Related papers: The generalized Phillips' spectra and new dissipat…
A kinetic equation for a system of elastic hard spheres or disks confined by a hard wall of arbitrary shape is derived. It is a generalization of the modified Enskog equation in which the effects of the confinement are taken into account…
We examine the validity of the kinetic description of wave turbulence for a model quadratic equation. We focus on the space-inhomogeneous case, which had not been treated earlier; the space-homogeneous case is a simple variant. We determine…
A new symplectic variational approach is developed for modeling dissipation in kinetic equations. This approach yields a double bracket structure in phase space which generates kinetic equations representing coadjoint motion under canonical…
During the set of direct numerical simulations of the forced isotropic turbulence of surface gravity waves in the framework of primordial dynamical equations, the universal inverse cascade spectrum was observed. The slope of the spectrum is…
All random wave fields possess a network of phase singularities. We show that while the phase statistics within speckle patterns is generic, the statistics of the motion of phase singularities differs substantially for diffusive and…
A strongly damped wave equation including the displacement depending nonlinear damping term and nonlinear interaction function is considered. The main aim of the note is to show that under the standard dissipativity restrictions on the…
In mean-field theory, the non-local state of fluid molecules can be taken into account using a statistical method. The molecular model combined with a density expansion in Taylor series of the fourth order yields an internal energy value…
1) A wave equation is derived from the kinetic equations governing media with rotational as well as translational degrees of freedom. In this wave the fluctuating quantity is a vector, the bulk spin. The transmission is similar to…
Variety of statistically steady energy spectra in elastic wave turbulence have been reported in numerical simulations, experiments, and theoretical studies. Focusing on the energy levels of the system, we have performed direct numerical…
Kinetic equations are analyzed for thermal degradation of polymers. The governing relations are based on the fragmentation-annihilation concept. Explicit solutions to these equations are derived in two particular cases of interest. For…
Wind-generated waves are often treated as stochastic processes. There is particular interest in their spectral density functions, which are often expressed in some parametric form. Such spectral density functions are used as inputs when…
In our previous studies we have examined solar wind and magnetospheric plasmas turbulence, including Markovian character on large inertial magneto-hydrodynamic scales. Here we present the results of statistical analysis of magnetic field…
The main goal of this work is to study systematically the quantum aspects of the interaction between scalar particles in the framework of Generalized Scalar Duffin-Kemmer-Petiau Electrodynamics (GSDKP). For this purpose the theory is…
Practical results gained from statistical theories of turbulence usually appear in the form of an inertial range energy spectrum $\mathcal{E}(k)\sim k^{-q}$ and a cut-off wave-number $k_{c}$. For example, the values $q=5/3$ and $\ell…
The nonlinear stage of the modulational (Benjamin - Feir) instability of unidirectional deep water surface gravity waves is simulated numerically by the firth-order nonlinear envelope equations. The conditions of steep and breaking waves…
We study experimentally the influence of dissipation on stationary capillary wave turbulence on the surface of a fluid by changing its viscosity. We observe that the frequency power law scaling of the capillary spectrum departs…
The observed Ekman spirals in the ocean are always "flatter" than that predicted by the classic theory. We propose that the universal flattening of Ekman spiral is mainly due to the damping associated with turbulent dissipation. Analytical…
We consider the whole-plane SLE conformal map f from the unit disk to the slit plane, and show that its mixed moments, involving a power p of the derivative modulus |f'| and a power q of the map |f| itself, have closed forms along some…
Reaction-diffusion problems are often described at a macroscopic scale by partial derivative equations of the type of the Fisher or Kolmogorov-Petrovsky-Piscounov equation. These equations have a continuous family of front solutions, each…
The complex form of Maxwell equations has been constructed as one equation for 3-dimensional complex A-vector. The real and imaginary parts of this vector are described with use of electric and magnetic tensions accordingly. With using a…