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In the report he submitted to the Académie des Sciences, Poisson imagined a set of concentric spheres at the origin of Earth's magnetic field. It may come as a surprise to many that Poisson as well as Gauss both considered the magnetic field to be constant. We propose in this study to test this surprising assertion for the first time, evoked by Poisson in 1826. First, we present a development of Maxwell's equations in the framework of a static electric field and a static magnetic field in order to draw the necessary consequences for the Poisson hypothesis. In a second step, we see if the observations can be in agreement with Poisson. To do so, we choose to compare (1) the polar motion drift and the secular variation of Earth's magnetic field, (2) the seasonal pseudo-cycles of day length together with those of the sea level recorded by different tide gauges around the globe and those of Earth's magnetic field recorded in different magnetic observatories. We then propose a mechanism, in the spirit of Poisson, to explain the presence of the 11-year cycle in the magnetic field. We test this mechanism with observations, and finally, we study closely the evolution of the g 1 , 0 coefficient of the International Geomagnetic Reference Field (IGRF) over time. [ABSTRACT FROM AUTHOR]

The Matrix Pencil method is used for extracting maximum information from the Electro-Magnetic disturbances emitted by power converters; these disturbances are manifested by an induced current in electric systems located in the power converter environs. The modeling of the power converter in time domain is realized by solving Maxwell's equations which allow determining the radiated electromagnetic field, Ampere's theorem is then used for computing the induced current in passive loops representing the victim system. In our work we also analyze the effect of the geometric configuration for both the passive loops and the power converter by extracting the poles and residues using Matrix Pencil method. [ABSTRACT FROM AUTHOR]

This paper presents a multi-physic analytical model for a permanent magnet assisted synchronous reluctance motor. The proposed model consists of: an electromagnetic model, an electrical model, a loss model, and a thermal model. The electromagnetic model is based on Maxwell's equations. Stator and rotor magnetic saturation is considered, as well as the effect of the magnetic bridges of the flux-barriers. The electrical model computes the terminal voltage and power factor. Copper loss and iron losses are also considered. The thermal model makes an estimation of the winding and magnet temperature. The goal is to compute the motor performances (average torque, voltage, power factor, efficiency etc.) for several current values and current angles. The analytical model results are compared with those from a finite element model and are subsequently validated by an experimental prototype. [ABSTRACT FROM AUTHOR]

The objective of this article is to discuss the existence and the uniqueness of a weighted extended B-spline-(WEB-spline) based discrete solution for the Maxwell equations in low frequency limit. The domain is composed of insulating and conducting regions. This problem has saddle point structure where the electric field in insulating region is the Lagrange multiplier that forces curl-free constraint on the magnetic field. [ABSTRACT FROM PUBLISHER]

The purpose of this article is to present a wider frame to treat the quasi-static limit of Maxwell's equations. We discuss the fact that there exists not one but indeed two dual Galilean limits, the electric and the magnetic one. We start by a re-examination of the gauge conditions and their compatibility with Lorentz and Galilean covariance. By means of a dimensional analysis on fields and potentials we first emphasize the correct scaling yielding the equations in the two limits. With this particular point of view, the gauge conditions of classical electromagnetism are continuity equations whose range of validity depend on the relativistic or Galilean nature of the underlying phenomenon and have little to do with mathematical closure assumptions taken without physical motivations. We then present the analysis of the quasi-static models in terms of characteristic times and visualize their domains of validity in a suitable diagram. We conclude by few words on the Galilean electrodynamics for moving media, underlying the transformation laws for fields and potentials which are valid in the different limits. [ABSTRACT FROM AUTHOR]

comparison is made between the treatment of magnetic fields in superconductors and normal materials. First some history is given, showing how early workers anticipated vortices. Later treatments tried to build a macroscopic theory using forces and torques on magnets. This was extremely unsatisfactory. Maxwell's equations for normal materials are derived using average fields. The differences between the applied field, the demagnetising field, the local field on an atom and H are made clear. The derivation in superconductors follows a different path and uses the theory of Evetts. Simple and rigorous derivations of the forces on bodies and magnetic energies are derived, with comments on less satisfactory treatments. This is extended to thermodynamic potentials including the Ginzburg-Landau free energy. [ABSTRACT FROM AUTHOR]

The complementary energy bounds of dual formulations on dual meshes for eddy current problems are investigated. Based on the algebraic discretization of Maxwell equations on the dual meshes using different working variables, two sets of dual formulations, both for the finite-element method (FEM) and the finite integral technique (FIT), can be derived. A rational comparison between these formulations and the circuit networks is performed. The complementary bounds of magnetic energy and power losses are studied through an example. The study shows that the energy bounds are due to the numerical discretization of the Hodge operators on dual meshes. The dependency of the upper and lower energy bounds on the field excitation is also illustrated. The relation of the numerical bounds of the global circuit elements to the dual mesh discretization is given. [ABSTRACT FROM AUTHOR]

We propose two improvements to the Reitzinger and Schöberl algebraic multigrid (AMG) method for solving the eddy current approximations to Maxwell's equations. The main focus in the Reitzinger/Schöberl method is to maintain null space properties of the weak δ×δ× operator on coarse grids. While these null space properties are critical, they are not enough to guarantee h-independent convergence of the overall multigrid method. We illustrate how the Reitzinger/Schöberl AMG method loses h-independence due to the somewhat limited approximation property of the grid transfer operators. We present two improvements to these operators that not only maintain the important null space properties on coarse grids but also yield significantly improved multigrid convergence rates. The first improvement is based on smoothing the Reitzinger/Schöberl grid transfer operators. The second improvement is obtained by using higher order nodal interpolation to derive the corresponding AMG interpolation operators. While not completely h-independent, the resulting AMG/CG method demonstrates improved convergence behavior while maintaining low operator complexity. [ABSTRACT FROM AUTHOR]

Provides information on a study which examined several three-dimensional eddy current formulations derived from dual system of Maxwell equations. Dual formulations of eddy current problems; Comparison of field and potential formulations; Conclusions.