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.

Calculation of equipotentials and flux lines in axially symmetrical permanent magnet assemblies by computer

Abstract: Two equivalent theoretical models of permanent magnets are used to develop algorithms for numerically computing the magnetic scalar potential and the magnetic vector potential in the vicinity of an axially symmetric array of pole pieces and permanent magnets. A computer program based on these algorithms calculates equipotential surfaces and flux lines in and around the magnets and pole pieces. In deriving the algorithm for numerically calculating the vector potential a relationship between the magnetic scalar potential and the vector potential was found which enables the program to calculate the vector potential from the scalar potential distribution and thus generate equipotentials and flux lines with only one iterative calculation. An algorithm which calculates the scalar potential of a "floating" pole piece, that is, one on which the scalar potential has not been specified, is developed. The vector potential around the pole piece is determined from the scalar potential calculation, and this information is used to calculate the vector potential and the flux lines within the pole piece. The computer program calculates the coordinates of all points at which the equipotential lines and flux lines cross the Liebmann net. This information is fed to a cathode ray tube plotter which generates a field plot. To deal with systems in which macroscopic currents are present as well as permanent magnets, the iterative Liebmann net calculation of the vector potential is developed, and a method of applying Neumann boundary conditions to the vector potential at high-permeability surfaces is described.

Scalar fields in Cosmology: dark matter and inflation

Abstract: Scalar fields have been widely used in cosmology during the last three decades, but it is until now that we have been able to fully understand their role as possible major matter components for the evolution of the Universe. Here we briefly present recent studies on scalar fields that show how their intrinsic properties are translated into observables related to the process of structure formation. In the first case, we consider a massive scalar field as a dark matter component, and present the corresponding mass power spectrum. It is confirmed that one of the distinctive features of the model is the suppression of structure at small cosmological scales. In the second case, we describe a generic method to find inflationary solutions without the need to be specific about the scalar potential. The method shows that single-field models of inflation can be classified in two groups according to their predictions of inflationary observables.

A Spherical Cap Harmonic Model of the Crustal Magnetic Anomaly Field in Europe Observed by Magsat

Abstract: The geomagnetic field observed in current-free regions above the Earth’s surface may be expressed as the gradient of a scalar potential satisfying Laplace’s equation Spherical cap harmonic analysis enables solution of Laplace’s equation, subject to boundary conditions appropriate to geomagnetic field analysis, in a region bounded by a spherical cap Magsat data within a spherical cap of half-angle 35° centred on latitude 45°N, longitude 10°E have been analysed for their crustal content The resulting estimates of the crustal vector field have been used to derive a spherical cap harmonic model of the crustal scalar potential The model contains 256 parameters and portrays wavelengths of 1000 km and above Vector anomaly maps derived from the model show several prominent features of which the largest is that in the Kursk region of the USSR The model has been used to correct both the vector and total intensity data on to a 2° by 2° grid at an altitude of 400 km Anomaly maps produced by contouring the grid averages are in good agreement with those derived from the model The major difference is for the vertical component of the anomaly field over the Kursk region of the USSR This is a high-amplitude short-wavelength feature which the model smooths

Orbit spaces of low‐dimensional representations of simple compact connected Lie groups and extrema of a group‐invariant scalar potential

Abstract: Orbit spaces of low-dimensional representations of classical and exceptional Lie groups are constructed and tabulated. We observe that the orbit spaces of some single irreducible representations (adjoints, second-rank symmetric and antisymmetric tensors of classical Lie groups, and the defining representations of F4 and E6) are warped polyhedrons with (locally) more protrudent boundaries corresponding to higher level little groups. The orbit spaces of two irreducible representations have different shapes. We observe that dimension and concavity of different strata are not sharply distinguished. We explain that the observed orbit space structure implies that a physical system tends to retain as much symmetry as possible in a symmetry breaking process. In Appendix A, we interpret our method of minimization in the orbit space in terms of conventional language and show how to find all the extrema (in the representation space) of a general group-invariant scalar potential monotonic in the orbit space. We also present the criterion to tell whether an extremum is a local minimum or maximum or an inflection point. In Appendix B, we show that the minimization problem can always be reduced to a two-dimensional one in the case of the most general Higgs potential for a single irreducible representation and to a three-dimensional one in the case of an even degree Higgs potential for two irreducible representations. We explain that the absolute minimum condition prompts the boundary conditions enough to determine the representation vector.