Surviving extrema for the action on the twisted SU(∞) one point lattice

We give a simplified construction of twist eating configurations, based on a theorem due to Frobenius. These configurations are defined through the equation:U U U ⁺ U ⁺ =exp(2in /N) withU SU(N), =1 tod andn an antisymmetric matrix with integer entries. In the (Twisted)-Eguchi-Kawai model they yield extrema some of which survive forN. Comparison is made with the Monte Carlo data of the internal energy in the small coupling region.     

Trace states and KMS states for approximately inner dynamical one-parameter groups of *-automorphisms

The usual definition of approximately inner one-parameter groups of *-automorphisms ofC*-algebras (approximately inner dynamical one-parameter groups) contains a slight asymmetry. When this asymmetry is corrected, we show that if an approximately inner dynamical one-parameter group hasKMS states forone value of inverse temperature =1/kT, then it hasKMS states for all values of . By the Powers-Sakai Theorem it is enough to show that there is a trace state. We obtain a trace state as a limit of a sequence of vector states with respect to a givenKMS state and thus solve a problem raised in [6].Supported by Odense University, Denmark     

К В. Ч. НАГРЕВУ РАЗРЕЖЕННОЙ ПЛАЗМЫ

[2]. . , . , . . . .     

High-temperature resistivity of Ti1-X Al X alloys

We have measured the high-temperature resistivities of dilute Ti_1-x Al _x alloys withx0.135 up to 1100 K (2.6 _D , where _D is the Debye temperature). We observe that possesses a strong downward deviation from a linear temperature-dependence at high temperatures (several hundred degrees Kelvin). Eventually, saturates to a constant. This non-Bloch-Grüneisen-like behavior is compared with the predictions of current theories.     

Electron microscope study of dislocations in slip bands of bent Fe-3·2% Si alloy single crystals

Dislocations in Fe-3·2% Si alloy single crystals deformed by bending are studied in this paper. The specimens were cut parallel to the slip plane into platelets, polished, and studied in places at various distances from the neutral plane with an electron microscope. A large number of jogs of various sizes was found on screw dislocations. Many loops are formed by the motion of dislocations with jogs and by the stopping of moving dislocations by obstacles. Some of them grow as a result of stress. The activity of sources on large jogs is stopped at an early stage by a cross slip. The formation and growth of loops increases the dislocation density and causes the growth of slip bands.

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Fe-3,2% Si

Fe-3,2% Si, , , . . , . . . .

     

The probability distribution of the velocities of gas molecules after collision with a rapidly moving rigid body

The above problem is met, for example, in the case of the collision of molecules of the atmosphere with an artificial earth satellite and leads to the problem of determining the probability distribution of the absolute value of the vector sum of a constant vector and a Maxwell vector (the latter being a vector, whose rectangular components are distributed normally, with the same standard deviation and mean value zero). The resultant probability density is given by equation (18), the complement to the distribution function by (24), the mean value by (27) and the variance by (31). These results are obtained by transforming the corresponding three-dimensional normal distribution to spherical co-ordinates and integrating over the co-ordinate angles and , which yields the required probability density; the other results are then obtained from it by the usual methods.

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, , (. . , ). (18), -(24), -(27) (31). , ; .

     

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.     

К ТЕОРИИ РЕЗОНАНСНОЙ МИГРАЦИИ ЭНЕРГИИ ВОЗ БУЖДЕНИЯ В ТВЕРДЫХ ТЕЛАХ

- - . - .     

Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits

We present and discuss the derivation of a nonlinear nonlocal integrodifferential equation for the macroscopic time evolution of the conserved order parameter (r, t) of a binary alloy undergoing phase segregation. Our model is ad-dimensional lattice gas evolving via Kawasaki exchange with respect to the Gibbs measure for a Hamiltonian which includes both short-range (local) and long-range (nonlocal) interactions. The nonlocal part is given by a pair potential ^dJ(|x–y|), >0 x and y in ^d, in the limit 0. The macroscopic evolution is observed on the spatial scale ^–1 and time scale ^–2, i.e., the density (r, t) is the empirical average of the occupation numbers over a small macroscopic volume element centered atr=x. A rigorous derivation is presented in the case in which there is no local interaction. In a subsequent paper (Part II) we discuss the phase segregation phenomena in the model. In particular we argue that the phase boundary evolutions, arising as sharp interface limits of the family of equations derived in this paper, are the same as the ones obtained from the corresponding limits for the Cahn-Hilliard equation.     

The metal-semiconductor transition in amorphous Si1−x Cr x films:T 0.19-contribution to the metallic conductivity

A detailed phenomenological re-analysis of previously published conductivity data, (T, x), is presented. It is based on the investigation of differences, (T, x ₁)–(T, x ₂). In this way, the cusp-like low-temperature term is amplified against the other temperature dependent contributions. This term can be described by wherep=0.19±0.03. It is present, if (4.2 K,x) exceeds 260 ^–1 cm^–1, at least up to (4.2 K,x)1350 ^–1 cm^–1 and forT60 K. But it is absent, if (4.2 K,x)180 ^–1 cm^–1. The disappearance of this contribution should be related to the metal-semiconductor transition, taking place atx _c 0.14. On the other hand, the presence of a term proportional toT ^1/2, as predicted by Altshuler and Aronov, seems unlikely.It is argued that the term should be related to the interplay of electron-electron interaction and disorder. The comparison with data from the literature shows that this contribution might also be present in heavily doped crystalline semiconductors.     

Magnetic relaxation spectrum of ferrites Mn x Fe3−x O4+γ

The initial permeability disaccommodation in ferritesMn _x Fe₃–xO₄₊ , 0·5x1, was studied in a temperature range around –200°C to +180°C. Four separate bands were found in the relaxation spectrum of these ferrites.

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Mn _x Fe_3–x O₄₊

Mn _x Fe_3–x O₄₊ , 0,5x1, –200°C +180°C. .

     

Основные соотношени я длн построения механических селект оров нейтронов

, . , , . . , , .     

Real-space renormalization group for directed percolation system

We use the recently proposed real-space renormalization group method to study the critical behavior of directed percolation system in two dimensions. The correlation length exponents and are found to be 1.76 and 1.15. These results are in good agreements with the best known values.     

The propagation of excitation energy in perturbed crystals

The process of the propagation of excitation energy in perturbed dielectric crystals with a weak bond between the atoms having zero permanent dipole moment is studied. It is shown that on certain assumptions this process of propagation can be regarded as the motion of a Frenkel exciton in the electrostatic field of the defect. Frenkel's exciton can be characterized in this case as a neutral polarizable particle having induced dipole moment equal to the change in the induced dipole moment of the crystal during the excitation of one of its atoms.

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, . , . .

     

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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, . , . , , . , . .

     

ЭЛЕКТРИЧЕСКАЯ ЭКВИВ АЛЕНТНАЯ СХЕМА ЗАТУХАЮЩИХ КОЛЕБАНИ Й СДВИГА ПЬЕЗОЭЛЕКТРИЧЕСКИХ СТЕРЖНЕЙ

n - , - .     

Bremsstrahlung spectrum in beta decay

The spectrum of the bremsstrahlung due to the complete slowing down in aluminium of beta particles belonging to the continuous spectrum, was calculated for an arrangement, in which the beta emitter is completely enclosed in an absorber. The Bethe-Heitler cross-section, corrected by an empirical factor, was used. A table is given which makes it possible to calculate bremsstrahlung spectra of beta emitters with their maximal energy between 0·6 MeV and 2·0 MeV; the necessary additional calculations are quite simple. The error in the calculation is practically determined by the uncertainty in the determination of the cross-section and is equal to about 10%.

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-

, - , , - . -, . , -, 0,6 –2,0 . . 10%.

     

Hydrogenated and irradiatedA15 Nb3Sn layers — Preparation,Rutherford scattering analysis,resistivity and superconductivity

Niobium films on sapphire were reacted in tin-vapour to Nb₃Sn with resistance ratiosR(297 K)/R(18.3 K) up to 6 and resistively measured superconducting transition temperaturesT _c up to 17.93 K. The composition Nb_3+z Sn_1–z H _x of electrolytically hydrogenated samples was determined depth dependent by Rutherford backscattering of 30 MeV³²S and simultaneous detection of recoiled protons. Considerable concentration gradients in the thin layers (0.27 m) were detected. The increase of resistivity with hydrogen content and the change in the temperature dependence of is analyzed. A correlation betweenT _c and ₀= is found: An increase of T _c =0.2 K at ₀25cm andx0.03 is followed by a drastic decrease toT _c <1.1 K at ₀80cm andx1. TheT _c vs. ₀ andT _c vs. (T) characteristic correlations are different from universal irradiation or preparation induced correlations. The discrepancies can be interpreted by a stiffening of phonon modes and a band-shifting caused by the hydrogen.     

Modelling of electron stream discharge

Particle-in-cell Monte Carlo code is used to simulate gas discharge initiated by a high current (I _e10kA) middle energy ( _e10keV) hot ( _e1 keV) electron stream. The generation of such an overthermal electron stream has been clearly demonstrated at the experimental REBEX facility during the relativistic electron beam-plasma interaction. When the electron beam (represented by1000 macroparticles) is injected into the drift tube filled by neutral gas (hydrogen,p=13.3–133 Pa) two different stages are observed. During the initial stage the arising Virtual Cathode (VC) is filled by hydrogen ions. The VC disappears when the quasineutrality of ionized gas is achieved. Then the severe exponential growth of electron and ion component of ionized gas is observed.List of symbols x distance from the left electrode [m] - t time [s] - v _x ,v _y velocity components [m/s] - g4(x) potential [Volt] - g4 _1/2(t) middle potential [Volt] - E(x) electric field [Volt/m] - Q _wall wall charge [C/m.m] - I current [C/s] - _tot total energy [J] - N number of macroparticles - f() energy distribution of electron macroparticles at the left electrode, is kinetic energy of macroparticle [eV]. Presented at 17^th Symposium Plasma Physics and Technology, Prague, June 13–16, 1995.     

Multifractal Power Law Distributions: Negative and Critical Dimensions and Other “Anomalies,” Explained by a Simple Example

Divergence of high moments and dimension of the carrier is the subtitle of Mandelbrot's 1974 seed paper on random multifractals. The key words divergence and dimension met very different fates. Dimension expanded into a multifractal formalism based on an exponent and a function f(). An excellent exposition in Halsey et al. 1986 helped this formalism flourish. But it does not allow divergent high moments and the related inequalities f()<0 and <0. As a result, those possibilities did not flourish. Now their time has come for diverse reasons. The broad 1974 definitions of and f allow <0 and f()<0, but the original presentation demanded to be both developed and simplified. This paper shows that both multifractal anomalies occur in a very simple example, which has been crafted for this purpose. This example predicts the power law distribution. It generalizes and f() beyond their usual roles of being a Hölder exponent and a Hausdorff dimension. The effect is to allow either f or both f and to be negative, and the apparent anomalies are made into sources of new important information. In addition, this paper substantially clarifies the subtle way in which randomness manifests itself in multifractals.