Showing papers on "Scalar potential published in 2002"
TL;DR: In this paper, the authors obtained the vacuum solutions for M-theory compactified on eight-manifolds with non-vanishing four-form flux by analyzing the scalar potential appearing in the three-dimensional theory.
Abstract: We obtain the vacuum solutions for M-theory compactified on eight-manifolds with non-vanishing four-form flux by analyzing the scalar potential appearing in the three-dimensional theory. Many of these vacua are not supersymmetric and yet have a vanishing three-dimensional cosmological constant.We show that in the context of type-IIB compactifications on Calabi-Yau threefolds with fluxes and external brane sources α'-corrections generate a correction to the supergravity potential proportional to the Euler number of the internal manifold which spoils the no-scale structure appearing in the classical potential. This indicates that α'-corrections may indeed lead to a stabilization of the radial modulus appearing in these compactifications.
495 citations
TL;DR: In this article, the authors obtained the vacuum solutions for M-theory compactified on eight-manifolds with non-vanishing four-form flux by analyzing the scalar potential appearing in the three-dimensional theory.
Abstract: We obtain the vacuum solutions for M-theory compactified on eight-manifolds with non-vanishing four-form flux by analyzing the scalar potential appearing in the three-dimensional theory. Many of these vacua are not supersymmetric and yet have a vanishing three-dimensional cosmological constant. We show that in the context of Type IIB compactifications on Calabi-Yau threefolds with fluxes and external brane sources alpha'-corrections generate a correction to the supergravity potential proportional to the Euler number of the internal manifold which spoils the no-scale structure appearing in the classical potential. This indicates that alpha'-corrections may indeed lead to a stabilization of the radial modulus appearing in these compactifications.
427 citations
TL;DR: It is shown that piles of smooth grains can be mapped onto a pile of unfrustrated rough grains, indicating that the problems of rough and smooth grains may be fundamentally distinct.
Abstract: The transmission of stress through a marginally stable granular pile in two dimensions is exactly formulated in terms of a vector field of loop forces, and thence in terms of a single scalar potential. This leads to a local constitutive equation coupling the stress tensor to fluctuations in the local geometry. For a disordered pile of rough grains this means the stress tensor components are coupled in a frustrated manner. In piles of rough grains with long range staggered order, frustration is avoided and a simple linear theory follows. We show that piles of smooth grains can be mapped onto a pile of unfrustrated rough grains, indicating that the problems of rough and smooth grains may be fundamentally distinct.
141 citations
TL;DR: In this article, a vector potential formulation for the solution of electromechanical boundary value problems is presented. But unlike the scalar potential formulation, which uses scalar electric potentials as nodal variables, the vector potential is derived from which components of electric displacement are derived.
Abstract: In this paper, a new finite-element formulation for the solution of electromechanical boundary value problems is presented. As opposed to the standard formulation that uses scalar electric potential as nodal variables, this new formulation implements a vector potential from which components of electric displacement are derived. For linear piezoelectric materials with positive definite material moduli, the resulting finite-element stiffness matrix from the vector potential formulation is also positive definite. If the material is non-linear in a fashion characteristic of ferroelectric materials, it is demonstrated that a straightforward iterative solution procedure is unstable for the standard scalar potential formulation, but stable for the new vector potential formulation. Finally, the method is used to compute fields around a crack tip in an idealized non-linear ferroelectric material, and results are compared to an analytical solution. Copyright © 2002 John Wiley & Sons, Ltd.
110 citations
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30 Sep 2002
TL;DR: In this paper, it was shown that there exists a soliton-like solution for real scalar fields with U(1) charges, which is called I-ball, and whose stability is ensured by the adiabatic invariance for the oscillating field.
Abstract: We find that there exists a soliton-like solution ``I-ball'' in theories of a real scalar field if the scalar potential satisfies appropriate conditions Although the I-ball does not have any topological or global U(1) charges, its stability is ensured by the adiabatic invariance for the oscillating field
94 citations
TL;DR: In this paper, the vector potential is used in both the conducting region and cutting domains to solve eddy-current problems in multiply connected regions, cuts have to be introduced to avoid multivalued problems of scalar potential.
Abstract: When using t-/spl Omega/ formulation for solving eddy-current problems in multiply connected regions, cuts have to be introduced to avoid multivalued problems of scalar potential. In this paper, the vector potential is used in both the conducting region and cutting domains. The cutting domains are composed of one layer of elements that fill the holes of conductors. In the cutting domains, the zero curl condition of the vector potential is strongly imposed by a constraint function. Such a method avoids the introduction of a fake conductor in the holes. To generate the cutting domains, an automatic cut generation algorithm is developed.
77 citations
TL;DR: In this article, the authors consider a five-dimensional supergravity model with SU(5) gauge symmetry and the minimal field content and find that the gauging of the U(1)R symmetry causes instabilities.
Abstract: We consider a five-dimensional supergravity model with SU(5) gauge symmetry and the minimal field content. Studying the arising scalar potential we find that the gauging of the U(1)R symmetry of the five-dimensional supergravity causes instabilities. Lifting the instabilities, the vacua are of anti-de-Sitter type and SU(5) is broken along with supersymmetry. Keeping the U(1)R ungauged the potential has flat directions along which supersymmetry is unbroken.
68 citations
TL;DR: In this article, the authors investigated the distribution of the scalar field in gravitational interaction with matter, assuming no singularities (like black holes) at the galaxy center, and concluded that a light non-interacting (or only selfinteracting) complex scalar fields is a promising candidate for galactic dark matter.
54 citations
TL;DR: In this article, a centrally fed ball antenna, 6 cm diameter, producing a pulsating 433.59 MHz spherical source charge, generated a wave, that was detected by an identical ball antenna.
Abstract: Theoretically scalar potential Φ waves with a longitudinal electric field in the direction of propagation must exist. A centrally fed ball antenna, 6 cm diameter, producing a pulsating 433.59 MHz spherical source charge, generated such a wave, that was detected by an identical ball antenna. The longitudinality of was demonstrated by intervening a cubic array of 9 half-wavelength wires, that absorbed the wave when the wires were parallel (but not when perpendicular) to the direction of propagation. The signal from the ball antenna source, placed 4.0 m above ground and receiver 4.4 m above ground, was measured as a function of distance, yielding satisfactory agreement with theory, including 2 expected interference minima produced by an image source induced in the Earth. Only waves can yield such an interference and can be reflected from the Earth's surface and vary as the inverse square of distance.
50 citations
TL;DR: In this article, a quantum lattice-gas model for simulating the time-dependent evolution of a many-body quantum mechanical system of particles governed by the non-relativistic Schrodinger wave equation with an external scalar potential is presented.
46 citations
TL;DR: Investigation of analytical solutions for the sphere suggests the parameter range in which this approximation might perform well and suggests ways of improving accuracy over an extended range, and the fundamental TSA formulation appears to be relatively robust.
Abstract: The problem of numerical modeling of electromagnetic induction (EMI) responses by metallic objects is complicated by the fact that transmitted fields may penetrate the target, but will often only do so slightly. The effect cannot be ignored, yet it is often grossly impractical to discretize the entire surface or volume of a target in space increments only on the order of a fraction of the skin depth. To deal with this problem, we retain a simple integral equation formulation in scalar potential for the region outside the target, where magnetic fields are quasi-static and irrotational. Within the target we apply only the divergence relation, /spl nabla//spl middot/H = 0. When the skin depth is small relative to the radius of curvature of the target (e.g., <0.1), we use the thin skin depth approximation (TSA), /spl part/H/sub n///spl part/n as /spl sim/-ikH/sub n/, just inside the target's surface, where k is the electromagnetic wavenumber inside the metal and n is the normal direction on the surface and pointing inside of metallic object. Examination of analytical solutions for the sphere suggests the parameter range in which this approximation might perform well and suggests ways of improving accuracy over an extended range. The fundamental TSA formulation appears to be relatively robust. Analysis indicates that it is insensitive to variation over the target's surface of primary field orientation relative to that surface, and that it is only dependent on the target's magnetic permeability through induction number. Implementing the TSA numerically, within the above divergence relation, allows us to express all quantities in terms of tangential magnetic field components and their tangential derivatives over the target surface. In principle, this closes the system completely in terms of the exterior scalar potential. Broad-band numerical simulations based on the TSA compare favorably with analytical and other numerical solutions.
TL;DR: In this article, the authors define the two dimensional Pauli operator and identify its core for magnetic fields that are regular Borel measures and extend the Aharonov-Casher theorem for magnetic field that are measures with finite total variation.
Abstract: We define the two dimensional Pauli operator and identify its core for magnetic fields that are regular Borel measures The magnetic field is generated by a scalar potential hence we bypass the usual A∈L
2
loc condition on the vector potential, which does not allow to consider such singular fields We extend the Aharonov–Casher theorem for magnetic fields that are measures with finite total variation and we present a counterexample in case of infinite total variation One of the key technical tools is a weighted L
2 estimate on a singular integral operator
TL;DR: In this paper, a coupled finite element (fe)-boundary element (be) approach for three-dimensional magnetic field problems is considered. But the authors focus on a coupled variational problem, where the constraints in the trial spaces are replaced by appropriate side conditions.
Abstract: We consider a coupled finite element (fe)–boundary element (be) approach for three-dimensional magnetic field problems. The formulation is based on a vector potential in a bounded domain (fe) and a scalar potential in an unbounded domain (be). We describe a coupled variational problem yielding a unique solution where the constraints in the trial spaces are replaced by appropriate side conditions. Then we discuss a Galerkin discretization of the coupled problem and prove a quasi-optimal error estimate. Finally we discuss an efficient preconditioned iterative solution strategy for the resulting linear system. Copyright © 2002 John Wiley & Sons, Ltd.
IMEC1
TL;DR: This paper deals with the software implementation, the treatment of interfaces and domain boundaries, scaling considerations, numbering schemes, and solver requirements on the simulation of on-chip high-frequency effects.
Abstract: This is the second paper in a series on the simulation of on-chip high-frequency effects. A computer-aided approach in three dimensions is advocated, describing high-frequency effects such as current redistribution due to the skin-effect or eddy currents and the occurrence of slow-wave modes. The electromagnetic environment is described by an electric scalar potential and a magnetic vector potential as well as a ghost field. The latter one guarantees a stable numerical implementation. This paper deals with the software implementation, the treatment of interfaces and domain boundaries, scaling considerations, numbering schemes, and solver requirements. Some illustrative examples are shown.
TL;DR: In this article, the authors derived the late time behavior of the bulk scalar field by analyzing the property of the retarded Green function and showed that the late-time behavior is dominated by a single (or a pair of) pole(s) in the Green function irrespective of the initial condition and of the signature of the potential of the field.
Abstract: Based on the recently proposed scenario of inflation driven by a bulk scalar field in the braneworld of the Randall-Sundrum (RS) type, we investigate the dynamics of a bulk scalar field on the inflating braneworld. We derive the late time behavior of the bulk scalar field by analyzing the property of the retarded Green function. We find that the late time behavior is basically dominated by a single (or a pair of) pole(s) in the Green function irrespective of the initial condition and of the signature of $m^{2}=V''(\phi)$, where $V(\phi)$ is the potential of the bulk scalar field. Including the lowest order back-reaction to the geometry, this late time behavior can be well approximated by an effective 4-dimensional scalar field with $m^2_{\mathrm{eff}}=m^2/2$. The mapping to the 4-dimensional effective theory is given by a simple scaling of the potential with a redefinition of the field. Our result supports the picture that the scenario of inflation driven by a bulk scalar field works in a quite similar way to that in the standard 4-dimensional cosmology.
TL;DR: In this paper, a family of (p+3)-dimensional brane worlds was constructed, where the brane has one compact extra dimension, the bulk has two extra dimensions, and the bulk closes regularly at codimension two submanifolds known as bolts.
Abstract: We construct a family of (p+3)-dimensional brane worlds in which the brane has one compact extra dimension, the bulk has two extra dimensions, and the bulk closes regularly at codimension two submanifolds known as bolts. The (p+1)-dimensional low energy spacetime Mlow may be any Einstein space with an arbitrary cosmological constant, the value of the bulk cosmological constant is arbitrary, and the only fields are the metric and a bulk Maxwell field. The brane can be chosen to have positive tension, and the closure of the bulk provides a singularity-free boundary condition for solutions that contain black holes or gravitational waves in Mlow. The spacetimes admit a nonlinear gravitational wave whose properties suggest that the newtonian gravitational potential on a flat Mlow will behave essentially as the static potential of a massless minimally coupled scalar field with Neumann boundary conditions. When Mlow is (p+1)-dimensional Minkowski with p ≥ 3 and the bulk cosmological constant vanishes, this static scalar potential is shown to have the long distance behaviour characteristic of p spatial dimensions.
TL;DR: In this article, the scalar potential of supergravity with matter was investigated and the extremum in the SU(1,1)/U(1) scalars was obtained for an arbitrary number of matter multiplets.
Abstract: We investigate the scalar potential of gauged N=4 supergravity with matter. The extremum in the SU(1,1)/U(1) scalars is obtained for an arbitrary number of matter multiplets. The constraints on the matter scalars are solved in terms of an explicit parametrisation of an
SO(6,6+n) element. For the case of six matter multiplets we discuss both compact and noncompact gauge groups.
In an example involving noncompact groups and four scalars we find a potential with an absolute minimum and a positive cosmological constant.
TL;DR: In this paper, a time-domain combined field integral equation (CFIE) is presented to obtain the transient scattering response from arbitrarily shaped three-dimensional (3D) conducting bodies.
Abstract: A time-domain combined field integral equation (CFIE) is presented to obtain the transient scattering response from arbitrarily shaped three-dimensional (3D) conducting bodies. This formulation is based on a linear combination of the time-domain electric field integral equation (EFIE) with the magnetic field integral equation (MFIE). The time derivative of the magnetic vector potential in EFIE is approximated with the use of a central finite-difference approximation for the derivative, and the scalar potential is averaged over time. The time-domain CFIE approach produces results that are accurate and stable when solving for transient scattering responses from conducting objects. The incident spectrum of the field may contain frequency components, which may correspond to the internal resonance of the structure. For the numerical solution, both the explicit and implicit schemes are considered and two different kinds of Gaussian pulses are used, which may or may not contain frequencies corresponding to the internal resonance. Numerical results for the EFIE, MFIE, and CFIE are presented and compared with those obtained from the inverse discrete Fourier transform (IDFT) of the frequency-domain CFIE solution. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 289–296, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10440
07 Apr 2002
TL;DR: The notions of discrete gradient vector field and of Smale-like decomposition for the domain of a d-dimensional scalar field are introduced and used to extract the most relevant features representing the topology of the field.
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.
TL;DR: For a given standard PT-symmetric Hamiltonian H = [p - A(x)]2/(2m) + V(x) with arbitrary complex scalar potential V and vector potential A, with x ∈ ℝ, this paper constructed an invertible antilinear operator τ such that H is τ-anti-pseudo-hermitian, i.e. H† = τHτ-1.
Abstract: For a given standard Hamiltonian H = [p - A(x)]2/(2m) + V(x) with arbitrary complex scalar potential V and vector potential A, with x ∈ ℝ, we construct an invertible antilinear operator τ such that H is τ-anti-pseudo-hermitian, i.e. H† = τHτ-1. We use this result to give the explicit form of a linear hermitian invertible operator with respect to which any standard PT-symmetric Hamiltonian with a real degree of freedom is pseudo-hermitian. Our results do not make use of the assumption that H is diagonalizable or that its spectrum is discrete.
TL;DR: In this article, the fundamental solutions for step-like point forces acting in three orthogonal directions and an instantaneous fluid point source in a fluid-saturated, porous, infinite solid of transversely isotropic elasticity and permeability were obtained.
Abstract: The fundamental solutions were obtained for step-like point forces acting in three orthogonal directions and an instantaneous fluid point source in a fluid-saturated, porous, infinite solid of transversely isotropic elasticity and permeability. After expressing the governing equations in the form of matrix in the Laplace space, we employed Kupradze's method together with the triple Fourier transforms. This method reduces the simultaneous partial differential equations with respect to three displacement components and a pore fluid pressure to a differential equation in terms of only one potential scalar function, which can be operationally solved in the transformed space. After the Laplace inversion of the potential, the residue theorem was applied to its Fourier inverse transform with respect to one of the transformation variables. The Fourier transforms with respect to two other variables were rewritten into the Hankel transforms. Copyright © 2002 John Wiley & Sons, Ltd.
TL;DR: In this paper, it was shown that if the scale of renormalization of the model is of order of the Planck mass, then a scalar field endowed with the scalar potential V = V0[cosh (λ √ κ0 Φ)− 1] can be a reliable model for dark matter in galaxies.
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TL;DR: In this article, necessary and sufficient conditions for the discreteness of spectrum and strict positivity of magnetic Schrodinger operators with a positive scalar potential were established in terms of Wiener's capacity and the local energy of the magnetic field.
Abstract: We establish necessary and sufficient conditions for the discreteness of spectrum and strict positivity of magnetic Schrodinger operators with a positive scalar potential. They are expressed in terms of Wiener's capacity and the local energy of the magnetic field. The conditions for the discreteness of spectrum depend on two functional parameters. One of them is a decreasing function of one variable whose argument is the normalized local energy of the magnetic field. This function enters the negligibility condition of sets for the scalar potential. We give a description for the range of admissible functional parameters which is precise in a certain sense.
In case when there is no magnetic field, our results extend the discreteness of spectrum and positivity criteria by A.Molchanov (1953) and V.Maz'ya (1973).
TL;DR: In this article, the exact solutions of the (2+1)-dimensional Dirac equation with a Coulomb potential and a scalar one are analytically presented by studying the second-order differential equations obtained from a pair of coupled first-order ones.
Abstract: The exact solutions of the (2+1)-dimensional Dirac equation with a Coulomb potential and a scalar one are analytically presented by studying the second-order differential equations obtained from a pair of coupled first-order ones. The eigenvalues are studied in some detail.
TL;DR: Effectes that could give astrophysical reconnection are discussed and a rational surface effect does not arise in astrophysics but does appear in periodic simulation codes.
Abstract: A magnetic evolution is ideal if it is consistent with the field being embedded in a perfectly conducting fluid. Faraday's law implies the evolution is ideal when the parallel component of the electric field is the derivative of a scalar potential, a condition that generically holds in any local region of space. Reconnection requires the non-existence of such a potential. In systems with two periodic directions, non-existence focuses reconnection onto the surfaces in which the magnetic field lines close on themselves, the rational surfaces. This rational surface effect does not arise in astrophysics but does appear in periodic simulation codes. Effects that could give astrophysical reconnection are discussed.
TL;DR: In this article, the role of baryons for the structure of dense matter in the Gross-Neveu model was investigated within a variational calculation, and a trial ground state at finite baryon density was constructed, which breaks translational invariance.
Abstract: Within a variational calculation we investigate the role of baryons for the structure of dense matter in the Gross-Neveu model. We construct a trial ground state at finite baryon density which breaks translational invariance. Its scalar potential interpolates between widely spaced kinks and antikinks at low density and the value zero at infinite density. Its energy is lower than the one of the standard Fermi gas at all densities considered. This suggests that the discrete gamma_5 symmetry of the Gross-Neveu model does not get restored in a first order phase transition at finite density, at variance with common wisdom.
TL;DR: In this paper, the authors studied holographic RG flows of N = 2 matter coupled AdS3 supergravities which admit both compact and non-compact sigma manifolds.
Abstract: We study holographic RG flows of N = 2 matter coupled AdS3 supergravities which admit both compact and non-compact sigma manifolds. For the compact case the supersymmetric domain wall solution interpolates between a conformal IR region and flat spacetime and this corresponds to a deformation of the CFT by an irrelevant operator. When it is non-compact, the solution can be interpreted as a flow between an UV fixed point and a non-conformal(singular) IR region. This is an exact example of a deformation flow when the singularity is physical. We also find a non-supersymmetric deformation flow when the scalar potential has a second AdS vacua. The ratio of the central charges is rational for certain values of the size of the sigma model. Next, we analyze the spectrum of a massless scalar on our background by transforming the problem into Schrodinger form. The spectrum is continuous for the compact case, yet it can be both continuous (with or without mass gap) and discrete otherwise. Finally, 2-point functions are computed for two examples whose quantum mechanical potentials are of Calogero type.
TL;DR: In this article, the authors show that the electric and magnetic fields are always the same and display the experimentally verified properties of causality and propagation at the speed of light, regardless of propagation characteristics.
Abstract: The main purposes of this paper are (i) to illustrate explicitly by a number of examples the gauge functions chi(x, t) whose spatial and temporal derivatives transform one set of electromagnetic potentials into another equivalent set; and (ii) to show that, whatever propagation or non-propagation characteristics are exhibited by the potentials in a particular gauge, the electric and magnetic fields are always the same and display the experimentally verified properties of causality and propagation at the speed of light. The example of the transformation from the Lorenz gauge (retarded solutions for both scalar and vector potential) to the Coulomb gauge (instantaneous, action-at-a-distance, scalar potential) is treated in detail. A transparent expression is obtained for the vector potential in the Coulomb gauge, with a finite nonlocality in time replacing the expected spatial nonlocality of the transverse current. A class of gauges (v-gauge) is described in which the scalar potential propagates at an arbitrary speed v relative to the speed of light. The Lorenz and Coulomb gauges are special cases of the v-gauge. The last examples of gauges and explicit gauge transformation functions are the Hamiltonian or temporal gauge, the nonrelativistic Poincare or multipolar gauge, and the relativistic Fock-Schwinger gauge.
TL;DR: In this article, a generalized variational principle of total energy functional is proposed to describe the magneto-thermo-elastic interaction of soft ferroelastic bodies with nonlinear magnetization under stationary thermal and magnetic fields.
TL;DR: In this article, numerical results for the dielectric polarizability of canonically shaped homogeneous scatterers: cube, tetrahedron, and octahedron are presented.
Abstract: This paper presents numerical results for the dielectric polarizability of canonically shaped homogeneous scatterers: cube, tetrahedron, and octahedron. The method is based on solving the integral equation for the static scalar potential on the surface of the scatterer by the method of moments. Easy-to-use interpolation formulas are given for the polarizabilities as a function of the permittivity. © 2002 John Wiley & Sons, Inc. Microwave Opt Technol Lett 32: 60–64, 2002.