Showing papers on "Scalar potential published in 1999"

Scale invariance, new inflation and decaying λ-terms

Abstract: Realizations of scale invariance are studied in the context of a gravitational theory where the action (in the first-order formalism) is of the form $S =\int L_1\Phi d^4 x +\int L_2\sqrt{-g} d^4x$ where Φ is a density built out of degrees of freedom, the "measure fields" independent of gμν and matter fields appearing in L1, L2. If L1 contains the curvature, scalar potential V(ϕ) and kinetic term for ϕ, L2 another potential for ϕ, U(ϕ), then the true vacuum state has zero energy density, when theory is analyzed in the conformal Einstein frame (CEF), where the equations assume the Einstein form. Global scale invariance is realized when V(ϕ)=f1eαϕ and U(ϕ)=f2e2αϕ. In the CEF the scalar field potential energy Veff(ϕ) has, in addition to a minimum at zero, a flat region for αϕ→∞, with nonzero vacuum energy, which is suitable for either a new inflationary scenario for the early universe or for a slowly rolling decaying Λ-scenario for the late universe, where the smallness of the vacuum energy can be understood ...

3D multifields FEM computation of transverse flux induction heating for moving-strips

Abstract: The numerical and experimental studies on induction heating of continuously moving strips in a transverse field are presented in this paper. The induced eddy current and its coupled thermal field in moving media is computed with FEM. The adopted mathematical model consists of a Fourier thermal conduction equation and a set of differential equations, which describes the steady-state eddy current problem in a configuration comprising a magnetic vector potential and an electrical scalar potential. The calculated results are in good agreement with the measurement.

Numerical modelling and design of electrical machines and devices

Abstract: 1 Introduction: 1.1 Numerical solution process. 2 Computer aided design in magnetics: 2.1 Finite element based CAD systems 2.2 Design strategies. 3 Electromagnetic fields: 3.1 Quasi stationary fields 3.2 Boundary value problem 3.3 Field equations in partial differential form. 4 Potentials and formulations: 4.1 Magnetic vector potential 4.2 Electric vector potential for conducting current 4.3 Electro-static scalar potential 4.4 Magnetic scalar potential 4.5 A? -formulation 4.6 AV-formulation 4.7 In-plane formulation 4.8 AV-formulation with v?B motion term 4.9 Gauge conditions 4.10 Subsequent treatment of the Maxwell equations. 5 Field computation and numerical techniques: 5.1 Magnetic equivalent circuit 5.2 Point mirroring method 5.3 The numerical solution of partial differential equations 5.4 Finite difference method 5.5 Finite element method 5.6 Material modelling 5.7 Numerical implementation of the FEM 5.8 Adaptive refinement for 2D triangular meshes 5.9 Coupling of field and circuit equations 5.10 Post-processing. 6 Coupled field problems: 6.1 Coupled fields 6.2 Strong and weak coupling 6.3 Coupled problems 6.4 Classification of coupled field problems. 7 Numerical optimisation: 7.1 Electromagnetic optimisation problems 7.2 Optimisation problem definition 7.3 Methods. 8 Linear system equation solvers: 8.1 Methods 8.2 Computational costs. 9 Modelling of electrostatic and magnetic devices: 9.1 Modelling with respect to the time 9.2 Geometry modelling 9.3 Boundary conditions 9.4 Transformations. 10 Examples of computed models: 10.1 Electromagnetic and electrostatic devices 10.2 Coupled thermo-electromagnetic problems 10.3 Numerical optimisation

The Geometry of Supersymmetric Quantum Mechanics

Abstract: One-dimensional sigma-models with N supersymmetries are considered. For conventional supersymmetries there must be N-1 complex structures satisfying a Clifford algebra and the constraints on the target space geometry can be formulated in terms of these. In the cases in which the complex structures are simultaneously integrable, a conventional extended superspace formulation is given, with the geometry determined by a 2-form potential for N=2, by a 1-form potential for N=3 and a scalar potential for N=4; for N>4 it is given by a scalar potential satisfying differential constraints. This gives explicit constructions of models with N=3 but not N=4 supersymmetry and of N=4 models in which the complex structures do not satisfy a quaternionic algebra. Generalisations with central terms in the superalgebra are also considered.

Numerical Models of Irrotational Binary Neutron Stars in General Relativity

Abstract: We report on general relativistic calculations of quasiequilibrium configurations of binary neutron stars in circular orbits with zero vorticity. These configurations are expected to represent realistic situations as opposed to corotating configurations. The Einstein equations are solved under the assumption of a conformally flat spatial 3-metric (Wilson-Mathews approximation). The velocity field inside the stars is computed by solving an elliptical equation for the velocity scalar potential. Results are presented for sequences of constant baryon number (evolutionary sequences). Although the central density decreases much less with the binary separation than in the corotating case, it still decreases. Thus, no tendency is found for the stars to individually collapse to black hole prior to merger.

The Galilean covariance of quantum mechanics in the case of external fields

Abstract: Textbook treatments of the Galilean covariance of the time-dependent Schrodinger equation for a spinless particle seem invariably to cover the case of a free particle or one in the presence of a scalar potential. The principal objective of this paper is to examine the situation in the case of arbitrary forces, including the velocity-dependent variety resulting from a vector potential. To this end, we revisit the 1964 theorem of Jauch which purports to determine the most general form of the Hamiltonian consistent with “Galilean-invariance,” and argue that the proof is less than compelling. We then show systematically that the Schrodinger equation in the case of a Jauch-type Hamiltonian is Galilean covariant, so long as the vector and scalar potentials transform in a certain way. These transformations, which to our knowledge have appeared very rarely in the literature on quantum mechanics, correspond in the case of electrodynamical forces to the “magnetic” nonrelativistic limit of Maxwell’s equations in the...

Forward problem solution for electrical conductivity imaging via contactless measurements.

Abstract: The forward problem of a new medical imaging system is analysed in this study. This system uses magnetic excitation to induce currents inside a conductive body and measures the magnetic fields of the induced currents. The forward problem, that is determining induced currents in the conductive body and their magnetic fields, is formulated. For a general solution of the forward problem, the finite element method (FEM) is employed to evaluate the scalar potential distribution. Thus, inhomogeneity and anisotropy of conductivity is taken into account for the FEM solutions. An analytical solution for the scalar potential is derived for homogeneous conductive spherical objects in order to test FEM solutions. It is observed that the peak error in FEM solutions is less than 2%. The numerical system is used to reveal the characteristics of the measurement system via simulations. Currents are induced in a 9x9x5 cm body of conductivity 0.2 S m(-1) by circular coils driven sinusoidally. It is found that a 1 cm shift in the perturbation depth reduces the field magnitudes to approximately one-tenth. In addition, the distance between extrema increases. Further simulations carried out using different coil configurations revealed the performance of the method and provided a design perspective for a possible data acquisition system.

Scattering of electrons on screw dislocations

Abstract: A previously established general framework for the description of long-wavelength quantum states of electrons in a crystal with topological defects is used to discuss the scattering of electrons on a screw dislocation. The corresponding Schr\"odinger equation contains contributions of the type of a vector potential as well as of a repulsive scalar potential. Together they give rise to modified Aharonov-Bohm interferences in the scattering amplitude, for which the far-field expression is calculated exactly.

Reconstruction of the plasma surface in a RFP in the presence of non-axisymmetric perturbations

Abstract: The non-axisymmetric analysis of the vacuum magnetic surface in a toroidal device is discussed assuming that the deviation from axisymmetry is a perturbation. The problem is particularly relevant to study the locked-mode phenomena due to internally resonant resistive magnetohydrodynamic (MHD) modes in reversed field pinch experiments. The general expressions which can be used for the magnetic reconstruction are derived according to two types of formalism: the flux function reconstruction and the magnetic scalar potential representation of the magnetic field. The measurements necessary to obtain a suitable magnetic reconstruction are discussed. In particular, it is found that a sufficient set of Br measurements is key information in obtaining the non-axisymmetric flux function. Such a set of measurements is presently lacking in the RFX reversed field pinch device. Nevertheless, based on an approximate solution of the Laplace equation for the magnetic scalar potential in the vacuum region outside the plasma, a method is derived by which the helical perturbation of the plasma magnetic surface can be computed with sufficient accuracy in RFX based on the measurements of a twin array of B coils only.

Method and system for numerical simulation of fluid flow

Abstract: A method of numerical simulation of fluid flow past a body. The physics of stationary flow is formulated in terms of a potential functional of at most four scalar fields: three Clebsch scalar fields and a density field. The physics of non-stationary flow is formulated in terms of an action that includes an action integral of a Lagrangian functional of the same four scalar fields and an initial and a final integral of a function of the same four scalar fields. The values of the fields are varied to extremize the potential functional or the action, under the constraint of appropriate boundary conditions. Potential functionals and Lagrangian functionals for compressible and incompressible flows with zero velocity normal to the surface of the body, and for potential flows, are described.

Self-similar collapse of a scalar field in higher dimensions

Abstract: This paper constructs the continuously self-similar solution of the spherically symmetric gravitational collapse of a scalar field in n dimensions The qualitative behaviour of these solutions is explained, and closed-form answers are provided where possible Equivalence of scalar field couplings is used to show a way to generalize minimally coupled scalar field solutions to the model with general coupling

Propagation of waves on a wire above a lossy ground-different formulations with approximations

Abstract: The characteristics of wave propagation guided by a single wire suspended in air above a lossy ground is studied with special regard to the distinction between the quantities: scalar potential, scalar potential to ground difference, and voltage to ground with their closed-form approximations of the correction terms. The propagation constant of the fundamental mode is addressed as is the difference in characteristic impedance depending on the formulation. The paper advocates the use of the magnetic vector potential together with the electric scalar potential and the complete solution for these in air and ground is given.

Duality and Hidden Symmetries in Gravitational Theories

Abstract: Duality is presently considered the key to the Holy Grail of String Theory— it is supposed to provide links between the five known different superstring theories in ten dimensions, hoped to be just different limits of one unique eleven dimensional theory [1]. The main role of duality is to relate two different regimes— e.g. one of weak and one of strong coupling— of these theories. In most cases duality is not a very precise concept, just because the strong coupling regime is a matter of speculation. This is rather different from the duality transformations in the gravitational theories considered in this work, which have a very precise meaning— not the least because we are dealing with classical field theories (compare, however, [2] and for a modest attempt to use duality symmetry in Quantum Gravity, see [3]). The historical example of all these dualities is the duality between electric and magnetic fields in electrodynamics, which, when expressed in terms of the field strength, is just an example of the mathematical notion of Hodge duality for differential forms. Actually, the source-free Maxwell equations are not only invariant under a discrete duality, but under a continous one-parameter group of duality rotations. It is this kind of transformations, which is the subject of this article. Whereas, in general, the electromagnetic duality rotations are an ‘on-shell’ symmetry, i.e. a symmetry of the equations of motion and not of the action, the situation changes,if one considers time-independent solutions. In this case also the magnetic field can be derived from a (pseudo) scalar potential and the duality rotations expressed in terms of scalar potentials become a bona fide "off-shell' symmetry of the "dimensionally reduced' three dimensional theory. This replacement of the vector potential by a scalar one has analogues in higher dimensions playing an important role in the construction of supergravity theories through the process of dimensional reduction. A typical example is the (pseudo) scalar "axion',obtained as the dual of a gauge field 2-form in 4 dimensions. This scalar axion combines nicely with another scalar,the dilaton to a doublet giving rise to an SL(2) group of non-linear duality transformations [4]. A particular element of this group,replacing the dilaton by its inverse,lies at the heart of string duality ("S- duality')[5],where the expectation value of the dilaton plays the role of a string coupling constant.

Implementing tri-potential approach in EMAP3D

Abstract: The Institute for Advanced Technology, The University of Texas at Austin has developed the finite element code EMAP3D which is capable of modeling coupled mechanical, thermal and electromagnetic diffusive processes with moving conductors. The Lagrangian dual potential formulation (magnetic vector potential and electrical scalar potential) was used in the earlier version of EMAP3D because it has the desirable property of being single-valued in multiply-connected regions. Using the magnetic vector potential for nonconducting regions requires solving for three unknowns at each node and results in large storage requirements and high computing cost. An alternative is to use the magnetic scalar potential, the third potential in the tri-potential formulation, in nonconducting regions. This requires solving for only one unknown at each node in nonconducting regions; however, the magnetic scalar potential is not single-valued in multiply-connected regions and the user is required to define appropriate branch cuts. A detailed Lagrangian tri-potential formulation is presented and compared to the dual potential formulation through the simulation of a typical railgun problem. The tri-potential approach shows distinct advantages in terms of model size, computing cost, and solution accuracy.

Supersymmetry of a spin 1/2 particle on the real line

Abstract: We study one dimensional supersymmetric (SUSY) quantum mechanics of a spin 1/2 particle moving in a rotating magnetic field and scalar potential. We also discuss SUSY breaking and it is shown that SUSY breaking essentially depends on the strength and period of the magnetic field. For a purely rotating magnetic field the eigenvalue problem is solved exactly and two band energy spectrum is found.

A surface impedance method for 3D time transient problems

Abstract: A new technique for modelling time transient thin skin depth eddy currents is presented. The nonconducting regions are modelled using conventional volume finite elements in terms of the magnetic scalar potential /spl psi/. The magnetic fields in the thin skin are determined approximately using 1D finite elements in terms of magnetic vector potentials, Most problems would result in one large volume matrix and many small 1D matrices. A staggered time transient solution to the two sets of equations in /spl psi/ and A is then carried out. A finite element implementation and some test examples are described.

Spherical and spheroidal shells as models in magnetic detection

Abstract: The expressions for the scalar potentials of prolate and oblate spheroidal shells immersed in a dc uniform magnetic field are obtained. The expressions for the induced dipole moment of the shells are also evaluated. The problem is solved by finding solutions for the Laplace equation that satisfy boundary conditions at the shell surfaces. The shell thickness effect on the induced dipole moment and on its orientation are evaluated, The results appear to be useful for the analysis and for the prediction of magnetic signatures of hidden ferromagnetic objects belonging to a relatively large family.

Quintessence and Supergravity

Abstract: In the context of quintessence, the concept of tracking solutions allows to address the fine-tuning and coincidence problems. When the field is on tracks today, one has $Q\approx m_{\rm Pl}$ demonstrating that, generically, any realistic model of quintessence must be based on supergravity. We construct the most simple model for which the scalar potential is positive. The scalar potential deduced from the supergravity model has the form $V(Q)=\frac{\Lambda^{4+\alpha}}{Q^{\alpha}}e^{\frac{\kappa}{2}Q^2}$. We show that despite the appearence of positive powers of the field, the coincidence problem is still solved. If $\alpha \ge 11$, the fine-tuning problem can be overcome. Moreover, due to the presence of the exponential term, the value of the equation of state, $\omega_Q$, is pushed towards the value -1 in contrast to the usual case for which it is difficult to go beyond $\omega_Q\approx -0.7$. For $\Omega_{\rm m}\approx 0.3$, the model presented here predicts $\omega_Q\approx -0.82$. Finally, we establish the $\Omega_{\rm m}-\omega_Q$ relation for this model.

A new approach to SP Computation-vector potential approach

Abstract: The steady current field is guided by two fundamental principles, i.e., the vanishing of the curl of the field strength and the vanishing of the divergence of current density, which originate from the conservation of energy and charge, respectively. In the prevailing approach, the first principle is assumed to be generally valid and, hence, the field strength is equated to the negative gradient of a scalar potential. The second principle is dropped at certain points, which are called current sources, that current is supposed to be injected from the outside. In the present paper, a different approach is proposed, in which the density of current is equated to the curl of a vector potential so that its divergence vanishes unconditionally while the curl of field strength assumes nonvanishing value at some points that are called curl sources. It is called the vector potential theory approach and shows its advantage over scalar potential theory in spontaneous potential (SP) computation. In the vector potential approach, the dipole layer disappears and SP is supposed to be generated by the curl source rather than the dipole layer. In the numerical computation, the numerical mode-matching method (NMM) is used. Hermite cubic interpolation rather than linear interpolation is employed in the basis function expansion of the simulated function. Eigenvectors to be solved for are composed of, not only the amplitudes, but also the slopes of the simulated function at nodal points.

Metric for an Oblate Earth

Abstract: In linearized general relativity the metric ofa body is described by a scalar potential and athree-vector potential. We here present a simpletransformation derivation of the linearized metric interms of these potentials, and calculate the exactscalar and vector potentials for a field with oblatespheroidal symmetry. The results for the externalpotentials do not depend on details of the densitydistribution inside the earth; both the scalar and vectorpotentials are fully determined by the total mass, thetotal angular momentum, and a radial parameter, all ofwhich are accurately known from observation. The scalar potential is accurate to roughly10-6 and the vector potential, which hasnever been accurately measured, should be accurate toabout 10-5. Applications include an accuratetreatmen t of the details of the motion of satellites, and theprecession of a gyroscope in earth orbit.

A study of the design for touch free linear eddy current brake

Abstract: This paper describes the performances of eddy current brake according to the design parameters. The characteristics are analyzed by using 2-dimensional Finite Element Method (2-D FEM) in order to predict the effect of the design parameters. The magnet stack width is determined from equivalent stack width that is calculated by solution of the field with scalar potential. The validity of available calculation program with FEM is achieved by comparing with experimental value. From the results, the optimized magnet configuration of the eddy current braking system is designed to obtain not only the maximum braking force but also the minimum attraction force.

High-resolution magnetic field numerical dosimetry for live-line workers

Abstract: Numerical modeling provides one means for the realistic assessment of the electric field and current density levels induced in the bodies of live-line utility workers during occupational exposure to 60 Hz nonuniform magnetic fields. An efficient scalar potential finite difference method is applied to anatomically-derived high-resolution heterogeneous human body conductivity models, to provide such estimates for four representative posture and exposure scenarios. Dosimetric data are presented in terms of volumetric maximum and root mean square fields induced in various tissue groups by unit current. The results scale linearly with total source current, which allows the data to be applied to arbitrary current levels.