The Robertson-Walker metric and the symmetries belong to the family of contracted Ricci collineations

It is shown that the general form of the Robertson-Walker cosmological metric admits symmetry properties that are members of the symmetry family of contracted Ricci collineations. A particular form for the conservation law generator given by _j [(–g)^1/2(T _i ^j –1/2 _i ^jT ) ⁱ ] = 0 following in consequence of these symmetries is obtained and interpreted.     

Multicomponent composites,electrical networks and new types of continued fraction I

The development of bounds on the complex effective conductivity tensor * (that relates the average current to the average electric field in a multicomponent composite) has been hindered by lack of a suitable continued-fraction representation for *. Here a new field equation recursion method is developed which gives an expression for * as a continued fraction of a novel form incorporating as coefficients the component conductivities and a set of fundamental geometric parameters reflecting the composite geometry. A hierarchy of field equations is set up such that the solutions of the (j+1)th-order equation generate the solutions of thejth-order equation. Consequently the effective tensor ^(j) associated with thejth-order field equation is expressible as a fractional linear matrix transformation of ^(j+1). These transformations combine to form the continued fraction expansion for *=⁽⁰⁾ which is exploited in the following paper, Part II, to obtain bounds: crude bounds on ^(j), forj1, give narrow bounds on *. The continued fraction is a generalization to multivariate functions of the continued fraction expansion of single variable Stieltjes functions that proved important in the development of the theory of Páde approximants, asymptotic analysis, and the theory of orthogonal polynomials in the last century. The results extend to other transport problems, including conduction in polycrystalline media, the viscoelasticity of composites, and the response of multicomponent, multiterminal linear electrical networks.     

On an internal symmetry for arbitrary dislocations in solids

We discuss an arbitrary distribution of dislocations moving in an anisotropic finite linear elastic solid. The field equations for theelastic strain tensor are decomposed into two independent systems of equations, the equations for acompatible elastic displacement fields and the equations for anincompatible elastic strain ^v . This can be done in such a way thats contains the full information on anisotropy, external forces, and boundaries, whereas ^v contains only a single material constant , which is related to a signal velocity , wherep is the mass density. In order to understand the symmetries of the ^v -field equations we introduce ac _T -relativistic space-time. As a consequence of certain hypothesis concerning the balance of eigenstresses for moving dislocations the Lorentz group becomes the symmetry group for the ^v -field equations. We call this aninternal symmetry. Thematerial symmetry of the field equations for the elastic displacement vectors which is defined by Hooke's tensor breaks this Lorentz symmetry for the complete elastic strain . Some conclusions for the dynamics of dislocations are discussed. It is found that Seeger's theory of kinks on dislocations describes elementary processes of this dynamics. Within the limits of the continuum model plasticity becomes a field theory with broken Lorentz symmetry.     

On Effective Conductivity on ℤ d Lattice

We study the effective conductivity _e for a random wire problem on the d-dimensional cubic lattice ^d , d2 in the case when random conductivities on bonds are independent identically distributed random variables. We give exact expressions for the expansion of the effective conductivity in terms of the moments of the disorder parameter up to the 5th order. In the 2D case using the duality symmetry we also derive the 6th order expansion. We compare our results with the Bruggeman approximation and show that in the 2D case it coincides with the exact solution up to the terms of 4th order but deviates from it for the higher order terms.     

Multicomponent composites,electrical networks and new types of continued fraction II

The outstanding problem of systematically developing rigorous bounds on the complex effective conductivity tensor * ofd-dimensional,n-component composites withn>2 is solved. The bounds incorporate information contained in successively higher order correlation functions which reflect the composite geometry. Explicit expressions are given for many of the bounds and some, but not all of them, are represented by nested sequences of circles in the complex plane that enclose, and in fact converge to, each diagonal element of *. They are derived from the fractional linear matrix transformations found in Part I that recursively link * with a hierarchy of complex effective tensors ^(j),j=0, 1, 2, ..., of increasing dimension,d(n–1) ^j . Elementary bounds on ^(j) confining the diagonal elements of ^(j) or its inverse to half-plane, wedge or open polygon regions of the complex plane, imply narrow bounds on * which converge to the exact value of * in the limit asj . When the component conductivities are real these bounds are more restrictive than the corresponding variational bounds. Besides applying to the effective conductivity *, the bounds extend to a wide class of matrix-valued multivariate functions called -functions, and thereby to conduction in polycrystalline media, viscoelasticity in composites, and conduction in multi-component, multiterminal, linear electrical networks. The analytic and invariance properties of -functions are explored and within this class of function most of the bounds are found to be optimal or at least attainable. The bounds obtained here are essentially a generalization to matrix-valued, multivariate functions of the nested sequence of lens-shaped bounds in the complex plane derived by Gragg and Baker for single variable Stieltjes functions.     

Transport phenomena in a plane shock wave

With the use of the nonpolynomial closure 1/ _z in the Mott-Smith approximation of the solution of the Boltzmann equation, we obtain a value of the density gradient in the limit of a very weak shock wave that is close to the correct value. For the determination of the transverse temperature gradient we calculated the _x ² / _z moment of the Mott-Smith collision integral. The effective values of viscosity and thermal conductivity in the limit of a very weak shock wave were calculated for inverse-power potentials and found to agree almost exactly with the Chapman-Enskog values. Such a comparison can serve as a criterion for the evaluation of different bimodal theories. Various bimodal theories give different values of viscosity and thermal conductivity, but all of them give 33 % too high a value of the Eucken ratio.     

R-Operator, Co-Product and Haar-Measure for the Modular Double of

A certain class of unitary representations of U_q((2,)) has the property of being simultanenously a representation of for a particular choice of (q). Faddeev has proposed to unify the quantum groups U_q((2,)) and into some enlarged object for which he has coined the name ``modular double'. We study the R-operator, the co-product and the Haar-measure for the modular double of U_q((2,)) and establish their main properties. In particular it is shown that the Clebsch-Gordan maps constructed in [PT2] diagonalize this R-operator.     

Study of the23Na EFG tensor as determined from first order NMR satellite lines near the ferroelectric phase transition of AgNa(NO2)2

The²³Na NMR first order quadrupolar satellite lines are detected and studied in AgNa(NO₂)₂ single crystals near the paraelectric-ferroelectric phase transition. Although the intensities of the satellites are small the components of the electric field gradient tensor (EFG) at the²³Na sites could be deduced from the angular dependence of the first order quadrupolar line splitting with respect to rotations around the three crystallographic axes by applying the Volkoff method. In the paraelectric phase the principal axes system of the EFG coincides with the crystallographic axes system whereas in the ferroelectric phase there is a strongly temperature dependent small non diagonal element _xz (T). The EFG principal components _xx and _yy are strongly influenced whereas the EFG principal component _zz is nearly not affected by the ferroelectric phase transition. The observed temperature dependences of the EFG components are related to the temperature variation of the normalized spontaneous polarizationS(T) by assuming a coupling term which is quadratic inS(T). Finally the problem of the intensities of the satellite lines is discussed.     

Some optimum parameters of golay detector of infra-red radiation

The relation for the sensitivity of the pneumatic detector based on the analysis of the thermal, pneumatic and optical parts of the instrument is derived. From this relation the optimum diameter of the flexible mirror and the optimum gas pressure in the detector cell are calculated.List of symbols used B brightness [sb] - C thermal capacity of absorbing membrane [cal cm^–2 grad^–1] - c specific heat of gas in cell [cal g^–1 grad^–1] - D diameter of grid [cm] - d diameter of flexible mirror [cm] - E illumination [ph] - F ₂ area of light spot [cm²] - F ₃ area of flexible mirror [cm²] - f,f ₁ focal distance [cm] - f ₀ chopping frequency of infra-red radiation [sec^–1] - h depth of cell [cm] - k radiation cooling constant [cal cm^–2 sec^–1 grad^–1] - k ₀ reflectivity of flexible mirror - k ₁,k ₂,k ₃,k ₄ constants - L total length of edge of half of grid [cm] - l distance between lens and flexible mirror [cm] - M, N constants - m refractive power of flexible mirror [cm^–1] - n number of grammolecules of gas in cell - P radiative power [cal sec^–1] - p,p ₀,p pressure, atmospheric pressure, change in pressure [dyne cm^–2] - R gas constant [erg grad^–1] - r coordinate - r ₀ radius of flexible mirror [cm] - r ₁,r ₂ radii of beam of rays [cm] - t tension of flexible mirror [dyne cm^–1] - , T, T _f absolute temperature and its change [grad] - V, V volume and increase in volume [cm³] - v coordinate - v ₀ maximum height of deflection of flexible mirror [cm] - x, x distance of object and image from focal planes [cm] - , angles - specific weight of gas at pressure of 1 atm. [g cm^–3] - absorption coefficient of infra-red radiation - thermal conductivity of gas [cal cm^–1 sec^–1 grad^–1] - v number of lines of grid per 1 cm [cm^–1] - radius of light spot on grid [cm] - T time constant [sec] - ₀, ₁, ₂, ₃ light flux and its change [lm]     

Hard-square lattice gas

We have studied the hard-square lattice gas, using corner transfer matrices. In particular, we have obtained the first 24 terms of the high-density series for the order parameter ₂– ₁. From these we estimate the critical activity to be 3.7962±0.0001. This is in excellent agreement with the earlier work of Gaunt and Fisher. It conflicts with the value 4.0 given by Müller-Hartmann and Zittartz's formula for the critical point of the antiferromagnetic Ising model in a field, so we conclude that this formula, while a good approximation, is not exact.     

Relativistic dynamics of interacting point particles: Central position of the Wheeler-Feynman scheme

The Wheeler-Feynman (WF) relativistic theory of interacting point particles, generalized by acceptance of an arbitrary spacelike interaction, is shown to possess a privileged status, reminiscent of the central force interactions occurring in Newtonian mechanics. This scheme is shown to be isomorphic to the classical one of the statics of interacting flexible current-carrying wires obeying the Ampère-Laplace (AL) formulas: to the tensionT (T ² =const) of the wire corresponds the momentum-energy pⁱ (p_ipⁱ=–c²m²) of the particle; to the Laplace linear force density –iH×dr corresponds the Lorentz force QH^ij dr_j; to the Laplace potential ir^–1 dr corresponds the WF potential Q(r²) drⁱ, etc. Among the differences, there is self-action in the AL scheme and no self-action in the WF scheme. A stationary energy principle in the AL scheme is isomorphic to Fokker's stationary action principle in the WF scheme.     

Point-contact measurements of CeB6 and CeCu6 in high magnetic fields

Epitaxial YBa₂Cu₄O₇-thin films with thec-axis oriented perpendicular to the film plane were prepared bydc-sputtering from a single stoichiometric target on (100) SrTiO₃-substrates. Typical values of the inductively measured superconducting transitions were about 90 K with a width less than 0.5 K. Critical current densities were measured on 5 to 10 m wide strips as function of magnetic field and temperature. The temperature dependences ofj _c follow a universal functionj _c(B,T)=j _c ^* (T=0,B)·(1–T/T _c (B)) with =1.5±0.1. ForB=0 andT=77 K we obtainedj _c =4·10⁶ A/cm². The field dependence of the resistive transitions was measured with the magnetic field parallel to thec-axis. The slope of the upper critical fieldB _c2 (T) was determined for different criteria. The carrier concentration evaluated from Hall-effect measurements was found to decrease linearly from one per unit cell at 240 K with decreasing temperature extrapolating nearly through zero forT=0. Highly resolved angular dependent measurements of the critical current density withB perpendicular to the current but tilted from thec-axis show a very strong and sharp enhancement ofj _c for the magnetic field parallel to the (CuO₂)-layers (Bc). Additionally to this phenomenon, which is caused by an intrinsic pinning mechanism due to the layered structure of high-T _c -superconductors the influence of the anisotropy of the upper critical field onj _c (B, T, ) is evident nearT _c .     

q-Weyl coefficients forU q (3) andq-Racah coefficients forSU q (2)

We show that theq-Weyl coefficients of the quantum algebraSU _q (3) are equal to theq-Racah coefficients of the quantum algebraSU _q (2) (up to a simple phase factor). Using aq-analog of the resummation procedure we obtain also theq-analogues of all known general analytical expressions for the 6j-symbols (or the Racah coefficients) of the quantum algebraSU _q (2) starting from one such formula.Presented at the 4th Colloquium Quantum groups and integrable systems, Prague, 22–24 June 1995.The research described in this publication was supported in part by Grants No. MB1000 and No. NRC000 from International Science Foundation.     

Non-Topological Multi-Vortex Solutions to the Self-Dual Chern-Simons-Higgs Equation

 In this article, we construct self-dual N-vortex solutions with a large magnetic flux Φ of (2+1)-dimensional relativistic Chern-Simons model, provided that the coupling constant κ is small and the cites of vorticity satisfies

a-b plane anisotropy of single-domain crystals of Bi2Sr2CaCu2O8

The polarized reflectance of thea-b plane of single-domain Bi₂Sr₂CaCu₂O₈ crystals is anisotropic above and belowT _c . The normal-state infrared conductivity is higher forEa whereas the high-frequency conductivity is higher alongb, particularly for transitions associated with the Bi–O layers. BelowT _c there is a definite anisotropy to the far-infrared absorption, with a finite absorption forEb down to 20 meV. This anisotropy of thea-b plane could be due either to anisotropy of the superconducting gap or to anisotropy of the midinfrared component to the conductivity.     

Generation of massive neutrinos by variable fields with allowance for mixing and radiative effects

The probabilities of the processesF v _i V _j andFB v _i V _j of generation of massive neutrinos by a variable electromagnetic field, due to the contribution of four-particle peaks in the one-loop approximation with allowance for mixing, are obtained. A comparative analysis is made of the quantities considered here and of generation mechanisms discussed earlier (F v _i V _j ) in the case of vacuum neutrino synchrotron emission.Moscow State Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 48–52, July, 1995.     

Spatial fluctuations in reaction-limited aggregation

A general method is used for describing reaction-diffusion systems, namely van Kampen's method of compounding moments, to study the spatial fluctuations in reaction-limited aggregation processes. The general formalism used here and in subsequent publications is developed. Then a particular model is considered that is of special interest, since it describes the occurrence of a phase transition (gelation). The corresponding rate constants for the reaction between two clusters of sizei and sizej areK _ij=ij (i, j=1, 2,). For thediffusion constants D _j of clusters of sizej the following class of models is considered:D _j=D if 1Js andD _j=0 ifj>s. The casess= ands< are studied separately. For the models= the equal-time and the two-time correlation functions are calculated; this modelbreaks down at the gel point. The breakdown is characterized by a divergence of the density fluctuations, and is caused by the large mobility of large clusters. For all models withs< the density fluctuations remain finite att _c, and the equal-time correlation functions in the pre- and in the post-gel stage are calculated. Many explicit and asymptotic results are given. From the exact solution the upper critical dimension in this gelling model isd _c=2.     

Classical equationsdN i /dr=1/2iε ijk [N j,N k ]

We study the first order system of equationsdN _i /dr=1/2i _ijk [N _j ,N _k ], where theN _i are classical, non-abelian gauge-Higgs fields with spherical symmetry. Exact solutions are constructed.Supported by the Hellenic National Research Foundation