Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge star is e...

The finite element approach can be considered as a tool for constructing finite dimensional systems of equations that approximate to field problems on the discrete level. Although the finite element technique is explained typically in terms of variational or weighted-residual approaches, another, less familiar way is available to introduce the same ideas geometrically. Using magnetostatics as a...

We have studied frustrated kagome arrays and unfrustrated honeycomb arrays of magnetostatically interacting single-domain ferromagnetic islands with magnetization normal to the plane. The measured pairwise spin correlations of both lattices can be reproduced by models based solely on nearest-neighbor correlations. The kagome array has qualitatively different magnetostatics but identical lattice...

In this article, we report on the simulation and realization of a magnetic circuit allowing to apply an axial magnetic field higher than 1 Tesla. The proposed electromagnet is used to investigate the influence of a magnetic field on the polarization behavior of a vertical-cavity-surface-emitting laser (VCSEL). A nonlinear polarization behavior can be experimentally observed for currents as low ...

We present a negative-norm least-squares method for axisymmetric divcurl systems arising from Maxwell’s equations for electrostatics and magnetostatics in three dimensions. The method approximates the solution in a two-dimensional meridian plane. To achieve this dimension reduction, we must work with weighted spaces in cylindrical coordinates. In this setting, a stable pair of approximation spa...

We report an experimental enhancement of the magnetic susceptibility of suspensions of particles that is related to the spatial distribution of the magnetic phase in the particles. At low field, the susceptibility of suspensions of nickel-coated diamagnetic spheres was approximately 75% higher than that of suspensions of solid nickel spheres with the same nickel content. This result was corrobo...

The problem of retrieving a static current density from knowledge of the magnetic field it produces at a plane is solved. This problem does not have a unique solution. However, there is a unique solution of the least L2 norm. The Fourier transform of the minimum norm current distribution is given in closed form. The minimum norm current distribution is a filtered version of any other current di...

Special relativity is reformulated as a symmetry property of space-time: Space-Time Exchange Invariance. The additional hypothesis of spatial homogeneity is then sufficient to derive the Lorentz transformation without reference to the traditional form of the Principle of Special Relativity. The kinematical version of the latter is shown to be a consequence of the Lorentz transformation. As a dy...

Special relativity is reformulated as a symmetry property of space-time: Space-Time Exchange Invariance. The additional hypothesis of spatial homogeneity is then sufficient to derive the Lorentz transformation without reference to the traditional form of the Principle of Special Relativity. The kinematical version of the latter is shown to be a consequence of the Lorentz transformation. As a dy...

| In this paper design sensitivity analysis is applied to solve the TEAM workshop problem 25. In order to justify the use of a gradient method, it is necessary to assume a continuously di erentiable dependence of the sti ness matrix on the design parameters. Since design sensitivity analysis is mainly applicable to optimization problems, where the geometrical parameters undergo small changes on...