Statistical-thermodynamical foundations of anomalous diffusion

It is shown that Tsallis' generalized statistics provides a natural frame for the statistical-thermodynamical description of anomalous diffusion. Within this generalized theory, a maximum-entropy formalism makes it possible to derive a mathematical formulation for the mechanisms that underly Levy-like superdiffusion, and for solving the nonlinear Fokker-Planck equation.Comment: 13 pages, 8 figures; to appear in special issue of Braz. J. Phys. as invited revie

Dynamical systems with time-dependent coupling: Clustering and critical behaviour

We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with autonomous dynamics. The system exhibits different dynamical regimes, with various forms of collective organization, controlled by the range of interactions and the dispersion of time scales in the evolution of the internal variables. In the limit of large interaction ranges, it reduces to an ensemble of coupled identical phase oscillators and, to some extent, admits to be treated analytically. We find and characterize a transition between ordered and disordered states, mediated by a regime of dynamical clustering.Comment: to appear in Physica

Effects of noise on the internal resonance of a nonlinear oscillator

We numerically analyze the response to noise of a system formed by two coupled mechanical oscillators, one of them having Duffing and van der Pol nonlinearities, and being excited by a self-sustaining force proportional to its own velocity. This system models the internal resonance of two oscillation modes in a vibrating solid beam clamped at both ends. In applications to nano- and micromechanical devices, clamped-clamped beams are subjected to relatively large thermal and electronic noise, so that characterizing the fluctuations induced by these effects is an issue of both scientific and technological interest. We pay particular attention to the action of stochastic forces on the stability of internal-resonance motion, showing that resonant oscillations become more robust than other forms of periodic motion as the quality factor of the resonant mode increases. The dependence on other model parameters - in particular, on the coupling strength between the two oscillators - is also assessed.Fil: Zanette, Damian Horacio. Comisión Nacional de Energía Atómica. Gerencia del Area de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Complex spatial organization in a simple model of resource allocation

A dynamical model for the distribution of resources between competing agents is studied. While global competition leads to the accumulation of all the resources by a single agent, local competition allows for a wider resource distribution. Multiplicative processes give rise to almost-ordered spatial structures, thourgh the enhancement of random fluctuations.Comment: 4 pages, 3 figures, preliminary versio