Magnetic field correlation tensor in spaces of constant curvature

The concept of statistical homogeneity and isotropy for vector fields in spatial sections of constant curvature was analyzed. Solenoidality conditions for a corresponding correlation tensor were obtained for positive and negative curvature. It was shown that these conditions differ from the corresponding condition for fields in Euclidean space.     

Two-component neutrino field and spherical symmetry in a space-time with curvature and torsion

The incompatibility of the spherical symmetry of a space-time with the presence of a “classical” i.e. not-quantized, 2-component neutrino field is extended from the purely Riemannian to the Riemann-Cartan geometry, corresponding to a space-time with curvature and torsion.     

Tensor analysis and curvature in quantum space-time

Introducing quantum space-time into physics by means of the transformation language of noncommuting coordinates gives a simple scheme of generalizing the tensor analysis. The general covariance principle for the quantum space-time case is discussed, within which one can obtain the covariant structure of basic tensor quantities and the motion equation for a particle in a gravitational field. Definitions of covariant derivatives and curvature are also generalized in the given case. It turns out that the covariant structure of the Riemann-Christoffel curvature tensor is not preserved in quantum space-time. However, if the curvature tensor _v (z) is redetermined up to the value of theL ² term, then its covariant structure is achieved, and it, in turn, allows us to reconstruct the Einstein equation in quantum space-time.     

Sectional curvature and the determination of the metric in space-time

It is shown that if the sectional (Riemannian) curvature function is given at all spacetime points, then, apart from a very special class of space-times, the metric is uniquely determined.     

Classification of the space-time curvature tensor,restricted case

Einstein field equations will be assumed in a certain restricted form. The problem to be solved consists, roughly, of the enumeration of all curvature tensors which satisfy these equations. Presented at the International Conference on Gravitation and Relativity, Copenhagen, July 1971.     

Surface tension with normal curvature in curved space-time

With an aim to include the contribution of surface tension in the action of the boundary, we define the tangential pressure in terms of surface tension and Normal curvature in a more naturally geometric way. For a thin shell approximation of a static spherically symmetric surface and for weak and slowly varying fields, the negative tangential pressure $\tau _{\alpha \beta }$ is chosen to be analogous to $S_{\alpha \beta },$ where $S_{\alpha \beta }$ is the classical surface tension. First, by a suitable choice of the enveloping surfaces, we show that the negative tangential pressure is independent of the four-velocity of a very thin hyper-surface. Second, using suitable definition of the normal curvature for such a surface layer, we relate the 3-pressure of a surface layer to the normal curvature and the surface tension. Third, using the fact that the tangential pressure on the surface layer is independent of the four-velocity and a central force interaction, we relate the surface tension $S_{\alpha \beta }$ to the energy of the surface layer. Four, we show that the delta like energy flows across the hypersurface will be zero for such a representation of intrinsic 3-pressure. Five, for the weak field approximation and for static spherically symmetric configuration, we deduce the classical Kelvin’s relation between surface tension, pressure difference and mean curvature from this sort of representation of negative tangential pressure $\tau _{\alpha \beta }$ in terms of surface tension $S_{\alpha \beta }$ and the normal curvature. Six, using the representation of tangential pressure in terms of surface tension and normal curvature, we write a modified action for the boundary having contributions both from surface tension and normal curvature of the surface layer. Also we propose a method to find the physical action assuming a reference background, where the background is not flat. (The $g_{\mu \nu }^{+}$ or just $g_{\mu \nu }$ has been chosen to represent the metric coefficent of the hypersurface of $V_{+}$ space which is time-like surface layer here. The $g_{\mu \nu }^{-}$ represents the metric coefficient of the space like hypersurface of $V_{-}$ space.)     

An effect of curvature of rotating diffuse objects on the dynamics of speckles produced in the diffraction field

The time correlation function is analyzed of the speckel intensity fluctuation produced in the Fresnel diffraction field from a rotating diffuse object under illumination of a Gaussian laser beam. The dependence of the curvature radius of the rotating diffuse object on the time correlation length of the speckle intensity fluctuation is especially explored by taking into account the size of the detecting aperture. The theoretical results are confirmed experimentally for detecting apertures with various sizes. It is shown that a detecting aperture with an appropriate size is required. It becomes useful for determining the radius of curvature of the rotating diffuse object from measurements of the time correlation length of the speckle intensity fluctuation.     

An electromagnetic field in the Plebanski space-time

The electromagnetic wave equation in the Plebanski space-time has been reduced to a one-dimensional wave equation with real short-range potential. We then find that the superradiance phenomenon occurs.     

Relativistic string model in a space-time of a constant curvature

The relativistic string model is investigated in a space-time of a constant curvature (de Sitter universe). The fundamental differential quadratic forms of the world surface of the string are considered as the dynamical variables. The coefficients of these forms obey two nonlinear equations $$\varphi _{,11} - \varphi _{,22} = e^\varphi \cos \theta + Ke^{ - \varphi } ,\theta _{,11} - \theta _{,22} = e^\varphi \sin \theta .$$ The Lax representation for this system is obtained.     

Combustion of volatile condensed systems during pressure decay

The combustion and extinction of volatile condensed systems during pressure decay are studied. In contrast to the existing theories of this phenomenon, where only the thermal inertia of the condensed phase (t _c -approximation) is considered, an analysis of the time-dependent behavior of the gas phase is also included. Extinction curves, i.e., dependence between the pressure decay depth and the pressure decay rate at which the burning of the propellant ceases are calculated. The analysis is performed within the framework of the Belyaev model. A comparison of the results with calculations based on the t _c -approximation shows that, at high pressures, the thermal inertia of the gas phase is of considerable importance.     

Riemannian curvature and the classification of the Riemann and Ricci tensors in space-time

Some theorems proved by Thorpe concerning the connection between the critical point structure of the Riemannian (sectional) curvature function and the Petrov classification are extended. A similar function is defined whose critical point structure is connected with the algebraic classification of the Ricci tensor.     

Magnetic field influence on coflow laminar diffusion flames

The behavior of a laminar methane air flame with a central methane jet and a surrounding air coflow is analyzed in a large range of fuel and air flow rates. Different regimes of flame stability are described from an anchored flame to a stable lifted flame which is destabilized before extinction. Influence of an upward increasing magnetic field generated by an electromagnet is then studied. Experimental measurements at different values of methane and air flow rates show that the flame lift-off height is decreased by the magnetic gradient. These effects are attributed to the magnetic force which develops on air via its action on the paramagnetic oxygen molecules. The magnetic force interacts with the air jet structures upstream of the flame and then influences the flame stability.     

Scalar field equation in Robertson-Walker space-time

The quantization of the scalar field is reconsidered in some of its basic elements in the context of the Robertson-Walker space-time. The integration of the generalized Klein-Gordon equation is performed by preliminary separation of the equation with the usual separation method. The orthonormal mode solutions are determined by the explicit integration of the resulting angular and radial equations and by standard properties of the time equation. The time evolution given by the standard cosmological model is briefly discussed.     

Magnetic anisotropic interactions of nuclei in condensed matter

This article examines some problems dealing with the anisotropy of the internuclei magnetic interactions in condensed matter, namely the properties and the experimental measurement of the magnetic shielding tensor σ and of the indirect nuclear spin-spin coupling tensor J. The symmetry of the tensors is examined, with a special emphasis of the possible existence of antisymmetric components. Experiments which may allow to measure the antisymmetric components of σ and J are presented. The number of independent components of the tensors, and the number of signals which may be observed in a solid-state N.M.R. experiment are discussed according to the local symmetry of the nuclei. The calculation of the σ and J tensor components using a perturbation theory from a complete molecular Hamiltonian is presented. For the indirect spin-spin coupling tensor the calculation is performed using a relativistic treatment. Some experimental results are given on the determination of the individual components of the σ and J tensors. For the latter only a very few data have been obtained in condensed matter. The use of the σ tensor anisotropy for examining some problems of special interest such as the hydrogen bonding or the orientation of large molecules in biological membranes is presented.     

Deuteron decay in the field of the nucleus

The amplitude of the A+d→n+p+A reaction was obtained on the basis of the diagram summation method for the particular configurations of the particle in the final state, when (i) the neutron and proton have a small relative energy, or (ii) one of the nucleons and the nucleus have a small relative energy. It was shown that from the analysis of the experimental data of the reaction A+d→n+p+A and by using the obtained formula the value of the spin-dependent and spin-independent parts of the nucleon-nucleus scattering amplitude can be found.     

Spinor field and nonmetricity of space-time

A study is made of the dynamics of a self-gravitating spinor field in a space with curvature and nonmetricity. It is shown that the nonmetricity of the space-time may induce a vector nonlinearity of cubic type in the equation of the spinor field. Also possible is the opposite effect in which such a nonlinearity of the spinor equation is compensated by the influence of the nonmetricity of space-time.Translated from Izvestiya Vysshikh Uchebnykh. Zavedenii, Fizika, No. 6, pp. 52–55, June, 1980.     

Long-range scalar field in conformally flat space-time

Consequences of a massless scalar field in conformally flat space-time are studied. Then a wide class of solutions of the scalar field is obtained.