Carlos Bruno Briozzo

Exact and asymptotic properties of multistate random walks

A method is presented which allows one to obtain explicit analytical expressions (both exact and asymptotic) for many of the physically interesting quantities related to a multistate random walk (MRW). The exact results include the Laplace-Fourier-transformed probability distribution (continuous time) and generating function (discrete time), and closed evolution equations for the propagators related to each “internal” state of the walker. Analytical expressions for the scattering dynamical structure function and the frequency-dependent diffusion coefficient are given as illustrations. Asymptotic approximations to the single-state propagators are derived, allowing a detailed analysis of the longtime behavior and the calculation of asymptotic properties by single-state random walk standard methods. As an example, analytical expressions for the drift and diffusion coefficients are given.

SIGNAL-TO-NOISE RATIO IN STOCHASTIC RESONANCE

We solve the Fokker-Planck equation for an overdamped Brownian particle in a periodically forced bistable potential by means of a path integral method, obtaining the propagators in the steepest-descent (small-noise) approximation. We compute the long-times asymptotic probability distribution, the asymptotic correlation functions, and the time-averaged spectral density, which allows us the immediate calculation of the signal to noise ratio, a directly measurable quantity useful to characterize the phenomenon of stochastic resonance. Our numerical algorithm is fast and runs on a desktop computer, and the results agree with experiments and with former theoretical calculations of the amplification factor; in addition it allows us to calculate the experimentally more accessible signal to noise ratio.

Stability of a Robertson-Walker universe against stochastic perturbations

Abstract The Einstein-Langevin equations for a Robertson-Walker universe in which a small stochastic perturbation is introduced in the deterministic equations of motion for the radius of the universe are analysed. We solve the associated nonlinear Fokker-Planck equation in the small noise limit using the Ω expansion and find that the cosmological constant plays an essential role in the long time stability of the model.

Exact generating function for the two-dimensional lattice Lorentz gas

We find the generating function for the two-dimensional lattice Lorentz gas by the resolvent matrix method introducing a direct procedure to calculate its elements. The asymptotic behaviour of properties as moments of the distribution and the probability of returning to the origin is analyzed in the discrete time formulation, and extended to continuous time; we also discuss briefly a disordered model. This result can be applied to a variety of physical problems.

Inertial effects on recurrent pattern formation in periodically driven Rayleigh–Bénard convection

Periodically driven Rayleigh–Benard convection is modelled by a vertical mode expansion of a mean field approximation to the Oberbeck–Boussinesq equations with thermal noise. The resulting model generalizes the Lorenz Model introduced by Ahlers, Hohenberg, and Lucke [Phys. Rev. A 32 (1985) 3493] including the continuous dependence on the horizontal wavenumber. The model is used to predict the order–disorder transition experimentally observed in the recurrent pattern formation near the convective onset, showing that the inclusion of inertial effects in the description of externally modulated pattern forming transitions, leads to theoretical predictions for the effects of thermal noise much closer to the experimental results than those of previous (purely dissipative) models.

EFFECT OF THERMAL NOISE ON THE CURRENT-VOLTAGE CHARACTERISTICS OF JOSEPHSON JUNCTIONS

We analyze the influence of thermal noise on the Shapiro steps appearing in the current-voltage characteristics of Josephson junctions. We solve the Fokker-Planck equation describing the system by a path integral method in the steepest-descent approximation, previously applied to the stochastic resonance problem. We obtain the Asymptotic Time-Periodic Distribution Pas(ϕ, t), where ϕ∈[0, 2π] and compute from it the voltage

Reactant Segregation: The Effect of Strong Space Disorder in Diffusion-Limited Bimolecular Reactions

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Extension of fast periodic transfer orbits from the Earth–Moon RTBP to the Sun–Earth–Moon Quasi-Bicircular Problem

, constructing the I-V characteristics. We find a defined “softening” of the Shapiro steps as temperature increases, for values of the system parameters in the experimentally accessible range.

Continuous-time random-walk model for superionic conductors

Quite recently, the non-classical kinetics of the diffusion-limited reaction processes for two species annihilation A+B→C (C: inert specie), has attracted considerable attention [1–7]. Such a process has been studied as a model of several different physical and chemical systems (ionic, electron-hole and defect recombination, matter-antimatter annihilation, etc.). An aspect pointed out almost a decade ago by Zeldovich and coworkers was the possibility of macroscopic segregation [8]. Several recent reviews have analyzed this and related aspects of such systems [9–12]. Among other problems, authors have been concerned with the influence of dimensionality, initial conditions, sources, conservation laws, etc. [1, 5, 6, 12]. Also the form of the kinetic or rate equations have received some attention [4, 7, 11 12 ,13].