Cloaks,editors, and bubbles: applications of spacetime transformation theory

Spacetime or ‘event’ cloaking was recently introduced as a concept, and the theoretical design for such a cloak was presented for illumination by electromagnetic waves [McCall et al., J. Opt. 2011]. Here it is described how event cloaks can be designed for simple wave systems, using either an approximate ‘speed cloak’ method, or an exact full‐wave one. Further, details of many of the implications of spacetime transformation devices are discussed, including their (usually) directional nature, spacetime distortions (as opposed to cloaks), and how leaky cloaks manifest themselves. More exotic concepts are also addressed, in particular concepts that follow naturally on from considerations of simple spacetime transformation devices, such as spacetime modeling and causality editors. A proposal for implementing an interrupt‐without‐interrupt concept is described. Finally, the design for a time‐dependent ‘bubbleverse’ is presented, based on temporally modulated Maxwell's Fisheye transformation device (T‐device) in a flat background spacetime.     

电磁学课程思政的探索与实践

为了落实"立德树人"的根本任务,将知识传授、能力培养、价值引领融为一体,在电磁学课程教学中开展了课程思政的探索.首先研究了基于课程思政理念的电磁学教学大纲与教学目标的修订、电磁学课程思政类型、准确提炼课程思政映射点的方法.其次探索了电磁学课程思政的几种方法和途径、电磁学教学内容及其课程思政映射点.实践表明电磁学课程思政...     

On linear electromagnetic constitutive laws that define almost‐complex structures

It is shown that not all linear electromagnetic constitutive laws will define almost‐complex structures on the bundle of 2‐forms on the spacetime manifold when composed with the Poincaré duality isomorphism, but only a restricted class of them that includes linear spatially isotropic and some bi‐isotropic constitutive laws. Although this result does not trivialize the formulation of the basic equations of pre‐metric electromagnetism, it does affect their reduction to metric electromagnetism by its effect on the types of media that are reducible, and possibly its effect on the way that such media support the propagation of electromagnetic waves.     

Wesson’s Induced Matter Theory with a Weylian Bulk

The foundations of Wesson’s induced matter theory are analyzed. It is shown that the empty—without matter—5-dimensional bulk must be regarded as a Weylian space rather than as a Riemannian one. Revising the geometry of the bulk, we have assumed that a Weylian connection vector and a gauge function exist in addition to the metric tensor. The framework of a Weyl–Dirac version of Wesson’s theory is elaborated and discussed. In the 4-dimensional hypersurface (brane), one obtains equations describing both fields, the gravitational and the electromagnetic. The result is a geometrically based unified theory of gravitation and electromagnetism with mass and current induced by the bulk. In special cases on obtains on the brane the equations of Einstein–Maxwell, or these of the original induced matter theory.     

Covariant hysteretic constitutive theory for Maxwell’s equations: application to axially rotating media

This paper explores a class of non-linear constitutive relations for materials with memory in the framework of covariant macroscopic Maxwell theory. Based on earlier models for the response of hysteretic ferromagnetic materials to prescribed slowly varying magnetic background fields, generalized models are explored that are applicable to accelerating hysteretic magneto-electric substances coupled self-consistently to Maxwell fields. Using a parameterized model consistent with experimental data for a particular material that exhibits purely ferroelectric hysteresis when at rest in a slowly varying electric field, a constitutive model is constructed that permits a numerical analysis of its response to a driven harmonic electromagnetic field in a rectangular cavity. This response is then contrasted with its predicted response when set in uniform rotary motion in the cavity.     

TheB (3) field as a link between gravitation and electromagnetism in the vacuum

The emergence of theB ⁽³⁾ field in vacuo has shown that electromagnetism is non-Abelian and similar in structure to gravitation. In this paper the Christoffel symbol used in general relativity is developed for electromagnetism in curvilinear coordinates: The former becomes describable as the antisymmetric part of the gravitational Ricci tensor. Therefore gravitation and electromagnetism are respectively the symmetric and antisymmetric parts of thesame Ricci tensor within a proportionality factor. Both fields are obtained from the Riemann curvature tensor, both are expressions of curvature in spacetime.     

Numerical treatment of realistic boundary conditions for the eddy current problem in an electrode via Lagrange multipliers

This paper deals with the finite element solution of the eddy current problem in a bounded conducting domain, crossed by an electric current and subject to boundary conditions appropriate from a physical point of view. Two different cases are considered depending on the boundary data: input current density flux or input current intensities. The analysis of the former is an intermediate step for the latter, which is more realistic in actual applications. Weak formulations in terms of the magnetic field are studied, the boundary conditions being imposed by means of appropriate Lagrange multipliers. The resulting mixed formulations are analyzed depending on the regularity of the boundary data. Finite element methods are introduced in each case and error estimates are proved. Finally, some numerical results to assess the effectiveness of the methods are reported.

     

An experimental confirmation of longitudinal electrodynamic forces

According to the conventional views of electromagnetic theory, as these are expressed in the Lorentz force law, all the forces which act on a current carrying metallic conductor are perpendicular to the current streamlines. However, over the years, from Ampère through Maxwell until the present day, there have been persistent claims that when current flows in a metallic conductor, there are mechanical forces acting along current streamlines which subject the conductor to tensile stress, and which are therefore capable of performing work in the direction of current flow. The problem of substantiating these claims has always lain in the difficulty of designing an experiment in which the effects are unambiguously demonstrated. The present paper describes an experiment which to a large extent removes these ambiguities, and which provides a compelling novel demonstration of forces acting along current streamlines. A force calculation based on Ampère's original electrodynamic force law is found to be consistent with the observed behaviour. Received 15 November 2000 and Received in final form 12 March 2001     

Elementary applications of quantum-electrokinematics theorem

Summary A preceding quantum-electrokinematics theorem obtained directly from the equations of Maxwell and of Schr?dinger-Pauli, connects, by means of an arbitrary irrotational vector fieldF the wave function of a many-particle system, the internal scalar and vector potentials and the electric permittivity, with the current density and scalar potential, or voltage, on the surface of the system itself. In particular it shows the role of the current due to the particle spin. By means of proper choices ofF, it can be used to find old and new relations and results which, in general, would be harder to get by other methods. In the present work the theorem is used to compute a new expression of the output current of cylindrical two-terminal devices which, in its turn, is applied to a few elementary cases relevant to a single particle. They concern bounded systems, in stationary state, and the drift and spin currents, in non-stationary states, of a free electron and of an electron in a uniform and constant magnetic field. We obtain that a bounded electron cannot induce current at the output terminals and that, in more general terms, the results given by the new approach in the case of ?small? sizes of the system, are very different from those obtained by means of the classical electrodynamics, whereas, as has to happen according to the classical limit principle, they tend to coincide for ?great? sizes of the system itself. So, a not well-defined value of the spin component along the motion axis of a free electron generates a time-dependent fluctuation of the current proportional to its steady value. In the presence of a homogenous magnetic field, rather, the electron spin and its not well-defined value can generate steady and time-dependent contributions of the current, respectively. We also find that the spin acts on the current partition between two contiguous surfaces. The proposed applications, even they are elementary, can have interest because many phenomena in many-particle systems can be reduced to deal with the motion of a single particle.     

Effect of colloidal charge discretization in the primitive model

The effect of fixed discrete colloidal charges in the primitive model is investigated for spherical macroions. Instead of considering a central bare charge, as it is traditionally done, we distribute discrete charges randomly on the sphere. We use molecular dynamics simulations to study this effect on various properties such as overcharging, counterion distribution and diffusion. In the vicinity of the colloid surface the electrostatic potential may considerably differ from the one obtained with a central charge. In the strong Coulomb coupling, we showed that the colloidal charge discretization qualitatively influences the counterion distribution and leads to a strong colloidal charge-counterion pair association. However, we found that charge inversion still persists even if strong pair association is observed. Received 30 June 2000 and Received in final form 28 November 2000