6 citations · 14 across the 8 of their papers we have counts for
6 papers · 1 filter
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…
A Variational Characterization of Fluid Sloshing with Surface Tension
Chee Han Tan, Christel Hohenegger, Braxton Osting
We consider the sloshing problem for an incompressible, inviscid, irrotational fluid in an open container, including effects due to surface tension on the free surface. We restrict…