Images of point charges in conducting ellipses and prolate spheroids

Tunable Plasmonic Nanoparticles Based on Prolate Spheroids

Metallic nanoparticles can exhibit very large optical extinction in the visible spectrum due to localized surface plasmon resonance. Spherical plasmonic nanoparticles have been the subject of numerous studies in recent years due to the fact that the scattering response of spheres can be analytically evaluated using Mie theory. However a major disadvantage of metallic spherical nanoparticles is ...

Shape factor extremes for prolate spheroids

Numerical simulation of the whispering gallery modes in prolate spheroids

In this paper, we discuss the progress in the numerical simulation of the socalled ‘whispering gallery’ modes (WGMs) occurring inside a prolate spheroidal cavity. These modes are mainly concentrated in a narrow domain along the equatorial line of a spheroid and they are famous because of their extremely high quality factor. The scalar Helmholtz equation provides a sufficient accuracy for WGM si...

tunable plasmonic nanoparticles based on prolate spheroids

metallic nanoparticles can exhibit very large optical extinction in the visible spectrum due to localized surface plasmon resonance. spherical plasmonic nanoparticles have been the subject of numerous studies in recent years due to the fact that the scattering response of spheres can be analytically evaluated using mie theory. however a major disadvantage of metallic spherical nanoparticles is ...

Mystery of Point Charges

We discuss the problem of finding an upper bound for the number of equilibrium points of a potential of several fixed point charges in Rn. This question goes back to J. C. Maxwell and M. Morse. Using fewnomial theory we show that for a given number of charges there exists an upper bound independent of the dimension, and show it to be at most 12 for three charges. We conjecture an exact upper bo...