A natural scalar field in the einstein gravitational theory

In a Riemannian space-time, the difference between the third-order tensor potentialH of the Riemann tensor (presented in a precedent paper) and the Lanczos generating function of the Weyl tensor is here shown to be characterized by a vectorV , obtained by contractionH . The significant role of such a vector, in the context of general relativity, is then discussed. Particular attention is paid to the scalar potential which characterizes the irrotational part ofV : such a scalar field satisfies a space-time wave equation of the Poisson type. Weak fields are also considered: in the particular case of a static metric, the scalar is found to be proportional to the classic Newtonian potential.This work was done in the sphere of activity of the C.N.R. Groups for mathematical research.     

Multiple coherent scattering of γ-radiation

Conclusions Multiplying (5) by 2d and integrating over angle, we get the relationship between the total flux and depth in the form , where .A similar result is obtained from integration of (11) over the angles and integration of (12) over the plane z = const. It thus follows that if we are interested in the angular distribution for in the first two cases and in the radial distribution for z in the third case, we can make an approximate estimate of the coherent scattering by eliminating the appropriate term from. This approach has been used in [15 etc.] but no indications were given of the conditions under which this is permissible.For problems in which small angles or small distances from the axis of a collimated source are important, allowance for the coherent scattering can change the result by an order of magnitude or more. For angles and it is possible to consider only the coherent scattering and to use (5), (11), and (12). For angles >gh and scattering >z, the contribution from coherent and incoherent scattering can be comparable. The kinetic equation must then be solved with allowance for both effects.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 129–132, May, 1973.     

Corrections to cluster-radius scaling for branched polymers and percolation

We report analyses of series enumerations for the mean radius of gyration for isotropic and directed lattice animals and for percolation clusters, in two and three dimensions. We allow for the leading correction to the scaling behaviour and obtain estimates of the leading correction-to-scaling exponent . We find -0.640±0.004 and =0.87±0.07 for isotropic animals in 2d, and =0.64±0.06 in 3d. For directed lattice animals we argue that the leading correction has= or= ; we also estimate =0.82±0.01 and 0.69 ±0.01 ind=2, 3 respectively. For percolation clusters at and abovep _c, we find (p _c) =0.58±0.06 and (p>p _c)=0.84±0.09 in 2d, and (p _c)=0.42±0.11 and (p>p _c)=0.41 ±0.09 in 3d.     

The Einstein 3-form Gα and its Equivalent 1-form Lα in Riemann–Cartan Space

We motivate the definition of the Einstein 3-form G by means of the contracted 2nd Bianchi identity. This definition contains the whole curvature 2-form. The L 1-form, defined via G = L ^*( ) ( is the Hodge-star, the coframe), is equivalent to the Einstein 3-form and contains all the information of the curvature 2-form relevant for the definition of the Einstein 3-form. A variational formula of Salgado on quadratic invariants of the L 1-form is discussed, generalized, and put into proper perspective.     

Gravity on a Parallelizable Manifold. Exact Solutions

The wave type field equation^a =^a, where ^ais a coframe field on a space-time, was recentlyproposed to describe the gravity field. This equationhas a unique static, spherically symmetric, asymptotically flat solution, whichleads to the viable Yilmaz–Rosen metric. We showthat the wave type field equation is satisfied by thepseudo-conformal frame if the conformal factor isdetermined by a scalar 3D-harmonic function. This functioncan be related to the Newtonian potential of classicalgravity. So we obtain a direct relation between thenon-relativistic gravity and the relativistic model: every classical exact solution leads to asolution of the field equation. With this result weobtain a wide class of exact, static metrics. We showthat the theory of Yilmaz relates to thepseudo-conformal sector of our construction. We derive also aunique cosmological (time dependent) solution of thedescribed type.     

On the existence of a local Hamiltonian in the Galilean invariant Lee Model

It is shown that there exists a selfadjoint Hamilton operator in the limit of local coupling for the Galilean invariant Lee Model. We discuss the scattering theory of this Hamilton operator in theV —N sector.     

Parametric dependence of the properties of pulsed-laser-deposited diamond-like carbon films

The properties of Pulsed-Laser-Deposited Diamond-Like Carbon (PLD DLC) films are studied as functions of the power density and the wavelength of the laser beam, and the incident angle of the beam relative to the normal of the target surface. All the films have a similar structure consisting of graphite particulates embedded in a continuous matrix, so the macroscopic performance of the films is determined by the overall contributions of the particulates and the matrix. The use of higher, shorter, or larger leads to an enhancement of the diamond-like characteristics and a simultaneous increase of the particulate density. These two effects give opposite contributions to the electrical conductivity _R, leading to the following results. (i) _R drops with increasing in the low range (region I) due to the stronger diamond-like nature of the matrix, but increases sharply after has exceeded a threshold _min as a result of the rapid increase in particulate density. (ii) In region I, the use of shorter or larger leads to a more diamond-like matrix, and this overwhelms the degradation effect caused by the slight increase in particulate density. The samples thus become more insulating. In the high region (region II), however, the use of shorter or larger gives rise to higher particulate density, thereby increasing the electrical conductivity.     

On the measure of the spectrum for the almost Mathieu operator

We obtain partial results on the conjecture that for the almost Mathieu operator at irrational frequency, , the measure of the spectrum,S(, , )=|4–2|. For ||2 we show that if _n is rational and irrational, then .Dedicated to Res Jost and Arthur WightmanResearch partially supported by U.S. NSF grant number DMS-8801918 and by BSF under grant number 88-00325     

Ferretti-Rajeev term and homotopy theory

We reduce Ferretti-Rajeev models to the usual sigma models with Chern-Simons terms (-terms), and show that whether is quantized or not corresponds to the fact ₄(G _j,n )₃(U(j))= or 0 of the topology in the process of our reduction. We also reconsider the topological invariance of the Chern classes in the language of the field theory.Partially supported by the Grant-in-Aid for Scientific Research, No. 04640088     

Statistical phase properties in a coherent state

The wave function of a harmonic oscillator is investigated under the assumption that the phase plays the role of a generalized coordinate. This wave function makes it possible to obtain all possible statistical information concerning the phase in a coherent state (moments of all orders). It is particularly simple to calculate cos and sin .Odessa State Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 7, pp. 748–760, July, 1991.     

ВЛИЯНИЕ СПЕКТРАЛЬНО ГО ПРОФИЛЯ ДУБЛЕТАKα 1 α 2 И ДИФРАКЦИОННОГО РАС ШИРЕНИЯ НА ИНТЕГРАЛЬ НУЮ ИНТЕНСИВНОСТЬ ДИФРА КЦИЙ ПРИ ВЫСОКИХ УГЛА Х БРЭГГА

, K _{1 2} LP . 75°85° K , . , <80°. ( , ) <83°. , 90° , , , . >83° , , .

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The influence of the spectral profile of theK₁₂ doublet and diffraction broadening on the integrated intensities of high angle diffractions

Relations are derived giving the influence of the spectral profile of theK _{1 2} doublet and the influence of diffraction broadening on the productLP of the Lorentz and polarization factor. The relations are used to calculate the numerical values of the corresponding corrections for the theoretical values of the integrated intensities of diffractions in the angular region 75°85° and for the most frequently usedK radiation of copper, cobalt and iron.It follows from the calculated values of the corrections that, due to the accuracy at present attainable in experimental measurements, the influence of the spectral profile in diffractions with an angle<80° can be neglected when calculating the theoretical values of the integrated intensities. The influence of diffraction broadening need not be taken into account in diffractions with an angle<83° even when the broadening is large (e. g. five-fold). As the angle approaches 90°, of eourse, the corrections for both above influences suddenly increase, particularly those for diffraction broadening, and their limitation becomes difficult and is not single-valued. For this reason the use of diffractions with angles>83° does not appear very suitable for solving problems based on exact measurement of the integrated intensities and their comparison with the corresponding theoretical values.

     

Влияние переменного магнитного поля на остаточное состоя ние магнитно — Мягких материалов

. .

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The influence of an alternating magnetic field on the remanent state of magnetically soft materials

A study is made of the influence of an alternating magnetic field of varying maximum amplitude on the remanent state, or rather, apparent remanent state of toroidal and open samples of metallic and non-metallic magnetically soft ferromagnetics. An interpretation of the corresponding dependences is given on the basis of Kondorski's conception of the composition of a polycrystalline jerromagnetic material.

     

High frequency gravitational radiation in Kerr-Schild space-times

Vaidya has obtained general solutions of the Einstein equationsR _ab= _{a b} by means of the Kerr-Schild metricsg _ab= _ab +H _{a b} . The vector field _a generates a shear free null geodetic congruence both in Minkowski space and in the Kerr-Schild space-time. If in addition it is hypersurface orthogonal, the Kerr-Schild metric may be interpreted as the background metric in a space-time perturbed by a high frequency gravitational wave. It is shown that Vaidya's solutions satisfying this additional condition are of only two types: (1) Kinnersley's accelerating point mass solution and (2) a similar solution where a space-like curve plays the role of the time-like curve describing the world line of the accelerating mass. The solution named by Vaidya as the radiating Kerr metric does not satisfy the hypersurface orthogonal condition.Supported in part by National Science Foundation Grant MPS 741029.     

Studium der Stationären und Laufenden Schichtung in der Entladung in Neon Mit Hilfe eines Lokalen Hochfrequenzfeldes

Zusammenfassung Es wurde ein Verfahren zur Erregung von stationären Schichten, der Schichtungswelle und der laufenden Schichten in der Gleichstromentladung ausgearbeitet, das auf der Einwirkung eines Hochfrequenzfeldes auf einen kurzen Abschnitt der positiven Säule beruht. Dieses Verfahren wurde zum Studium aller drei angeführten Schichtungsarten in Neon benützt, insbesondere jedoch zum Studium des Zusammenhanges zwischen den laufenden und den stationären Schichten.Bei stationären Schichten wurden zweifache Strukturen festgestellt und es wurde deren Abhängigkeit vom Entladungsstrom und von der Größe des erregenden Hochfrequenzfeldes verfolgt.Bei der Schichtungswelle wurde die Stelle deren Entstehung ermittelt und es wurde nachgewiesen, daß das Hochfrequenzfeld diese Welle lokal an der Stelle dessen Einwirkung auf die positive Säule hervorruft.Bei den laufenden Schichten wurde deren Resonanzfrequenz in Abhängigkeit vom Entladungsstrom und die Abhängigkeit der Wellenlänge der Schichten von der Frequenz untersucht.Es wurde festgestellt, daß der extrapolierte Wert der Wellenlänge für die Nullfrequenz erheblich niedriger ist als die Länge der stationären Schichten. Weiter wurde eine Übereinstimmung der Frequenz der laufenden Schichten in der Schichtungswelle mit der Resonanzfrequenz der künstlich hervorgerufenen laufenden Schichten festgestellt.

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, , . , . . , . . , . , .

     

Quantum field theory of anyons

For a Minkowski spacetime of dimension three, particles of arbitrary, real spin and intermediate (-) statistics, called anyons, are studied within the framework of relativistic quantum field theory. The localization properties of interpolating fields for anyons and the relation between the spin of anyons and their statistics are discussed on general grounds. A model of a quantum field theory exhibiting anyons is described. Our results might be relevant in connection with the fractional quantum Hall effect and two-dimensional models of high-T _c superconductors.     

Duality-invariant orthogonality relation between the magnetic monopole and associated quark charges

Duality invariance of the Dirac-Schwinger charge-symmetric theory for electromagnetism leads one to consider the complex-valued amplitudes ₁ and ₂ for the separation between the magnetic monopole and quarks in the logarithmic charge plane. It is observed that the orthogonality relation on the latter amplitudes, Re( ₁ ^* ₂)=0, is equivalent to the equation (ln 9 ^–1)(ln 2)=(1/2) ², which is indeed satisfied by the experimental value fora to within 0.027%. In addition to fixing the unit of electric charge at a primary physical value, the orientation of ₁, ₂ may also prescribe the Cabibbo angle to have the theoretical value 12.4438.     

Bunching phenomena during electron injection into the betatron II. Theory of starting conditions

A theory of the azimuthal bunching of electrons injected into the betatron is presented and compared with the experiments described in [1]. The bunching is treated as a small perturbation of the stationary beam.The stationary injected beam is replaced by the corresponding equilibrium beam of the same perveance so that the angular velocity spread of the injected electrons is proportional to the square root of the injection perveance.Self-consistent wave solutions for the perturbation of the stationary solution are then found. Equations giving the amplification of small density or energy disturbances along the beam are derived. These disturbances are assumed to be introduced by density or velocity modulation of the injected beam. The condition for the spontaneous occurrence of bunching is deduced by assuming that the disturbances do not vanish even when there is no modulation of the injected beam. The resulting expressions for the threshold perveance and the rise-time of the disturbance are in reasonably good agreement with the experiments. Such agreement may be considered as further verification of the statement made in [1] that the amplification of the disturbances is caused by the negative mass instability mechanism.

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, .

, . , [1]. . . , , . . , ., . , , . . , , [1].

     

Spectroscopic factors of9Be,10B and13C from (d,t) reactions

The differential cross sections of tritons from the (d, t) reaction on⁹Be,¹⁰B and¹³C targets have been measured in the angular range of 5° _LAB110° with relatively small errors, 5%. The experimental data were analysed in terms of the standard DWBA using both zero-range and exact finite-range approaches.     

Characteristics analysis of metal-clad and absorptive dielectric waveguides by a simple and accurate perturbation method

We present a simple and accurate method for characteristic analysis of metal-clad dielectric waveguides and absorptive waveguides. The real partN of the complex modal indexN=N + iN is obtained by solving the corresponding real eigenvalue equation, and the imaginary partN is given by (n/), where= + i is the complex dielectric constant of the absorptive layer, and N/ is obtained by numerical differentiation. The method is straightforward, and the cumbersome solution of complex transcendental equations is completely eliminated. Results for simple structures are in good agreement with those obtained by exact analysis.     

Stationary states of an electron in the field of a hole in an ionic crystal

An approximate solution is given of the Schrödinger equation for S-states of an electron in the field of a hole, when the potential energy of the electron has the form — e²/r [1+exp (–qr].

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s- , –e²/r [1+exp (–qr].