Topic
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.
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TL;DR: In this article, the eddy current equations are formulated in terms of H, instead of the more usual vector potential A, where a combination with a scalar potential is necessary in the non conducting regions.
Abstract: The eddy current equations are formulated here in terms of H [1] instead of the more usual vector potential A [2,3]. In both cases a combination with a scalar potential is necessary in the non conducting regions. In the case of A this leads to either a non symmetric or not positive definite system of equations to be solved. This is avoided by the formulation in H, but special elements have to be chosen in order to satisfy the interface conditions between the two regions. The construction of such elements on tetrahedra or rectangular blocks can be found in [4]. The construction for hexahedra, or more specifically, isoparametric bricks, is shown here. Compared to filling a hexahedron with tetrahedra, this method reduces the number of unknowns by a half. The computed approximations for the eddy currents are exactly non divergent.
99 citations
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TL;DR: In this paper, the authors consider type II string compactifications on Calabi-Yau orientifolds with fluxes and D-branes, and analyse the F-term scalar potential that simultaneously involves closed and open string modes.
Abstract: We consider type II string compactifications on Calabi-Yau orientifolds with fluxes and D-branes, and analyse the F-term scalar potential that simultaneously involves closed and open string modes. In type IIA models with D6-branes this potential can be directly computed by integrating out Minkowski three-forms. The result shows a multi-branched structure along the space of lifted open string moduli, in which discrete shifts in special Lagrangian and Wilson line deformations are compensated by changes in the RR flux quanta. The same sort of discrete shift symmetries are present in the superpotential and constrain the Kahler potential. As for the latter, inclusion of open string moduli breaks the factorisation between complex structure and Kahler moduli spaces. Nevertheless, the 4d Kahler metrics display a set of interesting relations that allow to rederive the scalar potential analytically. Similar results hold for type IIB flux compactifications with D7-brane Wilson lines.
99 citations
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TL;DR: In this article, the authors considered one-dimensional sigma-models with N supersymmetries and gave an extended superspace formulation, with the geometry determined by a 2-form potential for N = 2, by a 1-form for N=3, and by a scalar potential for n = 4.
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.
99 citations
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TL;DR: In this article, a novel procedure of formulating the three-dimensional magnetic field problem in heterogeneous materials in terms of the unknown scalar potential φ and a known analytical solution for a vector potential which is caused by the specified current densities in a homogeneous domain is presented.
Abstract: A novel procedure of formulating the three-dimensional magnetic field problem in heterogeneous materials in terms of the unknown scalar potential φ and a known analytical solution for a vector potential which is caused by the specified current densities in a homogeneous domain is presented. The analytical solution to the auxiliary problem is easily determined, and the resulting scalar formulation presents considerable economies against the more obvious but costly direct solution with a three-component vector potential A. Two-and three-dimensional examples assuming linear behavior of the material are given to assess the accuracy of the process, and indication is given of the nature of iterations required for nonlinear properties.
96 citations