Related papers: Exit-Times and {\Large $\epsilon$}-Entropy for Dyn…
An efficient approach to the calculation of the $\epsilon$-entropy is proposed. The method is based on the idea of looking at the information content of a string of data, by analyzing the signal only at the instants when the fluctuations…
The inverse structure functions of exit distances have been introduced as a novel diagnostic of turbulence which emphasizes the more laminar regions [1-4]. Using Taylor's frozen field hypothesis, we investigate the statistical properties of…
The numerical experiments of turbulence conducted by Gotoh et al. are analyzed precisely with the help of the formulae for the scaling exponents of velocity structure function and for the probability density function (PDF) of velocity…
A computational study of higher-order derivative ratios on a time interval leading to the enstrophy peak is presented in the case of the 3D Taylor-Green vortex, a benchmark problem in the simulation of turbulent flows. The main finding is…
We use the multifractal formalism to describe the effects of dissipation on Lagrangian velocity statistics in turbulent flows. We analyze high Reynolds number experiments and direct numerical simulation (DNS) data. We show that this…
An analytical expression of probability density function (PDF) of velocity fluctuation is derived with the help of the statistics based on generalized entropy (the Tsallis entropy or the R\'{e}nyi entropy). It is revealed that the derived…
We give conditions to prove the existence of an Extremal Index for general stationary stochastic processes by detecting the presence of one or more underlying periodic phenomena. This theory, besides giving general useful tools to identify…
Single file systems are simplified models to study effectively one-dimensional physical systems. Here we compute analytically the complete first exit time statistics for an ideal overdamped single file with absorbing boundary conditions.…
Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…
Turbulence may appear as a complex process with a multitude of scales and flow patterns, but still obeys simple physical principles such as the conservation of momentum, of energy, and the maximum entropy principle. The latter states that…
Energy dissipation rate is an important parameter for nearly every experiment on turbulent flow. Mathematically precise relationships between energy dissipation rate and other measurable statistics for the case of anisotropic turbulence are…
In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…
An analytical formula for the probability density function (PDF) of the velocity fluctuation in fully-developed turbulence is derived, non-perturbatively, by assuming that its underlying statistics is the one based on the generalized…
This paper analyses the turbulent energy cascade from the perspective of statistical mechanics, and relates inter-scale energy fluxes to statistical irreversibility and information-entropy production. The microscopical reversibility of the…
Using high-resolution direct numerical simulations, the height and Reynolds number dependence of higher-order statistics of the energy dissipation rate and local enstrophy are examined in incompressible, fully-developed turbulent channel…
A model to explain the statistics of the velocity gradients in the dissipation range of a turbulent flow is presented. The experimentally observed non-gaussian statistics is theoretically predicted by means of a thermodynamical analogy…
The principle of entropy increase is not only the basis of statistical mechanics, but also closely related to the irreversibility of time, the origin of life, chaos and turbulence. In this paper, we first discuss the dynamic system…
We use the mean exit time to quantify macroscopic dynamical behaviors of stochastic dynamical systems driven by tempered L\'evy fluctuations, which are solutions of nonlocal elliptic equations. Firstly, we construct a new numerical scheme…
A parallel pseudospectral code for the direct numerical simulation (DNS) of isotropic turbulence has been developed. The code has been extensively benchmarked using established results from literature. The code has been used to conduct a…
The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large…