Showing papers on "Scalar potential published in 1995"

A Lagrangian formulation for mechanically, thermally coupled electromagnetic diffusive processes with moving conductors

Abstract: In a moving physical system, field variables can be described by functions of time and initial (reference) positions of particles (Lagrangian description) or functions of time and current positions of particles (Eulerian description). Lagrangian formulation exhibits several advantages in modeling electromagnetic (EM) diffusion problems with moving conductors. It results in a symmetric coefficient matrix which reduces computational cost and central memory requirement. It also eliminates numerical instability at hypervelocity. In the simulation of EM launchers, Lagrangian formulation facilitates EM analyses including end (breech and muzzle) effects, and the effects of imperfect rails and structural deformation. A detailed Lagrangian formulation of mechanically, and thermally coupled electromagnetic diffusive processes with moving conductors is presented in this paper. It is based on the quasistatic Maxwell's equations in terms of dual potentials: magnetic vector potential and electric scalar potential. With the Coulomb gauge condition, magnetic vector potential is uniquely determined. The formulation has been implemented in the finite element program 'EMAP3D' (Electro-Mechanical Analysis Program in 3 Dimension). The thermally coupled electromagnetic simulation of a railgun is illustrated. The distributions of current density, magnetic field, and temperature are presented. Also the profiles of velocity and current are shown. >

Vacuum energy in smooth background fields

Abstract: We consider the ground-state energy of a scalar field in the background of a general potential which depends on one coordinate. We consider a general expression following from the analytical properties of the one-dimensional scattering matrix. We show that reflections give a positive and bound states a negative contribution to the ground-state energy and we calculate explicitly two simple examples, the square-well potential and a piecewise oscillatory potential. We demonstrate our formulae by an easy rederivation of the mass of the kink.

On calculation of 3-D eddy currents in conducting and magnetic shells

Abstract: The impedance type boundary conditions are derived for 3-D eddy currents in conducting and magnetic shells. These boundary conditions are then represented only in terms of magnetic field. This leads to a new magnetic scalar potential formulation for 3-D eddy currents in conducting and magnetic shells. This scalar potential formulation is reduced to weak Galerkin forms. The finite element discretization of these forms results in volume and surface "stiffness" matrices. >

T- Omega method using hierarchal edge elements

Abstract: The edge-element version of the T- Omega method is a 3D finite-element method for computing the fields in and around conducting and magnetic materials at power frequencies. The magnetic field is represented as the sum of two parts: the gradient of a scalar potential and, in the conductors, an additional vector field represented by Whitney edge elements. The method is powerful but uses only a low-order approximation of the magnetic field. The paper describes a version using higher-order polynomials. Three sets of trial function spaces are defined: a set of irrotational spaces and two sets of rotational spaces (one for the impressed coil field and one for the induced eddy currents). By combining spaces from the three sets, a number of representations for the magnetic field is possible on the same mesh. The simplest representation corresponds to the Whitney element; the most accurate is fully quadratic in each tetrahedron. Furthermore, as the spaces are hierarchically constructed, it is possible to mix elements of different types on the same mesh without violating continuity requirements. Results for two test problems are presented: an infinite, current-carrying copper plate, and a copper block in the airgap of a magnetic circuit. The results demonstrate that the higher-order elements give greater accuracy for a given computational cost.

Exact black-hole solution with self-interacting scalar field

Abstract: Einstein gravity minimally coupled to a self-interacting scalar field is investigated in the static and isotropic situation. We explicitly construct in partially closed form a new black-hole solution with exponentially decaying scalar hair. The symmetric interaction potential has both signs and a triple-well shape with a smooth but non-analytic minimum at vanishing field. We present numerical data as well as double-series expansions around spatial infinity.

Exact solution of the Dirac equation for a Coulomb and scalar potential in the presence of an Aharonov-Bohm and a magnetic monopole fields

Abstract: In the present paper the problem of a relativistic Dirac electron is analyzed in the presence of a combination of a Coulomb field, a 1/r scalar potential, as well as a Dirac magnetic monopole and an Aharonov–Bohm potential. Using the algebraic method of separation of variables, the Dirac equation expressed in the local rotating diagonal gauge is completely separated in spherical coordinates, and exact solutions are obtained. The energy spectrum is computed and its dependence on the intensity of the Aharonov–Bohm and the magnetic monopole strengths is analyzed.

Dual Description of the Superconducting Phase Transition

Abstract: The dual approach to the Ginzburg-Landau theory of a Bardeen-Cooper-Schrieffer superconductor is reviewed. The dual theory describes a grand canonical ensemble of fluctuating closed magnetic vortices, of arbitrary length and shape, which interact with a massive vector field representing the local magnetic induction. When the critical temperature is approached from below, the magnetic vortices proliferate. This is signaled by the disorder field, which describes the loop gas, developing a non-zero expectation value in the normal conducting phase. It therby breaks a global U(1) symmetry. The ensuing Goldstone field is the magnetic scalar potential. The superconducting-to-normal phase transition is studied by applying renormalization group theory to the dual formulation. In the regime of a second-order transition, the critical exponents are given by those of a superfluid with a reversed temperature axis.

Canonical measure and the flatness of a FRW universe

Abstract: We consider the claim of Hawking and Page that the canonical measure applied to Friedmann--Robertson--Walker models with a massive scalar field can solve the flatness problem, i.e. , regardless of inflation occurring or not. We point out a number of ways in which this prediction, which relies predominantly on post-Planckian regions of the classical phase space, could break down. By considering a general potential we are able to understand how the ambiguity for found by Page in the -theory is present, in general, for scalar field models when the potential is bounded from above. We suggest reasons why such potentials are more realistic, which then results in the value of being arbitrary. Although the canonical measure gives an ambiguity (due to the infinite measure over arbitrary scale factors) for the possibility of inflation, the inclusion of an input from quantum cosmology could resolve this ambiguity. This could simply be that due to a `quantum event' the Universe started small, and provided a suitable scalar potential is present an inflationary period could then be `near certain' to proceed in order to set infinitesimally close to unity. We contrast the measure obtained in this way with the more usual ones obtained in quantum cosmology: the Hartle--Hawking and tunnelling ones.

Dual description of the superconducting phase transition

Abstract: The dual approach to the Ginzburg-Landau theory of a Bardeen-Cooper-Schrieffer superconductor is reviewed. The dual theory describes a grand canonical ensemble of fluctuating closed magnetic vortices, of arbitrary length and shape, which interact with a massive vector field representing the local magnetic induction. When the critical temperature is approached from below, the magnetic vortices proliferate. This is signaled by the disorder field, which describes the loop gas, developing a non-zero expectation value in the normal conducting phase. It thereby breaks a {\it global} U(1) symmetry. The ensuing Goldstone field is the magnetic scalar potential. The superconducting-to-normal phase transition is studied by applying renormalization group theory to the dual formulation. In the regime of a second-order transition, the critical exponents are given by those of a superfluid with a reversed temperature axis.

Exact solution of the Dirac equation for a Coulomb and a scalar Potential in the presence of of an Aharonov-Bohm and magnetic monopole fields

Abstract: In the present article we analyze the problem of a relativistic Dirac electron in the presence of a combination of a Coulomb field, a $1/r$ scalar potential as well as a Dirac magnetic monopole and an Aharonov-Bohm potential. Using the algebraic method of separation of variables, the Dirac equation expressed in the local rotating diagonal gauge is completely separated in spherical coordinates, and exact solutions are obtained. We compute the energy spectrum and analyze how it depends on the intensity of the Aharonov-Bohm and the magnetic monopole strengths.

Heavy quark 1/m Q expansion of meson weak decay form factors in the relativistic quark model

Abstract: The method of systematical expansion in the inverse powers of the heavy quark masses of the weak current matrix elements between heavy meson states is developed in the framework of the relativistic quark model based on the quasipotential approach in quantum field theory. The comparison of the first and second order terms of this expansion with the structure predicted by the heavy quark effective theory imposes strong constraints on the form of the long-range confining potential of quark-antiquark interaction. It is found that the confinig\(q\bar q\) potential is effectively vector, while scalar potential is anticonfining and helps to reproduce the correct nonrelativistic limit. At large distances quarks have nonperturbative anomalous chromomagnetic moments. The obtained values of the potential parameters are in accord with the ones found in our previous consideration of meson masses and decay rates. We calculate the Isgur-Wise function. The first and the second order form factors within 1/mQ expansion.

Strong Constraints on the Parameter Space of the MSSM from Charge and Color Breaking Minima

Abstract: A complete analysis of all the potentially dangerous directions in the field-space of the minimal supersymmetric standard model is carried out. They are of two types, the ones associated with the existence of charge and color breaking minima in the potential deeper than the realistic minimum and the directions in the field-space along which the potential becomes unbounded from below. The corresponding new constraints on the parameter space are given in an analytic form, representing a set of necessary and sufficient conditions to avoid dangerous directions. They are very strong and, in fact, there are extensive regions in the parameter space that become forbidden. This produces important bounds, not only on the value of $A$, but also on the values of $B$ and $M_{1/2}$. Finally, the crucial issue of the one-loop corrections to the scalar potential has been taken into account in a proper way.

Relativistic nuclear matter with alternative derivative coupling models

Abstract: Effective Lagrangians involving nucleons coupled to scalar and vector fields are investigated within the framework of relativistic mean-field theory. The study presents the traditional Walecka model and different kinds of scalar derivative couplings suggested by Zimanyi and Moszkowski. The incompressibility (presented in an analytical form), scalar potential, and vector potential at the saturation point of nuclear matter are compared for these models. The real optical potential for the models are calculated and one of the models fits well the experimental curve from [minus]50 to 400 MeV while also giving a soft equation of state. By varying the coupling constants and keeping the saturation point of nuclear matter approximately fixed, only the Walecka model presents a first order phase transition for finite temperature at zero density.

A simple method to compute spherical harmonic coefficients for the potential model of the coronal magnetic field

Abstract: It is impossible to make a direct measurement of the coronal magnetic field from the ground. The coronal magnetic field is, then, usually inferred by extrapolation of the observed photospheric magnetic field. The so-called ‘potential model’ has been used for this extrapolation. We have to solve the Laplacian equation of the magnetic scalar potential. This magnetic scalar potential can be expanded into a spherical harmonic series. In this paper, new simple recursion formulae are proposed to solve the Laplacian equation; that is, to determine the spherical harmonic coefficients.

DC current distributions and magnetic fields using the T-omega edge-element method

Abstract: When steady currents flow in solid conductors, the current distributions are not known in advance, and a 3D finite-element analysis of the magnetostatic fields must also involve an analysis of the currents. To find the currents, either of two potentials can be used: the electric scalar potential or a vector potential T for the current density. The scalar potential has the disadvantage of producing a current density that is only approximately solenoidal, and is therefore incompatible with Ampere's Law for the magnetic field. The vector potential gives solenoidal currents. It may conveniently be found by applying the T-/spl Omega/ edge element method, an existing method for eddy current problems, in one of two ways: setting the frequency so low that the DC solution is obtained; or solving first for T, then for /spl Omega/. Either way, both the current distribution and the magnetic field are obtained, and the solution is ideally suited for subsequent transient analysis. Results from three test problems confirm the validity of the method. >

Flat directions in the scalar potential of the supersymmetric standard model

Abstract: The scalar potential of the Minimal Supersymmetric Standard Model (MSSM) is nearly flat along many directions in field space. We provide a catalog of the flat directions of the renormalizable and supersymmetry-preserving part of the scalar potential of the MSSM, using the correspondence between flat directions and gauge-invariant polynomials of chiral superfields. We then study how these flat directions are lifted by non-renormalizable terms in the superpotential, with special attention given to the subtleties associated with the family index structure. Several flat directions are lifted only by supersymmetry-breaking effects and by supersymmetric terms in the scalar potential of surprisingly high dimensionality.

Spontaneous CP violation in supersymmetric models with four Higgs doublets.

Abstract: We consider supersymmetric extensions of the standard model with two pairs of Higgs doublets. We study the possibility that {ital CP} violation is generated spontaneously in the scalar sector via vacuum expectation values (VEV`s) of the Higgs fields. Using a simple geometrical interpretation of the minimum conditions we prove that the minimum of the tree-level scalar potential for these models is always real. We show that complex VEV`s can appear once radiative corrections and/or explicit {ital soft} {ital CP}-violating terms are added to the effective potential.

The separability theorem revisited with applications to light scattering theory

Abstract: The separability theorem states that, given a linear partial differential equation and special coordinates allowing to find a family of separated solutions, all solutions of the equation can be obtained from linear combinations of the separated solutions. In developing a light scattering theory, it has been recently observed that the theorem may apparently fail. The separability theorem is therefore revisited and more general solutions than usually considered for the scalar wave equation and the Bromwich scalar potential equation, in cylindrical and spherical coordinates, are exhibited. Relevance to light scattering theory is discussed.

The structure and the small-scale intermittency of passive scalars in homogeneous turbulence

Abstract: Results generated by direct numerical simulations (DNS) are used to study the structure and the small-scale intermittency of a passive scalar contaminant in a homogeneous turbulent shear flow. Simulations are conducted of flows with and without a constant mean scalar gradient. In all cases, the probability density functions (PDFs) of the scalars adopt an approximate gaussian distribution at the final stages of mixing. In the presence of the mean gradient, the scalar fields yield a nearly identical asymptotic state independent of initial conditions. In these cases, the gradient of the fluctuating scalar field shows preferred directions of orientation with respect to the strain eigenvectors; and the mean transverse velocity conditioned on the scalar is linear. These fields also portray increased flatness and skewness of the scalar-difference field as the separation distance becomes small. Larger than gaussian tails are observed in the PDF of both the velocity- and the scalar-derivatives, and the intermittency of the scalar derivative is shown to be more pronounced in the presence of the mean scalar gradient. Conditional averages of the angle between the scalar gradient and the strain eigenvectors suggest that the scalar field may be viewed as a random gaussian background field superimposed with sporadic scalar structures which are responsible for intermittency. With this view, a Langevin transport equation is proposed for the mapping of the scalar derivative PDF from a gaussian reference field. This is done in the context of the “two-fluid” model of She (1990). With this model, the PDF of the scalar dissipation is produced and the results are compared with DNS data.

A Challenge for Magnetic Scalar Potential Formulations of 3-D Eddy Current Problems: Multiply Connected Cuts in Multiply Connected Regions which Necessarily Leave the Cut Complement Multiply Connected

Abstract: Formulations for making cuts for the magnetic scalar potential in 3-dimensional finite element meshes often assume a priori that cuts should render the nonconducting region simply-connected in order to have a single-valued scalar potential. Starting with the Biot-Savart integral and its interpretation through the Gauss linking number, this paper develops a (co)homology-based definition of cuts which make the scalar potential single-valued but do not guarantee simple connectivity. The variational problem resulting from an algorithm to compute the cuts is then discussed and used to reinforce the central theme of linking. The assumption of simple connectivity is examined in light of the relationship between homotopy and homology to show that it is over-restrictive and moreover, not related to Ampere’s Law.

On the essential self-adjointness of the relativistic hamiltonian with a negative scalar potential

Abstract: The relativistic quantum Hamiltonian H describing a spinless particle in an electromagnetic field is considered. H is associated with the classical Hamiltonian via Weyl’s correspondence. In the previous papers the second author has proved that H is essentially self-adjoint on if the scalar potential V(x) is a function bounded from below by a polynomial in x. In the present paper this result will be extended to show that H is essentially self-adjoint there if V(x) is bounded from below by -C exp a|x| for some positive constants C and a. Ameliorated is also the condition on the vector potential A(x). The result of this kind is quite different from that on the non-relativistic operator, i.e. the Schrodinger operator, but much closer to that on the Dirac operator.

Mass spectra from field equations. II. The electromagnetic contribution

Abstract: In the first article a method for finding a mass spectrum from a given field equation was developed. The method is extended here to provide for the self‐electromagnetic effect on the rest mass. The process is described by example: the method is applied here for the equations of a complex scalar field interacting with the electromagnetic field. A spectrum of charged‐particle masses is obtained. A quantum number for the charges of the mass levels appears. After some special assumptions about the dependence on the vector potential are made, there are finite electromagnetic contributions to the rest masses of the particle states.

Regular boundary integral solution with dual and complementary variational formulations applied to two‐dimensional Laplace problems

Abstract: Regular boundary integral elements are employed for the dual and complementary variational formulations of Laplace problems. The problems are defined only on the boundary as usual, but as in the manner of charge simulation method (CSM), the source terms are arranged outside the domain so that the singular integral can be avoided. The Laplace problems are analysed and the usefulness of the formulation is discussed in comparison with direct BEM. The scalar potential and electric displacement vector potential functions are used in the dual and complementary formulations, with which the upper and lower bounds of the system energy or the capacitance can also accurately be evaluated.

On a class of solvable Pauli-Schrödinger hamiltonians

Abstract: To every scalar potential for which the bound state problem of the Schrodinger equation can be (at least partially) solved it is possible to associate a new potential containing Pauli matrices and for which the associated Pauli-Schrodinger equation can also be solved to the same extent. The new system can be regarded as a finite break of the supersymmetry that the original system and its supersymmetric partner have.

Self-dual non-abelian vortices in a $\phi^2$ chern-simons theory

Abstract: We study a non-Abelian Chern-Simons gauge theory in $ 2+ 1$ dimensions with the inclusion of an anomalous magnetic interaction. For a particular relation between the Chern-Simons (CS) mass and the anomalous magnetic coupling the equations for the gauge fields reduce from second- to first order differential equations of the pure CS type. We derive the Bogomol'nyi-type or self-dual equations for a $\bphi^2$ scalar potential, when the scalar and topological masses are equal. The corresponding vortex solutions carry magnetic flux that is not quantized due to the non-toplogical nature of the solitons. However, as a consequence of the quantization of the CS term, both the electric charge and angular momentum are quantized.

A discussion of the uniqueness of a Laplacian potential when given only partial field information on a sphere

Abstract: Summary For a vector field defined by a scalar potential outside a surface enclosing all the sources, it is well known that the potential is defined uniquely if either the potential itself, or its derivative normal to the surface, is known everywhere on the surface. For a spherical surface, the normal derivative is the radial component of the field: the horizontal (vector) component of the field also gives uniqueness (except for any monopole contribution). This paper discusses the way other partial information of the field on the spherical surface can give a unique, or almost unique, knowledge of the external potential/field, bringing together and correcting previous work. For convenience the results are given in the context of the geomagnetic field B. This is often expressed in terms of its local Cartesian components (X, Y, Z), equivalent to (-Bo, Bθ,-Br); it can also be expressed in terms of Z and the vector horizontal component H= (X, Y). Alternatively, local ‘spherical polar’ components (F, I, D) are used, where F=|B|, the inclination I is the angle in the vertical plane downward from H to B, and the declination D is the angle in the horizontal plane eastward from north to H. Knowledge of X over the sphere gives a complete knowledge of the potential, apart from that of any monopole (which is zero in geomagnetism), and Y gives the potential except for any axially symmetric part (which can be provided by a knowledge of X along a meridian, or of H along any path from pole to pole). In terms of (F, I, D) the situation is more complicated; either For the total angle (I, D) needs to be known throughout a finite volume; for the latter, this paper shows how, in principle, the actual potential can be determined (except for an unknown scaling factor). Similarly D on the sphere also needs a knowledge of |H| on a line from (magnetic) pole to pole. We also discuss how these various properties affect the determination, by surface integration, of the Gauss coefficients of the field representation in terms of spherical harmonics.