Showing papers on "Scalar potential published in 2003"

Scalar hairy black holes and solitons in asymptotically flat spacetimes

Abstract: A numerical analysis shows that the Einstein field equations allow static and spherically symmetric black hole solutions with scalar-field hair in asymptotically flat spacetimes. When regularity at the origin is imposed (i.e., in the absence of a horizon) globally regular scalar solitons are found. The asymptotically flat solutions are obtained provided that the scalar potential $V(\ensuremath{\varphi})$ of the theory is not positive semidefinite and such that its local minimum is also a zero of the potential, the scalar field settling asymptotically at that minimum. The configurations, although unstable under spherically symmetric linear perturbations, are regular and thus can serve as counterexamples to the no-scalar-hair conjecture.

Identification of sources of potential fields with the continuous wavelet transform: Two-dimensional wavelets and multipolar approximations

Abstract: [1] We show new continuous wavelet-based transformation techniques of potential field maps and propose interpretation schemes for characterizing three-dimensional (3-D) sources having some finite extent. As in previous studies, we use wavelets derived from the Poisson kernel which generate a position-altitude representation of potential field data initially measured at one level above the ground. We use first-order or second-order wavelets to obtain wavelet transform parameters related to the 3-D analytic signals or 3 × 3 tensors of the data. We show how such parameters can be used to characterize the sources, first, by using the assumption of their local homogeneity and, second, by using multipolar expansions to estimate the sizes of the horizontal or vertical extent of the 3-D source. Thus we generalize to 3-D the Taylor expansion of upward continued 2-D analytic signals previously shown for the interpretation of profiles transformed using complex wavelets. Such a 3-D interpretation scheme based upon position-altitude representations has been developed to interpret the maps of scalar potential field anomalies (e.g., magnetic total field anomalies or vertical gravity anomalies) but can be also used for upward continued maps of vector or tensor of potential field anomalies as obtained by new surveys of the full tensor of gravity; this also concerns the interpretation of derived potentials considered in poroelasticity and electrokinetic in porous materials of the Earth. We illustrate the technique on synthetic data; in addition, a first application on aeromagnetic data from French Guyana shows the potential of the technique.

A nonlinear circuit coupled t-t/sub 0/-/spl phi/ formulation for solid conductors

Abstract: A new three-dimensional (3-D) finite element formulation based on the use of the magnetic scalar potential is proposed. It allows the description of multiply connected solid conductors coupled to electric circuits and to take into account the nonlinearities. Like the solutions using the magnetic vector potential, it is a general formulation and offers powerful solutions but at a lower cost.

Quantum Mechanics on Manifolds Embedded in Euclidean Space

Abstract: Quantum particles confined to surfaces in higher dimensional spaces are acted upon by forces that exist only as a result of the surface geometry and the quantum mechanical nature of the system. The dynamics are particularly rich when confinement is implemented by forces that act normal to the surface. We review this confining potential formalism applied to the confinement of a particle to an arbitrary manifold embedded in a higher dimensional Euclidean space. We devote special attention to the geometrically induced gauge potential that appears in the effective Hamiltonian for motion on the surface. We emphasize that the gauge potential is only present when the space of states describing the degrees of freedom normal to the surface is degenerate. We also distinguish between the effects of the intrinsic and extrinsic geometry on the effective Hamiltonian and provide simple expressions for the induced scalar potential. We discuss examples including the case of a 3-dimensional manifold embedded in a 5-dimensional Euclidean space.

Vector potential of the Coulomb gauge

Abstract: The vector decomposition theorem of Helmholtz leads to a form of the Coulomb gauge in which the potentials are expressed in a form that is totally instantaneous. The scalar potential is expressed in terms of the instantaneous charge density, the vector potential in terms of the instantaneous magnetic field.

Group theory approach to the Dirac equation with a Coulomb plus scalar potential in D+1 dimensions

Abstract: We generalize the Dirac equation to D+1 space–time. The conserved angular momentum operators and their quantum numbers are discussed. The eigenfunctions of the total angular momentums are calculated for both odd D and even D cases. The exact solutions of the D+1-dimensional radial equations of the Dirac equation with a Coulomb plus scalar potential are analytically presented by studying the Tricomi equations obtained from a pair of coupled first-order ones. The eigenvalues are also discussed in some detail.

Semantics of dyadic and mixed potential field representation for 3-D current distributions in planar stratified media

Abstract: The full spectral electric dyadic Green's function for three dimensional current distributions in planar stratified media can be obtained straight from Maxwell's equations. By following a physical reasoning analogous with the free space case but using general derivative relations for multilayered Green's functions, we derive a "basic" mixed potential form with a simple vector potential kernel but multiple scalar potential kernels, and also obtain the well established single scalar potential formulations with a dyadic vector potential kernel. Mixed potential forms are thus arrived at without the a priori introduction of scalar and vector potential, or choice of gauge condition. The nonuniqueness of the scalar potential kernel and the dyadic nature of the scalar and/or vector potentials are believed to be clarified by the proposed approach. A discussion of the different formulations focuses on physical meaning and numerical consequences for the solution of integral equations.

Regularization of spherical cap harmonics

Abstract: SUMMARY Spherical cap harmonic analysis has become a well-known technique for regional modelling of fields that can be expressed as the gradient of a scalar potential, such as for example the geomagnetic field and its secular variation. Up to now, the method has been regularized by a purely statistical technique: coefficients that are considered to be statistically insignificantly small are simply set to zero. This method lacks physical justification and ignores resolution; individual coefficients may be small but well-resolved, while coefficients with a large value may be poorly resolved. We implement the more physical regularization technique of minimizing a certain feature of the field, for example the field strength over the cap surface, analogous to the regularization techniques widely used in global spherical harmonic analysis. The mathematical difference between spherical cap harmonics (SCHA) and global spherical harmonics analyses (SHA) lies in the basis functions. While these are completely orthogonal in SHA, this is not the case in SCHA. This leads to the existence of certain linear combinations of coefficients that hardly contribute to the field, which makes the statistical rejection criterion meaningless. With the physical regularization the individual coefficients become meaningful, as we show by modelling the secular variation from a data set of 30 years of European observatory measurements, repeat station and ground vector surveys.

Coupled problem computation of 3-D multiply connected magnetic circuits and electrical circuits

Abstract: This paper presents the theory and the validation of a new finite-element formulation to realize the coupling between electrical circuits and multiply connected magnetic circuits, using a magnetic scalar potential as state variable. For this purpose, we used formulations in reduced magnetic scalar potential versus T/sub 0/ taking into account electrical circuits and a total magnetic scalar potential taking into account cuts.

Dynamics of a scalar field in a brane world

Abstract: We study the dynamics of a scalar field in brane cosmology. We assume that the scalar field is confined in our four-dimensional world. As for the potential of the scalar field, we discuss three typical models: (1) a power-law potential, (2) an inverse-power-law potential, and (3) an exponential potential. We show that the behavior of the scalar field is very different from that in conventional cosmology when the energy density square of the term dominates.

An algorithm to construct the discrete cohomology basis functions required for magnetic scalar potential formulations without cuts

Abstract: Magnetic scalar potential formulations without cuts require the definition of a set of basis functions for the cohomology structure of the magnetic field function space. This paper presents an algorithm to construct such a basis in the general case thanks to a properly chosen spanning tree. The algorithm is based on the topological properties of the discrete Whitney complex. It applies to static and dynamic problems.

Topological analysis and characterization of discrete scalar fields

Abstract: In this paper, we address the problem of analyzing the topology of discrete scalar fields defined on triangulated domains. To this aim, we introduce the notions of discrete gradient vector field and of Smale-like decomposition for the domain of a d-dimensional scalar field. We use such notions to extract the most relevant features representing the topology of the field. We describe a decomposition algorithm, which is independent of the dimension of the scalar field, and, based on it, methods for extracting the critical net of a scalar field. A complete classification of the critical points of a 2-dimensional field that corresponds to a piecewise differentiable field is also presented.

Local Friedel sum rule on graphs

Abstract: We consider graphs made of one-dimensional wires connected at vertices and on which may live a scalar potential. We are interested in a scattering situation where the graph is connected to infinite leads. We investigate relations between the scattering matrix and the continuous part of the local density of states, the injectivities, emissivities and partial local density of states. Those latter quantities can be obtained by attaching an extra lead at the point of interest and by investigating the transport in the limit of zero transmission into the additional lead. In addition to the continuous part related to the scattering states, the spectrum of graphs may present a discrete part related to states that remain uncoupled to the external leads. The theory is illustrated with the help of a few simple examples.

Enriching Volume Modelling with Scalar Fields

Abstract: A scalar field is a generalisation of a surface function in dimension Visualisation traditionally focuses on discrete specifications of scalar fields (eg, volume datasets) This paper discusses the role of continuous and procedural field specifications in volume visualisation and volume graphics, and the inter-operations between continuous and discrete specifications It demonstrates the different use of scalar fields through several modelling aspects, including constructive volume geometry and non-photorealistic textures, and presents our approaches to the creation of more photorealistic effects in direct volume rendering

General Brane Geometries from Scalar Potentials: Gauged Supergravities and Accelerating Universes

Abstract: We find broad classes of solutions to the field equations for d-dimensional gravity coupled to an antisymmetric tensor of arbitrary rank and a scalar field with non-vanishing potential. Our construction generates these configurations from the solution of a single nonlinear ordinary differential equation, whose form depends on the scalar potential. For an exponential potential we find solutions corresponding to brane geometries, generalizing the black p-branes and S-branes known for the case of vanishing potential. These geometries are singular at the origin with up to two (regular) horizons. Their asymptotic behaviour depends on the parameters of the model. When the singularity has negative tension or the cosmological constant is positive we find time-dependent configurations describing accelerating universes. Special cases give explicit brane geometries for (compact and non-compact) gauged supergravities in various dimensions, as well as for massive 10D supergravity, and we discuss their interrelation. Some examples lift to give new solutions to 10D supergravity. Limiting cases with a domain wall structure preserve part of the supersymmetries of the vacuum. We also consider more general potentials, including sums of exponentials. Exact solutions are found for these with up to three horizons, having potentially interesting cosmological interpretation. We give several additional examples which illustrate the power of our techniques.

Method for enhancing depth and spatial resolution of one and two dimensional residual surfaces derived from scalar potential data

Abstract: An improved method is disclosed for collecting or assembling scalar potential data measurements that are to be subsequently prepared as a surface representation for analysis via frequency domain transform filters. Measurements are made over a geographic reference region which extends in all cardinal directions from the center of some previously determined primary region. The reference dimensions must contain the primary region and must be plural multiples of the greatest depth to be considered in analyzing the contributions to the measurements. A combined or separate improved method for delineating or defining geospatial information contributing to a scalar potential surface is disclosed. This method is implemented using traditional statistical techniques to construct an histogram from the set of values comprising a surface representation. This histogram constitutes a Spatially Correlated Potential Spectrum for the surface. These combined and separate methods improve resolution of geological structures over depths and spatial extents under consideration.

An electrically conducting sphere in a three‐dimensional, alternating magnetic field

Abstract: The electrical vector and scalar potential as well as the underlying induced eddy current density of a conducting sphere exposed to an external, time-varying magnetic field are calculated. The external magnetic field is assumed to be generated by sinusoidally alternating current density distributions. Admitting arbitrary three-dimensional current density fields, this paper extends previous results on this subject. Among other things, these calculations prove that in a sphere there is no radial component of the induced eddy current density field. As an application of these results the impedance and power absorption of the sphere are derived. The impedance is the key for the contactless, inductive measurement of the electrical conductivity of metallic melts.

Scalar model of the glueball

Abstract: A scalar model of the glueball is offered. The model is based on the nonperturbative calculation of 2 and 4-points Green's functions. Approximately they can be expressed via a scalar field. On the basis of the SU(3) Yang-Mills Lagrangian an effective Lagrangian for the scalar field is derived. The corresponding field equations are solved for the spherically symmetric case. The obtained solution is interpreted as a bubble of the SU(3) quantized gauge field.

Using the vector potential in evaluating the likelihood of peripheral nerve stimulation due to switched magnetic field gradients

Abstract: The time-varying magnetic field gradients used in MRI can cause peripheral nerve stimulation (PNS) in human subjects, as a result of the electric fields induced in tissue. The local electric field, E, is given by E = - partial differential A/ partial differential t - nabla phi where A, is the vector potential and phi is the scalar electric potential generated by charges accumulated at boundaries between regions of different conductivity. Difficulties in calculating phi have led some investigators to use - partial differential A/ partial differential t alone as a predictor of the induced field. Here the spatial variation of - partial differential A/ partial differential t and E is investigated for the case of a simple spherical conductor exposed to time-varying gradients produced by two different gradient coils that generate identical internal magnetic fields, but very different vector potentials. The results indicate that the temporal derivative of A bears little relation to the induced electric field, and that consequently neglecting the effect of the scalar potential introduces significant errors in estimating the likelihood of PNS.

Singular compactifications and cosmology

Abstract: We summarize our recent results of studying five-dimensional Kasner cosmologies in a time-dependent Calabi-Yau compactification of Mtheory undergoing a topological flop transition. The dynamics of the additional states, which become massless at the transition point and give rise to a scalar potential, helps to stabilize the moduli and triggers short periods of accelerated cosmological expansion.

Domain wall dynamics of phase interfaces

Abstract: The statics and dynamics of a surface separating two phases of a relativistic quantum field theory at or near the critical temperature typically make use of a free energy as a functional of an order parameter. This free energy functional also affords an economical description of states away from equilibrium. The similarities and differences between using a scalar field as the order parameter versus the energy density are examined, and a peculiarity is noted. We also point out several conceptual errors in the literature dealing with the dynamical prefactor in the nucleation rate.

Charge and currents distribution in graphs

Abstract: We consider graphs made of one-dimensional wires connected at vertices, and on which may live a scalar potential. We are interested in a scattering situation where such a network is connected to infinite leads. We study the correlations of the charge in such graphs out of equilibrium, as well as the distribution of the currents in the wires, inside the graph. These quantities are related to the scattering matrix of the graph. We discuss the case where the graph is weakly connected to the wires.

The scalar sector in 331 models

Abstract: We calculate the exact tree-level scalar mass matrices resulting from symmetry breaking using the most general gauge-invariant scalar potential of the 331 model, both with and without the condition that the lepton number is conserved. Physical masses are also obtained in some cases, as well as couplings to standard and exotic gauge bosons.

Asymptotic analysis of the electrostatic wave equation in a toroidal plasma

Abstract: An analytical study is presented of the wave equation that describes the propagation of an electrostatic pulse in a cold plasma in a general magnetic equilibrium by means of a multiple spatial scale approach. This technique is strictly related with that discussed earlier by Zonca and Chen [Phys. Fluids B 5, 3668 (1993)], and, when applied to plasma instabilities, reduces to the well-known “ballooning formalism” [J. W. Connor, R. J. Hastie, and J. B. Taylor, Phys. Rev. Lett. 40, 396 (1978)]. A simplified equation for the scalar potential in the cold plasma limit will be derived and studied by applying the WKB asymptotic technique to describe the slow radial dependencies of the wave envelope, while the full-wave equation will be considered along the magnetic field lines. This ansatz can be entirely justified on the basis of spatial scale separation in the radial direction and for waves that have parallel group velocity faster than in the perpendicular direction. Thus, this approach could be viewed as a mixed WKB-full-wave technique.

An accurate broadband method of moments using higher order basis functions and tree-loop decomposition

Abstract: The method of moments (MoM) has been one of the most popular computational methods for the solution of electromagnetic scattering problems. While many MoM formulations are possible, the electric field integral equation (EFIE) formulation is of great importance as it can be applied to either closed or open structures. Unfortunately, at very low frequencies, naive EFIE implementations become inaccurate due to severe cancellation in the computation of the scalar potential. This work presents a method to create a loop-tree decomposition for the divergence-conforming higher-order triangular patch bases so that a single mesh can be used to gather broadband information. The proposed method is completely general, and works for any basis function order. In addition, frequency scaling of the impedance matrix was used to further lower its condition number and the right hand side was reformulated to alleviate subtractive cancellation.

Bound states of Klein-Gordon equation for scalar and vector linear potentials

Abstract: The s-wave bound state solutions of Klein-Gordon equation are obtained when a linear-type scalar potential is not less than its vector potential, and its solutions are expressed by the confluent hypergeometric function.

Two-dimensional gravity with an invariant energy scale and arbitrary dilaton potential

Abstract: We investigate a model of two-dimensional gravity with arbitrary scalar potential obtained by gauging a deformation of de Sitter or more general algebras, which accounts for the existence of an invariant energy scale. We obtain explicit solutions of the field equations and discuss their properties.