An Algorithm for Calculating Nonlinear Wave Processes in a Microwave Generator with Magnetic Insulation in the Three-Dimensional Case

In leading laboratories of the world intensive research on powerful microwave generators with magnetic self-isolation (MILO) is being carried out. In the present work the results of calculation and theoretical analysis of MILO, designed and tested in the Institute of Electromagnetic Research (IEMR), are given.

This paper presents the results of experimental studies of the influence of the geometry of the flow part of the chamber and the pressure at the inlet and outlet of the vortex-type generator on the intensity and nature of the occurrence of nonlinear wave and hydrodynamic processes.

Nonlinear waves in a liquid containing gas bubbles are considered in the three-dimensional (3D) case. The nonlinear evolution equation is given for a description of long nonlinear pressure waves. It is shown that in the general case the equation is not integrable. Some exact solutions for the nonlinear evolution equation are presented. The application of the Hirota method is illustrated for finding multi-soliton solutions for the nonintegrable evolution equation in the 3D case. The stability of the 1D solitary waves is investigated. It is shown that the 1D solitary waves are stable to transverse perturbations.

In this investigation, we concentrate on solving the regularized long-wave (RLW) and extended Fisher–Kolmogorov (EFK) equations in one-, two-, and three-dimensional cases by a local meshless method called radial basis function (RBF)–finite-difference (FD) method. This method at each stencil approximates differential operators such as finite-difference method. In each stencil, it is necessary to solve a small-sized linear system with conditionally positive definite coefficient matrix. This method is relatively efficient and has low computational cost. How to choose the shape parameter is a fundamental subject in this method, since it has a palpable effect on coefficient matrix. We will employ the optimal shape parameter which results from algorithm of Sarra (Appl Math Comput 218:9853–9865, 2012). Then, we compare the approximate solutions acquired by RBF–FD method with theoretical solution and also with results obtained from other methods. The numerical results show that the RBF–FD method is suitable and robust for solving the RLW and EFK equations.

The physical processes in a system relativistic microwave generator - power supply unit with a strong feedback are investigated. A computer model is constructed to calculate the output parameters of these systems substituted by equivalent circuits. A model is constructed for a linear induction accelerator based on magnetic elements intended for operation with relativistic magnetrons the nonlinear units of the equivalent circuit of which are calculated in the context of the theory of average motion.

In this paper, we present experimental results on the effect of nonlinear wave and cavitation processes occurring in flowing working parts of hydrodynamic generators of vortex and flat types with flow bodies of various shapes on the physicomechanical properties of a clay suspension. The model of the vortex-type generator with tangential and radial channels for feeding the working fluid of the generator, which is a flat channel with three bodies of flow around a cylindrical shape, was subjected to research.

Extreme wave runup at the Seisho Coast during Typhoons Faxai and Hagibis in 2019

Numerical estimation of the wave forces acting on a three-dimensional body on submerged breakwater

Non-linear waves on shallow water under an ice cover. Higher order expansions

A scientific session of the Physical Sciences Division of the Russian Academy of Sciences (RAS), entitled “Spintronics and nanomagnetism”, was held on 25 April 2012 at the conference hall of the Lebedev Physical Institute, RAS. The agenda of the session announced on the RAS Physical Sciences Division website www.gpad.ac.ru included the following reports: (1) Zvezdin A K, Zvezdin K A (Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow), Popkov A F (National Research University 'Moscow State Institute of Electronic Technology', Moscow) “Spin moment transfer effects and their applications in spintronics”; (2) Fraerman A A (Institute for Physics of Microstructures, Russian Academy of Sciences, Nizhny Novgorod) “Magnetic states and transport properties of ferromagnetic nanostructures”; (3) Panin V E, Egorushkin V E, Panin A V (Institute of Strength Physics and Materials Science, Siberian Branch of the Russian Academy of Sciences, Tomsk) “Nonlinear wave processes in a deformable solid as in a multiscale hierarchically organized system”. Papers based on oral reports 2 and 3 are presented below. • Magnetic states and transport properties of ferromagnetic nanostructures, A A Fraerman Physics-Uspekhi, 2012, Volume 55, Number 12, Pages 1255–1260 • Nonlinear wave processes in a deformable solid as in a multiscale hierarchically organized system, V E Panin, V E Egorushkin, A V Panin Physics-Uspekhi, 2012, Volume 55, Number 12, Pages 1260–1267

The article is devoted to the study of the scattering of nonlinear acoustic waves on cylindrical bodies. There was made a review of publications on the scattering of acoustic waves by inhomogeneities of the medium in the form of cylindrical bodies and shells. There were noted features of the small parameter method application in nonlinear acoustics. A three-dimensional model of the geometry of the problem in cylindrical coordinates was presented, nonlinear wave processes occurring between the falling plane and scattered cylindrical waves were described. The inhomogeneous wave equation is solved by the method of successive approximations of series expansion in a small parameter. An asymptotic expression for the acoustic pressure of a difference-frequency wave was obtained. A program for calculating scattering diagrams has been developed, and an algorithm for its operation is given. The acoustic pressure scattering diagram of a differential frequency wave on a rigid cylinder and its three-dimensional model are presented. The radius of convergence of the used method of expansion in a small parameter is determined.

Nonlinear wave processes during the propagation of a high-current electron beam in an ion-beam undulator

A nonlinear (in the cubic approximation) relaxation equation of state is derived for a rod containing cracks partially filled with an incompressible viscous liquid. The nonlinear effects of the self-action and interaction of low-and high-frequency longitudinal elastic waves propagating in such a rod are studied for the cases of identical and size-varied cracks. Linear and nonlinear acoustic parameters characterizing the self-action and interaction of elastic waves in a cracked rod are determined.

First Page

Nonlinear wave processes in a plasma with stationary random irregularities. Part II