85 citations · 285 across the 40 of their papers we have counts for
9 papers · 1 filter
An accelerated rearrangement method for two-phase composite optimization
Chiu-Yen Kao, Seyyed Abbas Mohammadi, Braxton Osting
We propose and analyze an Accelerated Rearrangement Method (ARM) for solving a class of nonconvex optimization problems involving two-phase composites. These problems include maxim…
A Semi-definite Optimization Method for Maximizing the Shared Band Gap of Topological Photonic Crystals
Chiu-Yen Kao, Junshan Lin, Braxton Osting
Topological photonic crystals (PCs) can support robust edge modes to transport electromagnetic energy in an efficient manner. Such edge modes are the eigenmodes of the PDE operator…
Extremal graph realizations and graph Laplacian eigenvalues
Braxton Osting
For a regular polyhedron (or polygon) centered at the origin, the coordinates of the vertices are eigenvectors of the graph Laplacian for the skeleton of that polyhedron (or polygo…
Dynamics and stationary configurations of heterogeneous foams
Dong Wang, Andrej Cherkaev, Braxton Osting
We consider the variational foam model, where the goal is to minimize the total surface area of a collection of bubbles subject to the constraint that the volume of each bubble is…
A maximal energy pointset configuration problem
Braxton Osting, Brian Simanek
We consider the extremal pointset configuration problem of maximizing a kernel-based energy subject to the geometric constraints that the points are contained in a fixed set, the p…
Extremal Spectral Gaps for Periodic Schrödinger Operators
Chiu-Yen Kao, Braxton Osting
The spectrum of a Schrödinger operator with periodic potential generally consists of bands and gaps. In this paper, for fixed m, we consider the problem of maximizing the gap-to-mi…
A diffusion generated method for computing Dirichlet partitions
Dong Wang, Braxton Osting
A Dirichlet -partition of a closed -dimensional surface is a collection of pairwise disjoint open subsets such that the sum of their first Laplace-Beltrami-Dirichlet eige…
Minimal Dirichlet energy partitions for graphs
Braxton Osting, Chris D. White, Edouard Oudet
Motivated by a geometric problem, we introduce a new non-convex graph partitioning objective where the optimality criterion is given by the sum of the Dirichlet eigenvalues of the…
Long-lived Scattering Resonances and Bragg Structures
Braxton Osting, Michael I. Weinstein
We consider a system governed by the wave equation with index of refraction , taken to be variable within a bounded region , and constant in $\mathbb R^…