4 citations · 8 across the 7 of their papers we have counts for
9 papers
Steklov eigenvalues of nearly circular area-normalized domains
Lucas Alland, Robert Viator
We consider Steklov eigenvalues of nearly circular domains in of fixed unitary area. In \cite{viator2018}, the authors treated such domains as perturbations of the disk, a…
Steklov eigenvalues of nearly hyperspherical domains
Chee Han Tan, Robert Viator
We consider Steklov eigenvalues of nearly hyperspherical domains in with . In previous work, treating such domains as perturbations of the ball, we pro…
Analyticity of Steklov Eigenvalues in nearly-hyperspherical domains in \mathbb{R}^{d+1}
Chee Han Tan, Robert Viator
We consider the Dirichlet-to-Neumann operator (DNO) on nearly-hyperspherical domains in dimension greater than 3. Treating such domains as perturbations of the ball, we prove the a…
Effective operators and their variational principles for discrete electrical network problems
Kenneth Beard, Anthony Stefan, Robert Viator +1
Using a Hilbert space framework inspired by the methods of orthogonal projections and Hodge decompositions, we study a general class of problems (called Z-problems) that arise in e…
Bloch Waves in High Contrast Electromagnetic Crystals
Robert Lipton, Robert Viator, Silvia Jimenez Bolanos +1
Analytic representation formulas and power series are developed describing the band structure inside non-magnetic periodic photonic three-dimensional crystals made from high dielec…
Steklov Eigenvalues of Nearly Spherical Domains
Robert Viator, Braxton Osting
We consider Steklov eigenvalues of three-dimensional, nearly-spherical domains. In previous work, we have shown that the Steklov eigenvalues are analytic functions of the domain pe…
Analyticity of Steklov eigenvalues of nearly-circular and nearly-spherical domains
Robert Viator, Braxton Osting
We consider the Dirichlet-to-Neumann operator (DNO) on nearly-circular and nearly-spherical domains in two and three dimensions, respectively. Treating such domains as perturbation…
Creating band gaps in periodic media
Robert Lipton, Robert Viator
We identify explicit conditions on geometry and material contrast for creating band gaps in 2-d photonic and 3-d acoustic crystals. This approach is novel and makes use of the elec…
Bloch Waves in Crystals and Periodic High Contrast Media
Robert Lipton, Robert Viator
Analytic representation formulas and power series are developed describing the band structure inside periodic photonic and acoustic crystals made from high contrast inclusions. Cen…