Related papers: Joint probability density with radial, tangential,…
We outline a statistical theory of turbulence based on the Lagrangian formulation of fluid motion. We derive a hierarchy of evolution equations for Lagrangian N-point probability distributions as well as a functional equation for a suitably…
In this paper, a multi-dimensional fractional wave equation that describes propagation of the damped waves is introduced and analyzed. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional…
Mathematical models based on probability density functions (PDF) have been extensively used in hydrology and subsurface flow problems, to describe the uncertainty in porous media properties (e.g., permeability modelled as random field).…
The Brownian motion of a particle in a one-dimensional periodic potential subjected to a uniform external force F is studied. Using the formula for the diffusion coefficient D obtained by other authors and an alternative one derived from…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
The behavior of a heavy tagged intruder immersed in a bath of particles evolving under ballistic annihilation dynamics is investigated. The Fokker-Planck equation for this system is derived and the peculiarities of the corresponding…
In this paper we present an integro-differential diffusion equation for continuous time random walk that is valid for a generic waiting time probability density function. Using this equation we also study diffusion behaviors for a couple of…
We consider classical solutions to the kinetic Fokker-Planck equation on a bounded domain $\mathcal O \subset~\mathbb{R}^d$ in position, and we obtain a probabilistic representation of the solutions using the Langevin diffusion process with…
In a previous work, a perturbative approach to a class of Fokker-Planck equations, which have constant diffusion coefficients and small time-dependent drift coefficients, was developed by exploiting the close connection between the…
In this study, we investigate the phenomenon of collective motion in binary mixtures of self-propelled particles. We consider two particle species, each of which consisting of pointlike objects that propel with a velocity of constant…
A wide range of physical problems can be described by randomly-oriented linear trajectories, including any system of objects, organisms, particles, or rays that follow a linear path. Dependent upon the particular random variables that…
Fractional generalized Langevin equation with external force is used to model single-file diffusion. It is found that for external force that varies with power law the solution for such a fractional Langevin equation gives the correct short…
We study the main properties of the solution of a Fokker-Planck equation characterized by a variable diffusion coefficient and a polynomial superlinear drift, modeling the formation of consensus in a large interacting system of individuals.…
A canonical structure compatible with the action of the Lorentz group can be obtained considering the energy and time as conjugate variables of an extended phase space. Scalar probability waves, describing free relativistic particles, are…
We study agitated frictional disks in two dimensions with the aim of developing a scaling theory for their diffusion over time. As a function of the area fraction $\phi$ and mean-square velocity fluctuations $\langle v^2\rangle$ the…
We investigate the motion of a run-and-tumble particle (RTP) in one dimension. We find the exact probability distribution of the particle with and without diffusion on the infinite line, as well as in a finite interval. In the infinite…
We investigate the dynamics of an inertial active Ornstein-Uhlenbeck particle suspended in a non-Markovian environment. The particle is additionally subjected to external forces, such as harmonic confinement and a magnetic field. Motivated…
A {\em propagation-dispersion equation} is derived for the first passage distribution function of a particle moving on a substrate with time delays. The equation is obtained as the continuous limit of the {\em first visit equation}, an…
We study stationary solutions to the continuity equation for weakly compressible flows. These describe non-equilibrium steady states of weakly dissipative dynamical systems. Compressibility is a singular perturbation that changes the steady…
In probability density function (PDF) methods a transport equation is solved numerically to compute the time and space dependent probability distribution of several flow variables in a turbulent flow. The joint PDF of the velocity…