A nonradiating linear combination of quasihomogeneous current correlations

Linear stability of the Lagrangian triangle solutions for quasihomogeneous potentials

In this paper we study the linear stability of the relative equilibria for homogeneous and quasihomogeneous potentials. Firstly, in the case the potential is a homogeneous function of degree −a, we find that any relative equilibrium of the n-body problem with a > 2 is spectrally unstable. We also find a similar condition in the quasihomogeneous case. Then we consider the case of three bodies an...

On Quasihomogeneous Curves

A hypersurface is said to be quasihomogeneous if in suitable coordinates with assigned weights, its equation becomes weighted homogeneous in its variables. For an irreducible quasihomogeneous plane curve, the equation necessarily becomes a two term equation of the form aY n + bX where n,m are necessarily coprime. Zariski, in a short paper, established a criterion for an algebroid curve to be qu...

Nonradiating surface sources.

The class of three-dimensional (3D) nonradiating sources to the inhomogeneous Helmholtz equation is generalized to include nonradiating surface sources that are localized on closed or infinite surfaces sigma and that generate no radiation throughout one of the two space regions whose common boundary is sigma. The class of non-radiating surface sources is shown to be identical to the class of so...

Reversing the Sign of Current-current Correlations

Nonradiating toroidal structures

Some basic properties of nonradiating systems are considered. A simple connection is established between the existence of residual electromagnetic potentials and the current density spectrum of the system. The properties of specific configurations based on toroidal and supertoroidal currents are modeled with the finite-difference timedomain method. Possible applications are discussed. A design ...