arXiv subjects

J. A. Scott

Publications and source records attributed to J. A. Scott.

4 recordsLinked to original sources

arXiv2026

An Introduction to Solving the Least-Squares Problem in Variational Data Assimilation

Variational data assimilation is a technique for combining measured data with dynamical models. It is a key component of Earth system state estimation and is commonly used in weather and ocean forecasting. The approach involves a large-scale generalized nonlinear least-squares problem. Solving the resulting sequence of sparse linear subproblems requires the use of sophisticated numerical linear algebra methods. In practical applications, the computational demands severely limit the number of iterations of a Krylov subspace solver that can be performed and so high-quality preconditioners are vital. In this paper, we present a numerical linear algebra perspective on variational data assimilation and discuss contemporary solution methods for the challenges posed by large-scale geophysical applications. The principal contribution is a focused treatment of the underlying linear algebraic subproblems, accompanied by a concise and clear introduction to the essential concepts of variational data assimilation and an extensive bibliography.

math.NA↗

arXiv2025

Coherent all-optical control of the germanium vacancy in diamond

The germanium vacancy in diamond (GeV) is a promising candidate for color center based quantum networking. Yet, like for other group-IV vacancy defects in diamond, achieving fast, high-fidelity qubit operations using traditional magnetic resonance techniques is experimentally challenging due to a weak magnetic dipole and susceptibility to thermally induced decoherence. Here, we perform all-optical control of the GeV and realize Rabi frequencies exceeding $\sim 20$~MHz. We do so by driving the two $Λ$-systems of the GeV simultaneously and apply this to probe the spin coherence ($T_2^*=224\pm14$~ns, $T_2^{\rm H}=11.9\pm0.3$~$μ$s). Our control scheme is applicable to other color centers and particularly, other group-IV defects for which, the scheme may be optimized to improve all-optical control in these systems.

cond-mat.mes-hall↗

arXiv2021

Quantum microscopy with van der Waals heterostructures

Quantum microscopes based on solid-state spin quantum sensors have recently emerged as powerful tools for probing material properties and physical processes in regimes not accessible to classical sensors, especially on the nanoscale. Such microscopes have already found utility in a variety of problems, from imaging magnetism and charge transport in nanoscale devices, to mapping remanent magnetic fields from ancient rocks and biological organisms. However, applications of quantum microscopes have so far relied on sensors hosted in a rigid, three-dimensional crystal, typically diamond, which limits their ability to closely interact with the sample under study. Here we demonstrate a versatile and robust quantum microscope using quantum sensors embedded within a thin layer of a van der Waals (vdW) material, hexagonal boron nitride (hBN). To showcase the capabilities of this platform, we assemble several active vdW heterostructures, with an hBN layer acting as the quantum sensor. We demonstrate time-resolved, simultaneous temperature and magnetic imaging near the Curie temperature of a vdW ferromagnet as well as apply this unique microscope to map out charge currents and Joule heating in graphene. By enabling intimate proximity between sensor and sample, potentially down to a single atomic layer, the hBN quantum sensor represents a paradigm shift for nanoscale quantum sensing and microscopy. Moreover, given the ubiquitous use of hBN in modern materials and condensed matter physics research, we expect our technique to find rapid and broad adoption in these fields, further motivated by the prospect of performing in-situ chemical analysis and noise spectroscopy using advanced quantum sensing protocols.

cond-mat.mes-hall↗

arXiv2013

On the effects of scaling on the performance of Ipopt

The open-source nonlinear solver Ipopt (https://projects.coin-or.org/Ipopt) is a widely-used software package for the solution of large-scale non-linear optimization problems. At its heart, it employs a third-party linear solver to solve a series of sparse symmetric indefinite systems. The speed, accuracy and robustness of the chosen linear solver is critical to the overall performance of Ipopt. In some instances, it can be beneficial to scale the linear system before it is solved. In this paper, different scaling algorithms are employed within Ipopt with a new linear solver HSL_MA97 from the HSL mathematical software library (http://www.hsl.rl.ac.uk). An extensive collection of problems from the CUTEr test set (http://www.cuter.rl.ac.uk) is used to illustrate the effects of scaling.

math.OC↗