Scalar potential

About: Scalar potential is a research topic. Over the lifetime, 3642 publications have been published within this topic receiving 78868 citations. The topic is also known as: potential.

On different approaches to calculating lightning electric fields

Abstract: Three different approaches to the computation of lightning electric fields are compared. These approaches are the traditional dipole (Lorentz condition) technique and two versions of the monopole (continuity equation) technique. The latter two techniques are based on two different formulations of the continuity equation, one used by Thottappillil et al. [1997] and the other by Thomson [1999], the difference between the formulations being related to different treatments of retardation effects. The three approaches involve the same expression for the vector potential but different expressions for the scalar potential. It is analytically shown that the three different expressions for the scalar potential are equivalent and satisfy the Lorentz condition. Further, the three approaches yield the same total fields and the same Poynting vectors. However, expressions in the three approaches for the individual electric field components in the time domain, traditionally identified by their distance dependence as electrostatic, induction, and radiation terms, are different, suggesting that explicit distance dependence is not an adequate identifier. It is shown that the so identified individual field components in the electric field equation in terms of charge density derived by Thottappillil et al. [1997] are equivalent to the corresponding field components in the traditional equation for electric field in terms of current based on the dipole technique. However, the individual field components in the electric field equation based on Thomson's [1999] approach are not equivalent to their counterparts in the traditional dipole technique equation. Further, in Thottappillil et al.'s [1997] technique and in the traditional dipole technique, the gradient of scalar potential contributes to all three electric field components, while in Thomson's [1999] technique it contributes only to the electrostatic and induction components. Calculations of electric fields at different distances from the lightning channel show that the differences between the corresponding field components identified by their distance dependence in different techniques are considerable at close ranges but become negligible at far ranges.

3-D Analytical Model for Axial-Flux Eddy-Current Couplings and Brakes Under Steady-State Conditions

Abstract: This paper presents a 3-D analytical model for axial-flux eddy-current couplings and brakes, leading to closed-form expressions for the torque and the axial force. The proposed model is valid under a steady-state condition (constant speed operation). It takes into account the reaction field due to induced currents in the moving conducting part. In order to simplify the analysis, we adopt the assumption of linearization at the mean radius, and the problem is then solved in 3-D Cartesian coordinates (curvature effects are neglected). The solution is obtained by solving the Maxwell equations with a magnetic scalar potential formulation in the nonconductive regions (magnets and air gap) and a magnetic field strength formulation in the conductive region (copper). Magnetic field distribution, axial force, and torque computed with the 3-D analytical model are compared with those obtained from the 3-D finite-element simulations and experimental results.

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

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

Comparison of magnetically induced elf fields in humans computed by FDTD and scalar potential FD codes

Abstract: This paper presents a comparison of the magnetically induced low frequency electric and current density fields within an anatomically realistic model of the full human body, as computed using two different numerical techniques. The first method is a full wave quasi-static finite-difference time-domain method. The second method is based on a representation of the first-order internal electric field in terms of a scalar conduction potential plus a vector potential for the lowest-order applied magnetic field. Each code was used to calculate the fields, induced by three orthogonal uniform magnetic fields, in a 7.2 mm-resolution human full-body model. Three-dimensional correlation coefficients of better than 99.8% were observed between results computed by the two methods. Individual edge electric fields typically agree to 3 significant digits.

E7(7) formulation of N = 2 backgrounds

Abstract: In this paper we reformulate N = 2 supergravity backgrounds arising in type II string theory in terms of quantities transforming under the U-duality group E7(7). In particular we combine the Ramond-Ramond scalar degrees of freedom together with the O(6,6) pure spinors which govern the Neveu-Schwarz sector by considering an extended version of generalised geometry. We give E7(7)-invariant expressions for the Kahler and hyperkahler potentials describing the moduli space of vector and hypermultiplets, demonstrating that both correspond to standard E7(7) coset spaces. We also find E7(7) expressions for the Killing prepotentials defining the scalar potential, and discuss the equations governing N = 1 vacua in this formalism.