Showing papers on "Scalar field published in 1983"

Nonlinear scalar field equations, I existence of a ground state

Abstract: 1. The Main Result; Examples . . . . . . . . . . . . . . . . . . . . . . . 316 2. Necessary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 319 3. The Constrained Minimization Method . . . . . . . . . . . . . . . . . . 323 4. Further Properties of the Solution . . . . . . . . . . . . . . . . . . . . 328 5. The \"Zero Mass\" Case . . . . . . . . . . . . . . . . . . . . . . . . . 332 6. The Case of Dimension N = 1 (Necessary and Sufficient Conditions) . . . . . 335 Appendix. Technical Results . . . . . . . . . . . . . . . . . . . . . . . . 338

Coherent scalar-field oscillations in an expanding universe

Abstract: Motivated by the cosmological importance of coherent (classical), scalar-field oscillations in the context of the invisible axion and the new inflationary-universe scenario, we analyze, in general, the classical evolution of a scalar field in an isotropic and homogeneous cosmology. For a scalar potential of the form $V(\ensuremath{\varphi})=a{\ensuremath{\varphi}}^{n}$, the energy density of the scalar-field oscillations decreases as ${R}^{\ensuremath{-}\frac{6n}{(n+2)}}$ when the oscillations are rapid compared to the expansion rate ($R=\mathrm{cosmic}\mathrm{scale}\mathrm{factor}$). We also investigate the effect of higher-order terms in the potential perturbatively, and analyze the decay of the coherent field oscillations due to quantum particle creation.

Lines of circular polarization in electromagnetic wave fields

Abstract: A monochromatic fully polarized electromagnetic wave propagating in free space possesses, in general, two families of singular lines ( C lines) on which the transverse field is circularly polarized. The distribution of polarization ellipses around a C line shows that it obeys the same classifi­cation scheme as the isotropic points of a two-dimensional symmetric tensor: that is, a given section of a C line may belong to one of three different line patterns and it may be elliptic or hyperbolic. In addition it may be left-or right-handed. However, the way in which the polarization ellipses are executed in time shows that C lines may also be regarded as singularities of phase, analogous to line dislocations or interference fringes in scalar waves. From this point of view, a given line is of edge or screw type, according to its orientation, or, more generally, is a curved line of mixed edge-screw type. The whole field is divided into regions of opposite hand by surfaces S of linear polarization, and each family of C lines is confined to just one of these regions.

Transport effects associated with turbulence with particular attention to the influence of helicity

Abstract: The action of turbulence on a passive convected scalar field (e.g. temperature) or vector field (e.g. the magnetic field in an electrically conducting fluid) is reviewed, with particular attention paid to anomalous effects that can arise through the influence of Coriolis forces in a rotating system on the statistics of the turbulence. The simplest such effect (which corresponds to a breaking of the Onsager symmetry relations) is a 'skew-diffusion' effect, i.e. the appearance of a component of turbulent heat flux perpendicular to the local mean temperature gradient. The famous alpha effect of magnetohydrodynamic dynamo theory is also in this category, as is the more subtle Radler effect (the appearance of a mean electromotive force perpendicular to the mean current in a plasma). These effects are all associated with the helicity of a turbulent flow, i.e. the correlation between the velocity field u(x,t) and the vorticity field omega (x,t)=curl u.

Scalar-tensor theories of gravitation: Foundations and prospects

Abstract: A generalization of Einstein's theory is discussed in which the gravitation is described by a tensor and a scalar field. The theory is more consistent with Mach's principle and less reliant on absolute properties of space. The modification involves a violation of the “strong principle of equivalence” on which Einstein's theory is based. In the original version of this new theory, the “constant” of gravitationG is varying and particle masses are fixed. Later on another version of the theory was given in whichG is truly a constant and the particle masses vary. The two versions are related by a conformal transformation. The physical and mathematical foundations of this theory have been discussed and the field equations have been derived. The astrophysical and cosmological consequences of the theory have been elaborately reviewed.

Turbulent time scales and the dissipation rate of temperature variance in the thermal mixing layer

Abstract: In a turbulent flow where the mechanisms and/or the importance of the generation processes of turbulent kinetic energy k and mean square scalar variance ∼(c2) are dissimilar, no simple connection exists between the turnover time scale of the fluctuating velocity and fluctuating scalar fields. To allow the computation of the turbulent scalar field in these situations a means of calculating the scalar time is required. Here, in an extension of work by Newman, Launder, and Lumley [J. Fluid Mech. 111, 217 (1981)], the time scale is obtained via a proposed transport equation for the dissipation rate of mean square scalar variance. The modeled equation has been applied successfully to the calculation of the spread of a thermal mixing layer in grid‐generated turbulence and the decay of temperature variance in a homogeneous field.

The initial value formulation of higher derivative gravity

Abstract: The initial value problem is considered for the conformally coupled scalar field and higher derivative gravity, by expressing the equations of each theory in harmonic coordinates. For each theory it is shown that the (vacuum) equations can take the form of a diagonal hyperbolic system with constraints on the initial data. Consequently these theories possess well‐posed initial value formulations.

Paraxial-wave optics and relativistic front description. II. the vector theory

Abstract: With the extension of the work of the preceding paper, the relativistic front form for Maxwell's equations for electromagnetism is developed and shown to be particularly suited to the description of paraxial waves. The generators of the Poincare group in a form applicable directly to the electric and magnetic field vectors are derived. It is shown that the effect of a thin lens on a paraxial electromagnetic wave is given by a six-dimensional transformation matrix, constructed out of certain special generators of the Poincare group. The method of construction guarantees that the free propagation of such waves as well as their transmission through ideal optical systems can be described in terms of the metaplectic group, exactly as found for scalar waves by Bacry and Cadilhac. An alternative formulation in terms of a vector potential is also constructed. It is chosen in a gauge suggested by the front form and by the requirement that the lens transformation matrix act locally in space. Pencils of light with accompanying polarization are defined for statistical states in terms of the two-point correlation function of the vector potential. Their propagation and transmission through lenses are briefly considered in the paraxial limit. This paper extends Fourier optics and completes it by formulating it for the Maxwell field. We stress that the derivations depend explicitly on the "henochromatic" idealization as well as the identification of the ideal lens with a quadratic phase shift and are heuristic to this extent.

Gaussian approximation for noncircular fibers

Abstract: The weak-guidance approximation, described in Chapter 13, greatly simplifies the determination of the modal fields of optical waveguides, because it depends on solutions of the scalar wave equation, rather than on vector solutions of Maxwell’s equations For circular fibers, with an arbitrary profile, the scalar wave equation must normally be solved by purely numerical methods We discussed the few profiles that have analytical solutions in Chapter 14 These solutions, including those for profiles of practical interest such as the step and clad power-law profiles, are given in terms of special functions or by series expansions, which usually necessitate tables or numerical evaluation to reveal the physical attributes of the modes

The energy-momentum tensor near a black hole

Abstract: The energy-momentum tensor for a conformally invariant scalar field near a Schwarzschild black hole in thermal equilibrium with radiation is found by a combination of analytical and numerical techniques Calculations are performed in the Euclidean section of the spacetime, and divergences isolated using the heat kernel expansion It is found that the results agree well with those of Candelas [1], but that there are significant differences from the Gaussian approximation of Page [2]

General Two Loop Beta Functions for Gauge Theories With Arbitrary Scalar Fields

Abstract: A renormalisation group beta function is defined for the scalar potential and is calculated to two-loop order for general gauge scalar field theories.

GRM: observing the terrestrial gravity and magnetic fields in the 1990's.

Abstract: NASA is proposing to launch a new geopotential fields exploration system called the Geopotential Research Mission (GRM). Two spacecraft will be placed in a circular polar orbit at 160 km altitude. Distances between these satellites will vary from 100 to 600 km. Both scalar and vector magnetic fields will be measured by magnetometers mounted on a boom positioned in the forward direction on the lead satellite. Gravity data will be computed from the measured change in distance between the two spacecraft. This quantity, called the range-rate, will be determined from the varying frequency (Doppler shift) between transmitter and receiver on each satellite. Expected accuracies (at the one-sigma level) are: gravity field, 1.0 milliGal, 5 cm geoid height; magnetics, scalar field 2 nT, vector to 20 arcsec, both resolved to less than 100 km. With these more accurate and higher resolution data, it will be possible to investigate the earth's structure from the crust (with the shorter wavelength gravity and magnetic anomalies) through the mantle (from the intermediate wavelength gravity field) and into the core (using the longer wavelength gravity and magnetic fields).

General vacuum-universe solutions in Brans-Dicke cosmology

Abstract: By a rescalation of the scalar field ϕ of the Jordan-Brans and Dicke cosmology, the general solutions of the Friedmannian ‘vacuum’ Universe are obtained. Only the flat space solution was previously known. Each solution is caracterized by the sign of the second time derivative of the rescaled field ψ≡ϕR3 (R being the scale factor of the Robertson-Walker line-element):\(\ddot \psi\) = 0 (flat space),\(\ddot \psi\) 0 (open space), so that the solutions are mutually exclusive. Of these, the open space one is damped-oscillatory andR attains its absolute minimum, equal to zero, in only one of the two ‘extreme’ cycles. Otherwise,R min remains positive. If the ϕ-field is dominant near the singularity, these solutions may have physical significance.