Showing papers on "Scalar potential published in 1989"
TL;DR: In this article, the method of calculating radiative corrections to the scalar potentials is reviewed, with an emphasis on renormalization group improvement of the potential, and the results are then applied to the standard model to derive stringent bounds on Higgs and fermion passes.
850 citations
TL;DR: The existence of bound states for the s-wave Klein-Gordon equation for vector and scalar Hulthen-type potentials is shown in this paper, provided that the potential size is large enough.
165 citations
TL;DR: In this article, a vector central-slice theorem is derived for the case of divergenceless 2D vector fields, which is a generalization of the scalar central slice theorem that plays a fundamental role in conventional tomography.
Abstract: Summary
We examine the problem of reconstructing a 2-D vector field v(x,y) throughout a bounded region D from the line integrals of v(x, y) through D. This problem arises in the 2-D mapping of fluid-flow in a region D from acoustic travel-time measurements through D. For an arbitrary vector field, the reconstruction problem is in general underdetermined since v(x, y) has two independent components, vx(x, y) and vy(x, y). However, under the constraint that v is divergenceless (▿ v = 0) in D, we show that the vector reconstruction problem can be solved uniquely. For incompressible fluid flow, a divergenceless velocity field follows under the assumption of no sources or sinks in D.
A vector central-slice theorem is derived, which is a generalization of the well-known ‘scalar’ central-slice theorem that plays a fundamental role in conventional tomography. the key to the solution to the vector tomography problem is the decomposition of the field v(x, y) into its irrotational and solenoidal components: v =▿φ+▿×ψ, where φ(x, y) and ψ(x, y) are scalar and vector potentials. We show that the solenoidal component ▿ x ψ can be uniquely reconstructed from the line integrals of v through D, whereas the irrotational component ▿φ cannot. However, when the field is divergenceless in D, the scalar potential φ solves Laplace's equation in D and can be determined by the values of v on the boundary of D. an explicit formula for φ from the boundary values of v is derived. Consequently, v(x, y) can be uniquely recovered throughout the region of reconstruction from the following information: line-integral measurements of v through this region and v measured on the boundary of this region.
106 citations
TL;DR: In this paper, the collision operator for a relativistic plasma is reformulated in terms of an expansion in spherical harmonics, which is used to calculate the electrical conductivity of a uniform electron-ion plasma with infinitely massive ions.
Abstract: The collision operator for a relativistic plasma is reformulated in terms of an expansion in spherical harmonics. In this formulation the collision operator is expressed in terms of five scalar potentials that are given by one‐dimensional integrals over the distribution function. This formulation is used to calculate the electrical conductivity of a uniform electron–ion plasma with infinitely massive ions.
88 citations
28 Mar 1989
TL;DR: In this article, it is demonstrated that it is possible to use a single continuous, continuous, scalar potential to solve magnetostatic problems in three dimensions without the loss of accuracy associated with the reduced potential.
Abstract: It is demonstrated that it is possible to use a single, continuous, scalar potential to solve magnetostatic problems in three dimensions without the loss of accuracy associated with the reduced potential. This method makes use of tetrahedral edge elements and does not require the initial calculation of the field of the currents in the absence of magnetic materials. The method requires no numerical integration, has no restrictions on the current flow or the iron topology, and needs the solution of only one matrix problem. Results obtained by the method for translational and axisymmetric problems agree well with those computed by two-dimensional analysis with a vector potential. The method can be used to obtain accurate flux densities in both air and iron regions of three-dimensional problems. >
84 citations
TL;DR: In this article, the authors employ the magnetic and electric fields as fundamental unknowns instead of the vector potential and scalar potential, and the proposed approach appears to be desirable for three-dimensional finite element analyses.
Abstract: This paper presents some mixed formulations for finite element analysis of magnetostatic and electrostatic problems We employ the magnetic and electric fields as fundamental unknowns instead of the vector potential and the scalar potential, and the proposed approach appears to be desirable for three-dimensional finite element analyses We also give brief comments on the use of the vector potential for the magnetostatic problem
59 citations
TL;DR: In this article, the relativistic mean field theory of nuclei is discussed for general scalar potential functions U ( φ ) with a minimum at zero scalar field φ = 0.
41 citations
TL;DR: In this article, the scattering state solutions of the s-wave Klein-Gordon equations with vector and scalar Hulthen type potentials are obtained both for regular and irregular boundary conditions.
38 citations
TL;DR: In this article, the de Rham complex is used to avoid reassembling large parts of the stiffness matrix in iterative computations involving constitutive laws which change with every iteration.
Abstract: The solvability, gauge invariance, and topological aspects of dual variational principles shed light on the difficulties that arise from the use of a vector potential in three dimensions in place of a stream function in two dimensions. These aspects reveal the central role of a relative de Rham complex in place of the usual Tonti diagram. By considering the 'spin complex' associated with the de Rham complex, it is seen that the helicity functional enables the scalar potential to be used in the dual role of a Lagrange multiplier which fixes the gauge of the vector potential. The metric and constitutive law independence of the helicity term is considered. The main purpose is to show how the invariant terms of the helicity functional can be used to avoid rebuilding (reassembling) large parts of the finite-element stiffness matrix in iterative computations involving constitutive laws which change with every iteration. The results are phrased in terms of differential forms. >
38 citations
28 Mar 1989
TL;DR: It is shown that a finite element discretization can make the problem reduce to that of harmonic functions subject to peculiar interelement constraints and the effective degrees of freedom in the element assembly are identified with topological constraints.
Abstract: A general approach to making cuts for magnetic scalar potentials that utilizes the formalism of algebraic topology and points to the external role played by mappings into circles was presented by D. Rodger and J.F. Eastham (1987). The author extends these previous results to practical algorithms by considering the variational formulation of harmonic maps into the circle and their numerical discretization by the finite element method. The harmonic map functional is nonquadratic and nonconvex. It is shown that a finite element discretization can make the problem reduce to that of harmonic functions subject to peculiar interelement constraints. Analyzing the continuity requirements of the harmonic map and the degrees of freedom in the interelement constraints which leave the discretized harmonic map functional invariant, the effective degrees of freedom in the element assembly are identified with topological constraints. The interelement constraints are then rephrased to make them amenable to well-known techniques of electric circuit theory. Finally, the entire development is summarized in the form of an algorithm. The results are important for the magnetic scalar potential analysis of eddy currents and nondestructive testing methodology in three dimensions. >
32 citations
TL;DR: A decoupled equation from the Rarita-Schwinger equation on an algebraically special vacuum space has been derived in this paper, where all the components of the field can be obtained from a scalar potential that obeys a wavelike equation.
Abstract: It is shown that previous results concerning test massless fields on algebraically special vacuum backgrounds can be extended to the case of massless spin‐ (3)/(2) Rarita–Schwinger fields. A decoupled equation is derived from the Rarita–Schwinger equation on an algebraically special vacuum space‐time and it is shown that all the components of the field can be obtained from a scalar potential that obeys a wavelike equation. In the case of type D metrics, identities of the Teukolsky–Starobinsky‐type are obtained. Some relations induced by Killing spinors are also included.
TL;DR: In this paper, the complete solution of the Rarita-Schwinger equation in terms of complex scalar potentials are obtained by means of Wald's method of adjoint operators.
Abstract: Expressions for the complete solution of the Rarita–Schwinger equation in terms of complex scalar potentials are obtained by means of Wald’s method of adjoint operators. The background space‐time is required to be an algebraically special solution of the Einstein vacuum field equations with cosmological constant or a solution of the Einstein–Maxwell equations such that one principal null direction of the electromagnetic field is geodetic and shear‐free.
01 Jan 1989
TL;DR: In this article, a spherical cap harmonic model of the crustal scalar potential has been used to correct both the vector and total intensity data on to a 2° by 2° grid at an altitude of 400 km.
Abstract: The geomagnetic field observed in current-free regions above the Earth’s surface may be expressed as the gradient of a scalar potential satisfying Laplace’s equation Spherical cap harmonic analysis enables solution of Laplace’s equation, subject to boundary conditions appropriate to geomagnetic field analysis, in a region bounded by a spherical cap Magsat data within a spherical cap of half-angle 35° centred on latitude 45°N, longitude 10°E have been analysed for their crustal content The resulting estimates of the crustal vector field have been used to derive a spherical cap harmonic model of the crustal scalar potential The model contains 256 parameters and portrays wavelengths of 1000 km and above Vector anomaly maps derived from the model show several prominent features of which the largest is that in the Kursk region of the USSR The model has been used to correct both the vector and total intensity data on to a 2° by 2° grid at an altitude of 400 km Anomaly maps produced by contouring the grid averages are in good agreement with those derived from the model The major difference is for the vertical component of the anomaly field over the Kursk region of the USSR This is a high-amplitude short-wavelength feature which the model smooths
28 Mar 1989
TL;DR: In this article, the authors present a method for modeling multiply connected regions based on the A-PSI field representation, where the magnetic vector potential A is used inside conductors, while the magnetic scalar psi is used to model nonconductors.
Abstract: The authors present a novel method for modeling multiply connected regions based in the A- psi field representation. The equations are solved in differential form using the finite element approximation. The magnetic vector potential A is used inside conductors, while the magnetic scalar psi is used to model nonconductors. Holes in eddy current regions are dealt with by adding one extra degree of freedom per hole. The proposed method is more economical (fewer unknowns) than previous solutions and is easily implemented in existing codes based on the A- psi method. >
TL;DR: In this article, the problem of coupling cuts for magnetic scalar potentials to cuts for stream functions describing currents on the orientable boundary of a good conductor or on thin, possibly nonorientable, conducting sheets is discussed.
Abstract: The problem discussed is that of coupling cuts for magnetic scalar potentials to cuts for stream functions describing currents on the orientable boundary of a good conductor or on thin, possibly nonorientable, conducting sheets. The solution of this problem is of interest both for its own sake and for the insight it gives into the general case of volume distributions of current. It is shown how the topological formalism clearly articulates the lumped parameter aspects. It is also shown that cuts for stream functions can be made on a nonorientable surface and that the discontinuities in the magnetic scalar potential can be systematically related to discontinuities in stream functions by a suitable choice of cuts. >
01 Mar 1989
TL;DR: In this paper, the authors studied multiply-connected regions with the use of magnetic scalar potentials and gave practical rules for the necessary "cuts" that are essential in numerical approaches to such problems.
Abstract: Magnetostatic problems in multiply connected regions are studied with the use of magnetic scalar potentials. Particular emphasis is given to the significance of the nontrivial topological structure of the region, for the mathematical formulation. Practical rules are given for the necessary 'cuts' that are essential in numerical approaches to such problems.
23 May 1989
TL;DR: In this article, a mixed potential surface integral equation formulation was used to compute the radiated emission from printed circuit traces that involve right-angular bends and gap discontinuities, and the results indicated good agreement between a quasistatic approximation of the trace current and a rigorous mixedpotential computation.
Abstract: A mixed (scalar and vector) potential surface integral equation formulation, originally developed for microstrip antennas by Mosig and Gardiol (1982), is used to compute the radiated emission from printed circuit traces that involve right-angular bends and gap discontinuities. Computed results for a gap-excited trace configuration loaded by a short circuit or an open circuit indicate good agreement between a quasistatic approximation of the trace current and a rigorous mixed-potential computation. >
TL;DR: In this paper, the role played by sophisticated scalar potential, dictated by spontaneous compactification, is analyzed and a fine-tuning is mandatory for achieving asymptotic flatness.
TL;DR: A general procedure for computing the capacitance coefficients of multilevel interconnections in multilayered dielectric medium is given and simple criteria are introduced to divide the interfaces into an optimum number of elementary parts.
Abstract: A general procedure for computing the capacitance coefficients of multilevel interconnections in multilayered dielectric medium is given. The electromagnetic concept of total charge density is applied. It makes it possible to obtain integral equations between scalar potential and charge density distributions. These equations are solved by the method of moments technique. To optimize the computational algorithm, special consideration is given to the limitation of the dimensions of the dielectric interfaces. Simple criteria are introduced to divide the interfaces into an optimum number of elementary parts. Theoretical results thus obtained agree closely with the experimental results from test vehicles. >
TL;DR: In this article, the Coulomb gauge is incorporated in the formulation and the normal component of the vector potential is set to zero on the interfaces between the vectorpotential and scalar-potential regions.
Abstract: Three-dimensional eddy-current problems with multiply connected conductors are formulated in terms of uniquely defined potentials. In the eddy-current-carrying regions, a magnetic vector potential and an electric scalar potential are used. These are coupled to a magnetic scalar potential in most parts of the nonconducting domain. However, in the nonconducting 'holes' in the conductors, a magnetic vector potential is used so that the region with the scalar description surrounds a simply connected domain. To ensure uniqueness of the vector potential, the Coulomb gauge is incorporated in the formulation and the normal component of the vector potential is set to zero on the interfaces between the vector-potential and scalar-potential regions. Solutions to two benchmark problems of the International TEAM Workshops involving multiply connected conductors are presented. The gain in computational time due to the use of unique potentials is pointed out. >
TL;DR: In this article, the method-of-moments impedance matrix (Z) was decomposed into three parts: a real inductance matrix (L) from the magnetostatic vector potential, a real elastance matrix from the electrostatic static scalar potential, and a complex impedance matrix of residual frequency-dependent contributions.
Abstract: As part of an investigation into methods for accelerating the process of filling the method-of-moments impedance matrix (Z), it was found that (Z) could be decomposed into three parts: a real inductance matrix (L) from the magnetostatic vector potential, a real elastance matrix (S) from the electrostatic static scalar potential, and a complex impedance matrix (z( omega )) of residual frequency-dependent contributions. By neglecting (z( omega )) at sufficiently low frequencies, static and quasi-static charge and current distributions were obtained. For electrically small antennas, a complete RLC circuit was obtained directly from a single quasi-static solution rather than as an approximate characterization of the impedance as a function of frequency. This gives a precise definition of the circuit parameters limiting the performance of electrically small antennas. >
TL;DR: It is shown that the two possible formulations for a divergence- and curl-free vector field, namely, in terms of a scalar or a two-form potential, are equivalent, both as free quantum field theories even in the presence of a background gravitational field and in their coupling to the gravitational field.
Abstract: We show that the two possible formulations for a divergence- and curl-free vector field, namely, in terms of a scalar or a two-form potential, are equivalent, both as free quantum field theories even in the presence of a background gravitational field and in their coupling to the gravitational field. An apparent disparity in the extrema of the actions in the Euclidean formulations of these theories is resolved by showing that if boundary conditions that are common to the two formulations (which are the only boundary conditions for which the two theories can be compared) are imposed the only extrema of either action has a zero value for the vector field and thus for the stress-energy tensor.
TL;DR: In this article, the 1/N energy formula for a spinless relativistic two-body system, which is subject to the attractive scalar potential - Λ 0/x2, was obtained by combining the analytic continuation towards n > 2 of 1/n energy results obtained previously for n < 2-Hamiltonians.
Abstract: Nonrelativistic energy formulae for the superposition between the attractive potential - λ0/x2 and the repulsive n > 2-potential γ(n)/xn have been established in N space dimensions, both to first and second order in 1/N. One proceeds by combining the analytic continuation towards n > 2 of 1/N energy results obtained previously for n < 2-Hamiltonians, with additional selection criteria implied by the related WKB-description. This leads to well-defined energy-levels relying on supercritical λ0-values. Finally, we find the 1/N energy formula for a spinless relativistic two-body system, which is subject to the attractive scalar potential - Λ0/x2.
01 Aug 1989
TL;DR: In this paper, a dual potential formulation for numerically solving the Navier-Stokes equations is developed and presented The velocity field is decomposed using a scalar and vector potential Vorticity and dilatation are used as the dependent variables in the momentum equations.
Abstract: A dual potential formulation for numerically solving the Navier-Stokes equations is developed and presented The velocity field is decomposed using a scalar and vector potential Vorticity and dilatation are used as the dependent variables in the momentum equations Test cases in two dimensions verify the capability to solve flows using approximations from potential flow to full Navier-Stokes simulations A three-dimensional incompressible flow formulation is also described An interesting feature of this approach to solving the Navier-Stokes equations is the decomposition of the velocity field into a rotational part (vector potential) and an irrotational part (scalar potential) The Helmholtz decomposition theorem allows this splitting of the velocity field This approach has had only limited use since it increases the number of dependent variables in the solution However, it has often been used for incompressible flows where the solution scheme is known to be fast and accurate This research extends the usage of this method to fully compressible Navier-Stokes simulations by using the dilatation variable along with vorticity A time-accurate, iterative algorithm is used for the uncoupled solution of the governing equations Several levels of flow approximation are available within the framework of this method Potential flow, Euler and full Navier-Stokes solutions are possible using the dual potential formulation Solution efficiency can be enhanced in a straightforward way For some flows, the vorticity and/or dilatation may be negligible in certain regions (eg, far from a viscous boundary in an external flow) It is possible to drop the calculation of these variables then and optimize the solution speed Also, efficient Poisson solvers are available for the potentials The relative merits of non-primitive variables versus primitive variables for solution of the Navier-Stokes equations are also discussed
TL;DR: In this article, the trace anomaly for massless self-interacting scalar fields propagating on a gravitational and a scalar field background is calculated using Fujikawa's path integral method.
Abstract: We calculate the trace anomaly for massless self-interacting scalar fields propagating on a gravitational and a scalar field background. This is done by using Fujikawa's path integral method.
TL;DR: In this article, the relativistic Dirac equation with scalar potential and fourth component of vector potential of the Woods-Saxon shape as well as of the Gaussian shape is considered, with the aim of determining the parameters of the potentials, i.e. well depths, range parameter and skin-thickness parameter for the Woods Saxon potential.
Abstract: The relativistic Dirac equation with scalar potential and fourth component of vector potential of the Woods-Saxon shape as well as of the Gaussian shape is considered, with the aim of determining the parameters of the potentials, i.e. well depths, range parameter and skin-thickness parameter for the Woods-Saxon potential. These parameters are determined by a least-squares fitting of the theoretically obtained ground-state binding energies to the experimentally known ones for a number of hypernuclei. Using the values of the parameters obtained, the ground-state binding energies of various hypernuclei are calculated and found to be in good agreement with the experimental ones.
01 Jan 1989
TL;DR: In the vicinity of an ICRH antenna strap, where there are no volume currents and a free space wavelength is much longer than the dimensions of interest, Ampere's law reduces to a curl-free condition on the magnetic field, allowing a magnetic scalar potential to be defined as mentioned in this paper.
Abstract: In the vicinity of an ICRH antenna strap, where there are no volume currents and a free‐space wavelength is much longer than the dimensions of interest, Ampere’s law reduces to a curl‐free condition on the magnetic field, allowing a magnetic scalar potential to be defined. This scalar potential is a solution of the three‐dimensional (3D) Laplace equation and satisfies the following boundary conditions on the magnetic field: (1) the line integral of the mgnetic field around the current strap is equal to the current flowing the strap and (2) the perpendicular component of the magnetic field vanishes at conductor surfaces (no flux penetrasion of perfect conductors). This formulation allows for the magnetic field solution of quite complex 3D geometries, such as poloidal current straps with asymmetric radial feeds or detailed Faraday shield geometries.
TL;DR: In this paper, the authors presented a method for the Dirac equation for a spherically symmetric potential with one spatial coordinate. But their method was restricted to the case of a potential depending on one space coordinate.
01 Jan 1989
TL;DR: In this paper, the inverse scattering problem for scalar wavefields is formulated in terms of timely separated pressure and shear wavefronts, each of which is characterized by a scalar potential.
Abstract: Elastic wave scattering by defects in solids can be interpreted in terms of timely separated pressure and shear wavefronts, each of which is approximately characterized by a scalar potential Formulation of the inverse scattering problem for scalar wavefields then yields a general solution via the backpropagation ansatz, if the defect can either be considered as a weakly scattering inclusion or a strongly scattering crack or void Holography, ALOK, SAFT, Echo Tomography and other algorithms for computed imaging turn out to be special solutions within this generalized diffraction tomography framework and therefore relate to each other in a quantitative way In addition, fast and powerful data processing alternatives like Fourier-Transform-SAFT are proposed and have recently been implemented for threedimensional computed imaging, either for planar or cylindrical measurement surfaces, the latter one relating to turbine shaft testing
01 Mar 1989
TL;DR: In this article, the authors reviewed vector potential and related methods for the simulation of both inviscid and viscous flows over aerodynamic configurations, and the advantages and disadvantages of several formulations are discussed and alternate strategies are recommended.
Abstract: Vector potential and related methods, for the simulation of both inviscid and viscous flows over aerodynamic configurations, are briefly reviewed. The advantages and disadvantages of several formulations are discussed and alternate strategies are recommended. Scalar potential, modified potential, alternate formulations of Euler equations, least-squares formulation, variational principles, iterative techniques and related methods, and viscous flow simulation are discussed.