Showing papers on "Scalar potential published in 1998"
TL;DR: In this article, the authors classify all potentials for which the scalar field energy density scales as a power law of the scale factor when the perfect fluid density dominates, and provide a complete analysis of exact solutions and their stability properties.
Abstract: An attractive method of obtaining an effective cosmological constant at the present epoch is through the potential energy of a scalar field. Considering models with a perfect fluid and a scalar field, we classify all potentials for which the scalar field energy density scales as a power law of the scale factor when the perfect fluid density dominates. There are three possibilities. The first two are well known; the much-investigated exponential potentials have the scalar field mimicking the evolution of the perfect fluid, while for negative power laws, introduced by Ratra and Peebles, the scalar field density grows relative to that of the fluid. The third possibility is a new one, where the potential is a positive power law and the scalar field energy density decays relative to the perfect fluid. We provide a complete analysis of exact solutions and their stability properties, and investigate a range of possible cosmological applications.
592 citations
TL;DR: In this article, an equation of state (EOSM) for strange stars is derived from an interquark potential, which has asymptotic freedom built into it, shows confinement at zero density (ρB=0) and deconfinement at high ρB, and gives a stable configuration for chargeless, β-stable quark matter.
266 citations
TL;DR: In this paper, the elastic field around a buried, strained quantum dot is solved with a scalar potential that obeys Poisson's equation and is analogous to the charge density and electric field.
Abstract: The elastic field around a buried, strained quantum dot is solved with a scalar potential that obeys Poisson’s equation. Standard methods from electrostatics can therefore be used. The lattice mismatch and displacement are analogous to the charge density and electric field. The dilation is proportional to the local lattice mismatch and therefore vanishes outside a dot. Expressions are also given for the piezoelectric potential. The results agree remarkably well with previous numerical calculations for a pyramidal dot. Thermoelasticity provides another analogy with many useful solutions available. These results are for an isotropic medium but cubic symmetry is considered briefly.
147 citations
TL;DR: In this article, it was shown that uniform electric fields can be represented by voltage sources in the transmission lines or at power system ground points, while realistic electric fields such as those produced by the auroral electrojet, cannot be represented with voltage sources at ground points.
Abstract: The methods used to model geomagnetically induced currents (GIC) on power systems depend on the nature of the electric field used as input. A uniform electric field, often used to simplify the modelling, is shown to have different properties from realistic nonuniform fields. Realistic fields which go to zero at infinity can be uniquely represented by the sum of the gradient of a scalar potential and the curl of a vector function. The scalar potential term is conservative and irrotational, while the vector term is nonconservative and solenoidal. In contrast, a uniform electric field can be represented simply by the gradient of a scalar potential. These different mathematical properties mean that modelling techniques derived for uniform fields may not work for realistic fields. This is examined using, as an example, the modelling of GIC produced in a conducting network at the surface of the Earth. It is shown that uniform electric fields can be represented by voltage sources in the transmission lines or at power system ground points. However, realistic electric fields, such as those produced by the auroral electrojet, cannot be represented by voltage sources at ground points and have to be represented by a voltage source in the transmission lines.
115 citations
TL;DR: In this article, four methods are presented and investigated on a 3D time harmonic eddy current problem, using the T,/spl Phi/-/spl Phi/ Phi/ finite element formulation, and the results obtained are compared with transient computation.
Abstract: Several possibilities are presented to deal with nonlinearity in ferromagnetic media in the case of time harmonic excitation in steady state, without losing simplicity in describing the potentials by means of complex peak values. The main idea is to introduce a fictitious time independent and inhomogeneous material to take into account the nonlinear relationship between the field quantities. Four methods are shown and investigated on a 3D time harmonic eddy current problem, using the T,/spl Phi/-/spl Phi/ finite element formulation. The vector potential is represented by means of edge elements and the scalar potential by nodal elements. The results obtained are compared with transient computation.
102 citations
TL;DR: In this article, the Bern-Kosower method was used to calculate the higher derivative expansion of the one-loop effective action for an external scalar potential, using the string-inspired Bern-inspired method in the first quantized path integral formulation.
70 citations
TL;DR: In this article, it was shown that for two-dimensional Schrodinger operators with a nonzero constant magnetic field perturbed by a magnetic field and a scalar potential, both vanishing arbitrarily slow at infinity, the eigenfunctions corresponding to the discrete spectrum decay faster than any exponential.
Abstract: For two dimensional Schrodinger operators with a nonzero constant magnetic field perturbed by a magnetic field and a scalar potential, both vanishing arbitrarily slow at infinity, it is proved that eigenfunctions corresponding to the discrete spectrum decay faster than any exponential. Under more restrictive conditions on the perturbations, even quicker decay is obtained.
58 citations
TL;DR: In this paper, a quasi-Newtonian dynamical model for a generic dust matter source field in a cosmological context is formulated with respect to a non-comoving Newtonian-like timelike reference congruence and investigated for internal consistency.
Abstract: Exact dynamical equations for a generic dust matter source field in a cosmological context are formulated with respect to a non-comoving Newtonian-like timelike reference congruence and investigated for internal consistency. On the basis of a lapse function N (the relativistic acceleration scalar potential) which evolves along the reference congruence according to , we find that consistency of the quasi-Newtonian dynamical equations is not attained at the first derivative level. We then proceed to show that a self-consistent set can be obtained by linearizing the dynamical equations about a (non-comoving) FLRW background. In this case, on properly accounting for the first-order momentum density relating to the non-relativistic peculiar motion of the matter, additional source terms arise in the evolution and constraint equations describing small-amplitude energy density fluctuations that do not appear in similar gravitational instability scenarios in the standard literature.
53 citations
TL;DR: In this paper, a multiple-time-scale expansion of reduced magnetohydrodynamic (MHD) equations is employed to evolve scalar potential quantities on a time scale associated with the parallel wave vector, which is the time scale of interest for MHD instability studies.
Abstract: A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Ad...
47 citations
TL;DR: In this paper, the ground wave propagation characteristics for a vertically polarized short electric dipole over a smooth spherical earth are reviewed, reducing the vector electromagnetic problem for the three-dimensional spherical geometry to an equivalent two-dimensional rectilinear scalar potential problem which is solved by spectral analysis and synthesis.
Abstract: An efficient novel algorithm is introduced for ground wave propagation problems. First, ground wave propagation characteristics for a vertically polarized short electric dipole over a smooth spherical earth are reviewed, reducing the vector electromagnetic problem for the three-dimensional spherical geometry to an equivalent two-dimensional rectilinear scalar potential problem which is solved by spectral analysis and synthesis. Alternative evaluations of the spectral integral yield ray optical and normal mode solutions, which are conventionally referred to as the Norton and Wait formulations, respectively. Combining these formulations in an efficient manner yields a hybrid algorithm which is constructed so as to account adaptively for the characteristics of ground wave propagation in interference, intermediate and diffraction regions (including mixed paths) for various source and/or receiver heights. Numerical comparisons are made with reference results obtained via the parabolic equation (PE) method, in parametric ranges where PE is reliable; this permits assessment of the effectiveness of the hybrid approach. © 1998 John Wiley & Sons, Ltd.
43 citations
TL;DR: In this article, exact dynamical equations for a generic dust matter source field in a cosmological context are formulated with respect to a non-comoving Newtonian-like timelike reference congruence and investigated for internal consistency.
Abstract: Exact dynamical equations for a generic dust matter source field in a cosmological context are formulated with respect to a non-comoving Newtonian-like timelike reference congruence and investigated for internal consistency. On the basis of a lapse function $N$ (the relativistic acceleration scalar potential) which evolves along the reference congruence according to $\dot{N} = \alpha \Theta N$ ($\alpha = {const}$), we find that consistency of the quasi-Newtonian dynamical equations is not attained at the first derivative level. We then proceed to show that a self-consistent set can be obtained by linearising the dynamical equations about a (non-comoving) FLRW background. In this case, on properly accounting for the first-order momentum density relating to the non-relativistic peculiar motion of the matter, additional source terms arise in the evolution and constraint equations describing small-amplitude energy density fluctuations that do not appear in similar gravitational instability scenarios in the standard literature.
TL;DR: In this article, an equivalence between the equations of the reluctance network method and the edge element method has been presented, where the edge values of magnetic vector potential represent the loop fluxes in reluctance network and magnetic scalar potential is determined in the centre of gravity of the element.
Abstract: Equivalence between the equations of the reluctance network method and the equations of the edge element method has been presented. The edge values of magnetic vector potential represent the loop fluxes in reluctance network Magnetomotive forces in the branches of the reluctance network are defined by the edge values of current vector potential. The magnetic scalar potential is determined in the centre of gravity of the element. The reluctance network formed by the edge element method contains mutual reluctances.
TL;DR: In this article, the authors give analytical expressions for the geometric potentials in the dark states of a driven $\stackrel{\ensuremath{\rightarrow}}{j}j\ensure-math{-}1$ transition and the dark state in the $\ stackrel{\ensemblemath{rightarrow}{1}1} 1$ system, for arbitrary electromagnetic fields.
Abstract: Quantum motion of atoms in light fields is described on the basis of adiabatic internal states. Forces arise due to the spatial variation of these states, which is determined by the electric field polarization. In a dark state, these are the only forces present. They are described by a geometric vector and a scalar potential. We give analytical expressions for the geometric potentials in the dark states of a driven $\stackrel{\ensuremath{\rightarrow}}{j}j\ensuremath{-}1$ transition and the dark state in the $\stackrel{\ensuremath{\rightarrow}}{1}1$ system, for arbitrary electromagnetic fields. For systems with velocity selective trapping states, the scalar geometric potential is inversely proportional to the field intensity squared. When the field has nodes the potential diverges. In one dimension, this constitutes an exact realization of the Kronig-Penney model.
TL;DR: In this paper, two solutions of the minimally coupled Einstein-scalar field equations, representing regular deformations of Schwarzschild black holes by a selfinteracting, static, scalar field were constructed.
Abstract: We construct two solutions of the minimally coupled Einstein–scalar field equations, representing regular deformations of Schwarzschild black holes by a selfinteracting, static, scalar field. One solution features an exponentially decaying scalar field and a triple-well interaction potential; the other one is completely analytic and sprouts Coulomb-like scalar hair. Both evade the no-hair theorem by having partially negative potential, in conflict with the dominant energy condition. The linear perturbation theory around such backgrounds is developed in general, and yields ! !
TL;DR: In this paper, a relativistic analogue of the quantum adiabatic approximation is developed for Klein-Gordon fields minimally coupled to electromagnetism, gravity and an arbitrary scalar potential.
Abstract: A relativistic analogue of the quantum adiabatic approximation is developed for Klein-Gordon fields minimally coupled to electromagnetism, gravity and an arbitrary scalar potential. The corresponding adiabatic dynamical and geometrical phases are calculated. The method introduced in this paper avoids the use of an inner product on the space of solutions of the Klein-Gordon equation. Its practical advantages are demonstrated in the analysis of the relativistic Landau level problem and the rotating cosmic string.
TL;DR: In this paper, the effect of a uniform intense terahertz radiation on hot-electron transport in semiconductors driven by a dc or slowly varying electric field of arbitrary strength was investigated.
Abstract: We investigate the effect of a uniform intense terahertz radiation on hot-electron transport in semiconductors driven by a dc or slowly varying electric field of arbitrary strength. Using a vector potential for the high-frequency field and a scalar potential for the dc or slowly varying field, we are able to separate the center-of-mass motion from relative motion of electrons and to distinguish the slowly varying part from the rapidly oscillating part of the center-of-mass velocity. Considering the fact that relevant transport quantities are measured over a time interval much longer than the period of the terahertz radiation field, we obtain a set of momentum and energy balance equations, without invoking a perturbational treatment of the electron-photon interaction. These equations, which include all the multiphoton processes, are applied to the examination of hot-carrier transport in a GaAs-based quantum well subjected to a weak or a strong dc bias and irradiated by a terahertz radiation of various frequency and strength in both the parallel and vertical configurations. Up to as many as |n|=50 absorption and emission multiphoton channels are included in the numerical calculation. The present approach turns out to be a very convenient and efficient tool to study the effect of an intense high-frequency radiation on dc or slowly varying carrier transport in semiconductors. Its applicable frequency range and its connection with previously developed balance-equation treatment are discussed.
TL;DR: In this article, the Anderson transition in three dimensions in a randomly varying magnetic flux is investigated by means of the transfer matrix method with high accuracy, and the results support the conventional classification of universality classes due to symmetry.
Abstract: The Anderson transition in three dimensions in a randomly varying magnetic flux is investigated in detail by means of the transfer matrix method with high accuracy. Both, systems with and without an additional random scalar potential are considered. We find a critical exponent of $
u=1.45\pm0.09$ with random scalar potential. Without it, $
u$ is smaller but increases with the system size and extrapolates within the error bars to a value close to the above. The present results support the conventional classification of universality classes due to symmetry.
TL;DR: In this article, the A/spl I.oarr/T/pl I.Oarr/t/splI.o arr/T /spl I this article formulation is applied on the computation of the 3D time-harmonic eddy current field of an induction furnace and is compared to other formulations as well.
Abstract: Most papers concerning the calculation of 3D eddy current problems are using a combination of a vector potential and a scalar potential to solve the electromagnetic field in conducting regions. This paper presents the A/spl I.oarr/T/spl I.oarr/ formulation using both the magnetic vector potential A/spl I.oarr/ and the electric vector potential T/spl I.oarr/ for the eddy current regions. Since nodal vector potentials with continuous normal components have accuracy problems at interfaces of regions with different permeabilities, edge elements are used for both potentials. The advantages of the presented formulation compared to the mentioned well-known formulations are described in detail. The formulation is applied on the computation of the 3D time-harmonic eddy current field of an induction furnace and is compared to other formulations as well.
TL;DR: In this article, the authors prove the cosmic no-hair conjecture for orthogonal, initially expanding Bianchi cosmologies in the theory with matter satisfying the strong and dominant energy conditions using the conformally equivalent Einstein field equations, with the scalar field having the full selfinteracting potential.
Abstract: We prove the cosmic no-hair conjecture for orthogonal, initially expanding Bianchi cosmologies in the theory with matter satisfying the strong and dominant energy conditions using the conformally equivalent Einstein field equations, with the scalar field having the full self-interacting potential. We assume that the universe is initially on the flat plateau of the potential and its initial kinetic energy is negligible with respect to its potential energy. We show, in particular, that the Bianchi IX universe asymptotically approaches de Sitter space provided that initially the scalar 3-curvature does not exceed the potential of the scalar field associated with the conformal transformation. Our proof relies on rigorous estimates of the possible bounds of the so-called Moss-Sahni function which obeys certain differential inequalities, and a non-trivial argument which connects the behaviour of this function to the evolution of the spatial part of the scalar curvature.
TL;DR: In this article, the spectrum of spherically symmetric Dirac operators with potentials tending to infinity at infinity under weak regularity assumptions was studied and it was shown that the positive part of the spectrum is purely discrete.
Abstract: We study the spectrum of spherically symmetric Dirac operators m three-dimensional space
with potentials tending to infinity at infinity under weak regularity assumptions. We prove that
purely absolutely continuous spectrum covers the whole real line if the potential dominates the
mass, or scalar potential, term. In the situation where the potential and the scalar potential are
identical, the positive part of the spectrum is purely discrete : we show that the negative half-line is
filled with purely absolutely continuous spectrum m this case.
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TL;DR: In this article, the authors investigated the global behavior of scalar field cosmological models with very hard potential walls via the simple example of an exponentially steep potential well and found that the solutions exhibit a non-trivial oscillatory behavior in the approach to an initial space-time singularity.
Abstract: The global behavior of scalar field cosmological models with very hard potential walls is investigated via the simple example of an exponentially steep potential well. It is found that the solutions exhibit a non-trivial oscillatory behavior in the approach to an initial space-time singularity. This behavior can be interpreted as being due to the inability of the scalar field to negotiate the walls of the steep potential well.
TL;DR: In this article, a line heat source that suddenly starts moving with a uniform velocity inside a thermoelastic semi-infinite medium with thermal relaxation of the type of Lord and Shulman is considered.
Abstract: This paper is concerned with the transient waves created by a line heat source that suddenly starts moving with a uniform velocity inside a thermoelastic semi-infinite medium with thermal relaxation ofthe type ofLord and Shulman The source moves parallel to the boundary surface which is traction-free. The problem is reduced to the solution of three differential equations, one involving the elastic vector potential, and the other two coupled, involving the thermoelastic scalar potential and the temperature. Using Fourier and Laplace transforms, the solution for the displacements have been obtained in the transform domain. The displacements have been calculated on the boundary surface for small time
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TL;DR: In this article, the authors studied the spectrum of spherically symmetric Dirac operators in three-dimensional space with potentials tending to infinity at infinity under weak regularity assumptions.
Abstract: We study the spectrum of spherically symmetric Dirac operators in three-dimensional space with potentials tending to infinity at infinity under weak regularity assumptions. We prove that purely absolutely continuous spectrum covers the whole real line if the potential dominates the mass, or scalar potential, term. In the situation where the potential and the scalar potential are identical, the positive part of the spectrum is purely discrete; we show that the negative half-line is filled with purely absolutely continuous spectrum in this case.
TL;DR: In this article, an extension of the Biot-Tolstoy (1957) exact time domain solution to the electromagnetic isovelocity or isorefractive wedge is described.
Abstract: The extension of the Biot-Tolstoy (1957) exact time domain solution to the electromagnetic isovelocity or isorefractive wedge is described. The TM field generated by a Hertzian electric dipole can be represented by a vector potential parallel to the apex of the wedge and a scalar potential necessitated by the three dimensionality of the magnetic field. The derivation of the former is exactly that of the pressure in the corresponding acoustic situation, and a more efficient version of the lengthy details is presented herein. A Lorentz gauge determines the scalar potential from the vector potential, and the diffracted field contains impulsive and "switch-on" terms that cannot be evaluated in closed form. The ratio of arrival times, at a given point, of the geometrical optics and diffracted fields provides a convenient parameter, in addition to the usual metric-related variable, for graphically displaying this scalar potential.
TL;DR: In this article, an error estimator based on the works of P. Ladeveze is presented to control the quality of finite element solutions in nonlinear magnetostatics.
Abstract: This paper presents an error estimator which enables control of the quality of finite element solutions in nonlinear magnetostatics. This method, based on the works of P. Ladeveze [1983, 1991] in mechanics, consists of constructing complementary admissible field from the one calculated by the finite element method. This method has been transposed in the cases of nonlinear vector and scalar potential 2D formulations. The results given by the proposed estimator are compared to the one based on two finite element solutions on two examples.
TL;DR: For an Abelian extended supergravity model, this paper investigated some important low energy parameters: tan�, Z − Zmixing angle, lightest CP-even Higgs mass bound, Zmass, and effective µ parameter.
Abstract: For an Abelian extended Supergravity model, we investigate some important low energy parameters: tan�, Z − Zmixing angle, lightest CP-even Higgs mass bound, Zmass, and effective µ parameter. By integrating the RGE's from string scale down to the weak scale we constuct the scalar potential, and analyze the quantities above at the tree- and one-loop levels by including the contributions of top squarks and top quark in the effective potential. PACS: 04.65.+e, 12.60.Jv
TL;DR: In this article, the authors presented a model for the dark matter in spiral galaxies, which is a result of a static and axial symmetric exact solution of the Einstein-Dilaton theory.
Abstract: We present a model for the dark matter in spiral galaxies, which is a result of a static and axial symmetric exact solution of the Einstein-Dilaton theory. We suposse that dark matter is a scalar field endowed with a scalar potential. We obtain that a) the effective energy density goes like $1/(r^2+r_{c}^{2})$ and b) the resulting circular velocity profile of tests particles is in good agreement with the observed one.
TL;DR: In this paper, a simplifying parametrization of the (l+1)thorder tensor of lth-order moments of the current density in terms of an lth order tensor bi1…il allows to derive all orders in the multipole expansions using only Cartesian coordinates of tensors.
Abstract: We derive the multipole expansions of the magnetostatic field and vector potential of an arbitrary steady current density. A simplifying parametrization of the (l+1)th-order tensor of lth-order moments of the current density in terms of an lth-order tensor bi1…il allows us to derive all orders in the multipole expansions using only Cartesian coordinates of tensors. We do not use a magnetic scalar potential or spherical harmonics. The field B(l)(r) of the lth-order magnetostatic multipole depends on only the 2l+1 independent components of the symmetric traceless part bi1…ils0 of bi1…il in exactly the same way as the field E(l)(r) of the lth-order electrostatic multipole depends on the lth-order symmetric traceless tensor ρi1…ils0 of multipole moments of the charge density. The vector potential that depends on only the symmetric traceless tensors bi1…ils0 differs from the vector potential in the Coulomb gauge. Our derivation shows that the fact that only the symmetric traceless part of bi1…il contributes to...
TL;DR: In this article, a three-dimensional method for the computation of the magnetic fields produced by thin ferromagnetic shells is presented, where the Integrodifferential equation is used to define the scalar potential distribution inside the magnetized region.
Abstract: In this paper we analyze a three-dimensional method for the computation of the magnetic fields, produced by thin ferromagnetic shells. Integrodifferential equation is used to define the scalar potential distribution inside the magnetized region. Magnetic field inside a thin shell is calculated using FEM. This method is shown to give accurate results for the field inside thin spherical shells in the wide range of the shielding factor.