fluids and biological rhythms. The phenomena of higher interest are the bifurcations, the synchronization and the instabilities in the parameter space. The changes of these properties with the appearance of stable and unstable manifolds and chaotic saddles in the phase space of the systems will be also investigated. We will investigate the properties of the attractors by applying metric (Lyapunov spectrum) and topological (parameter spaces, isoperiodic diagrams, topological planes, etc.) techniques. We will also study: the phase synchronization of complex chaotic attractors found in electrical circuits, such as the double scroll attractor of the Chua circuit. With new experimental and analysis techniques, we will study the formation of drops of water in regimen of low dripping rate with a high speed video camera. The coupling of bubbles forming from two close nozzles will be studied by measuring the bubbling pressure waves and the data will be analyzed with the technique of bi-spectral analysis that also will be applied to characterize the coupling of oscillating flames. A more extensive study of acoustic resonators will be carried out to verify if certain systems are in fact of intermediate statistics or if the distributions of nearest neighbors of the eigenvalues are affected by missing levels... (AU)