Showing papers on "Scalar (physics) published in 1991"

Pair production in a strong electric field.

Abstract: We investigate the mechanism of pair creation in scalar QED from spatially homogeneous strong electric fields in 1+1 dimensions. Solution of the semiclassical field equations shows particle creation followed by plasma oscillations. We compare our results with a model based on a relativistic Boltzmann-Vlasov equation with a pair-creation source term related to the Schwinger mechanism. The time evolution of the electric field and the current obtained from the Boltzmann-Vlasov model is surprisingly similar to that found in the semiclassical calculation.

A pure spin-connection formulation of gravity

Abstract: A new action principle, in which the only gravitational variables are an SL(2,C) connection and a scalar density, is derived for general relativity (GR) coupled to matter and for supergravity. In this form, GR appears as a non-metric, generally covariant gauge theory, the metric being reconstructed from the other fields in a solution. A similar non-metric action with a real SO(3,1) connection is also derived, however it involves an independent fourth rank tensor field representing the curvature.

The application of transport theory to visualization of 3‐D scalar data fields

Abstract: This paper describes a general visualization model for 3‐D scalar data fields based on linear transport theory that contains common volume rendering models as special cases and/or approximations. The concept of ‘‘virtual’’ particles for the extraction of information from data fields is introduced. The role of different types of interaction of the data field with those particles such as absorption, scattering, source, and color shift are discussed and demonstrated. Special attention is given to possible tools for the enhancement of interesting data features. Random distortions or noise of the data field are mapped onto the image plane in a well‐defined way such that picture processing methods can be used to reconstruct the appearance of the undistorted data set. Random texturing can provide visual insights as to the magnitude and distribution of deviations of related data fields, e.g., originating from analytic models and measurements, or in the noise content of a given data field. Hidden symmetries of a data set can often be identified visually by allowing it to interact with a preselected beam of ‘‘physical’’ particles with the attendant appearance of characteristic structural effects such as channeling.

Interface conditions for acoustic and elastic wave propagation

Abstract: The divergence theorem is used to handle the physics required at interfaces for acoustic and elastic wave propagation in heterogeneous media. The physics required at regular and irregular interfaces is incorporated into numerical schemes by integrating across the interface. The technique, which can be used with many numerical schemes, is applied to finite differences. A derivation of the acoustic wave equation, which is readily handled by this integration scheme, is outlined. Since this form of the equation is equivalent to the scalar SH wave equation, the scheme can be applied to this equation also. Each component of the elastic P‐SV equation is presented in divergence form to apply this integration scheme, naturally incorporating the continuity of the normal and tangential stresses required at regular and irregular interfaces.

Validity of the scalar Kirchhoff and Rayleigh–Sommerfeld diffraction theories in the near field of small phase objects

Abstract: Amplitude and phase in the diffraction near fields of small phase objects (bars with rectangular cross sections ≤λ2) are calculated according to the scalar Kirchhoff and Rayleigh–Sommerfeld diffraction theories. Results are compared with 3-cm microwave measurements. The agreement between calculation and measurement depends on the size of the phase objects because interference fields under certain circumstances will satisfy the Kirchhoff boundary conditions of the different diffraction theories.

On the charge and mass of particles in unitary quantum theory

Abstract: The scalar analogue of the main (principal) equation of the unitary quantum theory together with the Poisson equation are solved numerically in this paper. The value of the electrical charge and also the fine-structure constant are found, which are in good agreement with the experiment. The evaluation of the electrical form factor and the mass of such a particle is also carried out.

Kinetic roughening of interfaces in driven systems.

Abstract: We study the dynamics of an interface driven far from equilibrium in three dimensions. First we derive the Kardar-Parisi-Zhang equation from the Langevin equation for a system with a nonconserved scalar order parameter, for the cases where an external field is present, and where an asymmetric coupling to a conserved variable exists. The relationship of the phenomena to self-organized critical phenomena is discussed. Numerical results are then obtained for three models that simulate the growth of an interface: the Kardar-Parisi-Zhang equation, a discrete version of that model, and a solid-on-solid model with asymmetric rates of evaporation and condensation. We first make a study of crossover effects. In particular, we propose a crossover scaling ansatz and verify it numerically. We then estimate the dynamical scaling exponents. Within the precision of our study, the Kardar-Parisi-Zhang equation and the solid-on-solid model have the same asymptotic behavior, indicating that the models share a dynamical universality class. Furthermore, the discrete models exhibit a kinetic roughening transition. We study this by monitoring the surface step energy, which shows a dramatic jump at a finite temperature for a given driving force. At the same temperature, a finite-size-scaling analysis of the bond-energy fluctuation shows a diverging peak.

Occurrence of caustics for high-frequency acoustic waves propagating through turbulent fields

Abstract: Theoretical investigations of wave propagation in random media usually rely on a statistical approach. The interaction between the wave and the medium is expressed in terms of a random refractive index related to the fluctuations of the medium, which has been introduced in the Helmholtz equation. The equations which govern the second and higher moments of the transmitted sound pressure field are then deduced. Using a closure hypothesis for the index fluctuation, solutions may be obtained either by some analytical developments or by numerical integration. It is only recently that studies have been reported that make use of computer generated fields to simulate wave propagation in random media. However they are still limited to scalar random fields. Moreover, in acoustics, the presence of velocity components introduces additional effects of wave convection which cannot be described a priori by such a simplified approach.

Method of and system for displaying a scalar quantity distribution

Abstract: A scalar quantity distribution displaying method wherein shape information of an object to be displayed having a certain shape, and magnitudes of scalar quantities at sampling points lying on the object to be displayed are used for displaying scalar quantity magnitude distribution on the object to be displayed in terms of contour lines and/or a color map; the improvement therein comprising the fact that the distribution of the magnitudes of the scalar quantities is displayed by a graph simultaneously with the display presented in terms of the contour lines and/or the color map. Since the scalar quantity distribution is concurrently displayed, any singular value, etc. of the scalar quantity can be readily acknowledged.

Reconstruction of standard and inverse vector fields equivalent to a Rössler system.

Abstract: Ordinary diffential equations of continuous dynamical systems, or at least of equivalent systems, can be reconstructed from numerical scalar time series. Methods are exemplified for a R\"ossler band. Equivalent systems are standard and inverse systems, which are systematically investigated. Validations rely (i) qualitatively on comparisons between phase portraits and (ii) quantitatively on comparisons between generalized dimension spectra. By-products of the work are an information-compression scheme for time-series encoding and the introduction of squeezed systems that facilitate evaluations of generalized dimensions of small order q1.

The theoretical background of the fifth force

Abstract: Theoretical ideas of the fifth force(s) are reviewed, placing emphasis on the issue of how one can derive the two most important properties: the coupling strength roughly comparable with, or somewhat weaker than, gravity and the force-range of a macroscopic distance. Dilaton models, five-dimensional theory, and models of scalar fields induced from pseudoscalar fields as Nambu-Goldstone bosons of internal symmetries via CP violation are reanalyzed critically. All of these theories aim at predicting new types of phenomena to probe physics characterized by mass scales much higher than is accessible by other conventional means. Most of the theoretical predictions are shown to be consistent with effects expected to be discovered below the present experimental upper bounds. We are still waiting for more experiments with better sensitivity.

A scalar combustion model

Abstract: In this paper we introduce a simple combustion model and study its properties. The model supports both deflagration and detonation waves and exhibits instability. Our purpose is to introduce an admissibility criterion through the study of elementary waves, and use it to investigate the nonlinear stability and instability of flows with combustion waves. In particular, our model exhibits instability for unburnt states if the binding energy is sufficiently large. Because reactive gas flow is highly unstable, this aspect of our model is physically reasonable. The simplicity of our model allows us to make a fairly general study of solutions. A scalar value u is to represent a lumped quantity of the gas flow such as density, velocity or temperature, q, which denotes the binding energy of the reactive gas, equals a constant qo for unburnt gas and zero for burnt gas. A typical point in Lagrangian coordinates is denoted by x E R 1. In our model,

Field-dependent coupling strength for scalar fields

Abstract: Effective Lagrangians with a nonlinear coupling between the scalar density of the nucleons and the scalar meson field are investigated within the framework of relativistic mean-field theories. This phenomenological coupling acts as a field-dependent coupling strength and is supposed to take into account renormalization effects within a mean-field picture. The parameters of the model are adjusted to saturation properties of nuclear matter and predictions for the real part of the optical potential are compared with experimental data. For that relativistic and nonrelativistic optical model fits are examined and an experimental standard is deduced which covers the energy range from − 50 MeV to 1000 MeV. A definition for the real part of the optical potential is given which is not linear in the energy but has the proper limits for momentum zero and infinity. It is shown that for a special choice of the field-dependent coupling strength the meanfield theory can describe the nuclear equation of state and the momentum dependence of the single particle energy without further parameters up to momenta where the intrinsic structure of nucleon becomes relevant.

Homogeneous buoyancy‐generated turbulence

Abstract: If a random and statistically homogeneous density distribution is created in a fluid, a random motion of the fluid is subsequently generated by buoyancy forces. This motion is resisted by viscous stresses, while the density variation is smoothed by molecular diffusion of the relevant scalar property of the fluid. Furthermore, advective mixing generates smaller‐scale components of the scalar quantity, increasing the rate of smoothing. If the Reynolds number of the motion is sufficiently large, the motion becomes turbulent in the ordinary sense. Such turbulence may be said to be generated by an ‘‘active’’ conserved scalar quantity. To elucidate the nature of this buoyancy‐driven turbulence, we consider an infinite fluid that is initially at rest everywhere, with a given distribution of the conserved scalar quantity. In order to have a well‐defined initial state specified by a manageably small number of parameters, the initial distribution of the scalar is assumed to be statistically homogeneous and isotropi...

Comment on spectral statistics in elastodynamics

Abstract: Recently, a set of high eigenfrequencies of small aluminum blocks have been measured and analyzed quantitatively by using methods initially developed in nuclear physics on the basis of an analogy with random matrix theory [R. L. Weaver, J. Acoust. Soc. Am. 85, 1001 (1989)]. At the foundation of the application of random matrix theory is the (classical motion) ⇔ (finite frequency vibration) correspondence according to which the nature of classical geometrical acoustic trajectories determine the correspondence with random matrix theory and thereby the structure of the spectrum (classical chaos→GOE spectrum; regular motion→Poissonian spectrum). Although the classical geometrical acoustics trajectories are not chaotic in the system studied by Weaver, he finds a good agreement with the GOE prediction, in contradiction to the usual wisdom concerning the classical-vibration correspondence. It is suggested that this paradox stems from finite wavelength effects that introduce a coarse graining in the relevant classical dynamics. Interpreted in this way, Weaver’s results seem to confirm that the GOE spectrum initially studied for simple scalar Helmholtz equation may also be valid in the more complicated case of elastodynamics.

Some considerations on the elastic theory for nematic liquid crystals

Abstract: The elastic theory for nematic liquid crystals is critically analysed. After a review on the variational calculus formalism, the range of applicability of the Lagrangian method for the solution of practical problems is discussed. It is underlined that only a limited number of problems can be solved by means of a variational approach. The role at the Jacobi equation is also discussed. The importance of the non linear character of the K13-problem is analyzed in the framework of a simple molecular model. Finally, the principle of virtual work is applied to the elastic theory of nematic liquid crystals. Our analysis shows that the K13 elastic problem is an ill-posed one, since this problem can only be solved by means of a variational, or virtual work, approach by modifying the bulk elastic free energy and taking into account new terms quadratic in the second order deviatives. However it is necessary to remember that, in the proximity of a surface, a spatial variation of the density and of the scalar ...

Homonuclear scalar 6Li6Li spin–spin coupling: First direct observation and detection via the 6Li,6Li INADEQUATE experiment,

Abstract: A homonuclear 6Li,6Li spin–spin coupling has been directly measured in the case of the dimer of (E)-2-lithio-1-phenyl-1-o-lithiophenylpent-1-ene. This constitutes the first direct observation of such a parameter. The well known INADEQUATE experiment in its one- and two-dimensional versions is applied for the first time to a spin system of spin-1 nuclei. It is demonstrated that the experiment is very sensitive for the detection of 6Li,6Li spin–spin interactions, and thus provides a promising alternative to the COSY experiment and an additional tool for structural studies on organolithium compounds in solution.

Oscillations of a polarizable vacuum

Abstract: A classical basis for one-dimensional Schrodinger quantum theory is constructed from simple vacuum polarization harmonic oscillators within standard stochastic theory. The model is constructed on a two-dimensional phase configuration surface with phase velocity vectors that have a speed of light zitterbewegung behaviour character. The system supplies a natural Hermitian scalar product describing probability density which is derived from angular momentum considerations. The generality of the model which is extensive is discussed.

Transient combustion in a turbulent eddy

Abstract: A mathematical model of a local transient diffusion flame generated by mixing in a turbulent eddy is presented. It is intended ultimately as a computational “molecule” to be imbedded in numerical simulations of large scale reacting flows. The specific objective of the present analysis is to account explicitly for the modification of the local velocity field induced by the heat generation process. An “idealized” single step irreversible reaction model and a model treating the effects of real chemistry within the laminar flamelet approximation are considered. The convection diffusion equation for the mixture fraction and the mass conservation equation are analyzed using the experimental observation that specific volume is a piecewise linear function of mixture fraction. A Cole-Hopf transformation is used to reduce this equation to an incompressible form in terms of a new “pseudo mixture fraction” which can be related to all scalar properties using measured or idealized state relationships. Seven different fuels have been studied. Sample results for two of these are presented.

Identification of parameters in a moving model

Abstract: Although the problem of the identification of parameters in the classical scalar Preisach model, and in some field‐dependent models, has been solved, it is still an open question for the magnetization‐dependent models such as the moving model. In this paper we illustrate a solution for a scalar bivariate moving model for the case where the Preisach function is Gaussian with equal standard deviations in the two directions. The identification described is limited to the case where the nonzero values of a bivariate Preisach function, including its motion, are limited to one quadrant.

An algebraic approach to the propagation of waves and particles in layered media

Abstract: For the solution of a variety of physical problems in application to any medium it is very fruitful to split the medium in parts by introducing infinitesimal gaps. If a problem can be solved for one part, then after application of recurrent relations we obtain the solution for the whole medium. This approach is applied to the wave propagation in any periodic potential, to the diffraction of scalar radiation (neutrons, for example) from an ideal crystal and to the albedo of particles from a homogeneous medium filled with randomly distributed scatterers.

Ideal and quasi-ideal time focusing of charged particles

Abstract: Deals with the problem of the determination of scalar and vector potentials of electromagnetic fields providing time focusing of strongly diverging packs of charged particles (specific values of relative energy spread being about 100%, angular spread attaining tens of degrees). The problem is solved within the framework of static non-relativistic corpuscle optics. A theory of ideal time and space-time focusing encompassing and systematizing all known particular cases of such focusing is developed. Necessary and sufficient conditions of isochronous motion and requirements for inner symmetry of motion (the latter increasing with the growth of the quality of focusing) are determined. It is shown that the obtained results make it possible to realize an adequate choice of harmonic fields for constructing the time-of-flight apparatus. They can also be used to determine the accuracy of field sustaining according to the known time-focusing properties.

Quasi-classical trajectory-coherent approximation in quantum mechanics of a charged particle in a curved spacetime

Abstract: Using Maslov's complex sprout method the complete set of quasiclassical trajectory-coherent quantum states (TCS) for the Klein-Gordon equation in a curved spacetime in the presence of external electromagnetic and background scalar fields up to the order of O(32/) at to 0 was constructed. The approximate solutions Psi v are strongly peaked around the worldline neighbourhood of the charged particles. The method of reducing the initial Klein-Gordon equation to the Schrodinger type equation for which Psi v are exact solutions has been developed. In the quasi-classical trajectory-coherent approximation based on the ' gamma -reconstruction' technique the concept of the local time for a quantum scalar particle in a curved spacetime has been suggested. In general it has been stated that the constructed TCS Psi v permit the standard quantum-mechanical interpretation.

Vectorial Analysis of the Gaussian Beams of Light

Abstract: The scalar theory of Gaussian beams is an approximation to describe narrow beams of light. A vectorial analysis is required to describe the electromagnetic fields in the focal region with a small spot size. Maxwell's equations are solved to obtain the longitudinal as well as the transversal components of field vectors in a beam of light propagating along an axis. Solutions of the electromagnetic fields of either the plane-polarized-electric (and magnetic) or the transeverse-electric (and magnetic) modes are expressed in terms of Hermite-Gaussian functions. Magnitudes of the longitudinal field components in these modes are evaluated in particular.