On the Collective Motion in Globally Coupled Chaotic Systems

A mean-field formulation is used to investigate the bifurcation diagram for globally coupled tent maps by means of an analytical approach. It is shown that the period doubling sequence of the single site map induces a continuous family of periodic states in the coupled system. This type of collective motion breaks the ergodicity of the coupled map lattice. The stability analysis suggests that these states are stable for weak coupling strength but opens the possibility for more complicated types of motion in the regime of moderate coupling.Comment: 12 pages, Latex, 3 eps figures included also available "at http://athene.fkp.physik.th-darmstadt.de/public/wolfram.html" or "at ftp://athene.fkp.physik.th-darmstadt.de/pub/publications/wolfram/" Phys. Rep. in pres

Bifurcations in Globally Coupled Chaotic Maps

We propose a new method to investigate collective behavior in a network of globally coupled chaotic elements generated by a tent map. In the limit of large system size, the dynamics is described with the nonlinear Frobenius-Perron equation. This equation can be transformed into a simple form by making use of the piecewise linear nature of the individual map. Our method is applied successfully to the analyses of stability of collective stationary states and their bifurcations.Comment: 12 pages, revtex, 10 figure

Calculation of NMR Properties of Solitons in Superfluid 3He-A

Superfluid 3He-A has domain-wall-like structures, which are called solitons. We calculate numerically the structure of a splay soliton. We study the effect of solitons on the nuclear-magnetic-resonance spectrum by calculating the frequency shifts and the amplitudes of the soliton peaks for both longitudinal and transverse oscillations of magnetization. The effect of dissipation caused by normal-superfluid conversion and spin diffusion is calculated. The calculations are in good agreement with experiments, except a problem in the transverse resonance frequency of the splay soliton or in magnetic-field dependence of reduced resonance frequencies.Comment: 15 pages, 10 figures, updated to the published versio

Simple deterministic dynamical systems with fractal diffusion coefficients

We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic scattering process of the map can be changed by a control parameter. This induces a parameter dependence for the macroscopic diffusion coefficient. We calculate the diffusion coefficent and the largest eigenmodes of the system by using Markov partitions and by solving the eigenvalue problems of respective topological transition matrices. For different boundary conditions we find that the largest eigenmodes of the map match to the ones of the simple phenomenological diffusion equation. Our main result is that the difffusion coefficient exhibits a fractal structure by varying the system parameter. To understand the origin of this fractal structure, we give qualitative and quantitative arguments. These arguments relate the sequence of oscillations in the strength of the parameter-dependent diffusion coefficient to the microscopic coupling of the single scatterers which changes by varying the control parameter.Comment: 28 pages (revtex), 12 figures (postscript), submitted to Phys. Rev.

MICROSCOPIC EVALUATION OF THE TRANSPORT PARAMETERS OF SUPERFLUID 3He B

Les formules de Kubo pour les coefficients de transport de l'hydrodynamique phénoménologique de l'He3 superfluide ont été récemment données. Ici nous calculons ces paramètres dans l'approximation BCS en tenant compte des effets de couplage fort par une fonction de renormalisation Z(ω). En particulier, nous discutons la viscosité et la largeur de la raie RMN. Nous comparons nos résultats aux résultats expérimentaux.The Kubo formulas of the transport parameters of the phenomenological hydrodynamics of superfluid 3He, which have recently been given, are evaluated in the BCS approximation. Strong coupling effects are taken into account by renormalization function Z(ω). In particular the shear viscosity and the NMR line width are discussed and compared with experiments

Statistical approach to nonhyperbolic chaotic systems

info:eu-repo/semantics/publishe