Large-Deviation Principle for One-Dimensional Vector Spin Models with Kac Potentials

We consider the one-dimensional planar rotator and classical Heisenberg models with a ferromagnetic Kac potential J (r)=J(yr), J with compact support. Below the Lebowitz-Penrose critical temperature the limit (mean-field) theory exhibits a phase transition with a continuum of equilibrium states, indexed by the magnetization vectors m s, s any unit vector and m the Curie–Weiss spontaneous magnetization. We prove a large-deviation principle for the associated Gibbs measures. Then we study the system in the limit 0 below the above critical temperature. We prove that the norm of the empirical spin average in blocks of order ^–1 converges to m , uniformly in intervals of order ^–p , for any p 1. We also give a lower bound to the scale on which the change of phase occurs, by showing that the empirical spin average is approximately constant on intervals having length of order ^-1-with (0,1) small enough.     

Precipitation mechanism,shape, and bond with the matrix of γ′-phase particles in Ni36Cr12TiAl steel

It is shown that in discontinuous decomposition in Ni36Cr12TiAl steel, rodlike lamellae of the -phase are precipitated, which are coherently (possibly quasi-coherently) bonded to the matrix. It is concluded from data on the continuous precipitation of the -phase that continuous decomposition in this steel takes place in two stages: in the first, partially ordered zones are formed and, in the second, particles of the -phase.     

56,57,60CoFe NMR/ON,hyperfine anomalies and γ-factors of cobalt isotopes

The results of NMR/ON measurements on^56'57'60Co isotopes in iron are presented. To avoid the uncertainties caused by local demagnetizing field inhomogenities the measurements on two cobalt isotopes in one sample have been carried out. The values of nuclear-factor ratios ⁵⁷/ ⁶⁰ = 1.805 (20), ⁶⁰/ ⁵⁶ = 0.761 (20), ⁵⁶/ ⁵⁷ = 0.726 (20) and hyperfine anomalies⁵⁶⁶⁰ = -0.036 (10),^{60 57} = 0.017 (10) and⁵⁷⁵⁶ = 0.018 (10) have been calculated from the experimental results.     

Regge poles and π Δ (1236) photo production

The Regge-pole model is used to obtain expressions for the differential cross section and the polarization isobar-density matrix for the N (1236) process with an account of the , A₂, and trajectories.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 12, No. 6, pp. 103–106, June, 1969.     

(α, n) reactions in cascade γ-transitions

The ratios of the cross sections for the formation of the ground and isomeric states in reactions on¹⁰⁷Ag,¹⁰⁹Ag, and¹¹³In are calculated based on the assumption that at low energies the (, n) reaction proceeds via a) formation of the compound nucleus, b) evaporation of a neutron, and c) cascade -transitions. The number of cascade -quanta and the distribution of the excitation energy between the -quanta and the neutron is not postulated beforehand (as is usually done), but is calculated based on the statistical theory. By comparing with experiment, the parameter of the spin-dependence of the density of nuclear states is found. It is shown that the average number of -quanta in the cascade increases approximately linearly with the energy of the particles. The energy spectrum of the -quanta in the (, n) reaction is calculated. The distribution of -quanta has a maximum at low energies (1 MeV), which, as the energy of the primary particles is increased, moves slowly into the higher energy range while broadening at the same time.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 8, pp. 77–81, August, 1984.     

Radiation of relativistic electrons in a magnetic undulator

Expressions are obtained for the spectral-angular characteristics of the radiation in two limiting cases: 1 and 1 ( is the angle of deflection of the electron in the field, and is the energy of the electron in units of mc²). It is shown that in the latter case the maximum of the radiation occurs at higher harmonics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 88–91, October, 1973.In conclusion the authors thank Professor A. A. Sokolov for useful discussions.     

Nonlinear two-photon interaction in a strong magnetic field

Sections of nonlinear photon-photon scattering processes and merger of photons in the nucleus (Ze) (Ze) in a strong magnetic field are computed by using a developed two-dimensional formalism. Closed expressions are obtained for the sections with a graphical illustration of the results and they are compared with the case of no external fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 16–19, June, 1988.     

A dynamical system with integer information dimension and fractal correlation exponent

In this paper we construct a family {T }, 0<<1/2, of exact endomorphisms of [0, 1] such that the invariant measurem ofT is equivalent to Lebesgue measure but has fractal correlation exponent =2. This shows that an almost complete dichotomy can exist between the information dimension and the correlation exponent in observable dynamical systems.Research supported by the Natural Sciences and Engineering Research Council of Canada     

To the problem of KL→π0γγ decay

It is shown that the contribution of diagrams with intermediate state vector mesons to the K_L ⁰ amplitude, intensively discussed in literature in recent years, is close to zero provided that theSU(3) group breaking is taken into account. At the same time, the contribution of scalar mesons in the intermediate state is essential. The obtained estimates for Br(K_L ⁰) conform with the recent experimental data Br(K_L ⁰ )=(2·1 ± 0·6)×10^–6.Dedicated to the memory of our friend Prof. M. Gmitro.We wish to thank S. B. Gerasimov and A. B. Govorkov for useful discussions.     

Comparison between static and adiabatic coupling mechanisms for nonradiative multiphonon transitions in semiclassical approximation

Semiclassical versions of the static (diabatic) and adiabatic coupling schemes are applied to a two-level-one-mode system at total energies above the cross-over level. The corresponding rates of nonradiative multiphonon transitions reduce to alternativemonotonous dependences on the usual Landau-Zener parameter. Static coupling gives an increasing transition probability (per oscillation) of the familiar formP ^st() = 4. Adiabatic coupling associated with a sufficiently low mechanism-specific potential barrier of Born's type produces a decreasing transition probability of the formP ^ad() exp (–2). The underlying Beyond-Non-Condon calculation procedure shows that (1) the weak dependence of the pre-exponential factorP ^ad is a consequence of the-independent normalization of the electronic matrix element governing the non-adiabaticity operator and (2) the occurrence of the mechanism-specific tunnelling factor exp(–2) is due to the avoided crossing of adiabatic oscillator potentials. Ranges of applicability of both alternative coupling schemes are limited by comparison with earlier non-perturbational results.     

Analytical Electron Microscopy Examination of the γ′/γ Interfaces in a Ni-Based Superalloy

The investigation of microstructure and chemical composition of the and phases were performed in a Ni-base superalloy by means of analytical electron microscopy. The distribution of particular elements in the alloy was revealed using X-ray mapping in a transmission electron microscope. The detected concentration profiles of alloying elements at the / interface were relatively sharp in the case of cuboidal shape of the phase while they resembled the classical diffusion profile for the oval phase. The quantitative analysis of the phase revealed much higher content of Al and lower of Ti, W, Co and Mo in the oval precipitates compared to cuboidal ones. This result is attributed to the different solidification paths, which is eutectic for the cuboidal precipitates and peritectic for the oval precipitates.     

Production of neutral mesons in the reaction12C+12C at 2 GeV/u

A systematic study of neutral meson production in heavy-ion reactions at 2 GeV/u was started with a¹²C+¹²C experiment using the photon spectrometer TAPS. Special emphasis is put on the possible observation of the-meson in a heavy-ion reaction exploiting the decay channel ⁰.Presented at the International School-Workshop Relativistic Heavy-Ion Physics, Prague (Czech Republic), 19–23 September 1994.     

Critical exponents for the self-avoiding random walk in three dimensions

We compute by direct Monte Carlo simulation the main critical exponents, , ₄, andv and the effective coordination number for the self-avoiding random walk in three dimensions on a cubic lattice. We find both hyperscaling relationsdv=2– anddv– 2 ₄+=0 satisfied ind = 3.     

New derivation of Bardeen-Shockley formula for mobility of electrons in homopolar semi-conductors

The Bardeen-Shockley formula for the mobility of an electron or hole in a homopolar semi-conductor is derived in a different way to that in which its authors obtained it. The interaction energy of the electron with the acoustic lattice oscillations is derived in an original way. A new possibility for determining the energy gap is given.

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Hydrodynamic Limit of Brownian Particles Interacting with Short- and Long-Range Forces

We investigate the time evolution of a model system of interacting particles moving in a d-dimensional torus. The microscopic dynamics is first order in time with velocities set equal to the negative gradient of a potential energy term plus independent Brownian motions: is the sum of pair potentials, V(r)+ ^d J(r); the second term has the form of a Kac potential with inverse range . Using diffusive hydrodynamic scaling (spatial scale ^–1, temporal scale ^–2) we obtain, in the limit 0, a diffusive-type integrodifferential equation describing the time evolution of the macroscopic density profile.     

Current distributions in a two-dimensional random-resistor network

The current and logarithm-of-the-current distributionsn(i) andn(ln i) on bond diluted two-dimensional random-resistor networks at the percolation threshold are studied by a modified transfer matrix method. Thek th moment (–9k8) of n(ln i) i.e., ln i&^k, is found to scale with the linear sizeL as (InL)^(k). The exponents (k) are not inconsistent with the recent theoretical prediction (k)=k, with deviations which may be attributed to severe finitesize effects. For small currents, ln n(y)–, yielding information on the threshold below which the multifractality of (i) breaks down. Our numerical results for the moments of the currents are consistent with other available results.     

Resonant magnetopolaron effects in parabolic quantum wells in a tilted magnetic field

We study the resonant magnetopolaron effects in parabolic quantum wells in a tilted magnetic field. The renormalization of the first excited level, which is resonant with the ground state level plus one longitudinal-optical phonon is calculated at the resonance using an improved resonance approximation to be E= where is the polaron coupling constant. The exponent and the factor are calculated in dependence on the tilt angle of the magnetic field and the confinement energy.     

Honeycomb domain structure

A theory is given of a new structure produced when demagnetizing uniaxial single crystals (e.g. magnetoplumbite) in a field normal to thec axis. The experimental results fully support the theory on the assumption that domain structures produced under normal conditions are metastable. Methods are given by which stable structures can be prepared from such metastable ones. On the basis of these results opinions are expressed as to the nucleation of plate and honeycomb structures, produced either by reducing the field from saturation or by cooling below the Curie point.

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In conclusion the authors would like to thank C. Novák from the Institute of Technical Physics, Czechoslovak Academy of Sciences, for checking the calculation of the harmonic analysis and Z. Málek and J. Eousek for carefully reading the paper and for valuable remarks.     

Generalized Stefan-Boltzmann law

Thermodynamics arguments have been employed to derive how the energy density depends on the temperatureT for a fluid whose pressurep obeys the equation of statep = ( –1), where is a constant. Three different methods, among them the one considered by Boltzmann (Carnot cycle), lead to the expression = T/( –1), where is a constant. This result also appears naturally in the framework of general relativity for spacetimes with constant spatial curvature. Some particular cases are vacuum (p = –), cosmic strings (p= –1/3), radiation (p = 1/3), and stiff matter (p = ). It is also shown that such results can be adapted for blackbody radiation inN spatial dimensions.     

Локалъная чувствите лъностъ фотокатодов фотоумножителей

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The local sensitivity of photo-multiplier photo-cathodes

The influence of the non-uniform distribution of the sensitivity of a photo-multiplier photo-cathode on the spectrum shape of the output pulses from a scintillation detector is studied. Methods of scanning the local sensitivity and determining its distribution function are described. The theory was compared qualitatively with measurement on a slow-neutron detector from a mixture of zinc sulphate and boric acid.