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We derive the distribution function of work performed by a harmonic force acting on a uniformly dragged Brownian particle subjected to a rotational torque. Following the Onsager and Machlup's functional integral approach, we obtain the…
The article shows a bridge representation for the joint density of a system of stochastic processes consisting of a Brownian motion with drift coupled with a correlated fractional Brownian motion with drift. As a result, a small time…
A particle diffusing around a point of stable mechanical equilibrium in a static but non-conservative force field enters into a steady state characterized by circulation in the probability flux. Circulation in such a Brownian vortex is not…
We present a density functional based closure of the pair Smoluchowski equation for Brownian particles under shear flow. Given an equilibrium free energy functional as input the theory provides first-principles predictions for the…
The governing equations of Brownian rigid bodies that both translate and rotate are of interest in fields such as self-assembly of proteins, anisotropic colloids, dielectric theory, and liquid crystals. In this paper, the partial…
Stochastic dynamics in the energy representation is employed as a method to study non-equilibrium Brownian-like systems. It is shown that the equation of motion for the energy of such systems can be taken in the form of the Langevin…
Inertial particles in turbulent flows are characterised by preferential concentration and segregation and, at sufficient mass loading, dense particle clusters may spontaneously arise due to momentum coupling between the phases. These…
We review here the development of the general formalism for the study of fermion propagation in the presence of stochastic media. This formalism allows the systematic derivation of evolution equations for averaged quantities as survival…
We formulate the fractional Ricci flow theory for (pseudo) Riemannian geometries enabled with nonholonomic distributions defining fractional integro-differential structures, for non-integer dimensions. There are constructed fractional…
We consider stochastic Volterra integral equations driven by a fractional Brownian motion with Hurst parameter H > 1/2 . We first derive supremum norm estimates for the solution and its Malliavin derivative. We then show existence and…
In the paper we give consecutive description of functional methods of quantum field theory for systems of interacting q-particles. These particles obey exotic statistics and appear in many problems of condensed matter physics, magnetism and…
We find all factorized duality functions for a class of interacting particle systems. The functions we recover are self-duality functions for interacting particle systems such as zero-range processes, symmetric inclusion and exclusion…
Issues relevant to the flow chirality and structure are focused, while the new theoretical results, including even a distinctive theory, are introduced. However, it is hope that the presentation, with a low starting point but a steep rise,…
We review recent advances in imaging the flow of concentrated suspensions, focussing on the use of confocal microscopy to obtain time-resolved information on the single-particle level in these systems. After motivating the need for…
A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…
The paper suggests a way of stochastic integration of random integrands with respect to fractional Brownian motion with the Hurst parameter H> 1/2. The integral is defined initially on the processes that are "piecewise" predictable on a…
These notes contains an introduction to the theory of Brownian and diffusion local time, as well as its relations to the Tanaka Formula, the extended Ito-Tanaka formula for convex functions, the running maximum process, and the theory of…
In the last ten years, a number of ``Conventional Fluctuation Theorems'' have been derived for systems with deterministic or stochastic dynamics, in a transient or in a non-equilibrium stationary state. These theorems gave explicit…
We consider bifurcation of critical points from a trivial branch for families of functionals that are invariant under the orthogonal action of a compact Lie group. Based on a recent construction of an equivariant spectral flow by the…
New identities and congruences involving the ranks and cranks of partitions are proved. The proof depends on a new partial differential equation connecting their generating functions.