P. C. da Silva

Variance fluctuations in nonstationary time series: a comparative study of music genres

An important problem in physics concerns the analysis of audio time series generated by transduced acoustic phenomena. Here, we develop a new method to quantify the scaling properties of the local variance of nonstationary time series. We apply this technique to analyze audio signals obtained from selected genres of music. We find quantitative differences in the correlation properties of high art music, popular music, and dance music. We discuss the relevance of these objective findings in relation to the subjective experience of music.

Anomalous diffusion and anisotropic nonlinear Fokker–Planck equation

We analyse a N-dimensional anisotropic nonlinear Fokker–Planck equation by considering stationary and time-dependent solutions. The stationary solutions are obtained for very general situations, including those when the diffusion coefficients are spatial dependents. Time-dependent solutions are found in the absence of external force and with constant diffusion coefficients. When restricted to the bi-dimensional case, our investigation about time-dependent solutions focuses on situations where the diffusion coefficient are Dx∝|x|−θx and Dy∝|y|−θy with θx,θy∈R. In general, we verify an anomalous behavior induced in a given direction due to the other directions.

Nonlinear diffusion equation and nonlinear external force: Exact solution

The solutions of the nonlinear diffusion equation ∂tρ=r1−ND∂r{rN−1−θργ∂r[r−ηρν]}−r1−N∂r[rN−1Fρ] are investigated by considering the presence of an external force F which exhibits an explicit dependence on the distribution. First, the stationary case is considered; after that the dynamical case, i.e., the case dependent on time. The stationary solution is obtained by considering the external force F(r;ρ)=F1(r)+F2(r)[ρ(r)]ν+γ−1 and the result found is related to the distributions which emerge from the Tsallis statistics or the Boltzmann-Gibbs statistics. The dynamical solution is investigated by considering the external force F(r,t;ρ)=−k(t)r+K∕r1+θ+η[ρ(r,t)]γ+ν−1 and related to the Levy distributions in the asymptotic limit. In both cases, the solutions are expressed in terms of the q-exponentials and the q-logarithmics functions which emerge from the Tsallis formalism.

Recursive-search method for ferromagnetic ising systems: combination with a finite-size scaling approach

A method for obtaining critical properties of physical systems is presented. Based on a recursive relation involving a physical parameter of the system, it drives the system spontaneously to the critical point, providing an efficient way to estimate critical properties. The method is illustrated for several ferromagnetic Ising systems on well-known Bravais lattices. A finite-size scaling approach is performed, by applying the method on lattices of different sizes. The efficiency of the method is confirmed by evaluating critical temperatures, as well as critical exponents, that turn up to be in good agreement with those available in the literature, with a relatively small computational effort.

CRITICAL BEHAVIOR OF THE CONTACT PROCESS DELAYED BY INFECTION AND IMMUNIZATION PERIODS

We analyze the absorbing state phase transition exhibited by two distinct unidimensional delayed contact process (CP). The first is characterized by the introduction of an infection period and the second by an immune period in the dynamics of the original model. We characterize these CP by the quantities td (infection or disease period) and ti (immune period). The quantity td corresponds to the period interval an individual remains infected after being contaminated, while the period ti is the time interval an individual remains immune after being cured. We used Monte Carlo simulations to compute the critical parameters associated with the absorbing state phase transition exhibited by these models. We find two distinct power-law scale relations for the critical infection rate

Green function for a non-Markovian Fokker-Planck equation: comb-model and anomalous diffusion

\lambda_{{\rm in}}^{*} \propto t_{{\rm d}}^{-\mu_{{\rm d}}}

RECURSIVE SEARCH METHOD APPLIED TO A NONEQUILIBRIUM PHASE TRANSITION

and the critical cure rate

Non-Markovian Fokker-Planck equation: solutions and first passage time distribution.

\lambda_{{\rm cu}_{\rm c}}^{*} \propto t_{{\rm i}}^{-\mu_{{\rm i}}}

Self-organizing criticality and the method of automatic search of critical points

. For the CP delayed by the minimum infection period we find μd = 0.98, whil...

Multidimensional nonlinear diffusion equation: Spatial time dependent diffusion coefficient and external forces

We investigate solutions, by using the Green function approach, for a system governed by a non-Markovian Fokker-Planck equation and subjected to a Comb structure. This structure consists of the axis of structure as the backbone and fingers which are attached perpendicular to the axis. For this system, we consider an arbitrary initial condition, in the presence of time dependent diffusion coefficients and spatial fractional derivative, and analyze the connection to the anomalous diffusion.