47 citations · 231 across the 47 of their papers we have counts for
50 papers
Notes on the discretization of TV-NORM regularized inverse potential problems
L Baratchart, D P Hardin, C Villalobos-Guillén +1
We describe a method to discretize optimization problems arising in the regularization of linear inverse problem having compact forward operator defined on 3-D valued measures, com…
Universally Optimal Periodic Configurations in the Plane
Doug Hardin, Nathaniel Tenpas
We develop lower bounds for the energy of configurations in periodic with respect to a lattice. In certain cases, the construction of sharp bounds can be formulated…
Universal minima of discrete potentials for sharp spherical codes
Peter Boyvalenkov, Peter Dragnev, Douglas Hardin +2
This article is devoted to the study of discrete potentials on the sphere in for sharp codes. We show that the potentials of most of the known sharp codes attain the…
On polarization of spherical codes and designs
Peter Boyvalenkov, Peter Dragnev, Douglas Hardin +2
In this article we investigate the -point min-max and the max-min polarization problems on the sphere for a large class of potentials in . We derive universal lowe…
Asymptotics of -nearest neighbor Riesz energies
Douglas P. Hardin, Edward B. Saff, Oleksandr Vlasiuk
We obtain new asymptotic results about systems of particles governed by Riesz interactions involving -nearest neighbors of each particle as . These results i…
Dynamics of Particles on a Curve with Pairwise Hyper-singular Repulsion
Douglas Hardin, Edward B. Saff, Ruiwen Shu +1
We investigate the large time behavior of particles restricted to a smooth closed curve in and subject to a gradient flow with respect to Euclidean hyper-singula…