On generalized torsion two-forms in general relativity: a result of null tetrad formalism

The method of reduction of a connection form from a principal fibre-bundle to a sub-bundle is studied by considering the null tetrad formalism in space-time and discussing in detail the resulting Generalized Maurer-Cartan Structural Equations. Vacuum space-times satisfying Einstein field equations and admitting the vanishing of the induced curvature form in the reduced bundle are investigated. It is shown that these hypotheses imply the existence of a field surface orthogonal to a real null geodesic vector of the tetrad field. This work was carried out under the auspices of the National Group of Mathematical Physics of CNR.     

Statistical properties of one-dimensional inversion for the wave field diffracted by a two-dimensional phase screen

We study theoretically the statistical properties of one-dimensional wave-field inversions. We show that the real and imaginary parts of the logarithm of the normalized coherence function are the invariants of the inverted field if the field is measured on the statistical symmetry axis. Using these invariants, one can easily reconstruct two-point statistical moments of the phase distribution on the screen. We derive equations for the reconstruction of phase-distribution moments in the general case. Numerical simulations show that these equations can be solved by an iterative technique. The convergence range of the iteration method with variation in the parameters is studied. A. M. Obukhov Institute for Physics of the Atmosphere of the Russian Academy of Sciences, Moscow, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 3, pp. 234–242, March., 2000.     

Arbitrary order exactly divergence-free central discontinuous Galerkin methods for ideal MHD equations

Ideal magnetohydrodynamic (MHD) equations consist of a set of nonlinear hyperbolic conservation laws, with a divergence-free constraint on the magnetic field. Neglecting this constraint in the design of computational methods may lead to numerical instability or nonphysical features in solutions. In our recent work [F. Li, L. Xu, S. Yakovlev, Central discontinuous Galerkin methods for ideal MHD equations with the exactly divergence-free magnetic field, Journal of Computational Physics 230 (2011) 4828–4847], second and third order exactly divergence-free central discontinuous Galerkin methods were proposed for ideal MHD equations. In this paper, we further develop such methods with higher order accuracy. The novelty here is that the well-established H(div)-conforming finite element spaces are used in the constrained transport type framework, and the magnetic induction equations are extensively explored in order to extract sufficient information to uniquely reconstruct an exactly divergence-free magnetic field. The overall algorithm is local, and it can be of arbitrary order of accuracy. Numerical examples are presented to demonstrate the performance of the proposed methods especially when they are fourth order accurate.     

Contribution to the theory of optical constants in the vacuum ultraviolet and soft x-ray bands

A consistent exposition is presented of the theory of the dynamic response of an atom in the Thomas—Fermi model. The approach proposed is based on a system of Vlasov equations with a self-consistent field. These equations, supplemented by appropriate boundary conditions, describe the dynamic polarizability and photoabsorption of complex many-electron atoms.Theoretical Radiophysics Sector, Lebedev Physics Institute. Translated from Preprint No. 139 of the Lebedev Physics Institute, Academy of Sciences of the USSR, Moscow, 1989.     

Theories of gravitation with nonminimal coupling of matter and the gravitational field

The foundations of a theory of nonminimal coupling of matter and the gravitational field in the framework of Riemannian (or Riemann-Cartan) geometry are presented. In the absence of matter, the Einstein vacuum field equations hold. In order to allow for a Newtonian limit, the theory contains a new parameter l₀ of dimension length. For systems with finite total mass, l₀ is set equal to the Schwarzschild radius.Slightly extended version of a paper presented at the 14th Jena Seminar on Relativistic Physics, Georgenthal, November 15–21, 1982.     

Spatiotemporal characteristics of laser emission. I

The first chapter describes the general premises of the electrodynamic theory of the laser as a nonstationary nonlinear oscillatory system with spatially distributed parameters. Maxwell's equations are used to derive an equation for the complex amplitude of the electromagnetic field in a cavity filled with transversely inhomogeneous active medium. The self-conssitent analysis includes a simultaneous solution of the equations for the field and for the inverted population. In the second chapter, electrodynamic theory is applied to injection and electron-beampumped semiconductor lasers. The threshold characteristics, the field structure in the near and far zones, the lasing regimes of semiconductor lasers, and the influence of nonlinearity of the refractive index are considered.Division of Quantum Radiophysics, Lebedev Physics Institute. Translated from Preprint No. 33, Lebedev Physics Institute, Moscow, 1990.     

Study of electromagnetic field surface states in photonic crystals using the finite-difference method

Bulletin of the Lebedev Physics Institute - The properties of electromagnetic field surface states in globular photonic crystals are analyzed using numerical solution of Maxwell equations by the...     

On a generalization of the equations of electrodynamics

Both the field equations and the equations of motion of a charged particle in an electromagnetic field are generalized. The sense of the generalization consists in giving up the Lorentz condition on the field potentials. The basic conclusion is that, in addition to the charge and mass, the proper rotation of the particle (the spin) should belong to the characteristics of a particle in classical electrodynamics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 107–110, July, 1972.The author wishes to thank the participants of the Ivanov Inter-Institute Seminar on Mathematical and Theoretical Physics for discussion of the results of the present work.     

Classical and quantum conformal field theory

We define chiral vertex operators and duality matrices and review the fundamental identities they satisfy. In order to understand the meaning of these equations, and therefore of conformal field theory, we define the classical limit of a conformal field theory as a limit in which the conformal weights of all primary fields vanish. The classical limit of the equations for the duality matrices in rational field theory together with some results of category theory, suggest that (quantum) conformal field theory should be regarded as a generalization of group theory.On leave of absence from the Department of Physics, Weizmann Institute of Science, Rehovot 76100, Israel     

Field theory onR×S 3 topology. IV: Electrodynamics of magnetic moments

The equations of electrodynamics for the interactions between magnetic moments are written on R×S³ topology rather than on Minkowskian space-time manifold of ordinary Maxwell's equations. The new field equations are an extension of the previously obtained Klein-Gordon-type, Schrödinger-type, Weyl-type, and Dirac-type equations. The concept of the magnetic moment in our case takes over that of the charge in ordinary electrodynamics as the fundamental entity. The new equations have R×S³ invariance as compared to the Lorentz invariance of Maxwell's equations. The solutions of the new field equations are given. In this theory the divergence of the electric field vanishes whereas that of the magnetic field does not.Research supported in part by the Colgate Research Council and by the Center for Theoretical Physics, University of Maryland.     

Nonlinear Screening and the Metal–Insulator Transition in a Two-Dimensional Electron Gas

Russian Physics Journal - The density functional theory is used to study the nonlinear screening properties of a two-dimensional electron gas in a strong magnetic field. The Kohn-Sham equations for...     

Singularities in solutions of the Einstein equations for a static spherically symmetric field

Russian Physics Journal - The nature of the singularities in the solutions of Einstein's equations for a static spherically symmetric field is investigated as a function of the choice of...     

On a Nonlinear Effect in the Superconductivity Theory

Physics of the Solid State - Based on the solution of the hydrodynamic equations and Maxwell’s equations, we show that an external quasi-homogeneous magnetic field leads to the emergence of a...     

Field theory onR×S 3 topology. VI: Gravitation

We extend to curved space-time the field theory on R×S³ topology in which field equations were obtained for scalar particles, spin one-half particles, the electromagnetic field of magnetic moments, an SU₂ gauge theory, and a Schrödinger-type equation, as compared to ordinary field equations that are formulated on a Minkowskian metric. The theory obtained is an angular-momentum representation of gravitation. Gravitational field equations are presented and compared to the Einstein field equations, and the mathematical and physical similarity and differences between them are pointed out. The problem of motion is discussed, and the equations of motion of a rigid body are developed and given explicitly. One result which is worth emphazing is that while general relativity theory yields Newton's law of motion in the lowest approximation, our theory gives Euler's equations of motion for a rigid body in its lowest approximation.On leave from the Center for Theoretical Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel.     

Non-linear high-frequency waves in the magnetosphere

Using fluid theory, a set of equations is derived for non-linear high-frequency waves propagating oblique to an external magnetic field in a three-component plasma consisting of hot electrons, cold electrons and cold ions. For parameters typical of the Earth’s magnetosphere, numerical solutions of the governing equations yield sinusoidal, sawtooth or bipolar wave-forms for the electric field Article presented at the International Conference on the Frontiers of Plasma Physics and Technology, 9–14 December 2002, Bangalore, India.     

Field theory onR×S 3 topology. V:SU 2 gauge theory

A gauge theory on R×S ³ topology is developed. It is a generalization to the previously obtained field theory on R×S ³ topology and in which equations of motion were obtained for a scalar particle, a spin one-half particle, the electromagnetic field of magnetic moments, and a Shrödinger-type equation, as compared to ordinary field equations defined on a Minkowskian manifold. The new gauge field equations are presented and compared to the ordinary Yang-Mills field equations, and the mathematical and physical differences between them are discussed.On leave from Center for Theoretical Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel.     

The large-scale vortex structures in plasma-like media and the electric explosion of conductors

Formation of large-scale hydrodynamic convective patterns in plasma-like current-carrying media is considered. This process is shown to be described by the same equations, as Benard rolls, except that a temperature field must be replaced by a magnetic field. A simple low-mode model of spatial pattern formation for a case of cylindrical liquid-metal conductor with current is proposed and investigated. Nonlinear interaction of perturbations of the magnetic field and the velocity field results in an increase of effective conductor resistance even when transport coefficients are constant. In our opinion, it is this instability, that is of first importance at the initial stages of the electric explosion of conductors. In particular, it leads to conductor stratification and electric current interruption. (c) 1996 American Institute of Physics.     

A new Lagrangian for the vacuum einstein equations and its tetrad form

We give a modification of the Palatini Lagrangian for the free gravitational field that yields the vanishing of the torsion as a result of the field equations and requires only the assumption of the symmetry of the metric. We transcribe this Lagrangian into the tetrad formalism and show how the tetrad form of the Einstein field equations follows from it. Some remarks on possible generalization to a theory with nonvanishing torsion in the presence of matter conclude the paper.An earlier version of the results of this paper are found in [6].On leave from the Department of Physics, Boston University, Boston, Massachusetts.     

One solution of the problem of intrinsic energy of a point charge,as obtained within classical relativistic field theory

New equations are proposed for classical relativistic field theory, which insure a finite value for the intrinsic energy of a point charge.Mechanics and Physics Scientific Research Institute, Saratov State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 26–30, October, 1994.     

强流质子RFQ加速器高频数字低电平控制系统

强流质子RFQ加速器加速场的频率为352.2 MHz,加速场幅度和相位的精度分别要求控制在±1%和±1°的范围,为了达到这一要求,设计了一套数字低电平控制系统,该系统包括加速场的幅度和相位控制、腔体的谐振频率控制和高功率射频连锁保护3个部分。腔体采样信号的下变频及反馈激励信号的上变频由模拟器件来完成。幅相实时反馈处理过程采用数字I/Q解调的方法,在1块stratixⅡ的FPGA板上实现,板上另有3块DSP用于通信和协助FPGA进行数据处理。系统完成后与RFQ加速器进行联机调试,测试结果基本满足控制精度的要求。