РЕАКЦИЯ (γ, р) НА КАДМИИ И ОЛОВЕ

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(, p) Reaction on cadmium and tin

A study is made of the nuclear photoeffect on Sn and Cd where, in contrast to most of the experiments with this effect up to now, discrete rays were used. The paper complements paper [3], the experimental arrangement of which it has taken over. Several interesting results were obtained — particularly the discreteness of the energy spectrum and the unconventional form of the angular distribution. With tin, the top proton shell of which is completely occupied, the shape of the energy spectrum corresponds to the Wilkinson theory of gigant resonance; with cadmium the energy spectrum is similar to the evaporation spectrum. The angular distributions of the photoprotons of both elements do not satisfy the commonly used relations corresponding to existing theories of nuclear photoeffect. They can, however, be described quite well by empirical equations which contain associated Legendre polynomials of different orders. With both elements the results have features of both a direct and a collective process. The paper gives results, a satisfactory explanation of which would require a new theory including both types of processes.

     

Elastic stress around linear dislocation in anisotropic medium

Relations are derived for the elastic stress field around a linear dislocation in an infinite medium with general anisotropy. The strongly deformed material around the core of the dislocation is cut out in the shape of an elliptic cylinder. The conditions of a free surface are used on the boundary thus formed. The calculation of the field around a crack in a crystal, the model of which was proposed by Fujita in [9], is given as an example.

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The author thanks Dr. F. Kroupa for valuable discussions and all-round help in solving the problem and Z. Hemanová for performing the numerical calculations.     

An example of a generalized Brownian motion

We present an example of a generalized Brownian motion. It is given by creation and annihilation operators on a twisted Fock space ofL ²(). These operators fulfill (for a fixed –11) the relationsc(f)c ^* (g)–c ^* (g)c(f)=f,g1 (f, g L ²()). We show that the distribution of these operators with respect to the vacuum expectation is a generalized Gaussian distribution, in the sense that all moments can be calculated from the second moments with the help of a combinatorial formula. We also indicate that our Brownian motion is one component of ann-dimensional Brownian motion which is invariant under the quantum groupS U(n) of Woronowicz (with =v ²).     

Some Properties of the Bel and Bel-Robinson Tensors

The properties of the Bel and Bel-Robinson tensors seem to indicate that they are closely related to the gravitational energy-momentum. We present some new properties of these tensors which might throw some light onto this relationship. First, for any spacetime we find a decomposition of the Bel tensor in terms of the Bel-Robinson tensor and two other tensors, which we call the pure matter super-energy tensor and the matter-gravity coupling super-energy tensor. We show that the pure matter super-energy tensor of any Einstein-Maxwell field is simply the square of the usual energy-momentum tensor. This, together with the fact that the Bel-Robinson tensor has dimensions of energy density square, leads us to the definition of square root for the Bel-Robinson tensor: a two-covariant symmetric traceless tensor with dimensions of energy density and such that its square gives the Bel-Robinson tensor. We prove that this square root exists if and only if the spacetime is of Petrov type O, N or D, and its general expression is explicitly presented. The properties of this new tensor are examined and some interesting explicit examples are analyzed. Of particular interest are an invariant function that appears in the spherically symmetric metrics and an expression for the energy carried out by pure plane gravitational waves. We also examine the decomposition of the whole Bel tensor for Vaidya's radiating metric and Kerr-Newman's solution. Finally, we generalize the definition of square root to a factorization of the Bel-Robinson tensor and get the general solution for all Petrov types.     

Light yield of plastic scintillators in relation to the energy of external electrons

It is shown that the specific light yield of plastic scintillators irradiated with external electrons is not a constant quantity, owing to the probability of quenching at the surface of the scintillator. The degree of proportionality of plastic scintillators can be influenced by the choice of primary additive and its concentration.     

Massless and massive quanta resulting from a mediumlike metric tensor

We formulate a simple model of the primordial scalar field theory in which the metric tensor is a generalization of the metric tensor from electrodynamics in a medium. The radiation signal corresponding to the scalar field propagates with a velocity that is generally less thanc. This signal can be associated simultaneously with imaginary and real effective (momentum-dependent) masses. The requirement that the imaginary effective mass vanishes, which we take to be the prerequisite for the vacuumlike signal propagation, leads to the spontaneous splitting of the metric tensor into two distinct metric tensors: one metric tensor gives rise to masslesslike radiation and the other to a massive particle.     

On the Form of Parametrized Gravitation in Flat Spacetime

In a framework describing manifestly covariant relativistic evolution using a scalar time , consistency demands that -dependent fields be used. In recent work by the authors, general features of a classical parametrized theory of gravitation, paralleling general relativity where possible, were outlined. The existence of a preferred time coordinate changes the theory significantly. In particular, the Hamiltonian constraint for is removed From the Euler-Lagrange equations. Instead of the 5-dimensional stress-energy tensor, a tensor comprised of 4-momentum density mid flux density only serves as the source. Building on that foundation, in this paper we develop a linear approximate theory of parametrized gravitation in the spirit of the flat spacetime approach to general relativity. Using a modified form of Kraichnan's flat spacetime derivation of general relativity, we extend the linear theory to a family of nonlinear theories in which the flat metric and the gravitational field coalesce into a single effective curved metric.     

Algebraic classification of the matter tensor

A study is made of the matter tensor, which is constructed using only the energy tensor and the metric tensor and has all the algebraic properties of the Riemann tensor. The possible types of matter tensor are classified in the same way as Petrov's classification for the Weyl tensor, and the relationship between the matter tensor and the canonical forms of the corresponding energy tensors is established.Translated from Izvestiya VUZ. Fizika, No. 12, pp. 101–109, December, 1973.I thank V. I. Rodichev for discussing the results and for valuable comments.     

Bohm's quantum potentials and quantum gravity

A generally covariant theory, written in the spirit of Bohm's theory of quantum potentials, which applies to spinless, non interacting, gravitating systems, is formulated. In this theory the quantum state is coupled to the metric tensor g, and the effect of the quantum potential is absorbed in the geometry. At the same time, satisfies a covariant wave equation with respect to the very same g. This provides sufficient constraints to derive 11 coupled equations in the 11 unknowns: and the components of the metric tensor g_µv. The states of stable localized particles are identified, and vacuum-state solutions for both the Euclidean and the Lorentzian case are explicitly presented.     

Combinatorial expression for universal Vassiliev link invariant

A general model similar to R-matrix-type models for link invariants is constructed. It contains all R-matrix invariants and is a generating function for universal Vassiliev link invariants. This expression is simpler than Kontsevich's expression for the same quantity, because it is defined combinatorially and does not contain any integrals, except for an expression for the universal Drinfeld's associator.     

Geometrodynamics in multidimensional unified theory

The unified theory of gravitation and a Yang-Mills field is formulated as a dynamical theory of (r+3)-geometries presumed to be principal bundles with Riemannian metric. Beyond the usual constraint equations the second fundamental form should satisfy a third constraint equation. It is shown that they have a wormhole type solution describing a pair of Yang-Mills charges.Presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.     

Spatially Periodic Solutions in Relativistic Isentropic Gas Dynamics

We consider the initial value problem, with periodic initial data, for the Euler equations in relativistic isentropic gas dynamics, for ideal polytropic gases which obey a constitutive equation, relating pressure p and density , p=², with 1, 0<<c, where c is the speed of light. Global existence of periodic entropy solutions for initial data sufficiently close to a constant state follows from a celebrated result of Glimm and Lax (1970). We prove that given any periodic initial data of locally bounded total variation, satisfying the physical restrictions ||v₀||<c, where v is the gas velocity, there exists a globally defined spatially periodic entropy solution for the Cauchy problem, if 1<₀, for some ₀>1, depending on the initial bounds. The solution decays in L_loc¹ to its mean value as t.     

Deformation and annealing textures of rolled nickel single crystals

Textural and structural analysis is conducted on nickel single crystals of unstable orientation in a compression deformed (=83%) and annealed state. The formation of different deformation textures (DT) on opposite surfaces of compressed crystals is established. The relief and band structure corresponds to two-component DT {110} 112, observed in the compression plane. Annealing (573°K) leads to the appearance of recrystallization grains on the two component DT side {110} 112. Orientationally, the first recrystallization grains correspond to the intersection of the peripheral portions of the texture maxima associated with both components of DT. On the side with DT {123} 212, indications of recrystallization were not observed. Application of the texture method with defocus allowed the comparison of the state of the lattice in the regions of the crystal having different orientations. The experimentally observed inhomogeneity of the development of the structure for primary recrystallization is explained by the inhomogeneity of the deformed structure and by orientational factors.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 45–50, June, 1986.     

Freie Schwingungen einer vierteiligen Membran

Zusammenfassung Es handelt sich um eine aus vier Rechtecken von verschiedenen Materialien bestehende Membran, die durch eine allgemeine Anfangserregung in freie Schwingungen versetzt wird. Die angewandte klassische Lösungsmethode läßt sich auf noch allgemeinere Fälle erweitern. Die theoretischen Ausführungen werden erstens am Beispiel einer homogenen Membran erklärt und zweitens auf eine durch einen Momentanimpuls zur Schwingung gebrachte vierteilige Membran angewendet.

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Letter: Particle-like Behaviour of Some Bianchi Cosmologies: A Fundamental Unity in Nature?

We show that the equations of evolution of someBianchi cosmologies with equation of state p = (0 1) are formallysimilar to the equations of motion of a classical particle under the actionof suitably chosen potential functions. This appears topoint to a fundamental unity in Nature.     

Diffusion of electrons by temperature gradient in plasma of positive column

The inhomogeneous distribution of the concentration of charge carriers in a plasma as a rule excites the deflection of the electron temperature from the equilibrium state by means of a series of interconnected phenomena. In addition to the concentration gradient and the electric field, the temperature gradient also has an influence on the diffusion of electrons.It is shown that in the conditions of the positive column of a d-c discharge the influence of diffusion by a temperature gradient on the electron flux is the same in order of magnitude as the influence of diffusion due to a concentration gradient.

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In conclusion the authors thank V. Dvoák and K. Pátek for carefully reading the paper and for valuable remarks, and K. Wojaczek for valuable discussions.     

A variational principle giving gravitational “superpotentials,” the affine connection,Riemann tensor,and Einstein field equations

A first-order Lagrangian is given, from which follow the definitions of the fully covariant form of the Riemann tensorR _k in terms of the affine connection and metric; the definition of the affine connection in terms of the metric; the Einstein field equations; and the definition of a set of gravitational superpotentials closely connected with the Komar conservation laws [7]. Substitution of the definition of the affine connection into this Lagrangian results in a second-order Lagrangian, from which follow the definition of the fully covariant Riemann tensor in terms of the metric, the Einstein equations, and the definition of the gravitational superpotentials.Dedicated to Achille Papapetrou on the occasion of his retirement.     

Neighbours of Einstein's equations: Connections and curvatures

Once the action for Einstein's equations is rewritten as a functional of anSO(3, ) connection and a conformal factor of the metric, it admits a family of neighbours having the same number of degrees of freedom and a precisely defined metric tensor. This paper analyzes the relation between the Riemann tensor of that metric and the curvature tensor of theSO(3) connection. The relation is very complicated in general. The Einstein case is distinguished by the fact that two naturalSO(3) metrics on theGL(3) fibres coincide. In the general case the theory is bimetric on the fibres.     

A discussion of the Pseudo-Weyl-type metrics

We discuss the pseudo-Weyl vacuum field for which the two metric functions, and , depend on the three coordinates, z, andt. It is shown that no solutions exist that depend on all three coordinates. Consideration is given to the time-dependent metric of Einstein and Rosen and the same (null) result is shown to hold for that case. Thus, the most general solutions to the Weyl-type metric appear to be those already found by Weyl and by Einstein and Rosen.     

On the bimetric theory of gravitation

Rosen's bimetric theory is analyzed anew and is shown to have deficiencies if the space is assumed to be Riemannian. The problems are due mainly to the introduction of the flat metric , and the identification of the stress-energy tensor,T . It is indicated that if the Riemannian interpretation could be avoided the theory still holds promise as a viable theory of gravitation.