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Scalar Potential (scalar + potential)

Distribution by Scientific Domains

Engineering	50%

Selected Abstracts

Flux compactification of M-theory on compact manifolds with Spin(7) holonomy,

FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 11-12 2005
D. Constantin
At the leading order, M-theory admits minimal supersymmetric compactifications if the internal manifold has exceptional holonomy. The inclusion of non-vanishing fluxes in M-theory and string theory compactifications induce a superpotential in the lower dimensional theory, which depends on the fluxes. In this work, we check the conjectured form of this superpotential in the case of warped M-theory compactifications on Spin(7) holonomy manifolds. We perform a Kaluza-Klein reduction of the eleven-dimensional supersymmetry transformation for the gravitino and we find by direct comparison the superpotential expression. We check the conjecture for the heterotic string compactified on a Calabi-Yau three-fold as well. The conjecture can be checked indirectly by inspecting the scalar potential obtained after the compactification of M-theory on Spin(7) holonomy manifolds with non-vanishing fluxes. The scalar potential can be written in terms of the superpotential and we show that this potential stabilizes all the moduli fields describing deformations of the metric except for the radial modulus. All the above analyses require the knowledge of the minimal supergravity action in three dimensions. Therefore we calculate the most general causal ,, =1 three-dimensional, gauge invariant action coupled to matter in superspace and derive its component form using Ectoplasmic integration theory. We also show that the three-dimensional theory which results from the compactification is in agreement with the more general supergravity construction. The compactification procedure takes into account higher order quantum correction terms in the low energy effective action. We analyze the properties of these terms on a Spin(7) background. We derive a perturbative set of solutions which emerges from a warped compactification on a Spin(7) holonomy manifold with non-vanishing flux for the M-theory field strength and we show that in general the Ricci flatness of the internal manifold is lost, which means that the supergravity vacua are deformed away from the exceptional holonomy. Using the superpotential form we identify the supersymmetric vacua out of this general set of solutions. [source]

The reduced scalar potential in regions with permeable materials: Reasons for loss of accuracy and cancellation

INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 4 2007
S. Balac
Abstract Practical three-dimensional magnetic field problems usually involve regions containing current sources as well as regions with magnetic materials. For computational purposes, the use of the reduced scalar potential (RSP) as unknown has the advantage to transform a problem for a vector field throughout the space into a problem for a scalar function, thus reducing the number of degrees of freedom in the discretization. However, in regions with high magnetic permeability the use of the RSP alone usually results in severe loss in accuracy and it is recommended to use both the RSP and the total scalar potential. Using an asymptotic expansion, we investigate theoretically the underlying reasons for this lack of accuracy in permeable regions when using the RSP as a unique potential. Moreover, this investigation leads to an efficient numerical method to compute the magnetic field in regions with high magnetic permeability. Copyright © 2007 John Wiley & Sons, Ltd. [source]

The effect of the electrical anisotropy on the response of helicopter-borne frequency-domain electromagnetic systems

GEOPHYSICAL PROSPECTING, Issue 5 2004
Changchun Yin
ABSTRACT Helicopter electromagnetic (HEM) systems are commonly used for conductivity mapping and the data are often interpreted using an isotropic horizontally layered earth model. However, in regions with distinct dipping stratification, it is useful to extend the model to a layered earth with general anisotropy by assigning each layer a symmetrical 3 × 3 resistivity tensor. The electromagnetic (EM) field is represented by two scalar potentials, which describe the poloidal and toroidal parts of the magnetic field. Via a 2D Fourier transform, we obtain two coupled ordinary differential equations in the vertical coordinate. To stabilize the numerical calculation, the wavenumber domain is divided into two parts associated with small and large wavenumbers. The EM field for small wavenumbers is continued from layer to layer with the continuity conditions. For large wavenumbers, the EM field behaves like a DC field and therefore cannot be sensed by airborne EM systems. Thus, the contribution from the large wavenumbers is simply ignored. The magnetic fields are calculated for the vertical coaxial (VCX), horizontal coplanar (HCP) and vertical coplanar (VCP) coil configurations for a helicopter EM system. The apparent resistivities defined from the VCX, VCP and HCP coil responses, when plotted in polar coordinates, clearly identify the principal anisotropic axes of an anisotropic earth. The field example from the Edwards Aquifer recharge area in Texas confirms that the polar plots of the apparent resistivities identify the principal anisotropic axes that coincide well with the direction of the underground structures. [source]

On the efficient computation of closed-form Green's functions in planar stratified media

INTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 2 2008
A. G. Polimeridis
Abstract The spatial-domain Green's functions for the vector and scalar potentials in planar stratified media are cast into closed forms via a two-level approximation of their spectral-domain counterparts. The proposed methodology begins with the approximation of the spectral-domain Green's functions over large values of the spectral variable by complex exponentials, and continues with the approximation of the remainder by rational functions. Finally, the closed-form Green's functions in terms of spherical and cylindrical waves are derived, making use of some well-known integral identities. A key-feature of the proposed approach is that although it does not call for an analytical extraction of the quasistatic terms and the surface wave poles, it provides the means for the accurate description of both the near-field and far-field physics. Moreover, the rational function spectrum fitting proposed here overcomes the problem of the spurious singular behavior of the spatial-domain Green's functions because of the use of Hankel functions. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2008. [source]