相关论文: Power law dependence in a random differential equa…

Following the idea that dissipation in turbulence at high Reynolds number is by events singular in space-time and described by solutions of the inviscid Euler equations, we draw the conclusion that in such flows scaling laws should depend…

We investigate diffusion of excitation in one- and two-dimensional lattices with random on-site energies and deterministic long-range couplings (hopping) inversely proportional to the distance. Three regimes of diffusion are observed in…

We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…

Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…

We consider certain one dimensional ordinary stochastic differential equations driven by additive Brownian motion of variance $\varepsilon ^2$. When $\varepsilon =0$ such equations have an unstable non-hyperbolic fixed point and the drift…

Systems of differential equations with state-dependent delay are considered. The delay dynamically depends on the state i.e. is governed by an additional differential equation. By applying the time transformations we arrive to constant…

Maximum entropy (maxEnt) inference of state probabilities using state-dependent constraints is popular in the study of complex systems. In stochastic dynamical systems, the effect of state space topology and path-dependent constraints on…

We study the statistics of the amplitude of the synchronization error in chaotic electronic circuits coupled through linear feedback. Depending on the coupling strength, our system exhibits three qualitatively different regimes of…

We make the first steps towards a generic theory for energy spreading and quantum dissipation. The Wall formula for the calculation of friction in nuclear physics and the Drude formula for the calculation of conductivity in mesoscopic…

In this paper we study the fluctuations from the limiting behavior of small noise random perturbations of diffusions with multiple scales. The result is then applied to the exit problem for multiscale diffusions, deriving the limiting law…

A phenomenological model describing the time-frequency dependence of the power spectrum of thin plates vibrating in a wave turbulence regime, is introduced. The model equation contains as basic solutions the Rayleigh-Jeans equipartition of…

Consider a linear autonomous Hamiltonian system with a time periodic bound state solution. In this paper we study the structural instability of this bound state ^M relative to time almost periodic perturbations which are small, localized…

The theory of the depinning transition of elastic manifolds in random media provides a framework for the statistical dynamics of dislocation systems at yield. We consider the case of a single flexible dislocation gliding through a random…

Time evolution of a perturbed thermal state is studied in a quantum-mechanical system with O(N) symmetry. In the limit of large N, time dependence of O(N)-singlet expectation values can be described by classical equations of motion in a…

Under certain circumstances, the time behavior of a random walk is modulated by logarithmic periodic oscillations. The goal of this paper is to present a simple and pedagogical explanation of the origin of this modulation for diffusion on a…

We determine the late-time dynamics of a generic spin ensemble with inhomogeneous broadening - equivalently, qubits with arbitrary Zeeman splittings - coupled to a dissipative environment with strength decreasing as $1/t$. The approach to…

We investigate Brownian motion with diffusivity alternately fluctuating between fast and slow states. We assume that sojourn-time distributions of these two states are given by exponential or power-law distributions. We develop a theory of…

We investigate the distribution of relative velocities between small heavy particles of different sizes in turbulence by analysing a statistical model for bidisperse turbulent suspensions, containing particles with two different Stokes…

Power-law distributions occur in wide variety of physical, biological, and social phenomena. In this paper, we propose a statistical hypothesis test based on the log-likelihood ratio to assess whether two samples of discrete data are drawn…

In order to clarify how the statistical properties of earthquakes depend on the constitutive law characterizing the stick-slip dynamics, we make an extensive numerical simulation of the one-dimensional spring-block model with the rate- and…