9 papers
Numerical investigation of the generalized Jang equation coupled to conformal flow of metrics
Hollis Williams
A recent result of Jaracz has established nonexistence of global solutions to the coupled generalized Jang equation and zero divergence system which satisfy the asymptotic conditio…
Evolution of Hawking mass under perturbative spacetime uniformly expanding flows
Hollis Williams
We present a numerical investigation of the evolution of the Hawking mass for perturbed surfaces evolving under hypersurface-restricted uniformly expanding flows in Minkowski space…
Finite-Inertia Corrections and Breakdown of Gor'kov Theory in Acoustic Levitation of Droplets
Hollis Williams
Acoustic levitation is widely used for contactless droplet manipulation, yet the standard Gor'kov description obtained by time averaging the acoustic field lacks a quantitative val…
Geometry-controlled Onset of Inertial Drag in Granular Impact
Hollis Williams
The impact of solid intruders into granular media is commonly described by a combination of quasi-static resistance and an inertial drag force proportional to the square of the imp…
Nonabelian multiplicative integration and curvature obstructions for surface holonomy
Hollis Williams
Surface holonomy plays a central role in higher gauge theory, bundle gerbes and the geometric formulation of Wess--Zumino terms in string theory. In this work, we consider the rela…
A portable LED-based diamond magnetometer for outreach and teaching labs
Hollis Williams, Alex Newman, Stuart Graham +2
We present a compact, low-cost version of an NV center diamond magnetometer which replaces the standard green laser with a high-power LED. This modification improves safety, reduce…
An operator-based bound on information and disturbance in quantum measurements
Hollis Williams, Holger F. Hofmann
Quantum measurements can be described by operators that assign conditional probabilities to different outcomes while also describing unavoidable physical changes to the system. Her…
A note on asymptotic cones of graph-adapted smocked spaces
Hollis Williams
Smocked spaces, introduced by Sormani and collaborators as a generalization of pulled thread spaces, provide a broad class of metric quotients of Euclidean space. In this note we i…
Monotonicity of the Cheeger constant under Ricci flow on spheres
Hollis Williams
We study the behavior of the Cheeger isoperimetric constant under the Ricci flow on compact surfaces. For metrics on a surface diffeomorphic to , we show that the Cheeger cons…