In many different topics, the most significant digits of data series display a non-uniform distribution which points to an equiprobability of logarithms. This surprising ubiquitous property, known as the significant digit law, is shown here to follow from two similar, albeit different, scale...

The directed polymer in a 1+3 dimensional random medium is known to present a disorder-induced phase transition. For a polymer of length L, the high temperature phase is characterized by a diffusive behavior for the end-point displacement R<Superscript>2</Superscript> ∼L and by free-energy fluctuations of order ΔF(L)...</superscript>

We study two dynamical systems submitted to white and Gaussian random noise acting multiplicatively. The first system is an imperfect pitchfork bifurcation with a noisy departure from onset. The second system is a pitchfork bifurcation in which the noise acts multiplicatively on the non-linear...

With the aim of studying stochastic resonance (SR) in a double-well potential when the noise source has a spectral density of the form f<Superscript>-κ</Superscript> (with varying κ), we have extended a procedure introduced by Kaulakys et al. (Phys. Rev. E <Emphasis Type="Bold">70, 020101 (2004)). In order to achieve an analytical...</emphasis></superscript>

We investigate the behavior of energy fluctuations in several models of granular gases maintained in a non-equilibrium steady state. In the case of a gas heated from a boundary, the inhomogeneities of the system play a predominant role. Interpreting the total kinetic energy as a sum of...

The dynamics of a spatially extended system of two competing species in the presence of two noise sources is studied. A correlated dichotomous noise acts on the interaction parameter and a multiplicative white noise affects directly the dynamics of the two species. To describe the spatial...

We analyze in detail how the anomalous drift and diffusion properties of a particle evolving in an aging medium can be interpreted in terms of an effective temperature of the medium. From an experimental point of view, independent measurements of the mean-square displacement and of the mobility...

Detecting nonlinearity in financial time series is a key point when the main interest is to understand the generating process. One of the main tests for testing linearity in time series is the Hinich Bispectrum Nonlinearity Test (HINBIN). Although this test has been succesfully applied to a vast...

We consider different models of stochastic dissipative equations and theoretically compute the probability distribution functions (actually the associated large deviation functions) of the time averaged injected power required to sustain a nontrivial stationary state. We discuss the results and...

The influence of the periodic potential structure on the diffusion mechanism of a Brownian particle is studied using the Fokker–Planck equation. The equation is solved numerically by the matrix continued fraction method in order to calculate relevant correlation functions. In particular, jump...