Biomedical subjects
Publications and source records attributed to Angelo Vulpiani.
Discretization of phase space usually nullifies chaos in dynamical systems. We show that if randomness is associated with discretization dynamical chaos may survive and be indistinguishable from that of the original chaotic system, when an entropic, coarse-grained analysis is performed. Relevance of this phenomenon to the problem of quantum chaos is discussed.
The study of diffusion in Hamiltonian systems has been a problem of interest for a number of years. In this paper we explore the influence of self-consistency on the diffusion properties of systems described by coupled symplectic maps. Self-consistency, i.e., the backinfluence of the transported quantity on the velocity field of the driving flow, despite of its critical importance, is usually overlooked in the description of realistic systems, for example, in plasma physics. We propose a class of self-consistent models consisting of an ensemble of maps globally coupled through a mean field. Depending on the kind of coupling, two different general types of self-consistent maps are considered: maps coupled to the field only through the phase, and fully coupled maps, i.e., through the phase and the amplitude of the external field. The analogies and differences of the diffusion properties of these two kinds of maps are discussed in detail.
We study the behavior of two particles moving in a bistable potential, colliding inelastically with each other and driven by a stochastic heat bath. The system has the tendency to clusterize, placing the particles in the same well at low drivings, and to fill all of the available space at high temperatures. We show that the hopping over the potential barrier occurs following the Arrhenius rate, where the heat bath temperature is replaced by the granular temperature. Moreover, within the clusterized "phase" one encounters two different scenarios: For moderate inelasticity, the jumps from one well to the other involve one particle at a time, whereas for strong inelasticity the two particles hop simultaneously.
A discrete-time model of reacting evolving fields, transported by a bidimensional chaotic fluid flow, is studied. Our approach is based on the use of a Lagrangian scheme where fluid particles are advected by a two-dimensional symplectic map possibly yielding Lagrangian chaos. Each fluid particle carries concentrations of active substances which evolve according to its own reaction dynamics. This evolution is also modeled in terms of maps. Motivated by the question, of relevance in marine ecology, of how a localized distribution of nutrients or preys affects the spatial structure of predators transported by a fluid flow, we study a specific model in which the population dynamics is given by a logistic map with space-dependent coefficient, and advection is given by the standard map. Fractal and random patterns in the Eulerian spatial concentration of predators are obtained under different conditions. Exploiting the analogies of this coupled-map (advection plus reaction) system with a random map, some features of these patterns are discussed. (c) 2001 American Institute of Physics.