Research and Publications

My primary research interests are in applied analysis, PDE, and spectral theory in the context of wave propagation in optics and acoustics, with a particular interest in periodic problems. My PhD thesis at LSU revolved around an analytic representation formula for Bloch spectra corresponding to high-contrast photonic and acoustic crystals, culminating in a theorem providing criteria for opening band gaps in these materials with finite contrast ratios.

More recently, I have been interested in problems involving lossy magnetic photonic crystals and characterization of the scattering properties of magnetic-dielectric composites.

Publications and Preprints
  1. Bloch Waves in crystals and periodic high contrast media: Lipton, R. and Viator, R., ESAIM: Mathematical Modeling and Numerical Analysis, accepted June 16, 2016
  2. Creating Band Gaps in Periodic Media: Lipton, R. and Viator, R., Submitted for publication (Preprint)