Microstructure of fiber-like SiC/Si3N4 composite particulate

The microstructure of fiber-like SiC/Si₃N₄ composite particulate was investigated using high-resolution transmission electron microscopy techniques. The SiC/Si₃N₄ composite particulate consisted of a-SiC core and a -Si₃N₄ outer shell. Two kinds of composite particulate were distinguished when the observed orientation of the SiC core was <110>. In one type of the SiC/Si₃N₄ composite particulate, a crystal relationship of (111)-SiC | (102) -Si₃N₄ and (111)-SiC (114) -Si₃N₄ was identified; in the other type of the SiC/Si₃N₄ composite particulate, a crystal relationship of (111)-SiC (001) -Si₃N₄, and (111)-SiC (101) -Si₃N₄ was observed.     

Calculation of characteristics of benzene derivatives

The C₆H₅X compounds are considered as regards the energy and wave function _x as functions of within limits of –3 and +3, and also as functions of _cx within limits of 0. 5 and 1. 5. Convenient numerical tables are compiled.We are indebted to N.A. Prilezhaev and V.I. Danilov for extensive collaboration in this work.     

Letter: Gravitational Entropy of Constrained Instanton

The seeds for quantum creations of universes areconstrained gravitational instantons. For all compactconstrained instantons with a U(1) isometry, the period of the group parameter is identifiedas the reciprocal of the temperature. If remains a free parameter under the constraints, then theEuclidean action becomes the negative of the entropy. Asexamples, we perform the calculations forthe Taub-nut and Taub-Bolt-type models andstudy the quantum creation of the Taub-nutuniverse.     

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     

Phases of the number-theoretic spin chain

We present numerical and analytical evidence for a first-order phase transition of the ferromagnetic spin chain with partition functionZ()=(–1)/() at the inverse temperature _cr=2.     

Passive states and KMS states for general quantum systems

We characterize equilibrium states of quantum systems by a condition of passivity suggested by the second principle of thermodynamics. Ground states and -KMS states for all inverse temperatures 0 are completely passive. We prove that these states are the only completely passive ones. For the special case of states describing pure phases, assuming the passivity we reproduce the results of Haag et al.     

On the relation between classical and quantum statistical mechanics

Classical and quantum statistical mechanics are compared in the high temperature limit =1/kT0. While this limit is rather trivial for spin systems, we obtain some rigorous results which suggest (and sometimes prove) different asymptotics for continuous systems, depending on the behaviour of the two-body potential for small distances: the difference between suitable classical and quantum variables vanishes as ² for smooth potentials and as for potentials with hard cores.Supported in part by FAPESP. Permanent address: Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo, Brazil     

The spectrum of a quasiperiodic Schrödinger operator

The spectrum (H) of the tight binding Fibonacci Hamiltonian (H _mn= _m,n+1+ _m+1,n + _m,n v(n),v(n)= ((n–1)), 1/ is the golden number) is shown to coincide with the dynamical spectrum, the set on which an infinite subsequence of traces of transfer matrices is bounded. The point spectrum is absent for any , and (H) is a Cantor set for 4. Combining this with Casdagli's earlier result, one finds that the spectrum is singular continuous for 16.On leave from the Central Research Institute for Physics, Budapest, Hungary     

Current distributions in a two-dimensional random-resistor network

The current and logarithm-of-the-current distributionsn(i) andn(ln i) on bond diluted two-dimensional random-resistor networks at the percolation threshold are studied by a modified transfer matrix method. Thek th moment (–9k8) of n(ln i) i.e., ln i&^k, is found to scale with the linear sizeL as (InL)^(k). The exponents (k) are not inconsistent with the recent theoretical prediction (k)=k, with deviations which may be attributed to severe finitesize effects. For small currents, ln n(y)–, yielding information on the threshold below which the multifractality of (i) breaks down. Our numerical results for the moments of the currents are consistent with other available results.     

Bounds on the correlations and analyticity properties of ferromagnetic Ising spin systems

We consider a ferromagnetic Ising spin system isomorphic to a lattice gas with attractive interactions. Using the Fortuin, Kasteleyn and Ginibre (FKG) inequalities we derive bounds on the decay of correlations between two widely separated sets of particles in terms of the decay of the pair correlation. This leads to bounds on the derivatives of various orders of the free energy with respect to the magnetic fieldh, and reciprocal temperature . In particular, if the pair correlation has an upper bound (uniform in the size of the system) which decays exponentially with distance in some neighborhood of (,h) then the thermodynamic free energy density (,h) andall the correlation functions are infinitely differentiable at (,h). We then show that when only pair interactions are present it is sufficient to obtain such a bound only ath=0 (and only in the infinite volume limit) for systems with suitable boundary conditions. This is the case in the two dimensional square lattice with nearest neighbor interactions for 0<₀, where ₀ ^–1 is the Onsager temperature at which (,h=0) has a singularity. For >₀, (,h)/h is discontinuous ath=0, i.e. ₀=_c, where _c ^–1 is the temperature below which there is spontaneous magnetization.Research supported by AFOSR Contract # F 44620-71-C-0013.     

On the temperature dependence of the mean number of clusters

The random variable number of cluster defined on the configurations of a ferromagnetic Ising model at zero field and inverse temperature on a graphG is considered. The Gibbs average at=0 is proved to be greater than the one at>0 if the degree ofG is not greater than 3.     

Calculation of the force-dipole tensor for hydrogen in palladium and platinum

The force-dipole tensorP , also known as the elastic dipole and the double-force tensor, is calculated for hydrogen dissolved in palladium and platinum, using a microscopic model for the interaction potentials; the so-called effective medium theory. The force-dipole tensor describes the long range displacement field induced by hydrogen dissolved in the host metal lattice in the dilute limit. It can be related to the mean elastic hydrogen-hydrogen interaction energy and the critical temperatureT _c for the gas-liquid phase transition observed in systems such as PdH _x and NbH _x . Comparison show a fair agreement between theoretical and experimental values for the force-dipole tensor.     

On the distribution of recurrence times in nonlinear systems

A recent result on the recurrence properties of the sequence m=min_pZ |Mm–p| for irrational , together with a rather old, but little-known result by Florek and Slater on the recurrence properties of the sequence m mod 1 with respect to connected intervals in the interval [0, 1] show that integrable Hamiltonian systems with two degrees of freedom have at most three different recurrence times with respect to an arbitrary Poincaré section of the invariant tori in phase space. We discuss a possible extension of this result to arbitrary integrable systems with any number of degrees of freedom and propose the recurrence time spectrum as a new quantity for characterising simple and complex behaviour of general nonlinear systems.     

High-temperature polymorphism of tin

Using the methods of low-frequency internal friction, microhardness, differential thermal analysis, and x-ray diffraction analysis, the authors investigate the specifics of the high-temperature - polymorphic transformation in high-purity tin. The multistep nature of this transition, which is unusual for pure metals, is demonstrated. This transition is represented by a series of specific mixed phase transitions. The hypothesis is advanced that tin is transformed into its high-temperature modification through the formation of intermediate metastable phases, and a new scheme is proposed for this transformation. The lattice constants and melting temperature of one of the metastable phases are determined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 10–15, March, 1989.     

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.     

Derivation and solution of a low-friction Fokker-Planck equation for a bound Brownian particle

The low-friction region of an anharmonically bound Brownian particle is examined using systematic elimination procedures. We obtain an asymptotic expression for the spectrum of the Fokker-Planck operator. Asymptotic means both small anharmonicities and small friction constants compared to the oscillatory frequency . We conclude that Kramers' low-friction equation is generally valid only for 0<0.01 and has to be modified for 0.01 by including phase-dependent terms. From these the nonlinear part of the force field in connection with a finite temperature is shown to shorten the correlation time of the equilibrium velocity autocorrelation function and to renormalize the frequency of the corresponding spectral density.     

Exponential decay near resonance,without analyticity

We consider a quantum mechanical model which displays the behaviour associated with having a resonance or metastable state. The Hamiltonian depends on a parameter . When =0, there is an eigenstate ₀; when 0, ₀ dissolves into the continuous spectrum, showing approximate exponential decay. We prove this result without using dilatation analyticity. The model describes a two-state atom coupled to the quantized radiation field. The state space of the field is truncated, so that only the vacuum and one-photon states are included.This work was partially supported by NSF Grant DMS-8922941     

Three-Mode Entangled State Representation of Continuum Variables and Optical Four-Wave Mixing

We establish a new three-mode entangled state representation , of continuum variables, which make up a complete set. Using optical four-wave mixing and a beam splitter transform we can prepare , . Based on , a new number-difference--operational-phase uncertainty relation is established and the corresponding squeezing dynamics is discussed.     

HNC calculations of the partial structure factors of molten AgI

We have calculated the pair distribution functions and partial structure factors of molten AgI within the hypernetted chain (HNC) approximation. We have assumed that the effective interionic pair potentials are the same in the liquid and solid states, and have used the potentials constructed by Parrinello et al., which they used to describe both -AgI and the phase transition in AgI. The structure of molten AgI exhibits features similar to those of molten CuCl. Both of these salts melts from a superionic phase.     

The Crystallography of Interphase Boundaries Between Silicon Carbide and Silicon Nitride in Silicon Nitride—Silicon Carbide Particulate Composites

Interphase boundaries between 3C SiC grains and two different -Si₃N₄ morphologies in Si₃N₄–SiC composites have been studied by transmission electron microscopy. In general, boundaries between small -Si₃N₄ intragranular precipitates and surrounding SiC grains were relatively free of intergranular films, whereas boundaries between large -Si₃N₄ grains and adjacent SiC grains were invariably covered with thin intergranular films. Orientation relationships approximating to [110] 3C SiC [0001] -Si₃N₄ and (001) 3C SiC (10 0) -Si₃N₄ were found to dominate between 3C SiC grains and the intragranular -Si₃N₄ precipitates, but there was no evidence of any favoured orientation relationship between the large -Si₃N₄ grains and adjacent SiC grains. The rationale for special orientation relationships arising when there is no intergranular film present at 3C SiC–-Si₃N₄ interfaces is explored geometrically using the near-coincidence site lattice model, with the significant result that the dominant orientation relationships between 3C SiC grains and the intragranular -Si₃N₄ precipitates have low misfits relative to all other possible orientation relationships between 3C SiC and -Si₃N₄.