6 citations · 14 across the 16 of their papers we have counts for
7 papers · 1 filter
Maximizing the fundamental Laplace--Neumann eigenvalue on quadrilaterals
Ryoki Endo, Braxton Osting
We prove that among convex planar quadrilaterals of equal area, the square uniquely maximizes the first nonzero Laplace--Neumann eigenvalue. This is the quadrilateral case of the N…
A continuum limit for the PageRank algorithm
Amber Yuan, Jeff Calder, Braxton Osting
Semi-supervised and unsupervised machine learning methods often rely on graphs to model data, prompting research on how theoretical properties of operators on graphs are leveraged…
Interface dynamics for an Allen-Cahn-type equation governing a matrix-valued field
Dong Wang, Braxton Osting, Xiao-Ping Wang
We consider the initial value problem for the generalized Allen-Cahn equation, \[\partial_t Φ= ΔΦ-\varepsilon^{-2} Φ(Φ^t Φ- I), \qquad x \in Ω, \ t\geq 0,\] where is an $n\time…
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…
Spectral band degeneracies of rotationally invariant periodic Schrödinger operators
Rachael T. Keller, Jeremy L. Marzuola, Braxton Osting +1
The dynamics of waves in periodic media is determined by the band structure of the underlying periodic Hamiltonian. Symmetries of the Hamiltonian can give rise to novel properties…
A generalized MBO diffusion generated motion for orthogonal matrix-valued fields
Braxton Osting, Dong Wang
We consider the problem of finding stationary points of the Dirichlet energy for orthogonal matrix-valued fields. Following the Ginzburg-Landau approach, this energy is relaxed by…