Limiting behavior of asymptotically flat gravitational fields

Couch and Torrence suggest that the vacuum Einstein equations admit a larger class of asymptotically flat solutions than those exhibiting the peeling property. Starting with the assumption that , (d/dr) and (/x ^A ) , wherex ^A (A = 2, 3) are angular coordinates, they show that , where ₁ 2 and ₁<₀; , where ₂ 1 and ₁< ₁; and ₄ and ₃ peel as they would under the stronger peeling conditions. The Winicour-Tamburino energy-momentun and angular momentum integrals for these solutions, in general, diverge. In fact, since Couch and Torrence determine only the radial dependence of the solution, it is not clear that the solutions are well defined. We find that the stronger assumption , (d/dr) , and (/x ^A ) does result in well-defined solutions for which both the energy-momentum and angular momentum intergrals are not only finite but result in the same expressions as are obtained for peeling space-times. This assumption appears to be the minimal assumption that is necessary for investigating outgoing radiation at null infinity.In part based on a dissertation by Stephanie Novak and submitted to Syracuse University in partial fulfillment of the requirement for the Ph.D. degree.     

Eigenvalue Asymptotics for the Schrödinger Operator with a δ-Interaction on a Punctured Surface

Given n2, we put r=min . Let be a compact, C ^r -smooth surface in ⁿ which contains the origin. Let further be a family of measurable subsets of such that as . We derive an asymptotic expansion for the discrete spectrum of the Schrödinger operator in L ²( ⁿ ), where is a positive constant, as . An analogous result is given also for geometrically induced bound states due to a interaction supported by an infinite planar curve.     

Transport Properties of Kicked and Quasiperiodic Hamiltonians

We study transport properties of Schrödinger operators depending on one or more parameters. Examples include the kicked rotor and operators with quasi-periodic potentials. We show that the mean growth exponent of the kinetic energy in the kicked rotor and of the mean square displacement in quasiperiodic potentials is generically equal to 2: this means that the motion remains ballistic, at least in a weak sense, even away from the resonances of the models. Stronger results are obtained for a class of tight-binding Hamiltonians with an electric field E(t) = E ₀+ E ₁cos t. For with 3/2)$$ " align="middle" border="0"> we show that the mean square displacement satisfies for suitable choices of , E ₀, and E ₁. We relate this behavior to the spectral properties of the Floquet operator of the problem.     

Bound States in a Locally Deformed Waveguide: The Critical Case

We consider the Dirichlet Laplacian for astrip in with one straight boundary and a width , where $f$ is a smooth function of acompact support with a length 2b. We show that in the criticalcase, , the operator has nobound statesfor small .On the otherhand, a weakly bound state existsprovided . In thatcase, there are positive c ₁,c ₂ suchthat the corresponding eigenvalue satisfies for all sufficiently small.     

Unified fields of analytic space-time-energy

An analytic gravitational fieldZ (Z ^y ) is shown to include electromagnetic phenomena. In an almost flat and almost static complex geometryds ² =zdzdz of four complex variables z=t, x, y, x the field equationsR Rz = –(U U – Z ) imply the conventional equations of motion and the conventional electromagnetic field equations to first order if =(Z ^v) and =(z ) are expressed in terms of the conventional mass density function , the conventional charge density function , and a pressurep as follows: v=const=p/c ²–10^–29 gm/cm³.     

An Equation for the Dissipation Rate Correlation and Its Implications for the Intermittency Exponent μ in Turbulence

We derive an equation satisfied by the dissipation rate correlation function, for the homogeneous, isotropic state of fully-developed turbulence from the the Navier–Stokes equation. In the equal time limit we show that the equation leads directly to two intermittency exponents ₁=2– ₆ and ₂=z₄– ₄, where the 's are exponents of velocity structure functions and z₄ is a dynamical exponent characterizing the fourth order structure function. We discuss the contributions of the pressure terms to the equation and the consequences of hyperscaling.     

The energy gaps of fullerene C60 and C70 determined from the temperature dependent microwave conductivity

The dielectric constants of C₆₀ and C₇₀ powders have been measured in the temperature range from 150 K to 900 K using a microwave absorption method. From the temperature dependence of the electrical band gaps are found to be 1.86±0.1 eV for C₆₀ and 1.57±0.1 eV for C₇₀. Our method is not influenced by the possible generation of excitons. The results are discussed and related to theoretical predictions.     

Finite Range of Large Perturbations in Hamiltonian Dynamics

The dynamics defined by the Hamiltonian , where the _m are fixed random phases, is investigated for large values of A, and for . For a given P ^* and for , this Hamiltonian is transformed through a rigorous perturbative treatment into a Hamiltonian where the sum of all the nonresonant terms, having a Q dependence of the kind cos(kQ – nt + _m) with \Delta \upsilon$$ " align="middle" border="0"> , is a random variable whose r.m.s. with respect to the _m is exponentially small in the parameter . Using this result, a rationale is provided showing that the statistical properties of the dynamics defined by H, and of the reduced dynamics including at each time t only the terms in H such that , can be made arbitrarily close by increasing . For practical purposes close to 5 is enough, as confirmed numerically. The reduced dynamics being nondeterministic, it is thus analytically shown, without using the random-phase approximation, that the statistical properties of a chaotic Hamiltonian dynamics can be made arbitrarily close to that of a stochastic dynamics. An appropriate rescaling of momentum and time shows that the statistical properties of the dynamics defined by H can be considered as independent of A, on a finite time interval, for A large. The way these results could generalize to a wider class of Hamiltonians is indicated.     

On the Product of Real Spectral Triples

The product of two real spectral triples and , the first of which is necessarily even, was defined by A.Connes as given by and, in the even-even case, by . Generically it is assumed that the real structure obeys the relations , , , where the -sign table depends on the dimension n modulo 8 of the spectral triple. If both spectral triples obey Connes' >-sign table, it is seen that their product, defined in the straightforward way above, does not necessarily obey this -sign table. In this Letter, we propose an alternative definition of the product real structure such that the -sign table is also satisfied by the product.     

Phonon-Exchange Attraction. Optical Phonons and Type II Superconductivity, and d-Wave Cooper Pairs

The electron-pair density matrix (k ₁, k ₂; k ₃, k ₄, t) =: (1, 2; 3, 4, t) changes in time, following a quantum Liouville equation \rho (5,6;3,4,t) - < 5,6|v_c |3,4 >\rho (1,2,5,6,t)} \right]} } $$ " align="middle" border="0"> with : = 4\pi e^2 k_0 (\Omega q^2 )^{ - 1} \delta _{k_1 + k_2 ,k_3 + k_4 } \delta _{k_s - k_1 ,q} $$ " align="middle" border="0"> in the presence of a Coulomb interaction _c, where is the volume. If the virtual phonon exchange is in action, the density matrix is shown to change similarly with an effective interaction _e, \hfill \\ = |V_q |^2 \bar h\omega _q |(\varepsilon _3 - \varepsilon _1 )^2 - \bar h^2 \omega _q^2 |^{ - 1} \delta _{k_1 + k_2 ,k_3 + k_4 } \delta _{k_3 - k_1 ,q} \hfill \\ \end{gathered} $$ " align="middle" border="0"> , by using a time-dependent perturbation theory and a Markoffian approximation. The dominant longitudinal-acoustic-(optical)-phonon-exchange attraction at 0K is shown to be q-independent (-dependent). The results are used to discuss the Cooper pair size, the origin of type II superconductivity and the formation of d-wave Cooper pairs in the cuprates.     

Influence of a strong longitudinal static electric field on free carrier faraday effect in an n-type InSb at room temperature at submillimeter wave frequencies

The expression for free carrier Faraday rotation and for ellipticity , as the function of the applied parallel static electric field and static magnetic field for a given value of wave angular frequency and electron concentration N₀, are obtained and theoretically analyzed with the aid of one-dimensional linearized wave theory and Kane's non-parabolic isotropic dispersion law. It is shown that the maximum Faraday rotation occurs near the cyclotron resonance condition, which can be expressed as , where , , and . Here m^* and e denote the effective mass and charge of electron, respectively. _g is the forbidden bandgap of semiconductor. v₀ is the carrier drift velocity, which is a non-linear function of E₀ in high field condition. A possibility of a simple way of determining the non-linear v₀ vs E₀ characteristics of semiconductors by the measurement of Faraday rotation is also discussed.     

Superplasticity in A Zn-1·1 wt. % Al alloy

In the paper the results of the deformation behaviour study in a fine-grained Zn-1·1 wt. % Al alloy are presented. The influence of strain rate ranging from 4·2×10^–5 to 4·2×10^–2 s^–1 on the true stress — true strain curves, ductility and strain rate sensitivity was investigated at temperatures 295 K and 375 K. At both temperatures the superplastic behaviour was observed. The increase in temperature improved the superplastic properties and shifted the region of the superplastic behaviour to higher strain rates. The maximum values of ductilityA=700% and strain rate sensitivity parameter m=0·48 were established at 375 K at strain rates . The true stress — true strain curves were found to be influenced by a grain growth taking place during the deformation. The grain growth was also found to be responsible for significant differences in the parameterm values obtained from the log plots and from the strain rat-changes.     

Scaling characteristics of ac conductivity and dielectric function in fractal regime of the metal-insulator transition

An analysis of the ac conductivity _ac(), and the ac dielectric constant, (), of the metal-insulator percolation systems is presented in the critical regime near the transition threshold. It is argued that the polarization and relaxation of the finite fractal metallic clusters play dominant roles in controlling the dynamic response of the system on both sides of the threshold. The relaxation time constant of a fractal cluster is shown to scale with its size as withd _t = 4 – 2d +d _c + /, whered is tge Euclidean dimension, andd _c , , and are the scaling indices for the charging, the dc conductivity, and the correlation length respectively. The average time dependent response of the system is shown to scale with a new time scale , where is the correlation length and ₀ is a microscopic time constant. It is shown that at frequencies and with /d_t 1, in close agreement with experiments. The effects of the anomalous transport along the infinite cluster and the medium polarizability are also discussed.     

On equivalent-neighbour,random site models of disordered systems

Models of random systems whose Hamiltonian reads , where and _i ,=1,...,n are independent, identically distributed random variables are discussed.J _ij are assumed to be symmetric, with respect toJ ₀, random variables and also symmetric functions of components of . A question of dependence of a phase diagram on a probability distribution of is addressed. A class of distributions and interactionsJ _ij , which give rise to phase diagrams called typical is selected. Then a problem of obtaining typical phase diagrams, containing a certain region with an infinite number of pure phases, is studied.     

Na‐site energy of P2‐type NaxM O2 (M = Mn and Co)

P2‐type Na_xM O₂ (M = Mn and Co) is a promising cathode material for low‐cost sodium ion secondary batteries. In this structure, there are two different crystallographic Nai (i = 1 and 2) sites with different Coulomb potential $ (\varphi _i)$ provided by M^4–x and O^2–. Here, we experimentally determine a difference ${(\rm \Delta }\varepsilon \equiv \varepsilon _1 - \varepsilon _2)$ of Na‐site energies ${(}\varepsilon _i \equiv e\varphi {\kern 1pt} _i)$ based on the temperature dependence of the site occupancies. We find that ${\rm \Delta }\varepsilon \;{=}\;56\;{K}$ for Na_0.52MnO₂ is significantly smaller than 190 K for Na_0.59CoO₂. We interpret the suppressed ${\rm \Delta }\varepsilon $ in Na_0.52MnO₂ in terms of the screening effect of the Na⁺ charge. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Softening during and after the hot deformation of the AISI 321 steel with respect to practical applications

The softening processes during and after the hot deformation (850–1180 C) in AISI 321 stainless steel were studied with respect to true strains _D and true strain rates . The analysis of deformation curves indicates the occurrence of dynamic recrystallization for values of Zener-Hollomon parameterZ10¹⁵ s^–1. The retardation of static recrystallization by fine Ti(N, C) precipitates is documented by microstructure studies and by variations of annealing conditions.     

Power law scaling of the top Lyapunov exponent of a Product of Random Matrices

A sequence of i.i.d. matrix-valued random variables with probabilityp and with probability 1–p is considered. Leta() = a ₀ + O(), c() = c ₀ + O() lim ₀ b() = Oa ₀,c ₀, >0, andb()>0 for all >0. It is shown show that the top Lyapunov exponent of the matrix productX _n X _n-1...X ₁, = lim_n (1/n) n X _n X _n-1...X ₁ satisfies a power law with an exponent 1/2. That is, lim ₀(ln /ln ) = 1/2.     

Coordinates of the quantum plane as q-tensor operators in (\mathfrak{s}\mathfrak{u}(2)*\mathfrak{s}\mathfrak{u}(2))

The relation between the set of transformations of the quantum plane and the quantum universal enveloping algebra U _q (u(2)) is investigated by constructing representations of the factor algebra U _q (u(2))* . The noncommuting coordinates of , on which U _q (2) * U _q (2) acts, are realized as q-spinors with respect to each U _q (u(2)) algebra. The representation matrices of U _q (2) are constructed as polynomials in these spinor components. This construction allows a derivation of the commutation relations of the noncommuting coordinates of directly from properties of U _q (u(2)). The generalization of these results to U _q (u(n)) and is also discussed.     

Transient creep during transformation in Cd-Zn alloys

Transient creep of Cd-2 wt. % Zn and Cd-17·4 wt. % Zn alloys has been studied under different constant stresses ranging from 6·4 MPa to 12·7 MPa near the transformation temperature. The results of both compositions showed two transient deformation regions, the low temperature region (below 483 K) and the high temperature region (above 483 K). From the transient creep described by the equation _tr=Bt ⁿ, where _tr andt are the transient creep strain and time. The parametersB andn were calculated. The parameterB was found to change with the applied stress from 0·3×10^–4 to 3×10^–4 and from 0·6×10^–4 to 18×10^–4 for Cd-2 wt. % Zn and Cd-17·4 wt. % Zn, respectively. The exponentn was found to change from 0·8 to 0·95 for both alloys. The parameterB was related to the steady state creep rate through the equation , the exponent was found to be 0·5 for Cd-2 wt. % Zn and 0·6 for the eutectic composition. The activation energies of transient creep in the vicinity of the transformation regions (above 483 K) were found to be 50·2 kJ/mole for Cd-2 wt. % Zn and 104·7 kJ/mole for the eutectic composition characterizing the mechanisms of grain boundary diffusion and volume diffusion in Cd, respectively.