Projective geometry and special relativity

Some concepts of real and complex projective geometry are applied to the fundamental physical notions that relate to Minkowski space and the Lorentz group. In particular, it is shown that the transition from an infinite speed of propagation for light waves to a finite one entails the replacement of a hyperplane at infinity with a light cone and the replacement of an affine hyperplane – or rest space – with a proper time hyperboloid. The transition from the metric theory of electromagnetism to the pre‐metric theory is discussed in the context of complex projective geometry, and ultimately, it is proposed that the geometrical issues are more general than electromagnetism, namely, they pertain to the transition from point mechanics to wave mechanics.     

Semi‐analytical integration of the 8‐node plane element stiffness matrix using symbolic computation

The semi‐analytical integration of an 8‐node plane strain finite element stiffness matrix is presented in this work. The element is assumed to be super‐parametric, having straight sides. Before carrying out the integration, the integral expressions are classified into several groups, thus avoiding duplication of calculations. Symbolic manipulation and integration is used to obtain the basic formulae to evaluate the stiffness matrix. Then, the resulting expressions are postprocessed, optimized, and simplified in order to reduce the computation time. Maple symbolic‐manipulation software was used to generate the closed expressions and to develop the corresponding Fortran code. Comparisons between semi‐analytical integration and numerical integration were made. It was demonstrated that semi‐analytical integration required less CPU time than conventional numerical integration (using Gaussian‐Legendre quadrature) to obtain the stiffness matrix. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Co-Segregation Effects on Boundary Migration

We analyze the effect of co-segregation on the mobility of grain boundaries within the framework of the impurity drag theory originally proposed by Cahn and Lücke and Stüwe for an ideal solution. The new derivation extends this model to the case where there are two types of impurities (or three components in the alloy). Since the resultant expression for the boundary mobility is complicated, numerical solutions were obtained for several cases to show how co-segregation affects the boundary mobility. Depending on the relative diffusivities of the two impurities which are both attracted to the boundary, the mobility may either increase or decrease with increasing concentration of one of the impurities. When one of the impurities is attracted to the boundary and the other repelled from the boundary, increasing the concentration of the attractive impurity can lead to a sharp decrease in the boundary mobility.     

Analytic Properties of the Transition Admittance of an Infinite Plate in a medium and the Regularization of Boundary-Contact Integrals in Acoustics

A condition for regularization of boundary-contact integrals in two-dimensional problems of acoustics is considered. With an example of the simplest boundary-contact problem of acoustics, it is shown that a known sufficient condition for regularization is also a necessary one. The study of analytic properties of the transition admittance of an infinite plate that is in contact with a medium is conducted in order to obtain this statement. The considerations are carried out in general terms. The results obtained may be used in arbitrary models of plate theory, and they also may be adapted to boundary-contact problems of another physical nature. Bibliography: 9 titles.     

High energy asymptotics of the scattering amplitude for the Schrödinger equation

We find an explicit function approximating at high energies the kernel of the scattering matrix with arbitrary accuracy. Moreover, the same function gives all diagonal singularities of the kernel of the scattering matrix in the angular variables. This paper is dedicated to Jean-Michel Combes on the occasion of his sixtieth birthday.     

Modified Three-Dimensional Formulations of Bending Problems of Homogeneous Plates and Beams under Complex Fixing Conditions

Modified three-dimensional formulations of bending problems of homogeneous elastic plates and beams are considered. Modification of the known three-dimensional formulations reduces to using additional constraints imposed on displacement functions. An advantage of the formulations proposed is that complex fixing conditions of plates and beams can be taken into account.     

Application of quasi-steady-state plasma streams for simulation of ITER transient heat loads

The paper presents experimental investigation of energy characteristics of the plasma streams generated with quasi—steady—state plasma accelerator QSPA Kh-50 and adjustment of plasma paramenters from the point of view its applicability for simulation of transient plasma heat loads expected for ITER disruptions and type I ELMs. Possibility of generation of high-power magnetized plasma streams with ion impact energy up to 0.6 keV, pulse length 0.25 ms and heat loads varied in wide range from 0.5 to 30 MJ/m² has been demonstrated and some features of plasma interaction with tungsten targets in dependence on plasma heat loads are discussed.     

Dynamic holograms and optical limiting: Asymmetric two-wave interactions

The conditions for obtaining a high efficiency of energy exchange upon two-wave interactions in dynamic holograms are found by analysis and numerical simulation of a system of nonlinear equations. Use of an asymmetric scheme of beam interaction in a medium with two nonlinearities, one of which determines the amplitude and relaxation time of a grating and the other of which provides phase modulation of the interacting beams, is proposed. It is shown that such a scheme in combination with the specific properties of a medium makes it possible to radically reduce the requirements for the nonlinearity of a medium and the intensity of a light flux in limiting systems, as well as to significantly decrease the time of the transition process. As a result, it becomes possible to attain an efficiency of energy transfer higher than 90% and to increase the corresponding attenuation of a high-power beam by almost two orders of magnitude, which is of interest for optical limiting of intense light fluxes.