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 paper, a hybrid T-Omega method was proposed to solve eddy-current problems, where the finite element method is used in the conducting region while the boundary integral method (BIM) was used in free space.
Abstract: A hybrid T- Omega method to solve eddy-current problems is proposed. The finite-element method is used in the conducting region while the boundary integral method (BIM) is used in free space. The unknowns in the conducting regions are the electric vector potential T and the magnetic scalar potential Omega . Calculations for a test example concerning the current in an hollow sphere are performed, and field and current distributions are shown. The results confirm the usefulness of the MIXTER-T Omega code which uses the T Omega formulation and the coupling of FEM and BIM methods. >
20 citations
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TL;DR: In this article, the authors studied the spectrum of spherically symmetric Dirac operators in three-dimensional space with potentials tending to infinity at infinity under weak regularity assumptions.
Abstract: We study the spectrum of spherically symmetric Dirac operators in three-dimensional space with potentials tending to infinity at infinity under weak regularity assumptions. We prove that purely absolutely continuous spectrum covers the whole real line if the potential dominates the mass, or scalar potential, term. In the situation where the potential and the scalar potential are identical, the positive part of the spectrum is purely discrete; we show that the negative half-line is filled with purely absolutely continuous spectrum in this case.
20 citations
20 citations
TL;DR: In this paper, the problem of radiation from sources of arbitrary time dependence in a moving medium is treated, where the medium is assumed to be lossless, with permittivity e and permeability μ, and to move with constant velocity v with respect to a given inertial reference frame xyz.
Abstract: This paper treats the problem of radiation from sources of arbitrary time dependence in a moving medium. The medium is assumed to be lossless, with permittivity e and permeability μ, and to move with constant velocity v with respect to a given inertial reference frame xyz. It is shown how the Maxwell‐Minkowski equations for the electromagnetic fields in the moving medium can be integrated by means of a pair of vector and scalar potential functions analogous to those commonly used with stationary media. The wave equation associated with these potential functions is derived, and a scalar Green's function is defined to satisfy the same type of equation, with a delta‐function source term δ(r − r′) δ(t − t′), and the casuality condition. The solution for the Green's function is derived in closed form, by means of a Fourier integral method. The resulting Green's function is useful not only for calculating the fields from arbitrary sources in moving media, but also for its pedagogical value. It is simpler to un...
20 citations
TL;DR: In this article, the authors derived the full weak-lensing deflection angle valid on non-linear scales for any metric theory of gravity and showed that the only contributing term that is quadratic in the first order deflection is the expected Born correction and lens-lens coupling term.
Abstract: In this paper we examine cosmological weak lensing on non-linear scales and show that there are Newtonian and relativistic contributions and that the latter can also be extracted from standard Newtonian simulations. We use the post-Friedmann formalism, a post-Newtonian type framework for cosmology, to derive the full weak-lensing deflection angle valid on non-linear scales for any metric theory of gravity. We show that the only contributing term that is quadratic in the first order deflection is the expected Born correction and lens-lens coupling term. We use this deflection angle to analyse the vector and tensor contributions to the E- and B- mode cosmic shear power spectra. In our approach, once the gravitational theory has been specified, the metric components are related to the matter content in a well-defined manner. Specifying General Relativity, we write down a complete set of equations for a GR$+\Lambda$CDM universe for computing all of the possible lensing terms from Newtonian N-body simulations. We illustrate this with the vector potential and show that, in a GR$+\Lambda$CDM universe, its contribution to the E-mode is negligible with respect to that of the conventional Newtonian scalar potential, even on non-linear scales. Thus, under the standard assumption that Newtonian N-body simulations give a good approximation of the matter dynamics, we show that the standard ray tracing approach gives a good description for a $\Lambda$CDM cosmology.
20 citations