Frictional forces and resistance to the beginning of plastic deformation in Cu-Al solid solutions

Extension curves have been obtained for Cu-Al solid solutions in the microdeformation range 10^–6-10^–3. It is shown that the dependence of the resistance to microdeformation on the degree of this deformation is described by = ₀ ⁰ + A^1/2, where ₀ ⁰ is the resistance to the beginning of plastic deformation, and A = const. The stresses _F due to frictional forces are determined from the unloading curves. The dependences of ₀ ⁰ and _F on the Al concentration c in the alloy are studied. The ₀ ⁰ = f(c) and F = (c) dependences are analyzed in the light of current ideas regarding the nature of impurity strengthening. The grain size is shown to affect the resistance to microdeformation in Cu-Al alloys.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, Vol. 12, No. 5, pp. 94–103, May, 1969.     

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.     

Asymptotics of decay of correlations for lattice spin fields at high temperatures. I. The Ising model

We find the asymptotic decrease of correlations < _{A +y} , _B >,yZ ^v +1, |y|, in the Ising model at high temperatures. For the case when monomials _A and _B both are odd, using the saddle-point method, we find the asymptotics of the correlations for any dimension . For even monomials _A , _B we formulate a general hypothesis about the form of the asymptotics and confirm it in two cases: (1) =1 and the vectory has an arbitrary direction, (2)y is directed along a fixed axis and arbitrary . Here we use besides the saddle-point method, some arguments from scattering theory.     

The modular group and super-KMS functionals

Every normal, faithful, self-adjoint functional on a von Neumann algebraA canonically determines a one-parameter-weakly continuous *-automorphism group (the analog of the modular group) and a canonical ₂ grading onA, commuting with . We show that the functional satisfies the weak super-KMS property with respect to and Furthermore, we prove that and are the unique pair of a-weakly continuous one-parameter *-automorphism group and a grading of the algebra, commuting with each other, with respect to which is weakly super-KMS. The above results thus provide a complete extension of the theory of Tomita and Takesaki to the nonpositive case.Supported in part by the National Science Foundation under Grant DMS-8922002.     

Linear radiation transport in randomly distributed binary mixtures: A one-dimensional and exact treatment for the scattering case

Scattering effects are considered for radiative transfer within randomly distributed and binary mixtures in one dimension. The most general formalism is developed within the framework of the invariant imbedding method. The lengthL of the random sample thus appears as a new variable. One transmission coefficientT(L) suffices to specify locally the intensities. By analogy with the homogeneous situation, one introduces an effective opacity with T=(1+_eff L)^–1 fulfilling _eff<=p ₀₀+p ₁₁(0 and 1 refer, respectively, to the components involved in the mixture). Equality is reached whenL0, . Otherwise, _eff displays a deep transmission window. It is numerically expressed for three combinations of opacities (₀,₁) and average grain sizes (₀, ₁). These results are of crucial concern in optimizing an ICF compression for a pellet nonuniformly illuminated by intense laser or ion beams.     

Mixing properties,differentiability of the free energy and the central limit theorem for a pure phase in the Ising model at low temperature

For the Ising model with nearest neighbour interaction it is shown that the spin correlations _{A B} - _{A B} decrease exponentially asd(A, B) in a pure phase when the temperature is well belowT _c. This is used to prove that the free energyF(,h) is infinitely differentiable in and has one sided derivatives inh of all orders forh=0. The bounds are also used to prove that the central limit theorem holds for several variables such as e.g. the total energy and the total magnetization of the system, the limit distribution being gaussian with variances determined by the second derivatives ofF(,h).     

Determination of electrodynamical parameters of dielectric pipe-shaped materials using millimeter wave cavity

Employment ofE _0np modes of cylindrical cavity resonator for measurement of electrodynamical parameters of dielectric pipe-shaped materials in millimeter wavelength band is suggested. Dielectric permittivity and conductivity of a sample can be found by measuring the frequency shift and theQ-factor change of the resonator.Method of mode basis is used for the calculation of sample permittivity and conductivity . Measurements were carried out at 8mm wavelength and related calculations have demonstrated use and possibilities of the method in studying the dielectric properties of samples of cylindrical and other forms.     

The effects of inkomogeneous center structure on the shape of the ESR spectra of alkali-rich glasses

The paper considers the effect of nonuniform structure in the centers on the ESR spectrum for the case of axial anisotropy in the g factor; it is shown that if (² >² , _¦ >), the model enables one to describe fairly completely the spectrum of a glass containing 33% Na₂O and 67% SiO₂. Good agreement with all experimental evidence is not obtained for potassium silicate glasses.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 6, pp. 86–90, June, 1971.     

Contribution of quantum corrections and superconducting fluctuations to the magnetic field and temperature dependence of the conductivity in amorphous CuTi and CuZr alloys

We report conductivity measurements on Cu _x Ti_100–x and Cu _x Zr_100–x glasses as a function of magnetic field (0B6T) and temperature (1.5–5. At low temperatures the measured conductivity(T,B)= ₀+(T)+(B,T) is compared quantitatively with the predictions of diagrammatic perturbation theories including quantum interference effects, spin-orbit scattering and electron-electron interaction. We obtain a set of characteristic fields for inelastic and spin orbit scattering from both the magnetic field and the temperature dependence of the measured (T, B). Below about 4K the Coulomb interaction determines (T) in consistence with the Hall effect, whereas quantum interference processes and spin-orbit scattering dominate the magnetic field dependence. In case of Cu _x Zr_100–x , (B, T) can be explained by taking into account superconducting fluctuations (Maki-Thompson and Aslamasov-Larkin parts) in addition. Superconducting fluctuations dominate the temperature dependence as well. For high magnetic fields and lower temperatures (B/T>1T/K) we find discrepancies between experiment and calculations from perturbation theory.     

Correlation inequalities for the truncated two-point function of an Ising ferromagnet

We establish the following new correlation inequalities for the truncated twopoint function of an Ising ferromagnet in a positive external field: _j ; _l ^T _j ; _k ^T _k ; _l ^T , and _j ; _l ^T _{k K j} ; _k ^T _{k l} , whereK is any set of sites which separatesj froml. The inequalities are also valid for the pure phases with zero magnetic field at all temperatures. Above the critical temperature they reduce to known inequalities of Griffiths and Simon, respectively.NSERC Postgraduate Fellow, 1978–1981. Research supported in part by NSF Grant No. PHY-78-25390-A02.     

On the invariant measures for the two-dimensional euler flow

It is proven that the canonical Gibbs measure associated with a gas of vortices of intensity ± converges, in the limitN, 0,Nconst, to a Gaussian measure, which is invariant for the two-dimensional Euler equation.On leave from Dipartimento di Matematica Università di Roma Tor Vergata Roma, Italy.On leave from Dipartimento di Matematica Università di Roma La Sapienza, Roma, Italy.     

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.     

On the variation of hopping transport in amorphous silicon with preparation conditions

Thedc conductivity of amorphous silicon prepared by two successive ion bombardments at different temperatures has been measured as a function of temperature. The results may be expressed in terms of a generalized hopping formula =₀ exp [–(T ₀/T) ⁿ where the parameter set {n,T ₀, ₀} varies with the irradiation conditions. In particular, the hopping exponent has been found to assume the limiting values ofn1/4 at irradiation temperatures ofT _i100 K and ofn1/2 atT _i500 K, whereas intermediate values ofn have been observed for temperatures inbetween. It is concluded that thermally activated redistribution processes of radiation defects control the final state of disorder in the irradiated samples, which in turn determines the particular hopping characteristics. Within the framework of existing theories the two limiting cases can be explained to be due to a disordered solid of homogeneous and granular structure, respectively.     

Averaged electron Green function and CDW pinning in one-dimensional random potential

The averaged retarded electron Green functionG ⁺(,k) in 1d disordered metal is calculated using the Berezinsky diagram technique. Using the Gorkov's theory it is shown, that the substitution of inG ⁺ (,k) by the square of the external frequency atk=0 gives the dependence of Fröhlich conductivity _F(). This dependence describes the impurity pinning of CDW in 1d disordered metals. The good agreement of this dependence with experimental data Zeller et al. about _F() in quasi-1d conductor KCP is found     

Exact solutions of the SO(3)-invariant nonlinear O-model in the special theory of relativity

Exact solutions for the four-dimensional SO(3)-invariant-model are obtained using the relation between groups of isometric motions in the space-time V₄ and chiral space U_N. A means for separating corresponding solutions in the two-dimensional-model is found. It is shown that the classical instanton and meron solutions correspond to consistent rotation of V₄ and U₂, and a general solution for this case is obtained. Four-dimensional analogs of free fields for two-dimensional-models are considered using a local approach. A non-trivial general solution which diverges logarithmically is given for the SO(N)-invariant-model.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 22–26, October, 1985.In conclusion I would like to thank G. G. Ivanov for his statement of the problem and useful discussions and D. Maison from Munich for delivering study [10].     

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.     

Hydromagnetic laminar flow of a conducting fluid in an annulus in presence of a radial magnetic field

The object of the present paper is to study the MHD effects on the laminar flow of a viscous, incompressible and conducting fluid in an annulus with arbitrary time-varying pressure gradient and arbitrary initial velocity in presence of a radial magnetic field. Using finite Hankel transform, solutions for both the unsteady and steady flows under different prescribed pressure gradients have been found out.Notation H a constant characterising the intensity of the magnetic field - p hydrostatic pressure - _e magnetic permeability - coefficient of viscosity - kinematic coefficient of voscosity - conductivity of the medium - density - a radius of the inner cylinder - b radius of the outer cylinder - parameter - s positive root - J (sr) Bessel's function of first kind of ordergl - Y (sr) Bessel's function of second kind of order     

Mates toE=mc 2 and to the Heisenberg uncertainty relations

E=mc ² is found to be a special case ofE= ^±1cⁿ, where is any one of four susceptibilities, namely electric, magnetic, gravitational, and elastic. Letl be length,t time,t time dilation, andl a measure of Fitzgerald-Lorentz contraction. A particle is stated to be the manifestation of a collection of susceptibilities which arise when(l)/1=(t)/t. Then(E)/E=5 (t)/2t=±()/. Corresponding to susceptibility, special energy particles are postulated which exhibitSU(3) symmetry, Related to the susceptibilities are five new Heisenberg uncertainty relations. Three new conservation laws for particles are proposed.     

On the equivalence of different order parameters for Ising ferromagnets

In a recent note Barber showed, for a spin-1/2 Ising system with ferromagnetic pair interactions, that some critical exponents of the triplet order parameter _{i j k} are the same as those of the magnetization _i . Here we prove such results for all odd correlations and dispense with the requirement of pair interactions. We also prove that the critical temperatureT _c , defined as the temperature below which there is a spontaneous magnetization, is for fixed even spin interactionsJ _e independent of the way in which the odd interactionsJ _o approach zero from above. This is achieved by using only the simplest, Griffiths-Kelley-Sherman (GKS), inequalities, which apply to the most general many-spin, ferromagnetic interactions.Research supported in part by NSF Grant #MPS 75-20638.     

On the finite-size scalling equation for the spherical model

The mean spherical model with an arbitrary interaction potential, the Fourier transform of which has a long-wavelength exponent , 0<2, is considered under periodic boundary conditions and fully finite geometry ind dimensions, when <d<2. A new form of the finite-size scaling equation for the spherical field in the critical region is derived, which relates the temperature shift to Madelung-type lattice constants. The method of derivation makes use of the Poisson summation formula and a Laplace transformation of the momentumspace correlation function.On leave of absence from Institute of Mechanics and Biomechanics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria.