On the theory of fracture of solids submitted to powerful pulsed electron beams

The irradiation of solids by pulsed (of nanosecond periodicity) relativistic electron beams (also by powerful optic laser beams) led to the discovery of a new type of fracture /1–14/, entirely different from viscous or brittle fracture type produced by mechanical loads /15/. A theory based on the assumption of formation in a solid subjected to such irradiation of clusters of electrons that act as “knives” or “wedges” cutting the solid. Basic model problems of this theory are formulated.     

An Optimization algorithm computing the maximal singular number of a real matrix

The problem of calculating the maximal singular number of a given real matrix is considered. The existing solution methods are briefly surveyed. A new optimization-type algorithm for computing the maximal singular number is suggested and substantiated. Its rate of convergence is proved to be linear. A relationship between the row sums of the matrix and one of its singular numbers is established, and new localization theorems are proved. It is shown how the suggested algorithm is related to the Relay relation relaxation method. Exceptional situations in which the algorithm converges to a non-maximal singular number are described. A computational trick for avoiding such situations with fairly high reliability is suggested.     

Experimental study of variations in the thickness of a liquid film moving over the inner surface of a rotating cylinder

The behavior of a liquid layer moving in a mass-force field on the inner surface of a rotating vertical cylinder is studied experimentally. Free-surface profiles of the liquid moving under these conditions are constructed. An empirical dependence for the mean thickness of the film is obtained in criterial forms. The presence of a hydraulic jump in the lower part of the cylinder behind the entrance of the liquid onto the vertical surface is revealed. Tomsk, State Architectural-Building University, Tomsk 634003. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 65–71, November–December, 1998.     

An Approach for Building Dynamic Models of the Process of Disclosure of Transformable Space Structures

Doklady Physics - A universal approach to the creation of dynamic models for the disclosure of space structures is proposed, which makes it possible to study current and promising disclosure...     

The Hirota Method and Soliton Solutions to the Multidimensional Nonlinear Schrodinger Equation

Using the Hirota method, we obtain a 1-soliton solution to the (3+1)-dimensional nonlinear Schrodinger equation.     

Improving an estimate of the convergence rate of the seidel method by selecting the optimal order of equations in the system of linear algebraic equations

The Seidel method for solving a system of linear algebraic equations and an estimate of its convergence rate are considered. It is proposed to change the order of equations. It is shown that the method described in Faddeevs’ book Computational Methods of Linear Algebra can deteriorate the convergence rate estimate rather than improve it. An algorithm for establishing the optimal order of equations is proposed, and its validity is proved. It is shown that the computational complexity of the reordering is 2n ² additions and (12)n ² divisions. Numerical results for random matrices of order 100 are presented that confirm the proposed improvement.     

Convergence analysis of an optimization algorithm for computing the largest eigenvalue of a symmetric matrix

A new optimization algorithm for computing the largest eigenvalue of a real symmetric matrix is considered. The algorithm is based on a sequence of plane rotations increasing the sum of the matrix entries. It is proved that the algorithm converges linearly and it is shown that it may be regarded as a relaxation method for the Rayleigh quotient. Bibliography: 6 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 346, 2007, pp. 5–20.     

Macroscopic relativistic dynamics of hyperlight interactions of electrons

The general solution is given for the problem of the laws of motion of an electron in the field of a hyperlight electron in a medium with arbitrary initial conditions. Effective estimates of the time of approach of the electrons are found, which is of interest for the theory of self-contraction of intense electron beams.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 73–76, April. 1982.     

Analytical Estimates of the Motion and Elastic Vibrations of the Structures of Separated Fairing Flaps of Rocket-Space Systems

Doklady Physics - Equations are obtained, and a model is constructed for studying the dynamics of separation of fairing flaps of rocket and space systems. Based on the assumption that the angular...