85 citations · 285 across the 40 of their papers we have counts for
11 papers · 1 filter
A domain decomposition method for the directional contact angle hysteresis interval on doubly periodic rough surfaces
Zijie Lin, William M Feldman, Braxton Osting
We study wetting on a doubly periodic rough surface in three dimensions. Although the liquid-vapor interface meets the solid at the local Young's angle, microscale roughness can ca…
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…
High Spots for the Ice-Fishing Problem with Surface Tension
Nathan Willis, Chee Han Tan, Christel Hohenegger +1
In the ice-fishing problem, a half-space of fluid lies below an infinite rigid plate (``the ice'') with a hole. In this paper, we investigate the ice-fishing problem including the…
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…
Mean curvature, threshold dynamics, and phase field theory on finite graphs
Yves van Gennip, Nestor Guillen, Braxton Osting +1
In the continuum, close connections exist between mean curvature flow, the Allen-Cahn (AC) partial differential equation, and the Merriman-Bence-Osher (MBO) threshold dynamics sche…
Emergence of Periodic Structure from Maximizing the Lifetime of a Bound State Coupled to Radiation
Braxton Osting, Michael I. Weinstein
Consider a system governed by the time-dependent Schrödinger equation in its ground state. When subjected to weak (size ) parametric forcing by an "ionizing field" (time-varying…