Some critical exponent inequalities for percolation

For a large class of independent (site or bond, short- or long-range) percolation models, we show the following: (1) If the percolation densityP (p) is discontinuous atp _c , then the critical exponent (defined by the divergence of expected cluster size, nP _n (p) (P _c –P)^– asp p _c ) must satisfy 2. (2) or (defined analogously to, but asp p _c ) and [P _n (p _c ) (n ^–1–1/) asn ] must satisfy, 2(1 – 1/). These inequalities for improve the previously known bound 1(Aizenman and Newman), since 2 (Aizenman and Barsky). Additionally, result 1may be useful, in standardd-dimensional percolation, for proving rigorously (ind>2) that, as expected,P _x has no discontinuity atp _c .     

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.     

A contribution to the theory of the triple crystal diffractometer

The first part of the paper gives a general equation for triple-crystal arrangement with perfect crystals on the assumption that the third crystal is rotated. It is shown that in the case of perfect crystals the shape of the reflection curve is practically independent of the vertical divergence. The case of mosaic crystals is also solved and the possibility of rotation by other than the third crystal is considered. A method is proposed for investigating the imperfection of a crystal which is different from methods used up to now. The paper is supplemented by some experimental results.

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Влияние катодной обл асти на динамические свойства тлеющего разряда в во дороде

. . , , I-om 1957 .     

Change in primary extinction during decomposition of supersaturated solid solution II. Al-Cu 4% alloy-formation of G.P. zones

The change in integrated intensity of the (200) reflections of a solid solution during the formation of G.P. zones was measured and compared with the change in the character of the diffuse streaks corresponding to them. It was found that the. formation of G.P. zones does not lead to a decrease in primary extinction despite the great changes in the distribution of the copper atoms. It was shown that the formation of a precipitate accompanied by the formation of crystallographically incoherent boundaries greatly decreases the primary extinction.

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The van der Waals limit for classical systems

For a -dimensional system of particles with the two-body potentialq(r)+ ^v K(r) and density , it is proved under fairly weak conditions onq andK that the canonical pressure (, ) and chemical potential (, ) tend to definite limits when 0. The limiting functions are absolutely continuous and are given in terms of the derivative of the limiting free energy density which was found in Part I.     

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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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.     

Kinetic equation in the kinetic region of the dilute and nonuniform electron plasma

Mori's scaling method is used to derive the kinetic equation for a dilute, nonuniform electron plasma in the kinetic region where the space-time cutoff (b, t _c) satisfies _Dbl _f , _D t _{c f} , with _D the Debye length, _D ^–1= _p the plasma frequency, andl _f and _f the mean free path and time, respectively. The kinetic equation takes account of the nonuniformity of the order ofl _f and _D for the single-and the two-particle distribution function, respectively. Thus the Vlasov term associated with the two-particle distribution function is retained. This kinetic equation is deduced from the kinetic equation in the coherent region obtained by Morita, Mori, and Tokuyama, where the space-time cutoff of the coherent region satisfies _Dbr ₀, _Dt _{c 0}, withr ₀ the Landau length and ₀ the corresponding time scale.     

Long-range order in the XXZ model

The existence of long-range order is proved under certain conditions for the antiferromagnetic quantum spin system with anisotropic interactions (XXZ model) on the simple cubic or the square lattice. In three dimensions (the simple cubic lattice), finite long-range order exists at sufficiently low temperatures for any anisotropy(0) ifS1, and for 0<0.29 (XY-like) or>1.19 (Ising-like) ifS=1/2. In two dimensions (the square lattice), ground-state long-range order exists under the following conditions: for any anisotropy (0) ifS3/2; 0<0.032 (XY-like) or 0.67<<1.34 (almost isotropic) or>1.80 (Ising-like) ifS=1;>1.93 (Ising-like) ifS=1/2. We conjecture that the two-dimensional spin-1/2XY model (=0) has finite ground-state long-range order. Numerical evidence supporting this conjecture is given.     

Hyperbolic initial-boundary-value problem for magnetic flux compression by plane liners

Based on the (relativistic) Maxwell equations with displacement current E/t, the initial-boundary-value problem for the compression of an initially homogeneous magnetic fieldB={0,B(x,t),0} between a fixed liner atx=0 and a detonation-driven liner atx=s(t) is solved analytically. By homogenizing the boundary conditions at the moving boundary, the transient electromagnetic fields are shown to be a superposition of quasistatic elliptic (E/t=0) and hyperbolic (E/t0) wave solutions. The wave equation is solved by a Fourier expansion in time-dependent eigenfunctionsf _n =f _n [nx/s(t)] for the variable region 0xs(t), where the Fourier amplitudes _n (t) are determined by coupled differential equations of second order. It is concluded that the conventional elliptic flux compression theories (E/t=0) hold approximately for nonrelativistic liner speeds , whereas the hyperbolic theory (E/t0) is valid for arbitrary liner speeds .     

Pregalactic black holes: A new constraint

Pregalactic black holes accrete matter in the early universe and produce copious amounts of x radiation. By using observations of the background radiation in the x and wavebands we have been able to impose a strong new constraint upon their possible abundance. If pregalactic black holes are actually present, several outstanding problems of cosmogony can be resolved with typical pregalactic black hole masses of 100M. Significantly more massive holes cannot constitute an appreciable mass fraction of the universe and are limited by _PGBH(M)<10(M JM)^–1.This essay received an honorable mention (1978) from the Gravity Research Foundation.     

МОДЕЛИРОВАНИЕ ЭЛЕКТ РОННО-ОПТИЧЕСКИХ СИС ТЕМ С ОСЕВОЙ СИММЕТРИЕЙ П РИ ПОМОЩИ СЕТИ СОПРОТИВЛЕНИЙ

The paper explains the theory of modelling electrostatic fields by a resistance network. The conditions, which the resistance network must satisfy, are derived and the question of modelling electrodes of different shapes is solved. The finished network and the results obtained on it when modelling a jet for a linear h-f accelerator of electrons are described. Particular attention is paid to the influence of a space charge, the modelling of which is an advantage of this method.

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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.     

Privileged coordinate system in a Schwarzschild field

A basis is given for the idea that a Gaussian coordinate system is the most rational outside a singular sphere in a Schwarzschild field. It can also be extended into the matter below the singular sphere, describing a stationary distribution of matter with a density =A/r² at rR, where Rr_g.Astrophysics Institute, Kazakh Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 103–110, June, 1995.     

Determination of parameters in equation for ferromagnetic resonance of ferrites

The paper describes a new method for determining the parameters in the equation for ferromagnetic resonance — the internal effective field, the spectroscopic splitting factor and the saturation magnetization in polycrystalline magnetically isotropic ferrites. Relations are derived for calculating these parameters by means of the values of the resonance external static fields, which are obtained by measuring on samples having different geometrical shapes and differently arranged static and microwave magnetic fields. The advantages and disadvantages of the method and remarks on the experimental method are given. The paper ends with an example of measurement.

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The determination of the saturation magnetization of ferrites by the method described here was reported on at the Seminary on Ferrites in Microwave Technique, held by the Institute of Technical Physics, Czechoslovak Academy of Sciences, and the Research Institute of Communications Engineering of A. S. Popov, on November 25, 1959.     

Particle velocities faster than the speed of light

In connection with another article by the author, we show how it might be possible to travel faster than the speed of light. We show that for clocks and rods moving faster than the speed of light, we get instead of time dilation and Lorentz contraction, respectively, time contraction and Lorentz expansion, respectively. It is shown that this paper is in confirmation with earlier articles dealing with this subject.     

Nonvacuum taub-type cosmological model

The Einstein universe is a simple model describing a static cosmological spacetime, having a constant radius and a constant curvature, and, as is well known, it does not describe our universe. We propose a model which is an extension of Einstein's. Our metric, havingR × S ³ topology, describes a nonisotropic homogeneous closed (finite) universe of Bianchi type IX. This metric is similar to that of Taub, but is simpler. Unlike the Taub solution (which is a cosmological extension of the NUT solution), however, the universe described by our metric contains matter. Like the Taub metric, our metric has two positive constants (, T). The gravitational red shift calculated from our metric is given. Similarly to the Schwarzschild metric, which has a singularity atr = 2m, this metric has the same kind of singularity att = 2. The maximal extension of the coordinates in our metric is fairly analogous to that of the Schwarzschild metric.     

On two “self-creation” cosmologies

An attempt to produce a continuous creation theory by adapting the Brans-Dicke theory is described. The universe is seen to be created out of self-contained gravitational, scalar, and matter fields. However, the solution of the one-body problem reveals unsatisfactory characteristics of the theory, and in particular the principle of equivalence is severely violated. A second theory is described which retains the attractive features of the first theory and which does not fall foul of its objections. There do exist empirical tests for the theory which are described and which will require further examination. In the limit this theory approaches general relativity in every respect.Notation ² gf the invariant d'Alembertian - t ₀ Hubble time - H Hubble's constant - scalar field - coupling constant - T _M energy-momentum tensor of matter and nongravitational energy, and nonscalar field energy - T _M energy-momentum tensor of scalar field energy - T _M covariant form - T _M contravariant form - T _M mixed form - T _M T _M trace - T _{M ;} covariant differentiation - contravariant differentiation - T Ricci tensor - R curvature scalar (in tensorial equations) - Kronecker symbol - () a function of used in the text - density - p pressure - g the metric tensor - R(t) scale factor (in cosmological equations) - U the fluid 4-velocity (covariant) - U the fluid 4-velocity (contravariant) - functions differentiated once with respect to time ( , differenciated twice) - k the Robertson-Walker curvature constant=+1, 0, or –1 - proportional to - g gravitational coefficient - parameter - angle of deflection, or coordinate - angle of precession or coordinate - angle of precession - G _v the force density - ³( – _n (t)) the Dirac delta function - proper time - K an unknown function definingG - total angle of deflection - r ₀ minimum radius of approach of a light ray grazing the sun     

КРУГОВОЙ УСКОРИТЕЛЬ ЭЛЕКТРОНОВ С КОЛЬЦЕВ ЫМ волноводом

, 4 cm , E _8,1,1. 10 GHz. .

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Circular electron accelerator with toroidal wave-guide

A small electron model of a synchrotron with weak focusing and betatron injection was constructed and tested. In it the electrons are accelerated on a radius of 4 cm by a partial traveling wave in a rectangular toroidal resonator, excited in aE _8,1,1 mode. The source of the h-f power is a tunable impulse magnetron in the 10 GHz band. The possibility of synchronous acceleration of relativistic particles in a smooth toroidal wave-guide in the presence of a strong radial component of the h-f field was thereby confirmed experimentally.

     

Cosmological surrealism: More than “eternal reality” is needed

Inflationary cosmology makes the universe eternal and provides for recurrent universe creation, ad infinitum — making it also plausible to assume that our Big Bang was also preceeded by others, etc.. However, GR tells us that in the parent universe's reference frame, the newborn universe's expansion will never start. Our picture of reality in spacetime has to be enlarged.Wolfson Distinguished Chair in Theoretical Physics.Also on leave from the University of Texas, Center for Particle Physics, Austin, Texas.