Theory of percolation in fluids of long molecules

We use the reference interaction site model (RISM) integral equation theory to study the percolation behavior of fluids composed of long molecules. We examine the roles of hard core size and of length-to-width ratio on the percolation threshold. The critical density _c is a nonmonotonic function of these parameters exhibiting competition of different effects. Comparisons with Monte Carlo calculations of others are reasonably good. For critical exponents, the theory yields =2=2 for molecules of any noninfinite lengthL. WhenL is very large, the theory yields _cL ^–2. These predictions compare favorably with observations of the conductivity for random assemblies of conductive fibers. The threshold region where asymptotic scaling holds requires the correlation length (/ _c ) ^–v to be much larger thanL. Evidently, the range of densities in this region diminishes asL increases, requiring that density deviations from _c be no larger thanL ^–2. Otherwise, crossover behavior will be observed.     

Determination of the electron density at the Cu nucleus in Cu-Au alloys

The half-life of⁶⁴Cu in Cu–Au solid solutions has been measured as a function of the Cu concentration. Relative changes of electron densities (0)/(0) at the Cu nucleus are deduced. The observed nonlinear concentration dependence of (0)/(0) is discussed in terms of volume and charge transfer effects.     

The Ground State Energy of a Dilute Two-Dimensional Bose Gas

The ground state energy per particle of a dilute, homogeneous, two-dimensional Bose gas, in the thermodynamic limit is shown rigorously to be E₀/N=(2²/m)|ln(a²)|^–1, to leading order, with a relative error at most O(|ln(a²)|^–1/5). Here N is the number of particles, =N/V is the particle density and a is the scattering length of the two-body potential. We assume that the two-body potential is short range and nonnegative. The amusing feature of this result is that, in contrast to the three-dimensional case, the energy, E₀ is not simply N(N–1)/2 times the energy of two particles in a large box of volume (area, really) V. It is much larger.     

On the relative entropy

ForA any subset of () (the bounded operators on a Hilbert space) containing the unit, and and restrictions of states on () toA, ent _A (|)—the entropy of relative to given the information inA—is defined and given an axiomatic characterisation. It is compared with ent _A ^A (|)—the relative entropy introduced by Umegaki and generalised by various authors—which is defined only forA an algebra. It is proved that ent and ent ^S agree on pairs of normal states on an injective von Neumann algebra. It is also proved that ent always has all the most important properties known for ent ^S : monotonicity, concavity,w* upper semicontinuity, etc.     

Electrogravitational induction and rotation

The Faradayan hypothesis of inductive coupling of the electromagnetic and gravitational fields is briefly discussed. An experiment designed to test the hypothesis wherein samples are spun to see if any electrogravitational charge is induced is described. Results of the experiment are reported. They imply the induction of a charge density * for spinning samples that behaves as *=_ma, where _m is the mass density of an element of matter experiencing an acceleration a, and is the coupling coefficient for the hypothetical electrogravitational induction effect. In this experiment, is found to have the value(9.6±3.3)×10 ^–13 statcoulombs/dyne. Tests that seem to rule out explanations of the observed charges in terms of conventional charging mechanisms are considered.     

Self-diffusion in simple models: Systems with long-range jumps

We review some exact results for the motion of a tagged particle in simple models. Then, we study the density dependence of the self-diffusion coefficientD _N() in lattice systems with simple symmetric exclusion in which the particles can jump, with equal rates, to a set ofN neighboring sites. We obtain positive upper and lower bounds onF _N()=N{(1–)–[D_N()/D_N(0)]}/[(1–)]x for [0, 1]. Computer simulations for the square, triangular, and one-dimensional lattices suggest thatF _N becomes effectively independent ofN forN20.     

Spectrum of γ-Fluids: A statistical derivation

The spectrum of massless bosonic and fermionic fluids satisfying the equation of statep=(–1) is derived using elementary statistical methods. As a limiting case, the Lorentz-invariant spectrum of the vacuum (=0,p=–) is deduced. These results are in agreement with our earlier derivation for bosons using thermodynamics and semiclassical considerations.     

Contribution of the new vector mesons to the total cross section of hadron photoabsorption

The new vector mesons with mass 1.1 < M < 2 GeV as well as the ⁰,, ,, and mesons are included in the sum rules that relate the total cross section of hadron photoabsorption on the proton to the total cross sections for interaction of vector mesons with the proton. Satisfactory agreement with experiment is obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 108–111, September, 1977.     

First Order Asymptotics of Matrix Integrals; A Rigorous Approach Towards the Understanding of Matrix Models

We investigate the large N limit of spectral measures of matrices which relate to the Gibbs measures of a number of statistical mechanical systems on random graphs. These include the Ising and Potts models on random graphs. For most of these models, we prove that the spectral measures converge almost surely and describe their limit via solutions to an Euler equation for isentropic flow with negative pressure p()=–3^–123.     

Closed timelike smooth curves in the general theory of relativity

For a space-time which admits a closed timelike smooth curve it is estimated that 2 · 10^–24 · l ², where is the real time andl the spatial length associated with the timelike curve, and is the density of material.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 9, pp. 33–36, September, 1973.     

Reactive pulsed laser deposition and laser induced crystallization of SnO2 transparent conducting thin films

Transparent conducting SnO₂ thin films with a thickness between 1000–2000 Å were deposited on glass, quartz and silicon substrates using standard pulsed laser deposition techniques with two different targets (Sri and SnO₂) and with three different laser wavelengths (1.06, 0.532 and 0.266 ) from a Q-switched Nd: YAG laser. Tin dioxide films with optical transmission over most of the visible spectrum exceeding 80% were obtained using a Sn target and a background oxygen pressure of 20 Pa. The electrical resistivity () depended strongly on the substrate temperature during deposition, with the lowest values of of about 10^–2 -cm obtained when the substrate was maintained at 400°C during deposition. Using SnO₂ targets, predominantly amorphous phase SnO₂ films were deposited on Si substrates and then transformed into polycrystalline Sn₃O₄ by laser induced crystallization ( = 1.06 m). Whereas these later films were essentially non-conducting as deposited ( > 400 -cm), the electrical resistivity was permanently reduced after laser induced crystallization by a factor greater than 1000 to a value of approximately 4 × 10^–1 -cm.     

Some consequences of the nonlocalizability of space-time events

Space-time events are characterized by their coordinatesx from the classical point of view. The same events from the quantum-mechanical point of view should be described rather by the expectation value of coordinates X. The expectation value could be evaluated by introducing a density operator(x,x) associated with the event. In the case where(x,x) cannot be described by delta functions strictly monochromatic radiation does not exist. If localizability is limited by Planck's length there are no narrower spectral lines than 2× 10^–29 E ² (eV) whereE stands for the photon energy.On leave from the Institute of Nuclear Physics, Kraków, ul. Radzikowskiego 152, Poland.     

Analytic Properties of the Structure Function for the One-Dimensional One-Component Log–Gas

The structure function S(k; ) for the one-dimensional one-component log–gas is the Fourier transform of the charge–charge, or equivalently the density–density, correlation function. We show that for |k|j in the power series expansion of f(k; ) about k=0 is of the form of a polynomial in /2 of degree j divided by (/2)^j. The bulk of the paper is concerned with calculating these polynomials explicitly up to and including those of degree 9. It is remarked that the small k expansion of S(k; ) for the two-dimensional one-component plasma shares some properties in common with those of the one-dimensional one-component log–gas, but these break down at order k⁸.     

Relative change of the electron density at the Cu nucleus in Cu-Ag alloys

The decay constant of⁶⁴Cu in Cu–Ag solid solutions has been measured at various Cu concentrations. Deduced values of the relative changes of electron densities (0)/(0) at the Cu nucleus are given. The observed concentration dependence of (0)/(0) is discussed in terms of a volume effect and charge transfer from Cu to Ag.     

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.     

Magnetooptical light concentration by regular domain structures

Expressions are obtained for the diffracted field in the Fresnel and Fraunhoffer diffraction domains. It is shown that the field in the diffraction pattern is the superposition of two orthogonally polarized fields. The distribution of a field with polarization orthogonal to the incident radiation depends substantially on the domain structure parameters. Thus, for zeros of the function f ()=J₀((/)) assigned as radii of the annular domains, a magnetooptical light concentration in an annular image is possible, while for f()=cos(²/2R ₁ ² ) the light is concentrated at a point, i.e., the annular domain structure plays the part of a lens. The effects of light concentration are examined for both the case of annular systems and strip domains.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 31–38, October, 1978.     

TheN 7/5 law for charged bosons

Non-relativistic bosons interacting with Coulomb forces are unstable, as Dyson showed 20 years ago, in the sense that the ground state energy satisfiesE ₀–AN ^7/5. We prove that 7/5 is the correct power by proving thatE ₀–BN ^7/5. For the non-relativistic bosonic, one-component jellium problem, Foldy and Girardeau showed thatE ₀–CN^1/4. This 1/4 law is also validated here by showing thatE ₀–DN^1/4. These bounds prove that the Bogoliubov type paired wave function correctly predicts the order of magnitude of the energy.Work partially supported by U.S. National Science Foundation grant DMS 8600748Work partially supported by U.S. National Science Foundation grant PHY85-15288-A01Work supported by Alfred Sloan Foundation dissertation fellowship     

Dielectric properties of beryllia ceramics in the near-millimeter wavelength range

We report the refractive indices and absorption coefficients for four beryllia (BeO) ceramic samples. These dielectric properties have been measured over the range from 4 to 18 cm^–1 by use of a Michelson interferometer. The index n, follows the linear relationship n=0.6517 cm³/g×+0.7130 with density, , over the range 2.8<<3.0 g/cm³.     

A comment on an exact solution with a stiff equation of state

Recently, an analytical stellar model with a stiff equation of state and density distribution= _c (1-r ²/r _o ² ) was presented. We show that such a solution cannot exist.     

Computer simulation of shock waves in the completely asymmetric simple exclusion process

We study the evolution of the completely asymmetric simple exclusion process in one dimension, with particles moving only to the right, for initial configurations corresponding to average density _– ( ₊) left (right) of the origin, _{– +}. The microscopic shock position is identified by introducing a second-class particle. Results indicate that the shock profile is stable, and that the distribution as seen from the shock positionN(t) tends, as time increases, to a limiting distribution, which is locally close to an equilibrium distribution far from the shock. Moreover , withV=1– _–– ₊, as predicted, and the dispersion ofN(t), ²(t), behaves linearly, for not too small values of ₊– _–, i.e., , whereS is equal, up to a scaling factor, to the valueS _WA predicted in the weakly asymmetric case. For ₊= _– we find agreement with the conjecture .Dedicated to the memory of Paola Calderoni.