Effect of Finite Spectral Width on the Modulational Instability of Langmuir Waves described by a Nonlinear Schrödinger Equation

By using the two-point space correlation function an equation for the power spectral density for a random Langmuir field has been derived. The dispersion relation for a monochromatic wave is regained for a delta spectrum. For a Gaussian spectrum, the maximum growth rate is less than that for a monochromatic wave. For a “meander spectrum”, the growth rate is increased with the width of the spectrum in the first stage then decreased for further increase of the width.     

Numerical simulation of continuum models for fluid-fluid interface dynamics

This paper is concerned with numerical methods for two-phase incompressible flows assuming a sharp interface model for interfacial stresses. Standard continuum models for the fluid dynamics in the bulk phases, for mass transport of a solute between the phases and for surfactant transport on the interface are given. We review some recently developed finite element methods for the appropriate discretization of such models, e.?g., a pressure extended finite element (XFE) space which is suitable to represent the pressure jump, a space-time extended finite element discretization for the mass transport equation of a solute and a surface finite element method (SurFEM) for surfactant transport. Numerical experiments based on level set interface capturing and adaptive multilevel finite element discretization are presented for rising droplets with a clean interface model and a spherical droplet in a Poisseuille flow with a Boussinesq-Scriven interface model.     

Compact multireference wavefront sensor design

We present a compact optical design for a multireference Shack-Hartmann-based wavefront sensor (WFS) for multiconjugate adaptive optical systems. The key component of this WFS design is a field lenslet array that separates the exit pupil images in the sensing plane for all reference sources. An analytical method for WFS optical design is presented, and the optimal strategy for selecting optical components from a discrete set is outlined. The feasibility of the WFS design has been demonstrated for a prototype WFS system in a laboratory setup with five reference sources and two deformable mirrors representing a wavefront-distorting medium.     

The forced vibrational response of a rectangular parallelepiped with rigid-lubricated boundaries

The Green function for a rectangular parallelepiped with rigid-lubricated boundaries is developed by a normal mode approach, the free vibration solutions being used. Explicit solutions are presented for a concentrated impulse, which serves as a model for an acoustic emission stress wave, and for a concentrated step force. Numerical results for short times show good agreement with the infinite space solution. Analogous solutions are developed for the inverse boundary conditions.     

The experimental investigation of a glow discharge in a toroidal tube

A glow discharge in a toroidal tube with axial discharge current is investigated. The investigation was carried out for a discharge as a whole, not for electrodal zones and the positive column separately. The volt-ampere characteristics for different pressures and Paschen's curves for different gases were measured. The curves obtained are compared with analogous ones for a cylindrical tube. The conditions for the existence of a glow discharge in a toroidal tube and the processes passing there are discussed on the basis of the measured curves. The experiments were carried out in air, helium, argon and neon.     

Inertial Effects in Nonequilibrium Work Fluctuations by a Path Integral Approach

Inertial effects in fluctuations of the work to sustain a system in a nonequilibrium steady state are discussed for a dragged massive Brownian particle model using a path integral approach. We calculate the work distribution function in the laboratory and comoving frames and prove the asymptotic fluctuation theorem for these works for any initial condition. Important and observable differences between the work fluctuations in the two frames appear for finite times and are discussed concretely for a nonequilibrium steady state initial condition. We also show that for finite times a time oscillatory behavior appears in the work distribution function for masses larger than a nonzero critical value.     

Chiral symmetry breaking in an instantaneous approximation to Coulomb gauge QCD

We analyze the interplay between explicit and spontaneous chiral-symmetry breaking in Coulomb gauge QCD. Quark and pseudoscalar meson properties are investigated, using an instantaneous approximation to gluon exchange, with momentum-dependent coupling constants and current quark masses in agreement with the full QCD renormalization group equations. We show how a finite momentum-dependent constituent quark mass can be defined even for a confining interaction between the quarks, and derive an integral equation for this constituent mass from the renormalized Dyson-Schwinger equations. This equation is shown to be equivalent to a gap equation derived in a Bogoliubov-Valatin variational method from the model's hamiltonian. Including momentum-dependent current masses also ensures a finite value for the quark condensate. We report numerical results for a purely confining and for a Richardson potential for the Coulombic part of the quark-antiquark potential. Transverse gluons are included in the Breit approximation, neglecting retardation. As a confining Breit interaction leads to an infrared inconsistency in the model, and since there is mounting evidence for a dynamical gluon mass, such a mass is included. Numerical results for the constituent quark mass for one flavour, for different values of the current mass, are reported, together with the corresponding energy densities, quark condensates, pseudoscalar meson masses and pseudoscalar meson decay constants. The results are encouraging from a phenomenological point of view.     

Information capacity of optical fiber channels with zero average dispersion

We study the statistics of optical data transmission in a noisy nonlinear fiber channel with a weak dispersion management and zero average dispersion. Applying analytical expressions for the output probability density functions both for a nonlinear channel and for a linear channel with additive and multiplicative noise we calculate in a closed form a lower bound estimate on the Shannon capacity for an arbitrary signal-to-noise ratio.     

A Deformation-Theoretical Approach to Weyl Quantization on Riemannian Manifolds

By using a sheaf-theoretical language, we introduce a notion of deformation quantization allowing not only for formal deformation parameters but also for real or complex ones as well. As a model for this approach to deformation quantization, we construct a quantization scheme for cotangent bundles of Riemannian manifolds. Here, we essentially use a complete symbol calculus for pseudodifferential operators on a Riemannian manifold. Depending on a scaling parameter, our quantization scheme corresponds to normally ordered, Weyl or antinormally ordered quantization. Finally, it is shown that our quantization scheme induces a family of pairwise isomorphic strongly closed star products on a cotangent bundle.     

Brownian motion in periodic potentials; nonlinear response to an external force

The Brownian motion of particles in a periodic potential in response to a constant external force is investigated. By expanding the distribution function into Hermite-functions and into a Fourier-series, the Fokker-Planck-equation is transformed into a set of coupled equations for the expansion coefficients. These equations are solved by a continued fraction method for matrices. This continued fraction for the matrices converges for large, intermediate and even for very small damping constants. The mobility, the kinetic and potential energy for various damping constants and external forces are given for a cos-potential. The current-voltagecharacteristic of the Josephson tunneling junction is also shown.     

Scalar field potentials for closed and open cosmological models

We develop a technique for the reconstruction of the potential for a scalar field or a tachyon field, reproducing a given cosmological evolution in a closed and open isotropic cosmological models. Such potentials are explicitly written down for the cases of the evolutions driven by a generic barotropic fluid and by radiation plus a cosmological constant, for the case of a scalar field. For tachyon and pseudo-tachyon fields the potentials are reconstructed for some special cases, corresponding to particular values of the barotropic index.     

Intensity cross-correlation in light scattered by the rotational motion of macromolecules

Intensity cross-correlation in light scattered by the rotational motion of macromolecules is discussed in terms of pair- pair correlation. Expressions are given for a single pair for comparison with a rod, an equilateral triangle for comparison with a flat macromolecule, and a regular tetrahedron for comparison with other shapes. Anticorrelation occurs for the pair and triangle and correlation for the tetrahedron.     

Calculation of the luminescence of a finite volume with population inversion

Amplified luminescence is examined for a polished cylindrical rod. Nonlinear transport equations are used to examine the distribution of the emission along the rod and the mean density of the amplified luminescence. It is found that the probability of luminescence-induced transitions is of the same order as that for spontaneous transitions for a ruby rod. Calculations are presented for storage in a metastable level and for oscillation. Estimates are presented for the amplified luminescence from a cylinder with nonreflecting surfaces and also for a sphere.I am indebted to B. I. Stepanov for interest and valuable advice.     

Multi-STFT for adaptive SCPS phase determination

This paper presents a fast and reliable approach for phase modulo 2π-calculation from a single fringe pattern. It calculates correct phase values even for very complex and variable shape gradients based on a locally variable fringe period determined for the entire image. In the paper, a new two-step method for wrapped phase calculation is proposed. It is performed through the use of a method based on a multiple local fast Fourier transform for estimation of a local fringes period map and a 5-point spatial carrier phase shifting (SCPS) formula for phase modulo 2π-calculation. The described approach is verified by a correct demodulation of a real fringe pattern taken by a 3D-shape measurement system.     

Photorefractive Four-Wave Mixing Switches Utilizing Pockels Effect -Longitudinal and Lateral Switches-

We carried out detailed calculations for photorefractive wave-mixing switches based on one of three crystals with high electro-optic coefficients, namely, BaTiO₃, Strontium Barium Niobate (SBN (0.75)), and Potasium Sodium Strontium Barium Niobate (KNSBN). A comparison of results for the three crystals shows that a 0_-cut BaTiO³ crystal is suitable for a longitudinal switch and requires a voltage of about 80 for a 2-mm-thick crystal to induce sufficient phase mismatch. The electrodes must be transparent for the incident and diffracted beams. A 45_-cut SBN (0.75) crystal, however, is suitable for a lateral switch and requires a voltage of about 150 for a 1-mm-wide crystal. The electrodes do not need to be transparent.     

Moment problem for effect algebras

We present a solution to the moment problem for effect algebras, concerning mean values of all powers of an observable concentrated on the interval [0, 1] for states from a convex set. We give a solution for particular examples, e.g., for the set of all effect operators. We examine how this problem is related to a socalled E-property. Finally, we give a solution for observables studied in the operational approach to physical theories.     

Exact solution of a coagulation equation with a product kernel in the multicomponent case

In this paper, we obtain the general solution for the continuous Smoluchowski equation in the multicomponent case with a product kernel as a series expansion. The solution of the problem involves the Laplace transform in several dimensions. We obtain a nonlinear partial differential equation (PDE) of the advective kind generalizing the one previously given by other authors for the mono-component case.As in its relative mono-component case, gelation is produced at some point, the conditions for its occurrence being the same as those for the mono-component case, though substituting a sum of derivatives by a derivative in the Laplace transform field. We demonstrate that for a multicomponent particle size distribution (PSD) of multiplicative form, it is sufficient for one of the marginal PSDs to generate instantaneous gelation for the occurrence of instantaneous gelation in the multicomponent PSD.The general solution is applied to several specific cases, a discrete case that recovers a previously known solution, and another two continuous cases which can be used to check numerical methods designed to directly solve the Smoluchowski equation in more general cases.We have compared the solutions for the multicomponent PSD for constant, additive and product kernels and we conjecture about the relation existing between the functional forms for the solutions both in the mono-component and the multicomponent case.Finally, we have analysed the shape of the solutions for multicomponent PSD for constant, additive and product kernels for very small masses of components, obtaining a qualitatively different behaviour for the product kernel. This has effects in the mixing state of the sol phase as time passes.     

A path integral approach to inclusive processes

The single-particle inclusive differential cross-section for a reaction is written as the imaginary part of a correlation function in a forward scattering amplitude for in a modified effective theory. In this modified theory the interaction Hamiltonian equals in the original theory up to a certain time. Then there is a sign change and becomes nonlocal. This is worked out in detail for scalar field models and for QED plus the abelian gluon model. A suitable path integral for direct calculations of inclusive cross sections is presented. Received: 8 March 2000 / Published online: 6 July 2000     

Detection and discrimination of spectral peaks and notches at 1 and 8 kHz

The ability of subjects to detect and discriminate spectral peaks and notches in noise stimuli was determined for center frequencies fc of 1 and 8 kHz. The signals were delivered using an insert earphone designed to produce a flat frequency response at the eardrum for frequencies up to 14 kHz. In experiment I, subjects were required to distinguish a broadband reference noise with a flat spectrum from a noise with either a peak or a notch at fc. The threshold peak height or notch depth was determined as a function of bandwidth of the peak or notch (0.125, 0.25, or 0.5 times fc). Thresholds increased with decreasing bandwidth, particularly for the notches. In experiment II, subjects were required to detect an increase in the height of a spectral peak or a decrease in the depth of a notch as a function of bandwidth. Performance was worse for notches than for peaks, particularly at narrow bandwidths. For both experiments I and II, randomizing (roving) the overall level of the stimuli had little effect at 1 kHz, but tended to impair performance at 8 kHz, particularly for notches. Experiments III-VI measured thresholds for detecting changes in center frequency of sinusoids, bands of noise, and spectral peaks or notches in a broadband background. Thresholds were lowest for the sinusoids and highest for the peaks and notches. The width of the bands, peaks, or notches had only a small effect on thresholds. For the notches at 8 kHz, thresholds for detecting glides in center frequency were lower than thresholds for detecting a difference in center frequency between two steady sounds. Randomizing the overall level of the stimuli made frequency discrimination of the sinusoids worse, but had little or no effect for the noise stimuli. In all six experiments, performance was generally worse at 8 kHz than at 1 kHz. The results are discussed in terms of their implications for the detectability of spectral cues introduced by the pinnae.     

Ground state properties of a spinless Falicov-Kimball model; additional features

We have studied some energetic and structural ground state properties of a spinless Falicov-Kimball model. Using a method based on “Tchebycheff-Markoff inequalities”, we have calculated sharp upper and lower bounds for the ground state energy. These calculations lead to rigorous results for a special range of parameters, where we are able to give the exactf-level occupation pattern for a square lattice. The results for the “symmetric” case, where a superstructure occurs leading to a metal-insulator transition, have already been published. In this paper we present some additional results also for the “unsymmetric case” and study valence-transitions for fixed particle-number.