К ТЕОРИИ СПОНТАННОЙ Н АМАГНИЧЕННОСТИ ТОНКИХ СЛОЕВ. II. ЧАСТЬ)

- , . - . - - . , . 1956 .     

The matter-vacuum matching problem in general relativity

In a recent paper [1] methods were developed for studying the problem of matching matter and vacuum solutions of Einstein's field equations along timelike hypersurfaces in the axisymmetric stationary case. Criteria for the existence and uniqeness of perfect fluid sources for given vacuum fields were given in the form of a theorem. As an application, the existence of such Kerr-interior solutions could be proved at least in a full neighborhood of suitably chosen boundary surfaces.In this paper further investigations of this matching problem are made for some special cases. It is found that stationary rotating dust cannot be a source of the Kerr metric and the existence of rotating Schwarzschild sources is proved. These results are discussed together with further aspects of the general methods used.Work supported by the Deutsche Forschungsgemeinschaft.     

Замечание К теории по степенного возникновения подви жных слоев в плазме инертных газов

[1] t _B , t _B . , t _B , . .

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A note on the theory of the successive production of moving striations in the plasma of inert gases

Approximate expressions are derived on the basis of Pekárek's theoretical paper [1] for the period of the maximum t_B of a wave packet produced by the passage of a wave of stratification before the aperture of a photomultiplier, and for its time width in the half-height t_B. The relaxation time of a wave of stratification, following from the theory [1], can thus be calculated by means of the experimentally measured velocity of motion of the maximum of a wave packet u and its width t_B. The calculation is supplemented by numerical data on the magnitude of errors committed by using approximate expressions.

     

Ferromagnetic resonance in thin cobalt films

The paper gives the results of measuring ferromagnetic resonance on thin cobalt films, vacuum deposited on unheated glass slides. The values of the (g-factor, the width of the curve, the effective stress and uniaxial induced anisotropy were determined as a function of the thickness of the film from measurements of the ferromagnetic absorption in a magnetic field normal and parallel to the surface of the film. Measurements were carried out on a frequency of 9200 MHz and on film thicknesses of 180 to 1800 Å. A qualitative explanation of the observed dependences is given.

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, . , , g-, , , . 9200 MHz 180–1800 Å. .

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The author thanks V. Kamberský and Z. Málek, C. Sc., for providing some of the cobalt films and for help in depositing and measuring the thicknesses, S. Kadeková and M. Polcarová for valuable advice in determining the structure of the films, J. Míová for carefully plotting the results of measurements and Z. Málek and O. tirand for carefully reading the paper and for valuable discussions.     

Solutions without phase-slip for the Ginsburg-Landau equation

We consider the Ginsburg-Landau equation for a complex scalar field in one dimension and consider initial data which have two different stationary solutions as their limits in space asx±. If these solutions are not very different, then we show that the initial data will evolve to a stationary solution by a phase melting process which avoids phase slips, i.e., which does not go through zero amplitude.     

ТЕПЛОВАЯ ЭНЕРГИЯ ДИССОЦИАЦИИ И ОСНОВН ОЕ СОСТОЯНИЕF 2 + -ЦЕНТРОВ

+ - , , g - . , . .F ₂ ⁺ -. .     

The influence of the spectral asymmetry of X-ray emission lines on the results of studying defects in crystals by X-rays of different wavelength

Since the asymmetry of X-ray emission lines was found to influence the exact measurements of lattice parameters of powdered samples the author has revised the results she once obtained when carrying out exact measurements of the lattice parameter with radiations of various wavelengths for tungsten crystals containing admixtures of different elements. It is shown that with samples having an inhomogeneous distribution of the admixtures in the crystals the typical graphs of lattice parameter found originally remain when respecting the influence of the spectral asymmetry. On the other hand, with a sintered sample which has been homogeneized by long annealing the introduction of corrections to spectral asymmetry leads to an adjustment of the differences measured originally, for which it was difficult to find a probable explanation.

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

     

On the critical exponent for random walk intersections

The exponent _d for the probability of nonintersection of two random walks starting at the same point is considered. It is proved that 1/2<₂3/4. Monte Carlo simulations are done to suggest ₂=0.61 and ₃0.29.     

Standpoint cosmology

An unorthodox cosmology is based on a notion of standpoint, distinguishing past from future, realized through Hilbert-space representation of the complex conformai group for 3+1spacetime and associated coherent states. Physical (approximate) symmetry attaches to eight-parameter complex Poincaré displacements, interpretable as growth of standpoint age (one parameter), boost of matter energy-momentum in standpoint rest frame (three parameters) and displacement of matter location in a compact U(1)O(4)/O(3) spacetime attached to standpoint (four parameters). An initial condition (at big bang) is characterized by a huge dimensionless parameter that breaks dilation invariance. Four major length scales are recognized, called Planck, particle, lab, and Hubble, with separations controlled by ; all physical concepts, including spacetime, depend on wideness of scale separation.     

π0 → γγ in the Spinor Strong Interaction Theory

An expression for the decay rate (⁰ ) has been derived in the frameworkof the spinor strong interaction theory, a first-principles strong interaction theoryproposed some years ago as an alternative to low-energy QCD. The startingpoint is the SO(3) gauge-invariant action for two quark mesons which has beensuccessful in accounting for confinement, ^{+ +} , e⁺, and ⁰ e⁺, nonexistenceof the Higgs boson, and other low-energy mesonic phenomena. The quasi-four-quarkmeson equations developed for the decay of a vector meson into twopseudoscalar mesons V PP has been taken over here to apply to P(⁰) VV(^{+ –}) (plus ⁺ and ^– which annihilate each other). This mechanismin principle agrees with that of the assumption of vector meson dominance inthe literature. It, together with the effect of form factors, arises naturally in theformalism and need not be assumed. Equations for the perturbed vector mesonwave functions cannot be simply solved and an assumption has been made toobtain an estimate of their magnitude. Together with a constant associated withthe strong coupling obtained earlier from V() PP(K⁺K^–), the estimated decayrate is 19.2 eV, in order-of-magnitude agreement with data (7.74 eV).     

Effects of a positive cosmological constant on circular orbits in the reissner-nordström,schwarzschild, and kerr fields

Criteria for the existence and stability of circular orbits in a general stationary axisymmetric field are established using the equation of geodesic deviation. Circular orbits in the ReissnerNordström, Schwarzschild and Kerr fields, all with a positive cosmological constant included, are considered and the effects of are detailed.     

Gentle perturbations

By introducing a specific type of perturbation,A, in the Hamiltonian, we define a class of gently perturbed states, ,A, of a canonical ensemble, . The perturbations are chosen so as to preserve a relationship of the form ,A constant ×. Applications in ergodic theory and phase transitions are described.     

Radiation losses in completely ionized plasma

The losses caused by bremsstahlung during electron-ion and electron-electron collisions in a completely ionized plasma (in Born's approximation) are calculated. The calculation can be carried out analytically for a sufficiently dilute plasma (plasma with infinitely large Debay-Hückel radius). This assumption is satisfied very well by the known classification to actual controlled thermonuclear reaction. A dependence of the formI=an ². (1+3/2), wherea=0·73×10^–16 MeV.cm³.sec^–1,n is the number of ions per cm³ and =kT/mc ², is determined for the amount of energy radiated from 1 cm³ of plasma per sec. In the relativistic temperature regionkTmc ² the influence of electron-electron collisions begins to predominate. A number of important results concerning radiation losses in relativistic plasma will be published in a later paper.

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, ( ). ( -). . , I=an ². (1+3/2), =0,73. 10^–16 MeVcm²s^–1,n — =kT/mc ². kTmc ² . , .

     

On static and radiative space-times

The conformal constraint equations on space-like hypersurfaces are discussed near points which represent either time-like or spatial infinity for an asymptotically flat solution of Einstein's vacuum field equations. In the case of time-like infinity a certain radiativity condition, is derived which must be satisfied by the data at that point. The case of space-like infinity is analysed in detail for static space-times with non-vanishing mass. It is shown that the conformal structure implied here on a slice of constant Killing time, which extends analytically through infinity, satisfies at spatial infinity the radiativity condition. Thus to any static solution exists a certain radiative solution which has a smooth structure at past null infinity and is regular at past time-like infinity. A characterization of these solutions by their free data is given and non-symmetry properties are discussed.     

Positivity of entropy production in the presence of a random thermostat

We study nonequilibrium statistical mechanics in the presence of a thermostat acting by random forces, and propose a formula for the rate of entropy productione() in a state . When is a natural nonequilibrium steady state we show thate()0, and sometimes we can provee()>0.     

Hard gamma radiation in the decay of Lu176m

Gamma lines 1·05 MeV(4 × 10^–6 quanta/decay) and 1·14 MeV (9 × 10^–6 quanta/decay), giving evidence of the existence of a new level in Hf¹⁷⁶ with an energy of 1·14 MeV, were found in the decay of Lu^176m with a half-life of 3·7 hours, using the scintillation method. The component of the beta spectrum, exciting this level, has a maximum energy of 0·17 MeV and logft=8·3. The spin of this level proved to be equal to one. The level was interpreted as a single-particle neutron level withn ₀: 5/2^– (512),n ₁: 7/2^– (514);I=1⁺.

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- Lu^176m

Lu^176m 3,7 - 1,05 MeV (4.10^–6 /) 1,14 MeV (9.10^–6 / /), Hf¹⁷⁶ 1,14 MeV. -, , 0,17 MeV logft = =8,3. . cn ₀: 5/2^– (512),n ₁: 7/2^– (514);I = 1⁺h

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The authors thank L. K. Peker from the Leningrad State University for a helpful discussion of their results.     

Dark body and black hole horizons

The formula for the horizon of a Newtonian dark body is given and compared to that of a relativistic black hole: a Newtonian dark body has at least one hair.     

Low-temperature and long-time anomalies of a damped quantum particle

The time evolution of a damped quantum particle is discussed. Dissipation is modeled by the bilinear coupling to a set of harmonic oscillators. Using a functional integral technique that accounts for initial correlations between the particle and the reservoir, one can express the dynamics of the damped particle entirely in terms of equilibrium correlation functions. The long-time behavior of these correlations is determined for memory damping arising from the coupling to a reservoir with spectral densityI() at low frequencies, where > 0. The time evolution of nonequilibrium initial states of the damped particle is discussed. At finite temperatures an initially localized state is found to spread subdiffusively or superdiffusively, depending on . For > 2 the damping becomes ineffective for long times, and the width of a state grows kinematically. At zero temperature and for < 1, an initially localized state remains localized for all times. For 1 the state spreads, but with a slower rate than at finite temperatures. Study of arbitrary initial states indicates that the process is ergodic at finite temperatures only for 2 and at zero temperature for 1 2.     

ПРИГОТОВЛЕНИЕ И ХАРА КТЕР ПОВЕРХНОСТИ ПЛАСТИНОК AgBr

AgBr . , .     

The four laws of black hole mechanics

Expressions are derived for the mass of a stationary axisymmetric solution of the Einstein equations containing a black hole surrounded by matter and for the difference in mass between two neighboring such solutions. Two of the quantities which appear in these expressions, namely the area A of the event horizon and the surface gravity of the black hole, have a close analogy with entropy and temperature respectively. This analogy suggests the formulation of four laws of black hole mechanics which correspond to and in some ways transcend the four laws of thermodynamics.Research supported in part by the National Science Foundation.