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Showing papers on "Scalar potential published in 1984"


Journal ArticleDOI
TL;DR: In this article, a volume integral equation is formulated and solved by using the method of moments for calculating the electromagnetic scattering from and internal field distribution of arbitrarily shaped, inhomogeneous, dielectric bodies.
Abstract: A method for calculating the electromagnetic scattering from and internal field distribution of arbitrarily shaped, inhomogeneous, dielectric bodies is presented. A volume integral equation is formulated and solved by using the method of moments. Tetrahedral volume elements are used to model a scattering body in which the electrical parameters are assumed constant in each tetrahedron. Special basis functions are defined within the tetrahedral volume elements to insure that the normal electric field satisfies the correct jump condition at interfaces between different dielectric media. An approximate Galerkin testing procedure is used, with special care taken to correctly treat the derivatives in the scalar potential term. Calculated internal field distributions and scattering cross sections of dielectric spheres and rods are compared to and found in agreement with other calculations. The accuracy of the fields calculated by using the tetrahedral cell method is found to be comparable to that of cubical cell methods presently used for modeling arbitrarily shaped bodies, while the modeling flexibility is considerably greater.

887 citations


Journal ArticleDOI
TL;DR: In this paper, for spacetimes of arbitrary dimension, the general two-derivative gravity plus scalar field theory allowing anti-de Sitter space as a solution was considered.

243 citations


Journal ArticleDOI
TL;DR: In this paper, the conditions on the effective (de Sitter space) scalar potential that are required to obtain a successful new-inflationary-Universe scenario are codified into a general prescription, which ensures that sufficient inflation, density fluctuations of an acceptable magnitude, and reheating to a high enough temperature to produce the astrophysically observed baryon asymmetry result.
Abstract: The conditions on the effective (de Sitter space) scalar potential that are required to obtain a successful new-inflationary-Universe scenario are codified into a general prescription. These conditions ensure that sufficient inflation, density fluctuations of an acceptable magnitude, and reheating to a high enough temperature to produce the astrophysically observed baryon asymmetry result. We exemplify our prescription for a quartic potential and show that if the scalar field is a gauge singlet, then it is possible to tune the parameters of the potential to satisfy the conditions we have prescribed.

190 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated the possibility of spontaneous T violation arising from complex vacuum expectation values with calculable phases, assuming geometrical values, entirely determined by the symmetry of the scalar potential.

135 citations


Journal ArticleDOI
TL;DR: In this paper, a new coordinate system is defined on the scalar manifold of N = 8 supergravity, which enables one to obtain scalar potential, V, and the T-tensor in closed form in both N = 6 and n = 8 gauged supergravity.

126 citations


Journal ArticleDOI
TL;DR: In this article, the two parameter scalar potential of the gauged d = 7 simple (N = 2) supergravity theory has been analyzed and the latter provides a supersymmetric anti-deSitter background which is stable with respect to arbitrarily large fluctuations of the gravitational and scalar fields.

53 citations


Journal ArticleDOI
TL;DR: In this paper, the supersymmetric σ-model for an arbitrary hyper-Kahler manifold, and its minimal coupling to super-Yang-Mills theory, was constructed.

53 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that there are background solutions with abelian electric and magnetic fields and space-time geometry which is a product of two-dimensional anti-de Sitter space and the 2-sphere 2 × S 2.

52 citations


Journal ArticleDOI
TL;DR: In this article, an improved Vorticity-Vector Potential (VVPP) formulation is presented for incompressible flows in ducts of constant but arbitrary cross sections, which essentially removes the problem source by eliminating the necessity of a Scalar Potential.

46 citations


Journal ArticleDOI
TL;DR: In this paper, the exact solutions of the Dirac equation with a linear scalar confining potential in a uniform electric field are given, and it is found that, if the scalar potential is stronger than that of the electric field, confinement is permanent.
Abstract: The exact solutions of the Dirac equation with a linear scalar confining potential in a uniform electric field are given. It is found that, if the scalar potential is stronger than that of the electric field, confinement is permanent. On the contrary, if the electric field is strong enough, confinement is impossible due to the Klein paradox.

41 citations


Journal ArticleDOI
TL;DR: In this article, the shape factors necessary to compute the scalar magnetic potential from single and double layers and the magnetic fields from the single layers using integral equations with linear varying sources were given.
Abstract: Analytic formulas are given for the shape factors necessary to compute the scalar magnetic potential from single and double layers and the magnetic fields from the single layers using integral equations with linear varying sources. The formulas apply to triangular elements of the polyhedral body comprising the problem geometry. Several problems have been analyzed; the computed results compare favorably with existing approximate theory, experimental data, and other integral equation formulations.

Journal ArticleDOI
TL;DR: In this paper, the gauge-invariant approach to the potential via the Wilson loop is generalized, replacing the static sources by the appropriate Dirac currents, and the resulting expression is expanded with respect to l/m2 and then brought into a suitable form.
Abstract: The gauge-invariant approach to the potential via the Wilson loop is generalized, replacing the static sources by the appropriate Dirac currents. The resulting expression is expanded with respect to l/m2 and then brought into a suitable form. For the evaluation the only input we employ is the area law for large distances. This allows us to understand how the electric flux tube picture emerges in the case of moving quarks, and why magnetic terms do not contribute to spin-dependent corrections. The only surviving spin dependence is a spin-orbit term like that from a scalar potential, but with the opposite sign.

Journal ArticleDOI
M. L. Brown1
TL;DR: The algorithm is suitable for complex electromagnetic field problems where a magnetic scalar potential is to be calculated in a multiply connected region by an application of the Lebesgue Covering Theorem.
Abstract: An algorithm, for use on a digital computer, is explained for cutting multiply connected regions in three-dimensional space. The algorithm is suitable for complex electromagnetic field problems where a magnetic scalar potential, affected by current loops, is to be calculated in a multiply connected region. Problems in fluid dynamics with vorticity affecting a scalar potential, could also be attacked with this algorithm. Since finite element methods are ubiquitous in field calculations, the cuts of the space constructed by the algorithm should ideally correspond to the given discretization; this can be arranged by an application of the Lebesgue Covering Theorem, for which a second algorithm is provided.

Journal ArticleDOI
TL;DR: In this article, a vector potential arising from the motion of the lattice is introduced in addition to the scalar potential, which leads to a new Hamiltonian and a representation in which the important terms which lead to the experimentally observed spectroscopic changes with increasing temperature, are diagonal.
Abstract: Methyl groups in solids are representative of systems which exhibit tunnelling at low temperatures and thermally activated hopping motion at high temperatures. They exhibit very clearly all the features of the transition between free and thermally driven quantum tunnelling, the latter being describable in terms of classical hopping concepts. A satisfactory theoretical description has been lacking because the usual approaches, which treat the dynamic part of the scalar hindering potential by time-dependent perturbation theory are, the author suggest, incomplete. It is shown that a better description is possible if a vector potential arising from the motion of the lattice is introduced in addition to the scalar potential. This leads to a new Hamiltonian and a representation in which the important terms, which lead to the experimentally observed spectroscopic changes with increasing temperature, are diagonal. In this new representation a simple model emerges which exhibits most, if not all, of the observed experimental features. It also resolves an old problem: how to reconcile the quantum mechanical requirement that the rotation angles phi =0 and phi =2 pi are identical, with the classical assumption that they are distinguishable, and thus provides a bridge between the quantum and classical descriptions of rotation.

Journal ArticleDOI
TL;DR: In this article, the N = 2 scalar potential of the complex scalar fields in the adjoint representation, superpartners of the Yang-Mills gauge fields, splits into a conventional gauge contribution as well as in a superpotential term contribution proportional to the SO(2) gauge coupling of N =2 de Sitter supergravity.

Journal ArticleDOI
TL;DR: In this paper, the authors constructed the orbit space of low-dimensional representations of classical and exceptional Lie groups and tabulated the orbit spaces of two irreducible representations with different shapes, and showed that the observed structure implies that a physical system tends to retain as much symmetry as possible in a symmetry breaking process.
Abstract: Orbit spaces of low-dimensional representations of classical and exceptional Lie groups are constructed and tabulated. We observe that the orbit spaces of some single irreducible representations (adjoints, second-rank symmetric and antisymmetric tensors of classical Lie groups, and the defining representations of F4 and E6) are warped polyhedrons with (locally) more protrudent boundaries corresponding to higher level little groups. The orbit spaces of two irreducible representations have different shapes. We observe that dimension and concavity of different strata are not sharply distinguished. We explain that the observed orbit space structure implies that a physical system tends to retain as much symmetry as possible in a symmetry breaking process. In Appendix A, we interpret our method of minimization in the orbit space in terms of conventional language and show how to find all the extrema (in the representation space) of a general group-invariant scalar potential monotonic in the orbit space. We also present the criterion to tell whether an extremum is a local minimum or maximum or an inflection point. In Appendix B, we show that the minimization problem can always be reduced to a two-dimensional one in the case of the most general Higgs potential for a single irreducible representation and to a three-dimensional one in the case of an even degree Higgs potential for two irreducible representations. We explain that the absolute minimum condition prompts the boundary conditions enough to determine the representation vector.

Journal ArticleDOI
TL;DR: In this paper, a four component formulation is used to solve general three dimensional eddy currents, where the unknowns are the three components of magnetic vector potential A, and the scalar electric potential φ.
Abstract: A method to solve general three dimensional eddy currents is presented. A four component formulation is used. The unknowns are the three components of magnetic vector potential A, and the scalar electric potential φ. A discussion of the role of the scalar potential in insuring the continuity of the eddy currents is included. The method is formulated using eight noded brick finite elements. Several examples are given which illustrate the validity of the formulation.

Journal ArticleDOI
TL;DR: In this article, the relativistic imaginary optical potential is calculated to lowest order in nuclear matter for the exchange of σ-, ω- and π-mesons.

Journal ArticleDOI
TL;DR: In this paper, the authors compute finite temperature corrections to the scalar potential in maximally symmetric SU(N, 1) supergravity and show that in the large N limit, the zero temperature potential is only scaled by the thermal corrections.

Journal ArticleDOI
TL;DR: In this article, a method for finding the effective potential in an external gravitational field on the basis of the equation of a renormalized group is proposed, and the effect of quantum corrections on spontaneous symmetry violation is discussed.
Abstract: A method is proposed for finding the effective potential in an external gravitational field on the basis of the equation of a renormalized group. The effective potential is found in the single-loop approximation for the scalar field theory and for the asymptotically free theory containing non-Abelian calibration fields, scalars, and spinors with an arbitrary value of the parameter of nonminimal coupling between the scalar and gravitational fields. The effect of quantum corrections on spontaneous symmetry violation is discussed.

Journal ArticleDOI
TL;DR: In this article, the authors derived a multipole expansion for an interaction hamiltonian for a charged particle moving in a non-uniform static magnetic field and showed that the interaction Hamiltonian is proportional to the angular momentum as in the case of uniform magnetic field.
Abstract: Derives a multipole expansion for an interaction hamiltonian for a charged particle moving in a non-uniform static magnetic field. It is shown that the interaction hamiltonian is proportional to the angular momentum as in the case of uniform magnetic field. As a prelude to the final result a means of conversion is established between the scalar potential and the vector potential and multipole expansion of the magnetic vector potential inside a sphere of radius R is obtained.

Journal ArticleDOI
TL;DR: Franklin and Lidiard as mentioned in this paper extended the kinetic theory of isothermal solid state diffusion to describe atomic transport in such isothermal systems under the influence of external scalar potential fields (for example, electric, gravitational, centrifugal fields).
Abstract: The general formulation of the kinetic theory of isothermal solid state diffusion applicable to systems showing small degrees of vacancy and interstitial disorder that was presented in a previous paper (Franklin & Lidiard, Proc. R. Soc. Lond . A 389, 405-431 (1983)) is here extended to describe atomic transport in such isothermal systems under the influence of external scalar potential fields (for example, electric, gravitational, centrifugal fields). For steady fields the results verify the correctness of the phenomenological equations suggested for solid state transport processes by the theory of non-equilibrium thermodynamics and provide expressions for the phenomenological transport coefficients L ij in terms of microscopic quantities characterizing the defect species and their movements. In particular, it is shown that the same expressions for these transport coefficients are obtained from the atomic fluxes coming from ‘drift’ under applied fields, as from diffusion arising from imposed concentration gradients. The dielectric response function for use with time-dependent fields is also obtained. It is made up of two parts; one corresponding to the d. c. conductivity, the other to a set of Debye relaxation modes. It is demonstrated that the occurrence of association and dissociation reactions among the defects influences both the relaxation times and the strengths of these modes. A brief examination of the example of solute-vacancy pairs in a f. c. c. lattice shows that these influences can be substantial and qualitatively significant.

Journal ArticleDOI
TL;DR: In this article, a new method for approximating magnetostatic field problems is given, which is based on a volume integral formulation, and convergence results in actual computations are compared with results for the usual volume integral method used in GFUN3D.
Abstract: A new method for approximating magnetostatic field problems is given in this paper. The new method approximates the scalar potential for the magnetic intensity and is based on a volume integral formulation. The derivation of the new computational method uses the spectral properties of the relevant integral operator. The corresponding algorithm is similar to that obtained from coupled differential and boundary integral approaches. Conver- gence and stability theorems are proven. Finally, convergence results in actual computations are compared with results for the usual volume integral method used in GFUN3D. 1. Introduction. In this paper we define a new numerical method for magnetostatic field computation. We specifically consider the problem of calculating the nonlinear static field effects produced by the presence of iron-type materials. Applications for these problems occur in, for example, the design of accelerator and beam control magnets, fusion devices, electric motor design, and magnetic tape head design. A variety of numerical methods for the solution of magnetostatics problems have been proposed and some general purpose codes have been produced (1), (2), (4), (5), (8), (12), (13). For examples of magnetic field calculations, see (4), and the references therein. The magnetostatic field problem can be stated as an elliptic interface problem and the analysis presented in (3), (8) is applicable. Integral formulations of this problem have also been considered (6), (11). In this paper, a new scalar potential integral formulation of the nonlinear magnetostatic field problem is defined and analyzed. To motivate the new method, we give an analysis for constant permeability problems which shows that the large errors in the iron domain observed with the usual volume integral method lie in subspaces perpendicular to gradient functions. The new method is designed to eliminate errors of this type while generalizing to a method for nonlinear problems which exhibits uniform convergence in the iron domain even as the permeability becomes uniformly large. The new method is derived as a volume integral formulation which approximates the magnetic intensity H in terms of the gradient of a scalar potential. It is then

Journal ArticleDOI
TL;DR: In this paper, exact regular axisymmetric multi-wormhole solutions of the Einstein-Maxwell scalar field equations are generated from corresponding solution of the EIFE, and their interpretation as multi-particle systems is discussed.
Abstract: Exact regular axisymmetric multi-wormhole solutions of the Einstein-Maxwell scalar field equations are generated from corresponding solutions of the Einstein scalar field equations, and their interpretation as multi-particle systems is discussed.

Journal ArticleDOI
TL;DR: In this paper, the authors studied a homogenization problem for a time periodic boundary value problem concerning the quasi-stationary Maxwell equations with a non linear monotone magne tic characteristic.
Abstract: In this paper we study a homogenization problem for a time periodic boundary value problem concerning the quasi-stationary Maxwell equations with a non linear monotone magne tic characteristic. The main features of the problem are related to the vanishing of the conductivity inside each period so that the type of the equations is rapidly oscillating. The unknowns are a vector potential and a scalar potential. We show that the first one converges to zero up to terms of second order, while the second one converges to the solution of a suitable homogenized stationary equation (with time as a parameter). We show moreover that when the magnetic characteristic is linear and symmetric the second order terms in the asymptotic expansion of the vector potential can be identified and related to the time derivative of the limit scalar potential.

Journal ArticleDOI
TL;DR: In this article, a method for including into the expansion coefficients the effects of iron on coil systems is described. But this method is specifically orientated towards cylindrical symmetry and is not suitable for the case of axisymmetric conductors.
Abstract: The scalar potential of any system of axisymmetric conductors can be expressed in terms of Legendre polynomials. This paper describes a method for including into the expansion coefficients the effects of iron on coil systems. Although the basis of the method is taken from the Rutherford Laboratory program GFUN the approach is specifically orientated towards cylindrical symmetry. The iron is divided into small cylindrical elements for which the magnetisation and permeability are determined. These elements are then used to calculate the coefficients of the Legendre polynomial expansion of the potential due to the iron. The accuracy of the method is gauged by comparing the results with an analytical solution.

Journal ArticleDOI
TL;DR: In this paper, it was established that the inverse square relation is determined by more elementary properties of the field and of the source function to which it relates, and that the Newtonian gravitational and Coulombic electrostatic fields are the classical examples.
Abstract: Helmholtz’ theorem is a profound mathematical theorem which provides the definitive relationship between a vector field and mathematically defined source functions. The usual presentations of electromagnetic theory establish the principle sources of the electromagnetic field vectors, but leave the question of completeness unanswered, that is, whether all sources are included. Helmholtz’ theorem provides the basis for investigating the existence of other possible sources, and in at least one case shows a possible source not normally considered. Helmholtz’ theorem also provides a significant result pertaining to the meaning of the inverse square radial field, of which the Newtonian gravitational and Coulombic electrostatic fields are the classical examples. It can be established that the inverse square relation is determined by more elementary properties of the field and of the source function to which it relates.

Journal ArticleDOI
TL;DR: In this paper, a new potential ψ which is defined as the correlative potential is developed, which is different from the classical scalar potential ϕ and the vector potential developed by Helmholtz.
Abstract: This paper is a continuation of Paper [1]. 1. A new potential ψ which is defined as the correlative potential is developed in this paper. The potential ψ is different from the classical scalar potential ϕ and the vector potential\(A\) developed by Helmholtz. The new formulae of the solution of eqs.\( abla \times \mathop f\limits^ \to = \mathop \infty \limits^ \to . abla \cdot \mathop f\limits^ \to = p\) are given in terms of ψ. 2. In the time-varying electromagnetic field, two new retarded potentials, the electric type retarded correlative potential ψe and the magnetic type retarded correlative potential ψe, which are distinct from the classical retarded potentials\(A\) and ϕ, are used to solve Maxwell equations. The new formulae of solution of Maxwell equation are given in terms of ψe and ψm. 3. The methods for constructing a rotational field with given curl function (vorticity) is proposed.

Journal ArticleDOI
01 Nov 1984
TL;DR: In this article, the Schottky model is extended through the use of the Thomas-Fermi approximation; the relevant differential equation for the electric scalar potential is solved and through it an estimate of the work function for metals is obtained.
Abstract: The Schottky model is extended through the use of the Thomas-Fermi approximation; the relevant differential equation for the electric scalar potential is solved and through it an estimate of the work function for metals is obtained.

Journal ArticleDOI
TL;DR: In this paper, the basic equations for the vector potential method and for an extended scalar potential method are derived and the duality of both methods is shown. And the superior applicability of the ESP method for 3D magnetostatic field calculation is derived and recent results obtained for a superconducting coil are described.
Abstract: This paper addresses the problem of the numerical calculation of three-dimensional magnetostatic fields. The basic equations for the vector potential method and for an extended scalar potential method are derived and the duality of both methods is shown. The superior applicability of the extended scalar potential method for three-dimensional field calculation is derived and recent results obtained for a superconducting coil are described.