Related papers: Perturbation Theory Confronts Observations~: Impli…
We apply the methods of Field Theory to study the turbulent regimes of statistical systems. First we show how one can find their probability densities. For the case of the theory of wave turbulence with four-wave interaction we calculate…
In this paper, we study the edge behavior of Dyson Brownian motion with general $\beta$. Specifically, we consider the scenario where the averaged initial density near the edge, on the scale $\eta_*$, is lower bounded by a square root…
Rugged energy landscapes find wide applications in diverse fields ranging from astrophysics to protein folding. We study the dependence of diffusion coefficient $(D)$ of a Brownian particle on the distribution width $(\varepsilon)$ of…
We derive the time evolution of the density contrast to all orders of perturbation theory, by solving the Einstein equation for scale-invariant fluctuations. These fluctuations are represented by an infinite series in inverse powers of the…
Turbulent relative dispersion is studied theoretically with a focus on the evolution of probability distribution of the relative separation of two passive particles. A finite separation speed and a finite correlation of relative velocity,…
We elaborate the statistical field theory of Turbulence suggested in the previous paper \cite{M20a}. We clarify and simplify the basic Energy pumping equation of that theory and study mathematical properties of singular field configuration…
Diffusion of self-propelled particles in the presence of randomly distributed obstacles in three dimensions is studied using molecular dynamics simulations. It is found that depending on the magnitude of the propelling force and the…
The observed accelerated expansion of the Universe may be explained by dark energy or the breakdown of general relativity (GR) on cosmological scales. When the latter case, a modified gravity scenario, is considered, it is often assumed…
Within the framework of one-dimensional Laval-Dubrulle-Nazarenko type model for the Lagrangian acceleration in developed turbulence studied in the work [A.K. Aringazin and M.I. Mazhitov, cond-mat/0305186] we focus on the effect of…
A description of dislocations and disclinations defects in terms of Riemann--Cartan geometry is given, with the curvature and torsion tensors being interpreted as the surface densities of the Frank and Burgers vectors, respectively. A new…
We consider the evolution of relativistic perturbations in the Einstein-de Sitter cosmological model, including second-order effects. The perturbations are considered in two different settings: the widely used synchronous gauge and the…
In purely normal elastic rough surface contact problems, Persson's theory of contact shows that the evolution of the probability density function (PDF) of contact pressure with the magnification is governed by a diffusion equation. However,…
Properties of two equations describing the evolution of the probability density function (PDF) of the relative dispersion in turbulent flow are compared by investigating their solutions: the Richardson diffusion equation with the drift term…
We review the study of inhomogeneous perturbations about a homogeneous and isotropic background cosmology. We adopt a coordinate based approach, but give geometrical interpretations of metric perturbations in terms of the expansion, shear…
In this paper we study the evolution of density perturbations in the framework of Phase Coupling Gravity theory at the very early universe. We show that these perturbation display an exponential-like behaviour.
We describe two complementary formalisms designed for the description of probability density function (PDF) of the gradients of turbulent fields. The first approach, we call it adiabatic, describes PDF at the values much less than…
This paper uses dynamical invariants to describe the evolution of collisionless systems subject to time-dependent gravitational forces without resorting to maximum-entropy probabilities. We show that collisionless relaxation can be viewed…
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…
We present a numerical study of topological descriptors of initially Gaussian and scale-free density perturbations evolving via gravitational instability in an expanding universe. We carefully evaluate and avoid numerical contamination in…
Cosmological perturbation theory is crucial for our understanding of the universe. The linear theory has been well understood for some time, however developing and applying the theory beyond linear order is currently at the forefront of…