Advantages over conventional vector calculus makes the exterior differential forms an ideal framework for teaching and understanding Maxwell's equations
and the principles of electromagnetics.
. [DELTA] x E = -j[omega]B Faraday's law [DELTA] x H = J + j[omega]D Ampere's law [DELTA] x D = [[rho].sub.lambda] Gauss' law [DELTA] x B = 0 Gauss' law (magnetic)
MONK, Finite element methods for Maxwell's equations
, Oxford University Press, New York, 2003.
The geometry and material properties of the interconnects act as boundary conditions on the equations that describe these fields, Maxwell's equations
. In principle, an electromagnetic field solver could be used to predict the output waveforms when electromagnetic waves (the signals) encounter interconnects.
All the field solvers discussed are based on well-established numerical methods for solving Maxwell's equations
. Enough background material on the major numerical methods is offered to help the reader appreciate what is going on behind the surface.
The accuracy and physical significance of the classical Rayleigh-Sommerfeld and Kirchhoff diffraction integrals are assessed in the context of Sommerfeld's rigorous theory of half-plane diffraction and Maxwell's equations
. It is shown that the Rayleigh-Sommerfeld integrals are in satisfactory agreement with Sommerfeld's theory in most of the positive near zone, except at sub-wavelength distances from the screen.
The electron, as long as it remained in such an orbit, need not radiate light and would not violate the conditions of Maxwell's equations
Physicists explore skyrmions, tiny regions of reversed magnetization (named after Tony Skyrme who first proposed them during the 1960s) that cannot be described by Maxwell's equations
. Their topics include resonant X-ray scattering studies on skyrmions, imaging and tailoring chiral spin textures using spin-polarized electron microscopy, the formation and stability of individual skyrmions in confined geometries, novel topological resonant excitations of coupled skyrmions, and magnetic skyrmion channels: guided motion in potential wells.
According to auxiliary differential variables and Maxwell's equations
of CPML, the other relationship between field components and auxiliary differential variables is derived.
Unlike the regularity analysis for elliptic boundary value problems in domains with geometric singularities, where there exists a unified theory based on the shift theorem (see [1-3]), the regularity analysis of the solution of Maxwell's equations
has several interpretations.
The DGTD method developed here is based on the first-order Maxwell's equations
with electric field E and magnetic field H as variables
They cover vector analysis; static and dynamic fields and Maxwell's equations
; electromagnetic waves; computer-aided design; transmission lines and waveguides; electromagnetic radiation, interference, and noise in antennas; the influence of pair reactions on biological rhythms; and radio frequency electromagnetic fields from mobile phones.