Phonons in films

The oscillations of a film (lamina) with free boundaries are discussed. Calculations were performed and a computer analysis made of the dispersion curves for various types of oscillation. The results are presented here graphically. The density of states for phonons in a film is determined. The effects that the properties of phonons in films have on certain physical properties are discussed.Presented at the VI^th All-Union Conference on the Theory of Semiconductors.In conclusion, we are deeply grateful to M. Ya. Shirobokov for his valuable discussions and constant interest in the work, and to V. Metrikin for performing a great deal of computation. The authors are also very grateful to I. M, Lifshits for his fruitful discussion of the work and a number of valuable remarks.     

Production of light fermion–antifermion pairs in \gamma\gamma collisions

The corrections to in the standard model are calculated for arbitrary light fermions f. The relevant analytical results are listed in a form that is appropriate for practical applications, and numerical results for integrated cross sections are discussed. The corresponding QED corrections are generally of the order of some per mille for arbitrary energies. The weak corrections to are negligible below the electroweak scale, reach the percent level at a few hundred GeV, and grow to about at 2 TeV. The weak corrections to and production have a shape similar to the one for , but they are larger by factors of about 1.4 and 3, respectively. Received: 18 December 1998 / Revised version: 1 March 1999 / Published online: 18 June 1999     

A tapered beam finite element for rotor dynamics analysis

The stiffness, mass and gyroscopic matrices of a rotating beam element are developed, a cubic function being used for the transverse displacement. Shear deflection is included by use of end nodal variables of shear strain, along with transverse displacement and cross-section rotation; rotatory inertia effects are included in the energy functional to provide a Timoshenko beam formulation. The gyroscopic effects for small perturbations are linearized as a skew symmetric damping matrix. The formulation is implemented by numerical integration for a linearly tapered circular beam. A technique of reduction of the shear nodal variable prior to global assembly is shown to provide little loss in accuracy with reduced system bandwidth. Numerical comparisons for three previously published beam models are included, with results presented for the case of forward and reverse precession to verify the gyroscopic effects. The utility of the element in a general program for rotor dynamics analysis is identified.     

Hydrodynamics and time correlation functions for cellular automata

Hydrodynamic excitations in lattice gas cellular automata are described in terms of equilibrium time correlation functions for the local conserved variables. For large space and time scales the linearized hydrodynamic equations are obtained to Navier-Stokes order. Exact expressions for the associated susceptibilities and transport coefficients are identified in terms of correlation functions. The general form of the time correlation functions for conserved densities in the hydrodynamic limit is given and illustrated by some examples suitable for comparison with computer simulation. The transport coefficients are related to time correlation functions for the conserved fluxes in a way analogous to the Green-Kubo expressions for continuous fluids. The general results are applied for a one-component fluid and several types of binary diffusion. Also discussed are the effects of unphysical slow modes such as staggered particle or momentum densities.     

Random walks with nonnearest-neighbor transitions. II. Analytic one-dimensional theory for exponentially distributed steps in systems with boundaries

Exact analytic results for symmetric, nonnearest-neighbor random walks in one-dimensional finite and semiinfinite lattices are presented. Random walks with exponentially distributed step lengths are considered such that variation of a single parameter permits one to cover the whole range of step lengths from nearest-neighbor transitions to steps of aribtrary length. The generating functions for such lattices are derived and used to calculate a number of moment properties (mean first passage times, dispersion in the mean recurrence time). Since explicit expressions for the generating functions for these walks are obtained, additional moment properties can readily be calculated. The results found here for a finite system are compared to results found previously for a system with periodic boundary conditions. Two different semiinfinite systems are also considered.     

On the in-plane motion of thin,rotating ring segments

The equations governing the motion of a thin, circular ring, rotating about its polar axis, are derived under the restriction that plane sections remain plane and normal to the deformed centroidal curve. Simplified equations are then obtained for displacements that are small in comparison to the ring thickness, and for time scales that are comparable with the period of flexural vibration. Solutions are obtained for free vibration, and numerical results presented for the frequencies and mode shapes of a semi-circular ring fixed at both ends. The solution for forced motion is shown to be expressible as a modal expansion in these characteristic functions.     

Calculation of temporal, angular, and intensity characteristics of the sound field in a coastal area with an arbitrary bottom relief and a constant sound speed in the medium

Computational algorithms and some computed data are presented for the total sound field in a waveguide whose depth arbitrarily depends on two horizontal coordinates. The sound speed is supposed to be constant, and the bottom slopes are considered as small. The algorithm involves three steps. First, horizontal rays, i.e., horizontal projections of the real rays multiply bottom-and surface-reflected, are calculated. Second, the horizontal rays are set up to a point. Third, the real rays are set up to a point. The computational accuracy is analyzed for a homogeneous wedge lying on a halfspace. Calculations are carried out for a coastal region of the ocean.     

A linear code for the sawtooth and cat maps

The sawtooth maps are a one-parameter set of piecewise linear area preserving maps on the torus. For positive integer values of the parameter K they are automorphisms of the torus, known as the cat maps. We present a symbolic dynamics for these maps in which the symbols are integers. This code is related to a practical problem of the stabilisation of a system which is perturbed by impulses. The code is linear in the sense that an orbit and its code are linearly related, so it is not difficult to obtain a good approximation to one from the other in practice. A stationary stochastic process for generating the code is given explicitly. The theory uses Green function methods, which are also used to study ordered periodic orbits and cantori. The problems of using a similar code for arbitrary area preserving twist maps on the torus are briefly discussed.     

Superstrings with torsion

The conditions for spacetime supersymmetry of the heterotic superstring in backgrounds with arbitrary metric, torsion, Yang-Mills and dilaton expectation values are determined using the sigma model approach. The resulting equations are explicitly solved for the torsion and dilaton fields, and the remaining equations cast in a simple form. Previously unnoticed topological obstructions to solving these equations are found. The equations are shown to agree to leading order in perturbation theory with those derived in a field theory approach, provided one considers a more general ansatz than in previous analyses by allowing for a warp factor for the metric. Exact solutions with non-zero torsion are found, indicating a new class of finite sigma models. These solutions break the E_χ ⊗ E_χ or SO(32) gauge group down to a large variety of subgroups. Orbifolds with torsion are constructed. A perturbative analysis of the equations indicates a class of solutions whose existence has been recently argued for on other grounds. Brief comments are made on the implications for phenomenology.     

Asymptotic freedom,infrared convergence and supersymmetry

The conditions for infrared convergence and asymptotic freedom are investigated for a system in which (in order to produce a spontaneous breakdown) a supersymmetric matter-matter interaction is added to the supersymmetric Yang-Mills Lagrangian. It is found that, in contrast to conventional theory, the conditions imposed by the asymptotic freedom of the matter-matter interaction are not stringent, and are automatically satisfied for adjoint representations. The conditions for infrared convergence are also not too stringent. However the joint conditions for asymptotic freedom and infrared convergence turn out to be quite stringent. Nevertheless, a model is proposed which, subject to some reservations, appears to satisfy the joint conditions.     

Improved effective field treatment of the BEG model

A version of the effective field theory recently proposed by the author is applied to a study of the Blume-Emery-Griffiths model. The theory correctly accounts for all the single-kite kinematic relations and leads to results that are quite superior, and in some aspects crucially different, to those reported by other workers using a previous version of the formalism which was defective in its treatment of the kinematic relations. The critical temperature for the second-order phase transitions for a range of biquadratic exchange interactions and single-ion anisotropies is studied for the honeycomb, square and cubic lattices, and the tricritical points are also located. The magnetization curves are studied in depth for a range of interaction strengths, particularly in the vicinity where reentrant behaviour is predicted. The first-order transitions which can arise for a limited range of single-ion anisotropies are also studied, as well as the quadrupolar moment.     

Time-frequency analysis and modeling of the backscatter of categorized dolphin echolocation clicks for target discrimination

A set of dolphin echolocation clicks collected from an Atlantic bottlenose dolphin in Kaneohe Bay, Hawai'i from a previous experiment is examined in terms of their time and frequency characteristics. The center frequency and rms bandwidth are calculated for the clicks and these are clustered into four classes by using a model based on the Bayesian information criterion. The echo signatures are attained from a solid, elastic homogeneous sphere for each class of clicks from an acoustic scattering model. The results from the scattering model are compared to experimental values. The joint time-frequency content of the resulting echo signals is obtained by the reduced interference distribution (RID). The RIDs are plotted and examined for each signal class for four spherical targets of different material compositions. RID correlation values are obtained for a standard target versus comparison targets by using a time-frequency correlator. The results suggest that dolphins may discriminate by auditory inspection of the time-frequency information returned by the targets. The modification of the outgoing clicks and examination of time-frequency target information may be fundamental to a dolphin's ability to identify and discriminate targets.     

Brushed-on piezoelectric transducers

Design considerations and operation of vibration-sensitive transducers that are brushed into place are described. These transducers are made of a slurry of crushed piezoelectric ceramic and a liquid binding material that becomes rigid upon exposure to the air. The resulting hard coating is electroded and polarized in place prior to its use as a vibration-detecting transducer. The parameters for optimum particle size, concentration and electrode shape are determined for transducers that are suitable for detecting vibration. Feasibility of the technique is determined by its use in detecting ultrasonic vibration of small rigid members. The technique permits deposition of coats less than 1mm thick with a particle concentration of up to 77 percent of active material. The sensitivities obtained are compared to those of solid piezoelectric materials.     

Generic Bohmian Trajectories of an Isolated Particle

The generic Bohmian trajectories are calculated for an isolated particle in an approximate energy eigenstate, for an arbitrary one-dimensional potential well. It is shown that the necessary and sufficient condition for there to be a negligible probability of the trajectory deviating significantly from the classical trajectory at any stage in the motion is that the state be a narrowly localised wave packet. The properties of the Bohmian trajectories are compared with those in the interpretation recently proposed by García de Polavieja. The reasons why the latter tend to be much more nearly classical are discussed. The implications for other trajectory interpretations are considered.     

Calculation of critical states of superconducting multilayers based on numerical solution of the Ginzburg-Landau equations for superconducting plates

Numerical methods are used to analyze the Ginzburg-Landau equations for a superconducting plate carrying transport current in a magnetic field. Critical current is calculated as a function of the applied magnetic field strength for superconducting plates with different thicknesses. The relations between the field dependence of critical current and the distributions of order parameter, magnetic field, and supercurrent in a plate are analyzed. The field-dependent critical currents computed for plates are used to determine the critical current as a function of the applied magnetic field strength and local magnetic field and current distributions for multilayers in parallel magnetic fields. The constituent superconducting layers are assumed to interact only via magnetic field. A simple method is proposed for analyzing the critical states of multilayers in magnetic fields of arbitrary strength, based on elementary transformations of the critical current-density distribution over individual layers in zero applied magnetic field. The method can be used to analyze experimental results.     

Guiding of a one-dimensional optical beam with nanometer diameter

The concept of a one-dimensional optical wave and its waveguides are proposed for what is to our knowledge the first time. The proposed waveguides are principally new and named for one-dimensional optical waveguides. One-dimensional optical waveguides make it possible to guide very thin optical beams in the visible or the near-infrared region with a diameter in the nanometer range. The propagation properties are analyzed theoretically. The applications of the waveguides to optical devices in the nanometer range are discussed.     

Heisenberg equations of motion for spin-1/2 wave equation in general relativity

The Heisenberg equations of motion for the spin-1/2 wave equation in general relativity are obtained by a covariant procedure. They are found to be similar to the equations of motion for a classical pole-dipole test-particle in general relativity. The identification is complete when the Heisenberg equations are taken to be satisfied by the respective expectation values.     

超导电理论中的Гинзбург-Ландау方程的非局域推广

本文对Гинзбург-Ландау(ГЛ)方程的微观推导所需要的条件进行了分析。分析结果表明,对于Pippard型甚至是中间型超导体,ГЛ方程有效的温度范围都是相当狭窄的。为便于研究临界温度T_c附近比较宽的范围内,强磁场中各类超导体的性质,我们从Горьков的超导普遍方程出发,利用磁场存在时“正常金属格临函数”的非局域展式,导出了一个包含能隙函数和矢势的积分微分方程组。所得的方程对London型、中间型和Pippard型超导体在△t=(T_c-T)/T_c《1的温度区域中都同样适用。利用这个方程组,我们讨论了恒定外磁场中的半无限大超导体,给出了能隙函数和穿透深度的积分表达式。在London和Pippard两个极限下,积分被解析地作出了。对于Pippard型超导体,我们在T_c附近整个温度区域计算了能隙函数和穿透深度随磁场的变化。所得的结果表明,Pippard型超导体在磁场中的行为与ГЛ理论的预言有显著的不同。