Showing papers on "Scalar potential published in 1982"
CERN1
TL;DR: In this paper, spontaneous compactification in pure higher dimensional gravity was studied and examples for spontaneous compactment in pure high dimensional gravity were presented, and it was shown that invariant at least in second order of the curvature tensor have to be included in the action in order to stabilize the scalar potential.
74 citations
TL;DR: In this paper, a method for mapping the Sun's magnetic field B from the photosphere through the corona and interplanetary space is presented, which entails the derivation of B from a scalar potential within a current-free annular volume bounded inside by photosphere and outside by a prescribed nonspherical source surface to which B is made (as nearly as possible) perpendicular.
Abstract: A new method for mapping the Sun's magnetic field B from the photosphere through the corona and interplanetary space is presented. The method entails the derivation of B from a scalar potential within a current-free annular volume bounded inside by photosphere and outside by a prescribed nonspherical source surface to which B is made (as nearly as possible) perpendicular. As usual we obtain the potential for the part of B that arises from currents inside the Sun by fitting an expansion to the observed line-of-sight component of B at the photosphere. A second least-squares fit is introduced to obtain the part of B that arises from currents outside the source surface. Comparisons are made between this model and observed coronal and interplanetary structures. There is evidence that observation data underestimate the strength of photospheric polar magnetic fields.
52 citations
TL;DR: In this paper, the boundary conditions for the scalar potential and each of the components of the vector potential were determined for a two-dimensional eddy current problem with variable electric conductivity.
Abstract: In calculating eddy currents in a conductor by means of the vector potential for which the Coulomb Gauge is used, the scalar potential appears when the electric conductivity varies in the conductor, while it is not necessary for the case of the constant electric conductivity. As the field equation is a Helmholtz-type equation under the Coulomb Gauge condition, we must determine the boundary conditions for the scalar potential and each of the components of the vector potential. How to determine the boundary conditions is presented, together with an illustrative example of a two-dimensional eddy current problem with the variable electric conductivity.
50 citations
TL;DR: In this paper, the spatial gradient of geomagnetic perturbations at high latitudes is used to infer the ionospheric current distribution, and the ratio of ΔB∥ and ΔB⊥ depends on the height of satellite measurement and also on the electric conductivity of the ionosphere.
Abstract: MAGSAT data revealed the following characteristics of geomagnetic perturbations at high latitudes: Parallel (ΔB∥) and transverse (Δ B⊥→, especially geomagnetic east-west component) magnetic perturbations represent respectively scalar potential field (due primarily to electric currents within the ionosphere) and vector potential field (attributable to field-aligned currents and associated ionospheric currents). The spatial gradient of ΔB∥ is shown to be very useful to infer the ionospheric current distribution. The ratio of ΔB∥ and ΔB⊥ depends on the height of satellite measurement and also on the electric conductivity of the ionosphere.
27 citations
TL;DR: In this paper, the geomagnetic field in the near-earth magnetotail is discussed, taking into account the calculation of the field inside the magnetopause on the basis of the numerical integration of the Biot Savart integral.
Abstract: The geomagnetic field in the near-earth magnetotail is made up of three major contributions related to the dipole field, the magnetotail current system, and the magnetopause current system exclusive of the return currents in the magnetotail current system. The present investigation is concerned with the third contribution. The calculation of the magnetospheric field is discussed, taking into account the calculation of the field inside the magnetopause on the basis of the numerical integration of the Biot Savart integral. The representation of the field for distances greater than 10 earth radii on the dark side of the magnetosphere is considered. The field internal to the magnetopause is expressed as the negative gradient of a scalar potential which is expressed as a sum of solutions to Laplace's equation in cylindrical coordinates. The origin of coordinates is the earth.
23 citations
TL;DR: In this paper, a finite element equation system is set up for a non magnetic region using the Galerkin method, and the scalar potential φ is eliminated from the equation system in order to reduce the number of unknowns per node.
Abstract: A vector potential A and an electrical scalar potential φ are taken to describe the three dimensional eddy current problem. A finite element equation system is set up for a non magnetic region using the Galerkin method. The scalar potential φ is eliminated from the equation system in order to reduce the number of unknowns per node. Time dependent solutions for potentials and eddy currents can be obtained using a step by step procedure.
19 citations
TL;DR: In this paper, a finite element formulation based on a brick-shaped, second-order, subparametric finite element is proposed to solve complex scalar potential problems. But the authors do not consider the problem of complex Laplace's equation.
Abstract: Numerical solution methods for real conservative fields are abundant in the literature, but interest in complex potential problems has been very low. The author presents ideas that justify interest in complex scalar potentials. For instance, the ability to solve complex scalar potential problems is shown to be a prerequisite for the solution of general, three‐dimensional, magnetic vector potential problems. As another example, the electromagnetic properties of dielectrics, semiconductors, and magnetic materials can be described by complex material property tensors. The electric or magnetic scalar potential distribution in such media may be obtained from the complex Laplace’s equation. The paper examines three‐dimensional anisotropic complex potential problems and briefly describes a finite element formulation based on a brick‐shaped, second‐order, subparametric finite element. An example illustrates the method.
14 citations
TL;DR: In this paper, the scalar potential created by a point source is calculated numerically using the least-damped root approximation, which involves considering only two roots of the dispersion equation, corresponding to the oblique mode and to the cyclotron harmonic mode.
Abstract: Electrostatic radiation from a monopole antenna in a magnetoplasma is studied theoretically in the frequency range between the electron gyrofrequency and its second harmonic. The scalar potential created by a point source is calculated numerically using the least‐damped‐root approximation, which involves considering only two roots of the dispersion equation, corresponding to the oblique mode and to the cyclotron harmonic mode. The potential distribution can be understood as being due both to interference between these two modes and to diffraction of the cyclotron harmonic mode alone. Theoretical spatial distribution fit the experimental data. In particular, the theory confirms that cyclotron harmonic waves should be detectable in all directions from the source, as was observed experimentally. A good agreement with experimental data is shown by theoretical curves of constant phase and of constant amplitude. An approximate analytical model of the potential distribution is presented, and is compared with the numerical model and with experimental data. Finally, it is shown how such data can be interpreted to yield the electron density and temperature.
11 citations
TL;DR: In this article, the authors propose a fully conformal invariant theory describing gravity as a spontaneously broken theory, and show that Newton's constant is automatically generated at the tree approximation without introducing arbitrary forms for the scalar potential.
10 citations
TL;DR: In this article, the ground states of the supersymmetric SU(5) model were investigated and the explicit breaking of supersymmetry was shown to be tightly restricted to select the phenomenologically desired vacuum.
Abstract: We investigate in detail the groundstates of the supersymmetricSU(5) model. The explicit breaking of supersymmetry is shown to be tightly restricted to select the phenomenologically desired vacuum. If the model contains two or more generations, a breaking of supersymmetry by a cosmological constant yields a potential which is not bounded from below.
9 citations
TL;DR: In this article, the authors considered the linearized scalar potential formulation of the magnetostatic field problem in the parametric framework and proposed a reformulation of the continuous problem as a parametric boundary problem.
Abstract: We consider the linearized scalar potential formulation of the magnetostatic field problem in this paper. Our approach involves a reformulation of the continuous problem as a parametric boundary problem. By the introduction of a spherical interface and the use of spherical harmonics, the infinite boundary condition can also be satisfied in the parametric framework. The reformulated problem is discretized by finite element techniques and a discrete parametric problem is solved by conjugate gradient iteration. This approach decouples the problem in that only standard Neumann type elliptic finite element systems on separate bounded domains need be solved. The boundary conditions at infinity and the interface conditions are satisfied during the boundary parametric iteration.
TL;DR: In this article, the SU(2) Yang· Mills theory with scalar triplet was studied and the effective potential with one· loop correction was studied as a function of the magnetic field and a condensed scalar field.
Abstract: The effective potential with one· loop correction is studied as a function of the magnetic field and a condensed scalar field for SU(2) Yang· Mills theory with scalar triplet. For both cases of the massless scalars and the one of negative mass· squared, we obtain the same qualitative behaviors of the potentials. It is found that the minimum of the potential as a function of a magnetic field found by Savvidi changes to a mere saddle point when the condensation of the scalar is taken into account. The problem of the restoration of the broken symmetry is also discussed at a sufficiently large magnetic field.
TL;DR: An approach using finite element and augmented Lagrangian methods is presented, which takes into account the hysteresis loops of each material (head and medium) and improves the convergence time and the accuracy of the calculations.
Abstract: In order to optimize the design of conventional or thin film heads and to choose the more convenient medium, numerical analyses are generally used. Most of them use scalar potential or micromagnetic assumptions to simulate the head itself and the writing or reading processes. In order to improve the convergence time and the accuracy of the calculations with regard to the capabilities of the usual computers and to solve the complete problem, we have developed a method using the magnetic vector potential to make cleat the governing equations in the different steps of the writing process. An approach using finite element and augmented Lagrangian methods is presented, which takes into account the hysteresis loops of each material (head and medium).
TL;DR: In this article, the boundary condition contribution to the field equations is extended by solving term-by-term, and the inhomogeneous boundary conditions which appear are of a binary nature, i.e., they express relationships between potentials at distinct points.
Abstract: Many magnetic field problems involve axisymmetric boundary shapes, but excitations of an essentially arbitrary nonsymmetric nature. Often the current-carrying coils or conductors occupy a space sufficiently small to be considered as thin sheets or filaments. In such cases the magnetic field may be formulated in terms of a scalar potential, with inhomogeneous boundary conditions that account for the presence of current sheets. Any asymmetry of these boundary values can be accommodated by expanding the boundary condition contribution to the field equations as a series and solving term by term. The inhomogeneous boundary conditions which thus appear are of a binary nature, i.e., they express relationships between potentials at distinct points. Such conditions are readily included in a finite element model. The techniques for so doing are developed in detail, and a practical example of their application is given by way of illustration.
01 Jul 1982
01 Jan 1982
TL;DR: Magnetostatics is generally developed in a different manner from electrostatics as discussed by the authors, due to the fact that the magnetic field has zero divergence, whereas the electric field have zero curl.
Abstract: Magnetostatics is generally developed in a different manner from electrostatics. This is due to the fact that the magnetic field has zero divergence, whereas the electric field has zero curl.
26 Feb 1982
TL;DR: In this article, a description of a wavefront was obtained as a general solution of the eikonal equation by means of some standard techniques in differential geometry, which led to the description of the general caustic.
Abstract: Several years ago we published some results concerning the structure of geometrical wavefronts in a homogeneous medium. A description of a wavefront was obtained as a general solution of the eikonal equation. By means of some standard techniques in differential geometry this led to the description of the general caustic. This in turn led us to the study of the geometric aberrations of an optical system from a completely different point of view. These results also suggest an approach to the physics of. the Propagation of light in a homogeneous medium which ought to lead to a proper vector diffraction theory. Recall Hertz' approach to the problem of the spherical wavefront in which he transformed the Maxwell equations into wave equations for the vector and scalar potential functions. To apply these to the spherical wavefront he transformed the arguments of the aradient, divergence and curl operators to a spherical coordinate system. The near-field solution of the wave equation predicted the existence of the dipole oscillator. The farfield solution yielded the now well-known description of the polarization and energy distribution on a spherical wavefront. Present work involves applying these same techniques to the general wavefront obtained as a solution of the eikonal equation. The vector differential operators have been transformed to an appropriate generalized coordinate system. The wave equation for the Potential functions have been obtained and an intermediate integral has been found. As is stands at the present time the electric and magnetic vectors can be expressed in terms of this intermediate integral.© (1982) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
TL;DR: For a static dust distribution charged in both the electric and scalar sense, it was shown in this paper that the sum of squares of these two types of charge densities must be either greater than or equal to the square of the mass density, when the scalar potential is a function of the electrostatic potential.
Abstract: For a static dust distribution charged in both the electric and scalar sense the authors prove that the sum of squares of these two types of charge densities must be either greater than or equal to the square of the mass density, when the scalar potential is a function of the electrostatic potential. In the absence of either the electrical or scalar field the equality sign holds. In general, if there is no singularity in the matter distribution the three-space is conformally Euclidean. They show how to generate a special class of exact solutions of empty space in the presence of electrostatic and zero mass scalar fields and some properties are discussed. Finally they present two exact spherically symmetric solutions as examples.