Showing papers on "Scalar potential published in 1981"
TL;DR: In this article, a relativistic Hartree-Fock mean field approximation for symmetric nuclear matter was proposed, which is fully equivalent to the most general mean field and which is only the sum of a Lorentz scalar, of one component of an LSTM tensor and of the fourth component of a LRTM vector.
67 citations
TL;DR: In this article, the authors presented a model for a permanent magnet material that leads to a simplified energy functional and verified that this approach is appropriate for an axial-field electrical machine that has SmCo 5 magnets which have linear characteristics.
Abstract: The development of new types of permanent magnet material, particularly the rare earth-cobalt class, has created new interest in the design of electrical machines, torque couples, lifting magnets, and other electromechanical devices In all of these cases, the magnetic field is the medium for energy conversion The accurate computation of these magnetic fields is essential for realistic performance predictions at the design stage Techniques for field computation have generally been restricted to the two-dimensional closed form [1] and numerical analysis[2,3] However, permanent magnet electrical machine topologies are essentially three-dimensional [4], and, therefore, two-dimensional solutions may not yield the desired accuracy for certain applications A three-dimensional field distribution which uses a magnetic scalar potential function may be obtained by using finite element analysis[5,6] This paper presents a model for a permanent magnet material that leads to a simplified energy functional Although the method is generally applicable to nonlinear anisotropic magnets, such as alnicos, this paper has verified that this approach is appropriate for an axial-field electrical machine that has SmCo 5 magnets which have linear characteristics
31 citations
22 citations
TL;DR: In this article, a three dimensional scalar field solution is obtained through a two dimensional grid given cylindrical symmetry, the grid being excited by current injection at appropriate nodes as in the two dimensional vector potential grid.
Abstract: A three dimensional scalar field solution is shown obtainable through a two dimensional grid given cylindrical symmetry. A valid field solution is obtained within current elements, the grid being excited by current injection at appropriate nodes as in the two dimensional vector potential grid. Test results verifying the method for predicting end region flux is presented. Because of its unique field solution within current masses, the method is applicable to problems such as forces on conductors in the end region of a turbine generator.
19 citations
TL;DR: In this article, a general finite element solution of magnetostatic fields due to three-dimensional current sources, in axisymmetric geometries, in terms of the scalar magnetic potential is presented.
Abstract: This paper presents a general finite element solution of magnetostatic fields due to three-dimensional current sources, in axisymmetric geometries, in terms of the scalar magnetic potential. In the space occupied by the current sources, and there only, a correction field defined by a vector quantity must be added to the scalar potential field. Numerically, this correction field is obtained by using a vector potential which may be allowed to be divergenceless in the mean. Since the correction field is non-zero only in the current-carrying space, it is computationally relatively inexpensive to find. This method is used to predict the open-circuit and short-circuit magnetic fields in the end region of a turbine-generator. In order to assess the accuracy of the process, the magnetic fields are calculated and compared with the classical current-sheet approach and test measurements.
17 citations
15 Sep 1981
TL;DR: In this article, the drift shell is specified analytically (i.e., by an approximation given in closed form) in terms of the equatorial pitch angle, which offers an internal test for the absence of time-varying coefficients in the expansion of V.
Abstract: : We consider the adiabatic motion of electrons trapped in the model geomagnetic field derived from a scalar potential The drift shell is specified analytically (ie, by an approximation given in closed form) in terms of the equatorial pitch angle The 'radial gradient' is inferred from the diurnal variation of particle flux This procedure offers an internal test for the absence of time-varying coefficients in the expansion of V The pitch-angle distribution is directly observed at the noon meridian The parameters thus determined allow the pitch-angle distribution at other longitudes to be obtained from Liouville's theorem The results, at least for a well-studied test case, are comparable in quality to those obtained by more difficult methods, using a more complicated field model and the data from two spacecraft, ie, are in similarly good agreement with the observational data obtained at other longitudes In particular, we find that the maximum flux at alpha sub 0 = pi/2 occurs at noon (phi = pi) and that the maximum flux j(alpha sub 0, phi = 0) at midnight (phi = 0) occurs at alpha sub 0 not = pi/2
7 citations
TL;DR: In this article, a perturbation theory for an arbitrary bound state in the one-space and one-time dimension Klein-Gordon equation in the presence of a scalar potential and a vector (fourth component only) potential was presented.
Abstract: We present a perturbation theory for an arbitrary bound state in the one‐space and one‐time dimension Klein–Gordon equation in the presence of a scalar potential and a vector (fourth component only) potential by reducing it to a Ricatti equation with the method of logarithmic perturbation expansions. All corrections to the energies and wavefunctions, including corrections to the positions of the nodes in excited states, are expressed in quadratures in a hierarchical scheme, without the use of either the Green’s function or the sum over intermediate states.
6 citations
IBM1
TL;DR: In this article, a technique for enhancing the detail and resolution of 3D finite element magnetic field calculations for recording heads has been developed, which is often essential for recording head studies where the range of important linear dimensions can span three or four orders of magnitude.
Abstract: A technique for enhancing the detail and resolution of 3D finite element magnetic field calculations for recording heads has been developed. This approach (ZOOM) has proven useful for studying details of gap fringe fields for heads of arbitrary geometry. ZOOM involves performing a second finite element reduced scalar potential calculation within a rediscretized subvolume of particular interest using as boundary conditions the original FEM solution. Scalar potential values for new boundary mesh nodes are obtained by an appropriate interpolation scheme. ZOOM is often essential for recording head studies where the range of important linear dimensions can span three or four orders of magnitude. Discretization of such 3D structures to obtain high accuracy and detail in a single step is usually a practical impossibility. We have applied this technique to a study of side fringe fields of Winchester style heads with track side bevel angles of 45, 60, and 75 degrees. We report for the first time the computed side fringe field asymmetry arising from head structure asymmetry.
6 citations
TL;DR: In this paper, the properties of self-gravitating wave fields with integral spin (scalar and vector) compatible with a Godel type space are investigated and the simultaneous systems of Einstein's gravitational field equations and the equations corresponding to wave fields in Godel's metric are solved.
Abstract: The properties of self-gravitating wave fields with integral spin (scalar and vector), compatible with a Godel type space, are investigated. The simultaneous systems of Einstein's gravitational field equations and the equations corresponding to wave fields in Godel's metric are solved. For the scalar field, the solutions are obtained for different types of interaction Lagrangians for the gravitational and scalar fields. It is shown that for a massive vector field the relations obtained between the constants lead, within the scope of the strong gravitation theory, to the classical expression for the spin of elementary particles.
5 citations
01 Jan 1981
TL;DR: An aerodynamic prediction technique based on the full potential equation in conservation form is developed for the treatment of supersonic flows and exhibits a considerable improvement in computational efficiency and generality over an existing nonconservative full potential code.
Abstract: An aerodynamic prediction technique based on the full potential equation in conservation form is developed for the treatment of supersonic flows. This technique bridges the gap between simplistic linear theory methods and complex Euler solvers. A novel local density linearization concept and a second order accurate retarded density scheme, both producing the correct artificial viscosity, are introduced in developing an implicit marching scheme for solving the scalar potential. Results for conical flows over delta wings and a wing-body combination and for non-conical flows over bodies of revolution at angles of attack are compared with Euler and nonconservative full potential calculations and experimental data. The present formulation requires an order of magnitude less computer time and significantly less computer memory over Euler codes and exhibits a considerable improvement in computational efficiency and generality over an existing nonconservative full potential code.
3 citations
TL;DR: In this paper, a relativistic particle affected simultaneously by two static potentials, a Lorentz scalar and the time component of a four-vector potential, is discussed.
Abstract: We discuss a relativistic particle affected simultaneously by two static potentials, a Lorentz scalar and the time component of a four‐vector. We show that the scalar potential has effects on the motion of a particle that are distinctively different from those of a four‐vector potential. With the aid of an example we show that, in both classical and quantum mechanics, there are two inequivalent but compatible criteria of nonrelativistic behavior: (mean) kinetic energy much smaller than rest energy and nonrelativistic potential energy independent of total energy. The second of these is the correct condition for use of nonrelativistic methods, but it is the first that is usually invoked to justify their use. The two criteria are equivalent only when the scalar potential has a (mean) value much less in magnitude than the particle’s rest energy. If this condition is not satisfied, nonrelativistic formalisms such as ordinary Newtonian mechanics and the Schrodinger equation may be inadequate even if v/c is smal...
TL;DR: In this article, the meaning of the vector Vα which characterizes the difference between the two tensor potentials of the Riemann and of the Weyl tensor is studied.
Abstract: The meaning of the vector Vα which characterizes the difference between the two tensor potentials of the Riemann and of the Weyl tensor is here studied. In the context of general relativity, the equations satisfied by such a vector and by the scalar potential ϕ characterizing its irrotational part, are connected to the equation proposed by Cattaneo as a relativistic extension of the Gauss-Poisson classical one. The link between the vector potential Vα and the standard gravitational field is thus obtained, for static universes.
TL;DR: In this paper, a scalar potential representation for a P wave in an inhomogeneous medium is developed from ray theory and is shown to be generally applicable to both P and S waves.
TL;DR: In this article, a method for systematically constructing basis functions for two-dimensional field problems containing a strip conductor buried in stratified dielectrics is proposed, and the structure of the specific kernel or Green's function for the problem can be determined approximately.
Abstract: A new method for systematically constructing basis functions for two-dimensional field problems containing a strip conductor buried in stratified dielectrics is proposed. By applying a simplifying averaging process to the associated static problem, the structure of the specific kernel or Green's function for the problem can be determined approximately. An integral form of continuity equation is derived; general sets of quasi-eigenfunctions are established, which are orthogonal and complete in Hubert spaces L2(Ω, w). By substituting the specific information into the latter, the required quasi-eigenfunctions for the problem can be obtained. Hence, with both the edge condition and the continuity equation being satisfied simultaneously and with the inhomogeneity of dielectric constants being taken into account, these resultant functions form a particularly suitable expansion basis for the series solution to such physical quantities as scalar potential, induced surface charge, and surface current.
TL;DR: In this article, the equations of motion for a free electron laser with an electromagnetic pump field are presented, and a scalar potential representing an external static axial electric field for gain enhancement is included in the model.
Abstract: The equations of motion for a free electron laser with an electromagnetic pump field are presented. A scalar potential representing an external static axial electric field for gain enhancement has been included in the model. Equations governing gain and phase shift for each of the electromagnetic fields are given. The equation for the separatrix has been derived using the resonant particle concept and found to contain new terms. These expressions have been incorporated into a computer code which has been used to simulate several amplifier designs. The results of these designs and, in particular, the z-dependence of the accelerating voltage are discussed.
TL;DR: In this paper, the authors investigated the possibility of avoiding the introduction of a potential function and concentrating on the gravitational field vector itself and found that these vector integral representations are also suited for describing the gravity field of the earth.
Abstract: In the theory of gravitation, usually a potential function is introduced to describe the gravity field. This has the advantage that Green’s integral representations of potential theory can be used in a straight-forward manner. However, the introduction of a scalar potential also has some disadvantages. Although the potential can be associated with the work done when moving around a point mass in a gravitational field, it still is a somewhat artificial quantity that cannot directly and unambiguously be measured. This is in contrast with the gravitational field strength. In the present paper we investigate the possibility of avoiding the introduction of a gravitational potential and concentrate on the gravitational field vector itself. In that case, appropriate vector integral representations of the Green type have to be derived for the gravitational field. It turns out that these vector integral representations are also suited for describing the gravity field of the earth.
TL;DR: In this paper, a variational principle is proposed for finite element analysis of low intensity static magnetic field solutions, which leads to field equations and boundary conditions that characterize a magneticfield accounting for the presence of current, permanent magnetization and incident magnetic fields.
Abstract: A functional is presented that is useful in the finite element analysis of low intensity static magnetic field solutions. The variational principle is written in terms of a scalar potential function and, when minimized,leads to field equations andboundary conditions that characterize a magneticfieldaccounting for the presence of current, permanent magnetization,and incident magnetic fields. This variational principle finds applications in the fiiite element analysis of magnetic field problems.
TL;DR: In this article, Galerkin-type representations for the polarization vector P and the scalar potential φ in a dielectric solid were constructed for an ideal dipole, quadrupole and octapole.
TL;DR: In this paper, the impulse of the electric field defined has all the properties of a vector potential, and the observable vector field depends on the history of the electromagnetic field, which ensures the gauge invariance of the dynamics of charged particles.
Abstract: The impulse of the electric field defined has all the properties of a vector potential. This observable vector field depends on the history of the electromagnetic field. The gauge invariance of the dynamics of charged particles ensures that the instantaneous values of the electromagnetic field govern the motion.