Showing papers on "Magnetic potential published in 2003"
TL;DR: In this article, the state vector equations for three dimensional, orthotropic and linearly magneto-electro-elastic media are derived from the governing equations by eliminating σ x, σ y · τ xy, B x, B y, D x and D y.
158 citations
TL;DR: In this paper, the decay of unstable D$p$-branes when the world-volume gauge field is turned on was studied and a simple recipe to turn on the gauge fields in the boundary state was given.
Abstract: We study the decay of unstable D$p$-branes when the world-volume gauge field is turned on. We obtain the relevant Dp-brane boundary state with electric and magnetic fields by boosting and rotating the rolling tachyon boundary state of a D(p-1)-brane and then T-dualizing along one of the transverse directions. A simple recipe to turn on the gauge fields in the boundary state is given. We find that the effect of the electric field is to parametrically enhance coupling of closed string oscillation modes along the electric field direction and provide an intuitive understanding of the result in the T-dualized picture. We also analyze the system by using the effective field theory and compare the result with the boundary state approach.
119 citations
TL;DR: In this paper, the authors obtained multiple solutions to the nonlinear Schrodinger equation with an external magnetic field h i ∇ −A(x) 2 u+(U(x)-−E)u=f(x,u), x∈ R N, where N⩾2, A is a real-valued vector magnetic potential, U was a real electric potential function and the non-linear term f(t,t) grows subcritically in t.
107 citations
TL;DR: In this paper, the relativistic magnetic vector potential in the framework of the DKH theory is used for the calculations of magnetic properties without further expansion in powers of c 21.
Abstract: has been developed to study magnetic properties of molecules. The proposed Hamiltonian includes the relativistic magnetic vector potential in the framework of the DKH theory, and is applicable to the calculations of magnetic properties without further expansion in powers of c 21 . By combining with the finite-perturbation theory and the generalized-UHF method, new pictures of the magnetic shielding constant are derived. We apply the theory to calculations of the magnetic shielding constants of He isoelectronic systems, Ne isoelectronic systems, and noble gas atoms. The results of the present theory compare well with those of the four-component Dirac‐Hartree‐Fock calculations; the differences were within 3%. We note that the quasirelativistic theory that handles the magnetic vector potential at a nonrelativistic level greatly underestimates the relativistic effect. The so-called ‘‘picture change’’ effect is quite important for the magnetic shielding constant of heavy elements. The change in the orbital picture plays a significant role in the valence-orbital magnetic response as well as the core-orbital one. The effect of the finite nucleus is also studied using Gaussian nucleus model. The present theory reproduces the correct behavior of the finite-nucleus effect that has been reported with the Dirac theory. In contrast, the nonrelativistic theory and the quasirelativistic theory with the nonrelativistic vector potential underestimate the finite-nucleus effect. © 2003 American Institute of Physics. @DOI: 10.1063/1.1528933#
101 citations
TL;DR: In this article, the authors derived formulas for the gravity potential, field, and field gradient tensor for a polyhedral target body of a spatially linear density medium, and proposed new algorithms of improved error control over existing algorithms for the linear medium.
Abstract: Formulas for the gravity potential, field, and field gradient tensor are derived for a polyhedral target body of a spatially linear density medium. The formulas also define the magnetic potential and field in the case of a medium of spatially linear magnetization. This work generalizes existing solutions for the gravity field of a polyhedral target of linearly varying density.The formulas are analyzed for singularities and for numerical error growth. Error growth with increasing target distance is found to be higher than in the corresponding uniform polyhedral case. Examination of the error sources reveals that some error reduction is possible. On this basis, new algorithms of improved error control over existing algorithms are proposed for the linear medium. Computational results confirm the expected improvement.
85 citations
TL;DR: In this article, a method is developed to take the eddy currents in lamination stacks into account with the finite element method using the three-dimensional (3-D) magnetic vector potential magnetodynamic formulation.
Abstract: A method is developed to take the eddy currents in lamination stacks into account with the finite-element method using the three-dimensional (3-D) magnetic vector potential magnetodynamic formulation. It consists in converting the stacked laminations into continuums with which terms are associated for considering the eddy-current loops produced by both parallel and perpendicular fluxes. Two levels of accuracy are proposed. The best one is based on an accurate analytical expression of the eddy currents and makes the method adapted to a wide-frequency range, i.e., even for low skin depths in the laminations.
83 citations
TL;DR: In this paper, a 3D finite element formulation based on the use of the magnetic scalar potential is proposed, which allows the description of multiply connected solid conductors coupled to electric circuits and to take into account the nonlinearities.
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.
67 citations
TL;DR: In this paper, a model of an axisymmetric probe coil with a cylindrical ferrite core in the presence of a layered conducting half space is developed, where the boundary value problem is formulated in terms of the magnetic vector potential, which is expanded in a series of appropriate eigenfunctions.
Abstract: A model of an axisymmetric probe coil with a cylindrical ferrite core in the presence of a layered conducting half space is developed. The boundary value problem is formulated in terms of the magnetic vector potential, which is expanded in a series of appropriate eigenfunctions. The corresponding eigenvalues are the real roots of a function with the radius and the magnetic permeability of the core as parameters. The unknown coefficients of the series are computed by solving a matrix system, which is formed by applying the usual interface conditions. Expressions are derived for the induced eddy current density and the impedance of the coil. Numerical results for the latter are in good agreement with experimental data.
62 citations
TL;DR: 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 as discussed by the authors, i.e., the scalar potential is expressed in terms of the instantaneous charge density, and the vector potential is represented by the instantaneous magnetic field.
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.
59 citations
TL;DR: In this paper, transient numerical simulations of the temperature evolution during sublimation growth of SiC single crystals via physical vapor transport (also called the modified Lely method) including diffusion and radiation, investigating the influence of induction heating.
36 citations
TL;DR: In this article, the authors present an algorithm to construct a set of basis functions for the cohomology structure of the magnetic field function space, which is based on the topological properties of the discrete Whitney complex.
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.
TL;DR: An exact equation is derived for homogeneous isotropic magnetohydrodynamic (MHD) turbulent flows with nonzero helicity, which links the dissipation of magnetic helicity to the third-order correlations involving combinations of the components of the velocity, the magnetic field, and the magnetic potential.
Abstract: We derive an exact equation for homogeneous isotropic magnetohydrodynamic (MHD) turbulent flows with nonzero helicity; this result is of the same nature as the classical von Karman-Howarth (VKH-HM) formulation for the kinetic energy of turbulent fluids. Helical MHD is relevant to the astrophysical flows such as in the solar corona, or the interstellar medium, and in the dynamo problem. The derivation involves the new writing of the general form of tensors for that case, for either vectors or (pseudo)axial vectors. It is shown that, for general third-order tensors, four generating functions are needed when taking into account the nonmirror invariance of helical fluids, instead of two as in the fully isotropic case. The new equation obtained, denoted by VKH-HM, links the dissipation of magnetic helicity to the third-order correlations involving combinations of the components of the velocity, the magnetic field, and the magnetic potential. Finally, in the long-time and nonresistive limit, this relationship leads to a linear scaling with separation of the third-order tensor, correlating the two normal components of the electromotive force and of the magnetic potential.
TL;DR: In this paper, the electron-optical phase shift for a magnetized polyhedral nanoparticle, with either a uniform magnetization or a closure domain (vortex state), is computed using an analytical expression for the shape amplitude, combined with a reciprocal space description of the magnetic vector potential.
Abstract: A method is presented to compute the electron-optical phase shift for a magnetized polyhedral nanoparticle, with either a uniform magnetization or a closure domain (vortex state). The method relies on an analytical expression for the shape amplitude, combined with a reciprocal-space description of the magnetic vector potential. The model is used to construct two building blocks from which more complex structures can be generated. Phase computations are also presented for the five Platonic and 13 Archimedean solids. Fresnel and Foucault imaging mode simulations are presented for a range of particle shapes and microscope imaging conditions.
TL;DR: A constitutive model for dispersions of acicular magnetic particles has been developed by modeling the particles as rigid dumbbells dispersed in a solvent, and a transition from isotropic to nematic phases at equilibrium is predicted.
TL;DR: In this paper, the existence of nontrivial EYM solutions with a NUT charge in the presence of a negative cosmological constant is discussed and the boundary energy-momentum tensor and the mass of these configurations are calculated.
Abstract: We argue that the Einstein-Yang-Mills theory presents nontrivial solutions with a NUT charge. These solutions approach asymptotically the Taub-NUT spacetime. They are characterized by the NUT parameter, the mass, and the node numbers of the magnetic potential and present both electric and magnetic potentials. The existence of nontrivial Einstein-Yang-Mills solutions with a NUT charge in the presence of a negative cosmological constant is also discussed. We use the counterterm subtraction method to calculate the boundary energy-momentum tensor and the mass of these configurations. Also, dyon black hole solutions with a nonspherical event horizon topology are shown to exist for a negative cosmological constant.
TL;DR: In this paper, the spatial and temporal dynamics of a cold atom cloud in the conservative force field of a ferromagnetic guide, after laser cooling has been switched off suddenly, were studied.
Abstract: We have studied the spatial and temporal dynamics of a cold atom cloud in the conservative force field of a ferromagnetic guide, after laser cooling has been switched off suddenly. We observe outgoing 'waves' that correspond to caustics of individual trajectories of trapped atoms. This provides detailed information on the magnetic field, the energy distribution, and the spin states.
01 Jan 2003
TL;DR: In this paper, the eddy-current problem for the time-harmonic Maxwell equations in domains of general topology is solved by introducing a scalar "potential" for the magnetic field in the insulator part of the domain.
Abstract: The eddy-current problem for the time-harmonic Maxwell equations in domains of general topology is solved by introducing a scalar “potential” for the magnetic field in the insulator part of the domain. Indeed, since in general the insulator Ω I is multiply-connected, the magnetic field differs from the gradient of a potential by a harmonic field. We rewrite the problem in a two-domain formulation, in term of a scalar magnetic potential and a harmonic field in Ω I . Then the finite element numerical approximation based on this two-domain formulation is presented, using edge elements in the conductor and nodal elements in the insulator, and an optimal error estimate is proved. An iteration-by-sub domain procedure for the solution of the problem is also proposed.
TL;DR: In this paper, the Schrodinger operator H=(i∇+A)2 in the space L2(R3) with a magnetic potential A created by an infinite rectilinear current was considered and it was shown that the operator H is absolutely continuous, its spectrum has infinite multiplicity and coincides with the positive half-axis.
Abstract: We consider the Schrodinger operator H=(i∇+A)2 in the space L2(R3) with a magnetic potential A created by an infinite rectilinear current. We show that the operator H is absolutely continuous, its spectrum has infinite multiplicity and coincides with the positive half-axis. Then we find the large-time behavior of solutions exp (−iHt)f of the time dependent Schrodinger equation. Our main observation is that a quantum particle has always a preferable (depending on its charge) direction of propagation along the current. Similar result is true in classical mechanics.
TL;DR: In this article, the treatment of thin insulating layers between conducting regions is studied in the frame of dual three-dimensional (3-D) magnetodynamic finite element formulations, using either the magnetic field or the magnetic vector potential as the main unknowns.
Abstract: The treatment of thin insulating layers between conducting regions is studied in the frame of dual three-dimensional (3-D) magnetodynamic finite element formulations, using either the magnetic field or the magnetic vector potential as the main unknowns. The layers, of which the thickness is assumed to tend to zero, are represented by surface elements on which scalar potentials are defined and coupled with the main field of each formulation. At the discrete level, this coupling is rigorously done through a nodal and edge-elements coupling. Both passive and active conducting regions are considered, i.e., without or with applied voltage or current.
01 Jan 2003
TL;DR: In this paper, the authors derived a formula for the sensitivity of the measured voltage in terms of the magnetic vector potential A, which gives to an efficient method of sensitivity calculation using Finite Element Method.
Abstract: One of the major tools for both design and the image reconstruction of an MIT system are the spatial sensitivity analysis of the object space. This sensitivity analysis effectively maps the sensitivity of a particular excitation / detection coil pair to a small perturbation of the conductivity of the material in the object space. We derive a formula for the sensitivity of the measured voltage in terms of the magnetic vector potential A, which gives to an efficient method of sensitivity calculation using Finite Element Method.
TL;DR: In this article, the Schrodinger operator in 3 with a long-range magnetic potential associated with a magnetic field supported inside a torus was considered and the essential spectrum of S(λ) is an interval of the unit circle depending only on the magnetic flux across the section of.
Abstract: In this paper we consider the Schrodinger operator in 3 with a long-range magnetic potential associated with a magnetic field supported inside a torus . Using the scheme of smooth perturbations we construct stationary modified wave operators and the corresponding scattering matrix S(λ). We prove that the essential spectrum of S(λ) is an interval of the unit circle depending only on the magnetic flux across the section of . Additionally we show that, in contrast to the Aharonov–Bohm potential in 2, the total scattering cross-section is always finite. We also conjecture that the case treated here is a typical example in dimension 3.
Posted Content•
TL;DR: In this article, a generalised classical electrodynamics (CED) is proposed, such that scalar field effects are predicted and such that experiments can be performed in order to verify or falsify this generalised CED.
Abstract: Within the framework of Classical Electrodynamics (CED) it is common practice to choose freely an arbitrary gauge condition with respect to a gauge transformation of the electromagnetic potentials. The Lorenz gauge condition allows for the derivation of the inhomogeneous potential wave equations (IPWE), but this also means that scalar derivatives of the electromagnetic potentials are considered to be unphysical. However, these scalar expressions might have the meaning of a new physical field, S. If this is the case, then a generalised CED is required such that scalar field effects are predicted and such that experiments can be performed in order to verify or falsify this generalised CED. The IPWE are viewed as a generalised ~ Gauss law ~ ~
Patent•
23 May 2003
TL;DR: In this article, an aberration correcting device composed of quadruple electrostatic type quadrupoles, quadruple magnetic field types and quadruple octupole type octupoles was used to realize stable and optimum aberration correction and obtain a minimum probe diameter of a charged particle beam.
Abstract: PROBLEM TO BE SOLVED: To realize a charged particle beam apparatus equipped with an aberration correcting device which can realize stable and optimum aberration correction and obtain a minimum probe diameter of a charged particle beam. SOLUTION: Individual components are arranged so that a distance L 1 between a main surface of a last-stage multiple pole of an aberration correcting device C composed of quadruple electrostatic type quadrupoles 1, 2, 3, 4, magnetic field type quadrupoles 5, 6, of two steps superimposing a magnetic potential distribution similar to the electric potential distribution of the double electrostatic type quadrupoles 2, 3 at the center of the quadruple electrostatic type quadrupoles on the electric field distribution, and quadruple electrostatic type octupoles 11, 12, 13, 14, superimposing an octupole electric potential on the electric potential distribution of the quadruple electrostatic type quadrupoles 1, 2, 3, 4; and a main surface of a transfer lens 27a having a focal distance of f a becomes about f a , a distance L 2 between the main surface of the transfer lens 27a and a main surface of a transfer lens 27b having a focal distance of f b becomes about f a + f b , and a distance L 3 between the main surface of the transfer lens 27b and a forward focal distance FFP of an objective lens 7 becomes about f b . COPYRIGHT: (C)2004,JPO
TL;DR: In this article, the authors provide examples of how a computer algebra system can be used to investigate the motion of an electric charge in an electric or magnetic dipole field, and demonstrate the use of computer algebra for the same purpose.
Abstract: We provide examples of how a computer algebra system can be used to investigate the motion of an electric charge in an electric or magnetic dipole field.
TL;DR: In this paper, the authors discuss the methodological value of the potential formalism in electromagnetism and the advantages of potential-based computational approaches in EM analysis, and support the analysis of classical problems such as the radiation from a small dipole and the field propagation in waveguide structures: a waveguide bend and an H-plane filter.
Abstract: The theory of electromagnetic (EM) potentials is as old as the Maxwell equations, which treat the field vectors E and H directly. Yet the vector and scalar potentials are often regarded as nothing more than an auxiliary mathematical concept, which does not necessarily reflect a physically existing phenomenon. This widely accepted opinion does not have sound theoretical or experimental validation. The EM potentials are as "real" as the field vectors - they describe observable phenomena and play a crucial role in the explanation of light-matter interactions, radiation, and propagation. We discuss the methodological value of the potential formalism in electromagnetism and the advantages of the potential-based computational approaches in EM analysis. The key points of the discussion are supported by examples of the analysis of classical problems such as the radiation from a small dipole and the field propagation in waveguide structures: a waveguide bend and an H-plane filter. These examples include animations of the propagation of the EM-field potentials and the respective field vectors.
01 Jan 2003
TL;DR: In this paper, the free and forced flexural vibrations are investigated for rotors of electric motors operating in unsymmetrical magnetic fields, and the magnetic potential energy reserved in the air-gap is analytically derived and the unbalanced magnetic pull is obtained through the law of energy conservation.
Abstract: The free and forced flexural vibrations are investigated for rotors of electric motors operating in unsymmetrical magnetic fields The magnetic potential energy reserved in the air-gap is analytically derived and the unbalanced magnetic pull is obtained through the law of energy conservation With this excitation, the equations of motion of the unbalanced rotor are developed for nonlinear displacements response For small dynamic eccentricities, the equations of motion are simplified and the rotor is compared to a free Duffing oscillatory system The analytic solution for forced vibrations subject to residual mass-unbalance excitations is also obtained Jump phenomenon in the solution is pointed out, and the effects of initial eccentricity and flux density on the natural frequency are also investigatedCopyright © 2003 by ASME
15 Mar 2003
TL;DR: In this paper, the conditions for gauge independence of third-rank tensor properties that describe the response of a molecule in the presence of three perturbations, that is, external electric and magnetic field, and intramolecular nuclear magnetic dipoles, are discussed.
Abstract: Although electrodynamics is formally invariant in a gauge transformation, the values of some physical quantities, e.g., magnetic properties, depend on the approximation employed to calculate them. The conditions for gauge independence of third-rank tensor properties that describe the response of a molecule in the presence of three perturbations, that is, external electric and magnetic field, and intramolecular nuclear magnetic dipoles, are discussed. The relationships for invariance of the physical properties to a gauge translation are exactly the same as the constraints for charge conservation. They are expressed in terms of second-rank response properties, namely electric polarizabilities and electric shielding at the nuclei. An extended numerical test has been carried out to determine the Hartree–Fock limit for a series of quantities entering the gauge-invariance sum rules.
TL;DR: In this article, the behavior of magnetic potential near a point charge (fluxon) located at a curved regular boundary surface is shown to be essentially different from that of a volume point charge, and the field in the charge vicinity behaves accordingly, featuring generally two singular terms proportional to the inverse distance, in addition to the main inverse distance squared singularity.
Abstract: The behavior of the magnetic potential near a point charge (fluxon) located at a curved regular boundary surface is shown to be essentially different from that of a volume point charge. In addition to the usual inverse distance singularity, two singular terms are generally present. The first of them, a logarithmic one, is axially symmetric with respect to the boundary normal at the charge location, and proportional to the sum of the two principal curvatures of the boundary surface at this point, that is, to the local mean curvature. The second term is asymmetric and proportional to the difference of the two principal curvatures in question; it is also bounded at the charge location. Both terms vanish, apparently, if the charge is at a planar point of the boundary, and only in this case. The field in the charge vicinity behaves accordingly, featuring generally two singular terms proportional to the inverse distance, in addition to the main inverse distance squared singularity. This result is significant, in particular, for studying the interaction of magnetic vortices in type II superconductors.
TL;DR: In this paper, the authors present a detailed calculation of the electric and magnetic fields inside and outside the long solenoid without using the vector potential, and compare it with a solution given in an introductory textbook.
Abstract: Electromagnetic radiation exists because changing magnetic fields induce changing electric fields and vice versa. This fact often appears inconsistent with the way some physics textbooks solve particular problems using Faraday’s law. These types of problems often ask students to find the induced electric field given a current that does not vary linearly with time. A typical example involves a long solenoid carrying a sinusoidal current. This problem is usually solved as an example or assigned as a homework exercise. The solution offered by many textbooks uses the approximation that the induced, changing electric field produces a negligible magnetic field, which is only valid at low frequencies. If this approximation is not explicitly acknowledged, then the solution appears inconsistent with the description of electromagnetic radiation. In other cases, when the problem is solved without this approximation, the electric and magnetic fields are derived from the vector potential. We present a detailed calculation of the electric and magnetic fields inside and outside the long solenoid without using the vector potential. We then offer a comparison of our solution and a solution given in an introductory textbook.