Showing papers on "Scalar potential published in 1988"
DOI•
01 Sep 1988TL;DR: In this paper, an integral formulation for eddy-current problems in nomagnetic structures is presented, where the solenoidality of the current density is assured by introducing a current vector potential T. This potential possesses only two scalar components, as the gauge chosen to ensure its uniqueness is T. u = 0, where u is a prescribed vector field.
Abstract: An integral formulation for eddy-current problems in nomagnetic structures is presented. The solenoidality of the current density is assured by introducing a current vector potential T. This potential possesses only two scalar components, as the gauge chosen to ensure its uniqueness is T. u = 0, where u is a prescribed vector field. The discrete analogue of this gauge and the boundary conditions are directly imposed by the shape functions, exploiting the use of edge finite elements and the methods of network theory. In the frame of the integral methods, this approach seems the most adequate to analyse the eddy currents induced in both massive conductors and thin shells. In massive structures, the two degrees of freedom are to be compared to four of the usual integral methods which exploit the presence of a scalar potential to ensure solenoidality. On the other hand, the procedure naturally reduces to the stream function approach when applied to thin shells. Finally, an integration procedure which guarantees symmetry and positive-definiteness of the inductance matrix is proposed.
178 citations
TL;DR: In this paper, the authors examined the most general theory describing a real scalar field coupled to Einstein gravity in four dimensions and obtained a general non-trivial form of the Bianchi identities for this theory.
Abstract: The author examines the most general theory describing a real scalar field coupled to Einstein gravity in four dimensions. The author shows that the stress tensor of the scalar field always has the structure of a fluid stress tensor. In the case that the scalar field is minimally coupled to gravity, this reduces to a perfect-fluid structure. In addition, the author obtains a generally non-trivial form of the Bianchi identities for this theory, investigates the kinematics of the scalar field and shows how to extend the analysis to include complex scalars and scalar multiplets. Finally, the author discusses the ground-state solutions of the theory, with special attention given to the case when the scalar field potential is polynomial in the fields. The author shows that the gravity-scalar coupling has interesting consequences for the spontaneous breakdown of gauge symmetries and for the observable value of the cosmological constant.
164 citations
TL;DR: In this article, new constraints on parameters are found to avoid charge and/or color-breaking minima and instability of the scalar potential in the minimal low energy supergravity model.
93 citations
TL;DR: In this paper, it is shown that the vacuum of the theory is a dilute gas of instanton-anti-instanton molecules, and the scalar vev is fixed from this potential by the minimization procedure.
91 citations
TL;DR: The boundary element calculation of three-dimensional magnetostatic field problems using the reduced and total magnetic scalar potential formulation is described in this paper, based on a boundary integral equation that can be derived from Green's theorem.
Abstract: The boundary-element calculation of three-dimensional magnetostatic field problems using the reduced and total magnetic scalar potential formulation is described. The method is based on a boundary integral equation that can be derived from Green's theorem. Two regions, a current-free iron region and an air region including the source domains, are considered. The material properties of the iron are assumed to be linear and either isotropic or anisotropic (orthotropic). Two examples are investigated: a C-shaped magnet and an iron cylinder of finite length immersed in the magnetic field of a cylinder coil. >
51 citations
TL;DR: In this paper, a transient 3D finite element model is presented based on the solution of the magnetic scalar potential in nonconducting regions and the magnetic vector potential and an electric scalar capacity in eddy-current regions.
Abstract: A transient 3-D finite-element model is presented. The method is based on the solution of the magnetic scalar potential in nonconducting regions and the magnetic vector potential and an electric scalar potential in eddy-current regions. Multiply connected regions of magnetic scalar can be avoided by extending the region modeled by the magnetic vector potential to fill any holes in the conducting regions. The model was used to simulate the FELIX brick experiment. >
41 citations
TL;DR: In this paper, a class of models exhibiting breaking of N = 4 supergravitt with matter down to N = 1 or N = 2 supergravity at zero cosmological constant was constructed.
41 citations
TL;DR: In this article, two methods for using the magnetic vector potential for 3D eddy current calculation are treated, one continuous over the entire region and generally accompanies the electric scalar potential, and another discontinuous across the interface surface between different media.
Abstract: Two methods for using the magnetic vector potential for 3-D eddy current calculation are treated. One method uses the magnetic vector potential that is continuous over the entire region and generally accompanies the electric scalar potential. It has the advantage that no cutting is necessary for the multiply-connected-region problem. The other method uses the magnetic vector potential that is discontinuous across the interface surface between different media. This magnetic vector potential can be arranged so that the electric scalar potential does not appear in the equations when the conductivity is constant. It has the disadvantage that cutting is necessary for the multiply-connected-region problem. New boundary value problem formulations are given for both methods, precisely defining the interface and boundary conditions. >
36 citations
TL;DR: In this article, a finite-element computer code, EDDY3DT, has been developed using this A-V formulation, which is effective for problems involving anisotropic and discontinuous conductivities, cracks, and holes.
Abstract: Three-dimensional eddy current equations are formulated in terms of a magnetic vector potential A and an electric scalar potential V in the conductive regions and a reduced magnetic scalar potential Omega in the nonconductive region. A finite-element computer code, EDDY3DT, has been developed using this A-V formulation. Application to test problems and comparison with the analytical solutions or results by other methods show that the A-V formulation is effective for problems involving anisotropic and discontinuous conductivities, cracks, and holes. >
36 citations
TL;DR: In this article, the results obtained with several three-dimensional software packages for magnetostatic field calculation using the finite element method (FEM) are compared with regard to their accuracy and their computational time requirements.
Abstract: The results obtained with several three-dimensional software packages for magnetostatic field calculation using the finite-element method (FEM) are compared with regard to their accuracy and their computational time requirements. The packages are based on the vector potential (VPOT), the reduced scalar potential (RSP), and the total and reduced scalar potential (TSP+RSP), respectively. Results for an iron cylinder immersed in the field of a cylindrical coil are given. It is found that the finite-element formulation using a total and reduced scalar potential and the direct iteration method are useful for dealing with nonlinear magnetostatic field problems. >
36 citations
TL;DR: In this article, the authors review the theories that they have used to develop two finite-element software packages, one using a magnetic vector potential combined with an electric scalar potential in conducting regions and only the magnetic vector vector potential elsewhere.
Abstract: The authors review the theories that they have used to develop two finite-element software packages. One uses a magnetic vector potential combined with an electric scalar potential in conducting regions and only the magnetic vector potential elsewhere. The second formulation is based on an electric vector potential and a magnetic scalar potential whereby only the latter is used in conducting regions. A way to obtain unique solutions by satisfying the divergence condition of the vector potentials is shown. Calculations for several problems are reported, showing the efficiency of the codes. The pros and cons of both formulation are discussed. >
TL;DR: A semirelativistic equation which describes the relative motion of a Dirac particle and its antiparticle, interacting through a scalar potential, linearly dependent on the relative distance is investigated.
Abstract: A semirelativistic equation which describes the relative motion of a Dirac particle and its antiparticle, interacting through a scalar potential, linearly dependent on the relative distance, is investigated. The simplest case, corresponding to /sup 1/S/sub 0/ and /sup 3/P/sub 0/ solutions, of total angular momentum J = 0 and positive and negative parities, respectively, is easily worked out for massless constituents. The case of massive constituents, which gives rise to a different regime, is also examined together with other salient features of our approach. A treatment of the light- and heavy-meson J = 0 sectors is briefly discussed.
TL;DR: In this paper, the authors used the continuous and discontinuous magnetic vector potential for 3D eddy current calculation in both the simply and multiply connected regions, and proposed a formulation using the discontinuous vector potential to solve the simply-connected region problem.
Abstract: Formulations using the continuous and discontinuous magnetic vector potential for 3-D eddy current calculation in both the simply and multiply connected regions are presented. The formulation using the continuous magnetic vector potential does not need cutting for the multiply-connected-region problem, but it needs the electric scalar potential. The formulation using the discontinuous magnetic vector potential does not need the electric scalar potential for the simply-connected-region problem, but it needs cutting for the multiply-connected region problem, so additional computation is required. Thus the former may suite the multiply-connected-region problem, while the latter may suit the simply-connected region problem. >
TL;DR: In this paper, a package named VECTOR for solving 3-D eddy current problems is presented, which is a developmental version of the commercial package CARMEN and in the same way solves the vector diffusion equation, involving a modified vector potential, within conductors and the scalar Poisson equation, using a magnetic scalar potential, in non-eddy-current regions.
Abstract: A package named VECTOR for solving 3-D eddy current problems is presented. The package is a developmental version of the commercial package CARMEN and in the same way solves the vector diffusion equation, involving a modified vector potential, within conductors and the scalar Poisson equation, using a magnetic scalar potential, in non-eddy-current regions. It has been shown that this set of equations yields a unique solution for both the magnetic vector potential (and hence the currents) and the fields (which are derived from the magnetic potentials by differentiation). This package has recently been extended to solve transient problems, using simple time-stepping techniques. Some results using the package for problems with analytic solutions are given. >
TL;DR: In this article, the Dirac equation has been used to analyse cross sections and analyze power data for inelastic scattering of 800 MeV protons from low-lying states in 16 O, 24 Mg and 26 Mg.
TL;DR: In this paper, the authors pointed out an error in the time-dependent cosmological term and the scalar potential given by Lau and Prokhovnik and derived the correct forms for these quantities.
Abstract: Recently Lau & Prokhovnik (1986) have formulated a new scalar-tensor theory of gravitation which reconciles Dirac’s large numbers hypothesis with Einstein’s theory of general relativity. The present work points out an error in the time-dependent cosmological term and the scalar potential given by Lau and Prokhovnik. The correct forms for these quantities are derived. Further, a vacuum Robertson-Walker solution to the generalized field equations is obtained, under an anasatz that we propose, which illustrates that the theory is, in some sense, incomplete.
TL;DR: In this article, the authors deal with the four-component three-dimensional finite-element analysis of a flux concentration model with four thick conducting plates placed between a pair of AC-excited coils.
Abstract: The authors deal with the four-component three-dimensional finite-element analysis of a flux concentration model with four thick conducting plates placed between a pair of AC-excited coils. An improved formulation that's based on the Galerkin method is used. The distributions of flux densities, eddy currents and scalar potentials are calculated, and the results are discussed. The role of the scalar potential in the 3-D analysis is clarified. It is shown to be necessary when treating a model including conductors with any discontinuity or gaps in the streamlines similar to the flow of the impressed currents. >
TL;DR: In this article, the magnetic field of long, straight conductors of arbitrary polygonal cross section, carrying current of given volume density, is modeled in terms of a distribution of fictitious magnetization inside each conductor and an equivalent distribution of magnetic surface charge.
Abstract: The magnetic field of long, straight conductors of arbitrary polygonal cross section, carrying current of given volume density, is modeled in terms of a distribution of fictitious magnetization inside each conductor and a distribution of fictitious surface current, using the Amperian model for magnetized media. Subsequently, this magnetization is replaced by an equivalent distribution of fictitious magnetic surface charge. As a result, the field calculation is reduced to that of the field due to a long strip of finite width, with simple distributions of surface charge and current. An elementary formula is derived for the field produced by a conductor of arbitrary polygonal cross section carrying a uniformly distributed current. The amount of computation is subsequently reduced compared to that needed for other methods, since a Laplacian scalar potential can be used in the absence of volume current density in these models. >
TL;DR: In this paper, the rotational transform, aspect ratio, specific volume and helical ripple ratio are calculated for the l = 2 stellarator/ heliotron/ torsatron configurations ( l ; multipolarity of the field) for various values of m (m ; toroidal pitch number).
Abstract: Vacuum magnetic fields in helical configurations are analyzed by using the scalar potential which satisfies Laplace equation. By adding the axisymmetric toroidal and vertical magnetic fields to the helical field, the nested magnetic surfaces are constructed. The rotational transform, aspect ratio, specific volume and helical ripple ratio are calculated for the l =2 stellarator/ heliotron/ torsatron configurations ( l ; multipolarity of the field) for various values of m ( m ; toroidal pitch number). The magnetic sturface is optimized in regard to the rotational transform and the area surrounded by the outermost magnetic surface. The generation of the magnetic well and the increment of the confinement region by the vertical field are also discussed. Finally, the m =2 low aspect ratio system is discussed.
Book•
28 Nov 1988
TL;DR: In this paper, the authors proposed a method to compute the potential of a line charge from a given charge distribution, and the potential function of a general charge distribution from a particular charge distribution.
Abstract: 1 Elementary Concepts of Electric and Magnetic Fields.- 1.1 Flux and Flux Density of Vector Fields.- 1.2 Equations of Matter - Constitutive Relations.- 2 Types of Vector Fields.- 2.1 Electric Source Fields.- 2.2 Electric and Magnetic Vortex Fields.- 2.3 General Vector Fields.- 3 Field Theory Equations.- 3.1 Integral Form of Maxwells Equations.- 3.1.1 Faraday's Induction Law in Integral Form Vortex Strength of Electric Vortex Fields.- 3.1.2 Ampere's Circuital Law in Integral Form Vortex Strength of Magnetic Vortex Fields.- 3.1.3 Gauss's Law of the Electric Field Source Strength of Electric Fields.- 3.1.4 Gauss's Law of the Magnetic Field Source Strength of Magnetic Fields.- 3.2 Law of Continuity in Integral Form Source Strength of Current Density Fields.- 3.3 Differential Form of Maxwell's Equations.- 3.3.1 Faradays Induction Law in Differential Form Vortex Density of Electric Vortex Fields.- 3.3.2 Ampere's Circuital Law in Differential Form Vortex Density of Magnetic Vortex Fields.- 3.3.3 Divergence of Electric Fields Source Density of Electric Fields.- 3.3.4 Divergence of Magnetic Fields Source Density of Magnetic Fields.- 3.4 Law of Continuity in Differential Form Source Density of Current Density Fields.- 3.5 Maxwell's Equations in Complex Notation.- 3.6 Integral Theorems of Stokes and Gauss.- 3.7 Network Model of Induction.- 4 Gradient, Potential, Potential Function.- 4.1 Gradient of a Scalar Field.- 4.2 Potential and Potential Function of Static Electric Fields.- 4.3 Development of the Potential Function from a Given Charge Distribution.- 4.3.1 Potential Function of a Line Charge.- 4.3.2 Potential Function of a General Charge Distribution.- 4.4 Potential Equations.- 4.4.1 Potential Equations for Fields without Space Charges.- 4.4.2 Potential Equations for Fields with Space Charges.- 4.5 Electric Vector Potential.- 4.6 Vector Potential of the Conduction Field.- 5 Potential and Potential Function of Magnetostatic Fields.- 5.1 Magnetic Scalar Potential.- 5.2 Potential Equation for Magnetic Scalar Potentials.- 5.3 Magnetic Vector Potential.- 5.4 Potential Equation for Magnetic Vector Potentials.- 6 Classification of Electric and Magnetic Fields.- 6.1 Stationary Fields.- 6.1.1 Electrostatic Fields.- 6.1.2 Magnetostatic Fields.- 6.1.3 Static Conduction Field (DC Current-Conduction Field).- 6.2 Quasi-Stationary Fields (Steady-State) Fields.- 6.2.1 Quasi-Static Electric Fields.- 6.2.2 Quasi-Static Magnetic Fields.- 6.2.3 Quasi-Static Conduction Fields.- 6.2.4 Conduction Fields with Skin Effect.- 6.3 Nonstationary Fields, Electromagnetic Waves.- 6.3.1 Wave Equation.- 6.3.2 Retarded Potentials.- 6.3.3 Hertz Potentials.- 6.3.4 Energy Density in Electric and Magnetic Fields, Energy Flow Density in Electromagnetic Waves.- 7 Transmission-Line Equations.- 8 Typical Differential Equations of Electrodynamics and Mathematical Physics.- 8.1 Generalized Telegraphist's Equation.- 8.2 Telegraphist's Equation with a, b>0 c=0.- 8.3 Telegraphist's Equation with a>0 b=0 c=0.- 8.4 Telegraphist's Equation with b>0 a=0 c=0.- 8.5 Helmholtz Equation.- 8.6 Schroedinger Equation.- 8.7 Lorentz's Invariance of Maxwell's Equations.- 9 Numerical Calculation of Potential Fields.- 9.1 Finite-Element Method.- 9.2 Finite-Difference Method.- 9.3 Charge Simulation Method.- 9.4 Monte Carlo Method.- 9.5 General Remarks on Numerical Field Calculation.- A1 Units.- A2 Scalar and Vector Integrals.- A3 Vector Operations in Special Coordinate Systems.- A5 Complex Notation of Harmonic Quantities.- Literature.
TL;DR: Magnetic scalar potential theory is applied to a model of eddy-current detection of a surface-breaking flaw in a conductor as discussed by the authors, and a solution algorithm based on the boundary element method is outlined and demonstrated by application to a three-dimensional rectangular slot.
Abstract: Magnetic scalar potential theory is applied to a model of eddy-current detection of a surface-breaking flaw in a conductor. A general boundary integral equation for the potential is derived first in a form suitable for numerical solution. The problem is then specialized to a flaw in a perfectly conducting half-space. A solution algorithm based on the boundary element method is outlined and demonstrated by application to a three-dimensional rectangular slot. Methods for accounting for the effects of nonvanishing skin depth are discussed.
TL;DR: In this paper, two main theorems from the governing differential equations for the flow of sheet molding compounds in compression molding are proved, and the results are applied to problems of practical interest.
Abstract: Two main theorems are proved from the governing differential equations for the flow of sheet molding compounds in compression molding. The first states that among all possible velocity distributions which satisfy the incompressibility condition and the kinematic boundary condition at a fixed edge, the actual solution minimizes the instantaneous rate of work by the molding press. The second is a general representation theorem for the velocity solution in terms of two scalar potentials. One of these potentials satisfies Laplace's equation and the second satisfies Helmholtz's equation. Each of these theorems is applied to problems of practical interest. The variational theorem is used to obtain a simple approximate solution for the flow front progression in a rectangular charge which, for a limited range of parameters, agrees remarkably well with previous numerical solutions of the exact equations. The representation theorem is used to examine the form of the solution in the important practical limit of a thin cavity. This limit is a singular perturbation of the governing differential equations, with a boundary layer at the flow front. Nevertheless, it is possible to prove that the flow front progression in thin cavities depends only on the outer solution, which can be expressed in terms of just one scalar potential.
TL;DR: In this paper, the scalar potential gradient, the so-called source term of the partial differential equation, is treated as an extra unknown; in other words, this term is replaced by the total current of the conductor.
Abstract: Two approaches for analyzing steady-state skin effect phenomena in multiconductor systems are well established. In one method, the scalar potential gradient, the so-called source term of the partial differential equation, is treated as an extra unknown; in the other this term is replaced by the total current of the conductor. It is shown that in handling real-life transient problems the first approach is superior, since, in general, neither the potential gradient nor the total current of conductors are given explicitly, but only active electrical networks that terminate both ends of the multiconductor system. The geometry of that problem is assumed to be two-dimensional, neglecting effects due to the finite length of the conductors. For sake of brevity, material characteristics are treated as linear and isotropic, although nonlinearities are admissible. >
TL;DR: In this article, the boundary value problem for calculating the scalar magnetic potentials inside and outside of a helically symmetric solenoid is discussed, and the potentials can be expanded in infinite series of cylindrical harmonics.
TL;DR: In this paper, the problem of electromagnetic field interaction with viscous fluid without and with zero-mass scalar field has been studied, and exact solutions corresponding to the electromagnetic field interactions in presence of viscous fluids and zero mass scalar fields have been obtained subject to various physical conditions.
Abstract: The problem of electromagnetic field interacting with viscous fluid without and with zero-mass scalar field has been studied. It has been shown that electromagnetic field cannot interact with viscous fluid for spherically-symmetric Robertson-Walker metric. Exact solutions corresponding to the problem of electromagnetic field interactions in presence of viscous fluid and zero-mass scalar field have been obtained subject to various physical conditions. It presents a scope for the study of imperfect fluid FRW models showing the existence of the electromagnetic field due to the presence of zero-mass scalar field.
TL;DR: Two new exact solutions for the five-dimensional Kaluza-Klein field equations are generated, one without a magnetic field but with a scalar potential and the other with a gravitational potential as the Schwarzschild solution.
Abstract: Two new exact solutions for the five-dimensional Kaluza-Klein field equations are generated. The first one is a solution without a magnetic field but with a scalar potential. The second one is an exact solution with a gravitational potential as the Schwarzschild solution and a magnetic field containing a flux along the azimuthal direction and a scalar potential equal to one far away from a black hole.
01 Jan 1988
TL;DR: In this article, a vector potential formulation in the BEM for three-dimensional problems is described, which enables the coupling of BEM with the FEM easy, and some numerical results obtained by using the new formulation are reported.
Abstract: A new vector potential formulation in the BEM for three-dimensional problems is described. This formulation enables the coupling of the BEM with the FEM easy. Some numerical results obtained by using the new formulation are reported. Another boundary element formulation in terms of the magnetic field intensity and the scalar potential is also described. This approach has the advantage of reducing the number of unknown variables.
TL;DR: In this paper, a three-dimensional A-phi analysis of a cylinder-type concentration apparatus is presented, which attains compactness in size and high efficiency in flux concentration by assembling a conducting plate just inside one or several excitation windings.
Abstract: Three-dimensional A- phi analysis of a recently developed cylinder-type concentration apparatus is dealt with. The model used attains compactness in size and high efficiency in flux concentration by assembling a conducting plate just inside one or several excitation windings. A four-component direct finite-element calculation method is applied, and three-dimensional distributions of the flux density, eddy current, and scalar potential are obtained. The divided direct calculation method is compared with an iterative method previously used by the authors. >
TL;DR: In this article, a boundary method is developed for the computation of three-dimensional eddy-current distributions, where the electromagnetic field is described by the magnetic field intensity in conductive regions and the magnetic scalar potential in nonconductive regions.
Abstract: A boundary method is developed for the computation of three-dimensional eddy-current distributions. The electromagnetic field is described by the magnetic field intensity in conductive regions and by the magnetic scalar potential in nonconductive regions. The fundamental solutions of the relevant differential equations are used as trial functions to approximate the solution of the eddy-current problem. A method is obtained for finding the near-best positions of the singularities of the fundamental solutions using a nonlinear least-squares minimization technique. This method requires relatively few trial functions to obtain satisfactory accuracy. >