Off-campus Michigan Tech users: To download campus access theses or dissertations, please use the following button to log in with your Michigan Tech ID and password: log in to proxy server

Non-Michigan Tech users: Please talk to your librarian about requesting this thesis or dissertation through interlibrary loan.

Date of Award


Document Type

Master's report

Degree Name

Master of Science in Physics (MS)

College, School or Department Name

Department of Physics

First Advisor

Alexander B. Kostinski


We consider the question of optimal shapes, e.g., those causing minimal extinction among all shapes of equal volume. Guided by the isoperimetric property of a sphere, relevant in the geometrical optics limit of scattering by large particles, we examine an analogous question in the low frequency (electrostatics) approximation, seeking to disentangle electric and geometric contributions. To that end, we survey the literature on shape functionals and focus on ellipsoids, giving a simple proof of spherical optimality for the coated ellipsoidal particle. Monotonic increase with asphericity in the low frequency regime for orientation-averaged induced dipole moments and scattering cross-sections is also shown. Additional physical insight is obtained from the Rayleigh-Gans (transparent) limit and eccentricity expansions. We propose connecting low and high frequency regime in a single minimum principle valid for all size parameters, provided that reasonable size distributions of randomly oriented aspherical particles wash out the resonances for intermediate size parameters. This proposal is further supported by the sum rule for integrated extinction.