Numerical modeling of quasiplanar giant water waves

In this work we present a further analytical development and a numerical implementation of the recently suggested theoretical model for highly nonlinear potential long-crested water waves, where weak three-dimensional effects are included as small corrections to exact two-dimensional equations written in the conformal variables [V.P. Ruban, Phys. Rev. E 71, 055303(R) (2005)]. Numerical experiments based on this theory describe the spontaneous formation of a single weakly three-dimensional large-amplitude wave (alternatively called freak, killer, rogue or giant wave) on the deep water.Comment: revtex4, 8 pages, 7 figure

Two-dimensional nonstationary model of the propagation of an electron beam in a vacuum

A two dimensional nonstationary model of the propagation of a relativistic electron beam injected into a vacuum is considered. Collision effects are ignored and there are no external fields. Two types of the electron current propagation are shown from the computer simulation of the Maxwell-Vlasov equations

Branch cuts of Stokes wave on deep water. Part I: Numerical solution and Pad\'e approximation

Complex analytical structure of Stokes wave for two-dimensional potential flow of the ideal incompressible fluid with free surface and infinite depth is analyzed. Stokes wave is the fully nonlinear periodic gravity wave propagating with the constant velocity. Simulations with the quadruple and variable precisions are performed to find Stokes wave with high accuracy and study the Stokes wave approaching its limiting form with $2\pi/3$ radians angle on the crest. A conformal map is used which maps a free fluid surface of Stokes wave into the real line with fluid domain mapped into the lower complex half-plane. The Stokes wave is fully characterized by the complex singularities in the upper complex half-plane. These singularities are addressed by rational (Pad\'e) interpolation of Stokes wave in the complex plane. Convergence of Pad\'e approximation to the density of complex poles with the increase of the numerical precision and subsequent increase of the number of approximating poles reveals that the only singularities of Stokes wave are branch points connected by branch cuts. The converging densities are the jumps across the branch cuts. There is one branch cut per horizontal spatial period $\lambda$ of Stokes wave. Each branch cut extends strictly vertically above the corresponding crest of Stokes wave up to complex infinity. The lower end of branch cut is the square-root branch point located at the distance $v_c$ from the real line corresponding to the fluid surface in conformal variables. The limiting Stokes wave emerges as the singularity reaches the fluid surface. Tables of Pad\'e approximation for Stokes waves of different heights are provided. These tables allow to recover the Stokes wave with the relative accuracy of at least $10^{-26}$. The tables use from several poles to about hundred poles for highly nonlinear Stokes wave with $v_c/\lambda\sim 10^{-6}.$Comment: 38 pages, 9 figures, 4 tables, supplementary material

On the Quantum Kinetic Equation in Weak Turbulence

The quantum kinetic equation used in the study of weak turbulence is reconsidered in the context of a theory with a generic quartic interaction. The expectation value of the time derivative of the mode number operators is computed in a perturbation expansion which places the large diagonal component of the quartic term in the unperturbed Hamiltonian. Although one is not perturbing around a free field theory, the calculation is easily tractable owing to the fact that the unperturbed Hamiltonian can be written solely in terms of the mode number operators.Comment: 12 pages, LATEX, no figures, to appear in Phys. Rev.

Condensation of classical nonlinear waves

We study the formation of a large-scale coherent structure (a condensate) in classical wave equations by considering the defocusing nonlinear Schr\"odinger equation as a representative model. We formulate a thermodynamic description of the condensation process by using a wave turbulence theory with ultraviolet cut-off. In 3 dimensions the equilibrium state undergoes a phase transition for sufficiently low energy density, while no transition occurs in 2 dimensions, in analogy with standard Bose-Einstein condensation in quantum systems. Numerical simulations show that the thermodynamic limit is reached for systems with $16^3$ computational modes and greater. On the basis of a modified wave turbulence theory, we show that the nonlinear interaction makes the transition to condensation subcritical. The theory is in quantitative agreement with the simulations

Studying the utilization techniques of ammonium hexafluorosilicate

The utilization techniques of ammonium hexafluorosilicate have been proposed and studied. Thermodynamic calculations of equilibrium gas phase compositions of topaz concentrate fluoridation reaction and reaction of (NH4)2SiF6 absorption by ammonium hydroxide were given. Experimental investigations in studying gas phase composition were carried out. The sublimation process of ammonium hexafluorosilicate as well as the process of its dissolving in ammonia water with silicon dioxide obtaining was studie

Methodological Aspects of Formation of Chart of Accounts

The study identified three types of charts of accounts: the chart of accounts oriented to financial accounting, which is based on the matrix method of building, classification of accounts is based on the principles of the balance sheet and the traditional definition of financial results; the chart of accounts, which assumes detailing the cost accounting and allocating additional classes of accounts to determine the financial results of the production; the chart of accounts of the integrated accounting, allowing the formation of multi-sector information and the data exchange between the accounted subsystemsyesBelgorod State Universit