Related papers: Thermalization of random motion in weakly confinin…
Persistence is defined as the probability that the local value of a fluctuating field remains at a particular state for a certain amount of time, before being switched to another state. The concept of persistence has been found to have many…
The PDFs for energy dissipation rates created in a high resolution from $4096^3$ DNS for fully developed turbulence are analyzed in a high precision with the PDF derived within the formula of multifractal probability density function theory…
We consider a thermal particle which is diffusing in velocity-space and in a weakly confining potential characterized by the inverse hyperbolic sine function of the particle velocity $v$ and the control parameter $v_c$. The stationary state…
The evolution of probability distribution functions (PDFs) of continuous density, velocity and velocity derivatives ( deformation tensor) fields in the theory of cosmological gravitational instability are considered. We show that in the…
We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially-dependent diffusion coefficient of the form $D(x)\sim |x|^c$, at constant temperature. The particle's probability distribution function…
Dispersion of a passive scalar from concentrated sources in fully developed turbulent channel flow is studied with the probability density function (PDF) method. The joint PDF of velocity, turbulent frequency and scalar concentration is…
The probability density function (PDF) of velocity fluctuations is studied experimentally for grid turbulence in a systematical manner. At small distances from the grid, where the turbulence is still developing, the PDF is sub-Gaussian. At…
We calculate the probability distribution function (PDF) of an overdamped Brownian particle moving in a periodic potential energy landscape $U(x)$. The PDF is found by solving the corresponding Smoluchowski diffusion equation. We derive the…
We present an overview of recent works on the statistical description of turbulent flows in terms of probability density functions (PDFs) in the framework of the Lundgren-Monin-Novikov (LMN) hierarchy. Within this framework, evolution…
We show that for weakly dependent random variables the relative entropy functional satisfies an approximate version of the standard tensorization property which holds in the independent case. As a corollary we obtain a family of…
In this paper, we investigate and develop a new approach to the numerical analysis and characterization of random fluctuations with heavy-tailed probability distribution function (PDF), such as turbulent heat flow and solar flare…
Under ideal conditions, the probability density function (PDF) of a random variable, such as a sensor measurement, would be well known and amenable to computation and communication tasks. However, this is often not the case, so the user…
Many thermodynamic instabilities in one dimension (e.g. DNA thermal denaturation, wetting of interfaces) can be described in terms of simple models involving harmonic coupling between nearest neighbors and an asymmetric on-site potential…
Diffusive transport of a particle in spatially correlated random energy landscape having exponential density of states has been considered. We exactly calculate the diffusivity in the nondispersive quasi-equilibrium transport regime and…
Based on the theory of continuous time random walks (CTRW), we build the models of characterizing the transitions among anomalous diffusions with different diffusion exponents, often observed in natural world. In the CTRW framework, we take…
The microcanonical statistical mechanics of a set of self-gravitating particles is analyzed in mean-field approach. In order to deal with an upper bounded entropy functional, a softened gravitational potential is used. The softening is…
We study the problem of a Brownian particle diffusing in finite dimensions in a potential given by $\psi= \phi^2/2$ where $\phi$ is Gaussian random field. Exact results for the diffusion constant in the high temperature phase are given in…
We consider thermodynamics of the excluded volume particles at finite temperature and chemical potential, in the low density approximation. We assume Boltzmann statistics and study the influence of the excluded volume on an ideal gas…
The celebrated Sutherland-Einstein relation for systems at thermal equilibrium states that spread of trajectories of Brownian particles is an increasing function of temperature. Here, we scrutinize diffusion of underdamped Brownian motion…
A standard calculation of the energy density of heavy stable particles that may pair-annihilate into light particles making up thermal medium is performed to second order of coupling, using the technique of thermal field theory. At very low…