Spectral properties of a class of operators associated with conformal maps in two dimensions

Iff is a rational map of the Riemann sphere, define the transfer operator by Let also be the Banach space of functions for which the second derivatives are measures. Ifg andg satisfies a simple integrability condition (implying thatg vanishes at critical points and multiple poles off) then is a bounded linear operator on . The essential spectral radius of can be estimated and, under suitable conditions, proved to be strictly less than the spectral radius. Similar estimates for more general operators are also obtained.     

The lattice spacings of equilibrium solid solutions of silver in aluminium

This paper describes the measured dependence of the lattice spacings of equilibrium Al-Ag solid solutions on temperature and composition. The form of the lattice spacing composition curve is found to differ considerably from that for the supersaturated Al-Ag solid solutions. The differences between the spacings of equilibrium and quenched Al-Ag solid solutions plotted against the electron concentration yield a curve similar to that constructed from the analogous measurements on Al-Zn given by Ellwood. The differences can be attributed to the influence of changes accompanying the increased solute clustering introduced by quenching the solid solutions into the supersaturated state.

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Al-Ag . , Al-Ag . Al-Ag, (. . , ), Al-Zn, , . , .

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The author wishes to express her thanks to Ing. J. Lagek for his care in carrying out the chemical analysis of the aluminium-silver alloys. The careful density measurements of these alloys made by J. Bednfi [are greatly appreciated.     

On maximal surfaces in asymptotically flat space-times

Existenc of maximal and almost maximal hypersurfaces in asymptotically flat space-times is established under boundary conditions weaker than those considered previously. We show in particular that every vacuum evolution of asymptotically flat data for the Einstein equations can be foliated by slices maximal outside a spatially compact set and that every (strictly) stationary asymptotically flat space-time can be foliated by maximal hypersurfaces. Amongst other uniqueness results, we show that maximal hypersurfaces can be used to partially fix an asymptotic Poincaré group.Supported in part by the NSF grant PHY 8503072 to Yale University     

Heat-pulse induced energy transfer in ruby

It is shown that heat pulses, generated by current pulses in thin metal films, may be a powerful tool in the investigation of energy transfer dynamics in solids. Application to ruby shows clearly that the energy transfer from the single ions to the pairs is limited by the energy diffusion in the single ion system contrary to prior ideas. The time constants for the single ion—single ion energy migration and for the transfer from a single ion to a nearby pair could be estimated to be 250µs and 4µs, respectively, for 1.35% doped ruby.Project of the Sonderforschungsbereich 65, Frankfurt-Darmstadt, supported by the Deutsche Forschungsgemeinschaft     

On the geometrization of electrodynamics

This paper develops the conjecture that the electromagnetic interaction is the manifestation of the torsion of spacetime. This conjecture is made feasible by the natural separation of the connection ^v into gravitational and electromagnetic parts ^v and ^v , respectively, related to the metric and to the torsion. When ^v is neglected in front of ^v , the affine geodesics are shown to become the equations of motion of charged particles with Lorentz force, for an appropriate choice of . Since ^v contains the factor q/m, neutral particles do not see the torsional part of the connection and behave as if were zero, i.e., as in Einstein's theory of gravity (the same effect is obviously obtained for charged particles when ^{v v} ).In addition to the factor q/m, the velocity of the test particle appears in . This indicates that the appropriate context for this problem is to be found in velocity-dependent connections. The velocities are now coordinates and become the actual velocities of the test particles only in the system of equations that one solves for obtaining the affine geodesics in connections of this type.When written with differential forms, the combination of Maxwell's equations and of the pertinent form of the torsion suggests geometric field equations for electrodynamics. As for the gravitational part of the connection, it can be made to obey equations similar in form to the Einstein field equations. A unified geometric theory of electrodynamics and gravitation spontaneously emerges. The present state of the theory does not yet permit us to ascertain whether the right-hand side of the fully geometric, gravitational field equations corresponds to the energy-momentum tensor.     

Exponential decay of the power spectrum of turbulence

The analyticity on a strip of the solutions of Navier-Stokes equations in 2D is shown to explain the observed fast decay of the frequency power spectrum of the turbulent velocity field. Some subtleties in the application of the Wiener-Khinchine method to turbulence are resolved by showing that the frequency power spectrum of turbulent velocities is in fact a measure exponentially decaying for frequency ±. Our approach also shows that the conventional procedures used in analyzing data in turbulence experiments are valid even in the absence of the ergodic property in the flow.     

Modeling of the Electric-Field Dynamics in the Atmosphere Using the Test-Structure Method

We propose the test-structure method for modeling of electric-field pulsations in the atmosphere. Numerical calculations necessary for interpretation of the behavior of experimental spectra and structure functions of the electric field are performed. Analysis of experimental data shows that the aeroelectric-field strength, being a nonlocal quantity, is formed by an inhomogeneous distribution of space charges surrounding the observation point. Quantitative assessments of the state of the atmospheric boundary layer, electro-gas-dynamic turbulence and convection parameters are discussed on the basis of spectral and structure functions of the electric field. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 8, pp. 648–660, August 2005.     

A class of exact solutions for doubly anharmonic oscillators

The solution of a difference equation in the form of an infinite continued fraction is used to obtain a class of exact solutions for the eigenfunctions and eigenvalues of doubly anharmonic oscillators described by potentials of the type (1/2)²x²+(1/4)x⁴+(1/6)x⁶, n>0, provided certain constraints on the couplings are satisfied. The class is denumerably infinite but not complete.     

Defect of the five-thirds law using the Wiener-Hermite expansion

Application of the refined Wiener-Hermite expansion with moderate to high Reynolds numbers Re to homogeneous, isotropic turbulence is presented. The results show a defect to Kolmogorov's five-thirds law, increase in the absolute value of the exponent comparable with many theoretical predictions. Midrange spectra up to fluctuation Reynolds numbers of 10⁸ show little, if any, dependence of the defect on Re, as long as the initial spectra do not deviate too far from their equilibrium states. The renormalization scheme has also been proven to have no effect on the final shape of the spectrum.     

Complementary influence of electric and magnetic fields on the sample voltage oscillations ofP-type ultrapure germanium

We report on a previously not observed behaviour of oscillations of the voltage over a hyperpure germanium sample, when increasing the sample current from 0.05 to 13 A, for a number of transverse magnetic fields ranging from 697 to 1746 gauss. The sample temperature was 7.54 K±0.02 K. For each magnetic field the first observed peaks in the frequency spectrum of the sample voltage go to chaos by the period-doubling route and simultaneously shift to lower frequencies (first scenario). Superimposed upon this chaotic spectrum a new peak emerges, which again shifts to lower frequencies with increasing sample current (second scenario). A complementary effect of the sample current and the magnetic field is detected for four properties: firstly, the sudden onset of high resistance in the current versus voltage diagram, secondly, the transition between the two frequency scenarios described above, thirdly the presence of certain frequencies in the sample voltage spectra and fourthly the occurrence of an amplitude maximum for the principal frequency of the first scenario. It is shown that the first two transitions are interrelated.     

Luminescence in the systems ZnS-CuAlS2 and ZnS-AgAlS2

ZnS-CuAlS₂ and ZnS-AgAlS₂ phosphors (denoted by CuAl and AgAl) have blue, green, and red emission bands. The excitation spectra of these bands have characteristic peaks. The effects of activator concentration on the parameters of the emission and excitation spectra are examined.     

A refinement of Simon's correlation inequality

A general formulation is given of Simon's Ising model inequality: whereB is any set of spins separating from . We show that _b can be replaced by _{b A} whereA is the spin system insideB containing . An advantage of this is that a finite algorithm can be given to compute the transition temperature to any desired accuracy. The analogous inequality for plane rotors is shown to hold if a certain conjecture can be proved. This conjecture is indeed verified in the simplest case, and leads to an upper bound on the critical temperature. (The conjecture has been proved in general by Rivasseau. See notes added in proof.)Work partially supported by U.S. National Science Foundation grant PHY-7825390 A01     

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.     

On the theory of scattering of electromagnetic waves in media with space-time velocity fluctuations

We express the effective permittivity tensor for a medium that is, on the average, motionless and nonstationary. It is shown that fast time pulsations of velocity lead to an increase in the average wave field and in the propagation velocity of an electromagnetic wave. Using a computer, we compare the surfaces of the frequency spectra of the strength of the scattered field for the Gaussian and diffusion components of the solenoidal velocity field. Dips are shown to emerge in the frequency spectrum that corresponds to the diffusion correlation function as the velocity pulsation increases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 9, pp. 1091–1095, September, 1996.     

Bifurcation phenomena near homoclinic systems: A two-parameter analysis

The bifurcations of periodic orbits in a class of autonomous three-variable, nonlinear-differential-equation systems possessing a homoclinic orbit associated with a saddle focus with eigenvalues ( ±i,), where ¦/¦ < 1 (Sil'nikov's condition), are studied in a two-parameter space. The perturbed homoclinic systems undergo a countable set of tangent bifurcations followed by period-doubling bifurcations leading to periodic orbits which may be attractors if ¦/¦ < 1/2. The accumulation rate of the critical parameter values at the homoclinic system is exp(-2¦/¦). A global mechanism for the onset of homoclinicity in strongly contractive flows is analyzed. Cusp bifurcations with bistability and hysteresis phenomena exist locally near the onset of homoclinicity. A countable set of these cusp bifurcations with scaling properties related to the eigenvalues±i of the stationary state are shown to occur in infinitely contractive flows. In the two-parameter space, the periodic orbit attractor domain exhibits a spiral structure globally, around the set of homoclinic systems, in which all the different periodic orbits are continuously connected.     

Multicomponent field theories and classical rotators

It is shown that aD-component Euclidean quantum field, =(¹,...,^D), with ||⁴+|²| interaction, can be obtained as a limit of (ferromagnetic) classical rotator models; this extends a result of Simon and Griffiths from the caseD=1. For these Euclidean field models, it is then shown that a Lee-Yang theorem applies forD=2 or 3 and that Griffiths' second inequality is valid forD=2; a complete proof is included of a Lee-Yang theorem for plane rotator and classical Heisenberg models. As an application of Griffiths' second inequality forD=2, an interesting relation between the parallel and transverse two-point correlations is obtained.Research supported in part by the National Science Foundation under grant NSF MPS 74-04870.     

Estimation of the uncertainty of mmw six-port reflectometer

Estimation of the uncertainty of six-port reflectometer is a difficult job especially in higher mmw band for lack of standard terminations. In this paper a novel approach of estimating the uncertainty by using software in stead of those hardly availeble hardware is discribed.     

Statistical mechanics of nonlinear wave equations. 3. Metric transitivity for hyperbolic sine-gordon

McKean and Vaninsky proved that the canonical measuree ^–H d Q d P based upon the Hamiltonian of the wave equation ² Q/t ² - ² Q/x ² +f(Q) = 0 with restoring forcef(Q)=F'(Q) is preserved by the associated flow ofQ andP =Q , and they conjectured that metric transitivity prevails,always on the whole line, and likewise on the circleunless f(Q)=Q orf(Q)=shQ. Here, the metric transitivity is proved for the whole line in the second case. The proof employs the beautiful d'Alembert formula of Krichever.     

THe mechanism of the amplification of moving striations in a d-c discharge

To determine the mechanism of the amplification of moving striations one starts out from the processes which [3] showed to be decisive for the production of stratification of the plasma of a positive column. An analysis of the influence of other processes shows that the main processes leading to the decay of space charges and thus to a smoothing out of the inhomogeneities and thereby to the attenuation of the periodic structure, cannot by overcome by ionization phenomena caused by changes in the concentration of electrons but only partially compensated.It was found that the process which can lead to the predomination of the processes of amplification over the attenuation is the process of the spatial shift of the temperature deflections of the electrons with respect to the additional electric field, which is expressed in a simplified way by Eq. (12).By solving the extremely simplified basic equations it is proved that under favourable conditions this displacement can lead to both a time and a spatial amplification of the striations. Such a possibility is also verified quantitatively by substituting numerical values into the formulae obtained.

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, [3] . , , , , , ., , (12). , , . .

     

Distribution of roots of random real generalized polynomials

The average density of zeros for monic generalized polynomials, , with real holomorphic ,f _k and real Gaussian coefficients is expressed in terms of correlation functions of the values of the polynomial and its derivative. We obtain compact expressions for both the regular component (generated by the complex roots) and the singular one (real roots) of the average density of roots. The density of the regular component goes to zero in the vicinity of the real axis like |lmz|. We present the low- and high-disorder asymptotic behaviors. Then we particularize to the large-n limit of the average density of complex roots of monic algebraic polynomials of the form with real independent, identically distributed Gaussian coefficients having zero mean and dispersion . The average density tends to a simple,universal function of =2nlog|z| and in the domain coth(/2)n|sin arg(z)|, where nearly all the roots are located for largen.