Energy and momentum in general relativity

In general relativity, conservation of energy and momentum is expressed by an equation of the form /x= 0, where –gT represents the total energy, momentum, and stress. This equation arises from the divergence formula dV _v = (/x ^v )d ⁴ d. Here we show that this formula fails to account properly for the system of basis vectors e(x). We obtain the (invariant) divergence formula e dV _v = e (/x ^v + )d ⁴ d. Conservation of energy and momentum is therefore expressed by the covariant equation (/x ^v ) + = 0. We go on to calculate the variation of the action under uniform displacements in space-time. This calculation yields the covariant equation of conservation, as well as the fully symmetric energy tensor . Finally, we discuss the transfer of energy and momentum, within the context of Einstein's theory of gravitation.     

An Equilibrium Lattice Model of Wetting on Rough Substrates

We consider a semi-infinite 3-dimensional Ising system with a rough wall to describe the effect of the roughness r of the substrate on wetting. We show that the difference of wall free energies (r)= _AW(r)– _BW(r) of the two phases behaves like (r)r(1), where r=1 characterizes a purely flat surface, confirming at low enough temperature and small roughness the validity of Wenzel's law, cos (r)r cos (1), which relates the contact angle of a sessile droplet to the roughness of the substrate     

ЗАТУХАНИЕ КОЛЕБАНИЙ ЧАСТИЦ В ОБЩЕМ ПОЛЕ С ПЕРИОДИЧЕСКОЙ СТРУКТУРОЙ I

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The damping of particle oscillations in a general field with periodic structure I

A liner theory is derived, discussing the dynamics of particles in the region of an equilibrium orbit in a general electromagnetic field, which forms a periodic system. The total particle damping is determined from the Hamiltonian found and from dissipative forces brought out by a classical reaction radiation. Relations for the damping of the synchrotron oscillations are derived from the study of the appropriate phase space.

     

A note on the divergence of a series for multiple beam interference in a thin metallic film

The paper deals with the problem of the anomalous divergence of an infinite geometric series of complex amplitudes, pointed out by Berning. It is shown that the paradox is of a formal mathematical nature and has no consequences for multiple beam interference as a method of derivation.

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The connection between low-gradient form of the positive column in oxygen and moving striations

The method of sliding photomultipliers was used to study the connection between two forms of the positive column in oxygen — the so-called low-gradientT-form and the highgradientH-form — and the presence of moving striations in the positive column. It was shown that in theT-form of a positive column striations are always present which move from the cathode to anode with a velocity of several thousand metres/sec. The highgradient form of theH-positive column, on the other hand, is not striated. The non-single-valuedness of the value of the longitudinal electric field in a discharge in oxygen is thus explained by the presence or absence of phenomena of a time variable character.

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— - H - — . , - , /. , , . , , , .

     

Determinism in space-time

Generalizing a definition given by Budic and Sachs we define the set (M) of deterministic points of a space-timeM, and show that (M) Ø implies thatM admits compact achronal slices. Further we give a new characterization of space-times with (M)=M. The relation between determinism, existence of particle horizons, and visible Cauchy surfaces is investigated.     

More inequalities for critical exponents

A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequalitydv +2 2–. Others are 1 1 +v, 1 1 , 1,d 1 + 1/ (for d),dv, ₃ + (for d), ₄ , and _{2m 2m+2} (form 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.NSF Predoctoral Fellow (1976–1979). Research supported in part by NSF Grant PHY 78-23952.     

Anisotropy of the low temperature resistivity of hexagonal single crystalline spin glass systems

The impurity contribution to the resistivity in zero field (T) of dilute hexagonal single crystals of ZnMn, CdMn and MgMn has been studied in the mK range on samples cut parallel () and perpendicular () to thec-axis, using a SQUID technique for the measurements. Typical spin glass behavior is found in (T) as well as (T) for all alloys, with Kondo like logarithmic increases at higher temperatures and maxima atT _m at lower temperatures, indicating the influence of impurity interactions. The differences in the corresponding isotropic resistivity _poly(T) between the three systems can qualitatively be understood within the framework of a theoretical model by Larsen, describing (T) as a function of universal quantitiesT/T _K and _RKKY/T _K , where _RKKY is the RKKY-interaction strength andT _K the Kondo temperature. With respect to the two lattice directions studied, the behavior of (T and (T is anisotropic in the Kondo regime as well as in the range where ordering becomes important. While the anisotropy in the Kondo slope can be understood by an anisotropic unitarity limit, the understanding of the anisotropy in region where impurity interactions are important remains problematic.Dedicated to Prof. Dr. S. Methfessel on the occasion of his 60th birthday     

The energy-momentum gravitational pseudotensor and Kerr-Schild metrics

It is shown that the Landau-Lifshitz pseudotensor vanishes for any Kerr-Schild metricg =n + 2Hl l satisfying the conditionS l =0. Some solutions verifying this condition are indicated.     

Feynman integral and complex classical trajectories

Let _t be an analytic solution of the Schrödinger equation with the initial condition . Let _t be the solution of the Schrödinger equation with the initial condition =, where is an analytic function. When 0, then _t (x) _t (x)¹ ( _t (x)), where _t (x) trajectory starting from x. We relate this result to Feynman's sum over trajectories and complex stochastic differential equations.     

ПЛОТНОСТЬ ТОКА В АНОД НЫХ ПЯТНАХ ИСКРОВЫХ РАЗРЯДОВ В ВОЗДУХЕ ПР И АТМОСФЕРНОМ ДАВЛЕН ИИ

annapamyp, . .     

Fractal drums and then-dimensional modified Weyl-Berry conjecture

In this paper, we study the spectrum of the Dirichlet Laplacian in a bounded (or, more generally, of finite volume) open set R ⁿ (n1) with fractal boundary of interior Minkowski dimension (n–1,n]. By means of the technique of tessellation of domains, we give the exact second term of the asymptotic expansion of the counting functionN() (i.e. the number of positive eigenvalues less than ) as +, which is of the form ^/2 times a negative, bounded and left-continuous function of . This explains the reason why the modified Weyl-Berry conjecture does not hold generally forn2. In addition, we also obtain explicit upper and lower bounds on the second term ofN().     

Измерение некоторых нейтронных спектров методом ядерных эмулъсий

. Ra+Be . , , . 8.     

ОПРЕДЕЛЕНИЕ ПОСТОЯН НЫХ ДВУХПАРАМЕТРОВЫ Х РЕШЕТОК МЕТОДОМ ОТНО ШЕНИЙ

. . - 10^–4.     

Bemerkung zur Theorie der Elektrolumineszenz in ZnS-Kristallen

Zusammenfassung Nach Zalm sind die Kristalle von ZnS mit einer dünnen Halbleiterschicht bedeckt, aus der auf Grund des Tunneleffekts Elektronen in den Kristall eindringen können. Im vorliegenden Artikel wird vorausgesetzt, da die Elektrolumineszenz bei der Rekombination dieser Elektronen mit den ionisierten Aktivatorzentren eintritt, die sich im Kristall zu Beginn eines jeden Zyklus vorfinden, und die Folgen dieser Voraussetzung werden mit den experimentell erhaltenen Daten verglichen.

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ZnS

ZnS , . , , ; .

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Dieser Artikel entstand aus einer Diplomarbeit, die im Physikalischen Institut der Tschechosl. A. d. W., Prag, ausgearbeitet wurde.

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Abschlieend möchte ich RNDr. Miroslav Trlifaj für seine zahlreichen wertvollen Hinweise wie auch für sein Interesse an dieser Arbeit danken.     

A possible test of quantum electrodynamics by means of polarization effects in electron-nucleon scattering

The differential cross-section is given for the electromagnetic scattering of polarized relativistic electrons on polarized nucleons. The finite size of each particle is taken into account by means of two form-factors. The effect of the possible non-punctiform structure of the electron on the polarization effects in scattering is discussed. It is shown that the internal structure of the anomalous magnetic moment of the electron would show itself in the cross-section by terms depending on the transversal polarization of the incident electrons.

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Summary of results of a diploma-thesis for the degree of graduate physicist.

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In conclusion the author wishes to express his sincere gratitude to prof. V. Votruba and J. Kvasnica for suggesting this problem, for helpful discussions and valuable advice.     

Diffraction from modulated structures. V. Numerical calculations of diffuse intensity

Numerical calculations of the intensityI(h)/M ²,I(h)/M as well as the interference functions(h)/M and(h) in the vicinity of (200) and (800) matrix reciprocal lattice points for both the periodic and quasiperiodic (monodisperse and polydisperse) models of modulated structures are presented.     

Slowing down of retrieval in the hopfield model

The variation of the convergence time, as a function of the storage capacity is studied numerically for systems ranging in size fromN=1000 toN=16,000 neurons. is found to increase likeexp[–A(_c–)] as one nears the critical storage capacity _c =0.142=0.002.     

The influence of elastic deformation on the magnetostriction constant of nickel and iron-nickel alloys

The dependence of the magnetostriction constant of different materials in the form of a wire on the elastic elongation was measured. With pure nickel the magnetostriction constant is independent of the elastic deformation. All three alloys of iron and nickel and the triple alloy Fe-Ni-Co exhibit a linear dependence on the deformation, which differs for different crystallographic texture. In two iron-nickel alloys the dependence of the magnetostriction constants of the single crystal on the elastic deformation was calculated from measurements on polycrystals having different crystallographic textures. In the triple alloy Fe-Ni -Co a considerable linear decrease in the volume magnetostriction with the elastic elongation was also found. The observed changes can be explained by assuming the influence of the lattice deformation on the spinorbital interaction in alloys.

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. . - Fe-Ni-Co , . - . , Fe-Ni-Co . - .

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A preliminary report on some of the results of this paper was given at the conference on magnetism in Kyoto (Japan) in September 1961.

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In conclusion the authors thank Z. Frait C. Sc. and S. Libovický for remarks, J. Míová for help in the measurements, members of the chemical department of our institute for annealing and analyzing the samples and members of the Metal Research Institute in Panenské Beany for their exceptional helpfulness in preparing the wires.     

ГЕОМАГНИТНЫЙ ЭФФЕКТ ШИРОКИХ ЛИВНЕЙ КОСМИ ЧЕСКИХ ЛУЧЕЙ

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