Kinetics of contact melting under conditions of non-steady-state diffusion

The average rate ¯v_n of contact melting under conditions of non-steady-state diffus ion was measured for 8 metallic systems using a procedure in which a crystal-liquid-crystal nonconvection system could be produced. It is shown that when the experimental data on ¯v_n are suitably reduced, it is possible to obtain the rate ¯v_S of contact melting in the steady state. v_n and v_S are calculated in the same systems, using equations derived by the authors. The calculated data on ¯v_n and on its temperature dependence agree satisfactorily with the experimental data. The coefficients of heterodiffus ion in metallic melts with large component concentrations are calculated using the experimental data for ¯v_n.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 13–17, December, 1970.     

Pauli-Dirac matrix generators of Clifford Algebras

This article presents a Pauli-Dirac matrix approach to Clifford Algebras. It is shown that the algebra C₂ is generated by two Pauli matrices i₂ and i₃; C₃ is generated by the three Pauli matrices ₁, ₂, ₃; C₄ is generated by four Dirac matrices ₀, ₁, ₂, ₃ and C₅ is generated by five Dirac matrices i₀, i₁, i₂, i₃, i₅. The higher dimensional anticommuting matrices which generate arbitrarily high order Clifford algebras are given in closed form. The results obtained with this Clifford algebra approach are compared with the vector product method which was described in a recent article [Found. Phys. 10, 531–553 (1980) by Poole, Farach and Aharonov] and with the Dirac, Rashevskii and Ramakrishnan methods of matrix generation.Supported by the National Science Foundation under Grant ISP-80-11451.     

Pulsed laser deposition of non-stoichiometric silicon nitride (SiNx) thin films

Silicon nitride (SiN_x) thin films of various stoichiometries (x) were prepared on Si (100) substrates applying the Nd:YAG (=1064 nm) pulsed laser deposition (PLD) process in the shaded off-axis technique at room temperature. The specific arrangement of this technique with perpendicular target (Si) and substrate surfaces and a metallic screen in between guarantees very low particulate (droplet) deposition and, thus, excellent surface qualities. Compared to the usually used on-axis deposition technique consisting of a parallel arrangement of the target and substrate surface, the coating surface covered with particulates is about 100 times lower reaching a maximum of 0.2% on 400 nm thick films. The variation the N₂ partial pressure affects the nitrogen content and the silicon bonding structure of the films analysed by means of SIMS and XPS, respectively. As a consequence the optical properties (e.g.m refractive index) are tailorable in a wide spectral range between 250 and 1200 nm. PACS 81.15.Fg; 78.20.Ci     

Exact expressions for row correlation functions in the isotropicd=2 ising model

We present exact explicit expressions for the row spin-spin correlation functions _{00 n}0 in the isotropicd= 2 Ising model, in terms of elliptic integrals, forn 5. We also give a general structural formula for _{00 n}0.     

Electron emission from Al,Pt, Ag,and Au surfaces under the action of resonant photons with λ=2537 and 1850 Å

An original variant of an electronic device is described, which can be used for gamma-process selection under ionized gas conditions. The device is based on a Hanley and Schaffernicht electron gun. Selection of photons and metastable atoms is performed by a quartz tube located in axial symmetry with the primary electron gun. The desired signal is measured from the flow of secondary electrons emitted from Al, Pt, Ag, and Au surfaces under the action of resonant photons radiated from the levels Hg(6³P₁) and Hg(6¹P₁). For =2537 Å the following values were obtained for _ph 9.1, 3.8, 1.1, 0.25. Analogous values of _ph for =1850 Å were equal to 45.5, 10.8, 6.5, 3.2. The _ph values are in units of 10^–4.Translated from Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 68–74, December, 1987.     

Fock representations of the affine Lie algebraA 1 (1)

The aim of this note is to show that the affine Lie algebraA ₁ ⁽¹⁾ has a natural family _, ,v of Fock representations on the spaceC[x _i,y _j;i andj ], parametrized by (,v) C ². By corresponding the highest weight _, of _, to each (,), the parameter spaceC ₂ forms a double cover of the weight spaceC₀C –₁ with singularities at linear forms of level –2; this number is (–1)-times the dual Coxeter number. Our results contain explicit realizations of irreducible non-integrable highest wieghtA ₁ ⁽¹⁾ -modules for generic (,v).     

Acoustic properties of amorphous SiO2 and PdSiCu,and of crystalline Ag,NbTi and Ta at very low temperatures

With the vibrating reed and vibrating wire techniques we have investigated the acoustic properties of vitreous silica (SiO₂, Suprasil I) and of amorphous PdSiCu as well as of polycrystalline Ag, NbTi and Ta at frequencies of 100 Hz/2<6 kHz and at temperatures of 0.1 mKT1 K. The relative change of sound velocity v/v of SiO₂ shows saturation effects, strain amplitude dependence, as well as an unexpected temperature dependence below its maximum atT<50 mK. For PdSiCu we observe that below a certain temperature, which depends on the applied strain, the temperature dependence of the sound velocityv deviates from the logarithmic behavior observed at higher temperatures and reaches an almost constant value atT<1 mK. In the same temperature rangeQ ^–1 does not remain constant but steadily decreases. The acoustic properties of the two amorphous materials at finite strain show substantial deviations from the standard tunneling model. Some of the observed anomalies can be explained taking into account the change of population of the tunneling systems energy states and a nonlinear relaxation absorption. For polycrystalline Ag we find v/v lnT andQ ^–1T ^1/3 over three decades inT atT<100 mK; it shows low-temperature acoustic properties which are strikingly similar to those of amorphous materials. The temperature and strain dependencies of the acoustic properties of polycrystalline superconducting NbTi and Ta resemble those obtained for SiO₂. These results indicate that there are basically no differences in the low-temperature acoustic properties of polycrystals and amorphous materials.     

Trapping,percolation, and anomalous diffusion of particles in a two-dimensional random field

We analyze from first principles the advection of particles in a velocity field with HamiltonianH(x, y)=¯ V ₁ y–¯ V ₂ x+W ₁ (y)-W ₂ (x), whereW _i , i=1, 2, are random functions with stationary, independent increments. In the absence of molecular diffusion, the particle dynamics are very sensitive to the streamline topology, which depends on the mean-to-fluctuations ratio=max(|¯V₁¦/; ¦¯V₂|/), with =|W ₁ |^21/2=rms fluctuations. Remarkably, the model is exactly solvable for 1 and well suited for Monte Carlo simulations for all , providing a nice setting for studying seminumerically the influence of streamline topology on large-scale transport. First, we consider the statistics of streamlines for=0, deriving power laws for p_nc(L) and (L), which are, respectively, the escape probability and the length of escaping trajectories for a box of sizeL, L » 1. We also obtain a characterization of the statistical topography of the HamiltonianH. Second, we study the large-scale transport of advected particles with > 0. For 0 < < 1, a fraction of particles is trapped in closed field lines and another fraction undergoes unbounded motions; while for 1 all particles evolve in open streamlines. The fluctuations of the free particle positions about their mean is studied in terms of the normalized variablest ^– v/2[x(t)–x(t)] andt ^–v/2 [y(t)-(t)]. The large-scale motions are shown to be either Fickian (=1), or superdiffusive (=3/2) with a non-Gaussian coarse-grained probability, according to the direction of the mean velocity relative to the underlying lattice. These results are obtained analytically for 1 and extended to the regime 0<<1 by Monte Carlo simulations. Moreover, we show that the effective diffusivity blows up for resonant values of ) for which stagnation regions in the flow exist. We compare the results with existing predictions on the topology of streamlines based on percolation theory, as well as with mean-field calculations of effective diffusivities. The simulations are carried out with a CM 200 massively parallel computer with 8192 SIMD processors.     

Dynamics of vector spin glasses: The Gabay-Toulouse line

The dynamics of ann-component vector spin glass with infinite range interactions are investigated near and above the Gabay-Toulouse (GT) line. The local transverse susceptibility _T for 0 varies along the whole GT lineT _c1 (H) as ^v , with a field and temperature independent critical exponentv=1/2. The longitudinal susceptibility _L () remains analytic for all (T, H)T _c1 (H), except for a cross-over fromv=1 tov=1/2 forH0 at the freezing temperatureT=T _f . The dynamic susceptibilities _T () and _L () are already coupled above the GT line via self-energy terms. BelowT _c1 (H), this coupling is strongly enhanced by other mechanisms.     

On the photo-electroluminescence of ZnS-Cu

The influence of weak ultra-violet irradiation on the brightness waves of electroluminescence is investigated for two types of ZnS-Cuphosphors. The observed effects (increase in brightness in the primary peak and its phase shift, the disappearance of the secondary peak) are explained on the basis of present-day conceptions on electroluminescence.

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ZnS-Cu

ZnS-Cu. ( , ) .

     

Thes-f model with Coulomb repulsion: Thermodynamics of two atomic cluster. Spin 1/2

A cluster of two atoms described by thes-f model with Coulomb repulsion has been considered. The interaction between localized 4f electrons (S=1/2) is taken in the molecular field approximation. The thermodynamic quantities like magnetization, specific heat and correlation functions n , n , S ^z n , S ^z n , S ^z (n –n ), n n and S ⁺ a ⁺ a as functions of temperature are presented for different band fillingN=0, 0.5, 1, 1.5, 2. The dependence of Curie temperature onN is calculated. The phase diagram forN=1 (T=0K) shows the possibility of existence of two phases: paramagnetic and ferromagnetic.The Curie temperature and the specific heat as functions ofN exhibit similar trends as found in experiments on doped magnetic semiconductors.     

Measurement of Optical Constants of CVD-Diamond for Short-Wavelength Far-Infrared Lasers

A diagnostic system using short-wavelength far-infrared (FIR) lasers (40–70 m in wavelength) is now being developed for high density and large volume plasmas. In the wavelength region, a CVD-diamond is the excellent materials for optical windows of the laser and the plasma vessel and beam splitters of a multichannel interferometer. To design these optical elements, the optical constants (refractive index n, absorption coefficient and transmissivity T) of the CVD-diamond have been measured precisely by using FIR lasers of 48-, 57- and 71-m in wavelength. As an example, the result for 57.1511 m light is n = 2.383(1) ± 0.002, = 0.19 ± 0.05 cm^-1 and T = 97.5 ± 1.5% at 1.023 mm in thickness.     

Un phénomène de concentration évanescente pour des flots non-stationnaires incompressibles en dimension deux

We consider a sequencev of non-stationary solutions of the incompressible 2D-Euler equation, locally bounded inL ². We prove that if the defect measure is supported in a one-dimensional set (³) of some special type (which we call finite type), the weak limitv ofv is a solution of the Euler equations: our theorem is of the type concentration-cancellation.     

Convergence of Chorin-Marsden product formula in the half-plane

Consider a viscous incompressible fluid in the half-plane and letu _t be a solution of the Navier-Stokes equation. In this paper we prove that the product formula (E _t/n G _t/n u) ⁿ u ₀, whereE _t is the Euler flow,G _t is the heat flow and is a suitable operator describing the vorticity production due to the boundary, converges uniformly tou _t in the limitn .Research supported by Ministero della Pubblica Istruzione, CNR contract No. 84.00016.02 and GNFM     

Induced geometry and confinement

A classical, Poincaré invariant dynamical system is developed which contains, besides the natural metric _v , an induced metricg _v that is generated by a real scalar dynamical field. It is shown that scalar fields whose dynamics are governed by the induced metric can be consistently introduced. Also, point particles which follow timelike quasi-geodesic trajectories can be introduced. The reaction forces acting ong _v due to the presence of these fields and particles are computed. A discussion of causality and geometrical confinement is given.     

Absolute Continuity of Vitali–Hahn–Saks Measure Convergence Theorems

In this paper, we prove the following improved Vitali–Hahn–Saks measure convergence theorem: Let (L, 0, 1) be a Boolean algebra with the sequential completeness property, (G, ) be an Abelian topological group, be a nonnegative finitely additive measure defined on L, {_n: n N} be a sequence of finitely additive s-bounded G-valued measures defined on L, too. If for each a L, {_n(a)}_{n N} is a -convergent sequence, for each nN, when { (a)} convergent to 0, {_n(a)} is -convergent, then when { (a)} convergent to 0, {_n(a)} are -convergent uniformly with respect to nN     

Debye temperature of alkali halide crystals

The Debye temperature _D is calculated from the elastic constants for 18 alkali halide crystals. Comparison of the results with calorimetric data _D reveals an agreement within the experimental error. The temperature dependence of _D is determined for NaCl, NaBr, KCl, and KBr crystals from the elastic constants, and this dependence is compared with the calorimetric data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 3, pp. 89–94, March, 1971.     

Stochastic coupling and thermodynamic inequalities

Let ₁ and ₂ be thermodynamic Gibbs measures on ^m and ⁿ , respectively. Diffusions are constructed having ₁, and ₂ as invariant measures. These diffusions are then coupled; inequalities between expectations of certain random variables on the two spaces result.Partially supported by NSF-MCS 74-07313-A03     

Experimental investigation of infrared fluorescence of molecular gases under the action of CO2-laser radiation

In the paper, the experimental investigation is carried out of the IR fluorescence of organic substances of different classes in the range 600–3000 cm^–1 under the action of the continuous radiation of a CO₂ laser with a power of 40 W/cm². The procedure is given for obtaining the fluorescence spectra. For all the substances investigated, the magnitudes of the effective absorption cross section were determined experimentally at the generation frequency of the laser. Fluorescence is observed only in the case when _v 0; if _v 0, fluorescence is absent. It is shown that the fluorescence intensity depends significantly on the magnitude of the absorption cross section at the laser frequency. A comparison of the fluorescence and absorption spectra shows that only vibrations allowed in the IR region appear in the emission; in a number of cases, a sharp increase of the fluorescence intensity of certain overtones and compound vibrations is observed: when the frequencies are multiples of the laser emission.Translated from Izvestiya Uchebnykh Zavedenii, Fizika, No. 3, pp. 50–53, March Vysshikh 1979.     

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 .