arXiv subjects

Andrew Williamson

Publications and source records attributed to Andrew Williamson.

4 recordsLinked to original sources

arXiv2018

A counterexample to De Pierro's conjecture on the convergence of under-relaxed cyclic projections

The convex feasibility problem consists in finding a point in the intersection of a finite family of closed convex sets. When the intersection is empty, a best compromise is to search for a point that minimizes the sum of the squared distances to the sets. In 2001, de Pierro conjectured that the limit cycles generated by the $\varepsilon$-under-relaxed cyclic projection method converge when $\varepsilon\downarrow 0$ towards a least squares solution. While the conjecture has been confirmed under fairly general conditions, we show that it is false in general by constructing a system of three compact convex sets in $\mathbb{R}^3$ for which the $\varepsilon$-under-relaxed cycles do not converge.

math.OC↗

arXiv2017

Targeted numerical simulations of binary black holes for GW170104

In response to LIGO's observation of GW170104, we performed a series of full numerical simulations of binary black holes, each designed to replicate likely realizations of its dynamics and radiation. These simulations have been performed at multiple resolutions and with two independent techniques to solve Einstein's equations. For the nonprecessing and precessing simulations, we demonstrate the two techniques agree mode by mode, at a precision substantially in excess of statistical uncertainties in current LIGO's observations. Conversely, we demonstrate our full numerical solutions contain information which is not accurately captured with the approximate phenomenological models commonly used to infer compact binary parameters. To quantify the impact of these differences on parameter inference for GW170104 specifically, we compare the predictions of our simulations and these approximate models to LIGO's observations of GW170104.

gr-qc↗

arXiv2004

The Structure and Stokes Shift of Hydrogenated Silicon Nanoclusters

We evaluate the optical gap and Stokes shift of several candidate 1 nm silicon nanocrystal structures using density functional and quantum Monte Carlo (QMC) methods. We find that the combination of absorption gap calculations and Stokes shift calculations may be used to determine structures. We find that although absorption gaps calculated within B3LYP and QMC agree for spherical, completely hydrogenated silicon nanocrystals, they disagree in clusters with different surface bonding networks. The nature of the Stokes shift of the ultrabright luminescence is examined by comparing possible relaxation mechanisms. We find that the exciton which reproduces the experimental value of the Stokes shift is most likely a state formed by a collective structural relaxation distributed over the entire cluster.

cond-mat.mtrl-sci↗

arXiv1999

Addition spectra of quantum dots: The role of dielectric mismatch

Using atomistic pseudopotential wave functions we calculate the electron and hole charging energies of InAs quantum dots. We find that the charging energies depend strongly on the dielectric constant epsilon_out of the surrounding material, and that when the latter is smaller than the dielectric constant of the dot the electron-electron and hole-hole interactions are dominated by surface-polarization effects. We predict the addition energies and the quasi-particle gap as a function of size and epsilon_out. We find excellent agreement with recent single-dot tunneling spectroscopy data for epsilon_out=6.

cond-mat.mtrl-sci↗