Showing papers on "Scalar (physics) published in 1977"

Absorbing boundary conditions for acoustic and elastic wave equations

Abstract: Boundary conditions are derived for numerical wave simulation that minimize artificial reflections from the edges of the domain of computation. In this way acoustic and elastic wave propagation in a limited area can be efficiently used to describe physical behavior in an unbounded domain. The boundary conditions are based on paraxial approximations of the scalar and elastic wave equations. They are computationally inexpensive and simple to apply, and they reduce reflections over a wide range of incident angles.

A model for viscoelastic fluid behavior which allows non-affine deformation

Abstract: A continuum theory of viscoelasticity is developed which allows non-affine deformation, defined in an appropriate manner. The constitutive equation is a generalization of that obtained from molecular theory with the addition of one scalar parameter which becomes important for large deformations. The theory is applied to simple shear flows, the scalar parameter being determined to match certain experimental data. The theory shows good agreement with all data examined. The paper concludes with the development of a general non-affine thermodynamic theory.

Stress-tensor conformal anomaly for scalar, spinor, and vector fields

Abstract: The conformal trace anomalies for massless scalar, "neutrino," and photon fields propagating in an arbitrary Riemannian space-time are derived. They are seen to be a consequence of the subtraction, during renormalization, of a finite term, $\ensuremath{\sim}\mathrm{ln}({m}^{2}{L}^{2})$, which violates the scale invariance of the massless theory. A general derivation of the scalar anomaly is given based on the $\ensuremath{\zeta}$-function regularization developed earlier.

The prediction of turbulent diffusion flame fields and nitric oxide formation

Abstract: Several contributions are made to the numerical modelling of turbulent diffusion flames. The use of Favre averaging to account for the strong density differences is developed and together with the Favre form of the k el turbulence model is used to predict the flow and composition fields in hydrogen/air diffusion flames. The form of the probability density functions is found to have little effect on the velocity and conserved scalar mean fields but is more significant in determining mean temperatures and molecular species compositions. Nitric oxide formation is computed by means of the theory which relates non-equilibrium O-atom concentrations to the fine scale fluctuations in the turbulence. The results show much improvement over the equilibrium O-atom theory. Nitric oxide concentrations are particularly sensitive to the form of the probability density function.

Are Particle Rest Masses Variable? Theory and Constraints from Solar System Experiments

Abstract: We consider the possibility that particle rest masses may vary in spacetime. According to arguments originated by Dicke, if this is the case various null experiments indicate that all masses vary in the same way. Their variation relative to the Planck-Wheeler mass defines a universal scalar rest-mass field. We construct the relativistic dynamics for this field based on very general assumptions. In addition, we assume Einstein's equations to be valid in Planck-Wheeler units. A special case of the theory coincides with Dicke's reformulation of Brans-Dicke theory as general relativity with variable rest masses. In the general case the rest-mass field is some power $r$ of a scalar field which obeys an ordinary scalar equation with coupling to the curvature of strength $q$. The $r$ and $q$ are the only parameters of the theory. Comparison with experiment is facilitated by recasting the theory into units in which rest masses are constant, the Planck-Wheeler mass varies, and the metric satisfies the equations of a small subset of the scalar-tensor theories of gravitation. The results of solar system experiments, usually used to test general relativity, are here used to delimit the acceptable values of $r$ and $q$. We conclude that if cosmological considerations are not invoked, then the solar-system experiments do not rule out the possibility of rest-mass variability. That is, there are theories which agree with all null and solar-system experiments, and yet contradict the strong equivalence principle by allowing rest masses to vary relative to the Planck-Wheeler mass. We show that the field theory of the rest-mass field can be quantized and interpreted in terms of massless scalar quanta which interact very weakly with matter. This explains why they have not turned up in high-energy experiments. In future reports we shall investigate the implications of various cosmological and astrophysical data for the theory of variable rest masses. The ultimate goal is a firm decision on whether rest masses vary or not.

New Lorentz-invariant system with exact multisoliton solutions

Abstract: A Lorentz-invariant equation is derived for a scalar complex field in two-dimensional space-time. Exact two-soliton solutions are obtained for this equation and can be generalized in trivial fashion to include the case of N solitons.

A note on the body force integral of classical elastostatics

Abstract: A method of accounting for the influence of body force, which involves a surface rather than a volume integral, is shown to be available whenever the body force is derivable from a scalar with constant Laplacian.

A note on the inverse scattering problem in quantum field theory

Abstract: We study the set of local fields φ describing the dynamics of a scalar, massless particle. It turns out that these fields are relatively local to the free, massless, scalar fieldA if the massless particle does not interact. This leads to a simple algebraic characterisation of interacting fields in the above framework.

Interaction of isovector scalar mesons with simple sources

Abstract: A variational procedure using coherent states is shown to be superior to previous methods for treating the interaction of charged or isovector mesons with a static source. The technique is then applied to interaction with a Schr\"odinger field.

Null Field Approach to Scalar Diffraction. II. Approximate Methods

Abstract: We develop from our generalized null field method a generalization of the Kirchhoff, or physical optics, approach to diffraction theory. Corresponding to each particular null field method there is a corresponding physical optics approximation, which becomes exact when one of the coordinates being used is constant over the surface of the scattering body. We show how to improve these approximations by a computational procedure which is more efficient than those introduced in the previous paper. The reradiations from our physical optics surface sources more nearly satisfy the extinction theorem the deeper they penetrate the interiors of scattering bodies. We find that we have to introduce a new definition of the parts of a body’s surface that are directly illuminated and shadowed, and we suggest that this may be more apposite in general than the usual definition. The computational examples presented herein indicate that useful approximations to surface source densities are obtained in the umbra and penumbra of bodies. These examples also show that our scattered fields are in several particulars superior to those obtained from the conventional Kirchhoff approach. It is important to choose that physical optics approximation most appropriate for the scattering body in question.

Neutron slowing down and transport in a medium of constant cross section. I. Spatial moments

Abstract: Some aspects of the problem of neutron slowing down and transport have been investigated in an infinite medium consisting of a single nuclide scattering elastically and isotropically without absorption and with energy‐independent cross sections. The method of singular eigenfunctions has been applied to the Boltzmann equation governing the Laplace transform (with respect to the lethargy variable) of the neutron flux. Formulas have been obtained for the lethargy dependent spatial moments of the scalar flux applicable in the limit of large lethargy. In deriving these formulas, use has been made of the well‐known connection between the spatial moments of the Laplace‐transformed scalar flux and the moments of the flux in the ’’eigenvalue space.’’ The calculations have been greatly aided by the construction of a closed general expression for these ’’eigenvalue space’’ moments. Extensive use has also been made of the methods of combinatorial analysis and of computer evaluation, via FORMAC, of complicated sequenc...

Stationary axially symmetric coupled Einstein-Maxwell-scalar fields

Abstract: Solutions of the stationary axially symmetric coupled Einstein-Maxwell-scalar field equations can be generated from the corresponding static vacuum solutions, and in special cases they can be reduced to the already known static or stationary solutions by suitably choosing an integration constant.

Bound-state effective potential formulation of dynamical symmetry breaking

Abstract: We propose an approximation procedure for studying dynamical symmetry breaking that closely parallels scalar field models of spontaneous symmetry breaking. We focus our attention on the role a deep scalar bound state plays in effecting a phase transition. We show that a viable approximation to the effective potential must contain all one-particle-reducible bound-state pole structures. This dictates a Dyson equation for the self-energy even in the simplest approximation. For theories with 4-field interactions this can reduce to a closed-form Hartree approximation. We look at trilinear interactions where the Dyson integral equation is intractible because of its nonlinearity. Without linearizing the Dyson equation we extract a bound-state contribution to the effective potential. We end up with a generalized effective potential that is a function of classical fields representing the bound state. We show that this contribution displays the proper phase transition when the theory becomes unstable due to a composite tachyon.

Spherical Diffuse Yukawa Sources in Relativity

Abstract: A system containing only two diffuse massless sources (bearing a uniform ratio) of two different short range scalar fields is studied, according to Einstein's gravitational theory. One field is attractive, the other is repulsive. The distribution is in static equilibrium with spherical symmetry. A class of solutions of the field equations is obtained, where the solutions are nonsingular and have simple physical interpretation. A Schwarzschild-type gravitation is found at infinity, with the mass parameter solely arising from the scalar fields; these rapidly disappear with a Yukawa-type behaviour. The stability of the system is briefly stated, and the applicability of the model to large or small physical systems is pointed out.

Massless propagators on the light cone

Abstract: The propagators of free spin-0 and spin-1/2 fields are considered in two-dimensional light-cone coordinates. It is shown by explicit construction that although the differential equations for the propagators are identical to those conventionally obtained the solutions differ from the usual space-time form by the addition of terms dependent only upon the ''time'' coordinate. The results obtained are confirmed by recourse to the usual plane-wave expansions of the scalar and spinor fields.

Scalar propagators in a pseudoparticle field

Abstract: We derive the propagators for massless scalar particles of isospin \textonehalf{} and 1 in the field of an SU(2) pseudoparticle.