Eugenie Hunsicker

Eugenie Hunsicker, Hengguang Li, Victor Nistor et al.

Let $V$ be a potential on $\RR^3$ that is smooth everywhere except at a discrete set $\maS$ of points, where it has singularities of the form $Z/ρ^2$, with $ρ(x) = |x - p|$ for $x$ close to $p$ and $Z$ continuous on $\RR^3$ with $Z(p) > -1/4$ for $p \in \maS$. Also assume that $ρ$ and $Z$ are smooth outside $\maS$ and $Z$ is smooth in polar coordinates around each singular point. We either assume that $V$ is periodic or that the set $\maS$ is finite and $V$ extends to a smooth function on the radial compactification of $\RR^3$ that is bounded outside a compact set containing $\maS$. In the periodic case, we let $Λ$ be the periodicity lattice and define $\TT := \RR^3/ Λ$. We obtain regularity results in weighted Sobolev space for the eigenfunctions of the Schrödinger-type operator $H = -Δ+ V$ acting on $L^2(\TT)$, as well as for the induced $\vt k$--Hamiltonians $\Hk$ obtained by restricting the action of $H$ to Bloch waves. Under some additional assumptions, we extend these regularity and solvability results to the non-periodic case. We sketch some applications to approximation of eigenfunctions and eigenvalues that will be studied in more detail in a second paper.

Eugenie Hunsicker, Hengguang Li, Victor Nistor et al.

Let $V$ be a {\em periodic} potential on $\RR^3$ that is smooth everywhere except at a discrete set $\maS$ of points, where it has singularities of the form $Z/ρ^2$, with $ρ(x) = |x - p|$ for $x$ close to $p$ and $Z$ is continuous, $Z(p) > -1/4$ for $p \in \maS$. We also assume that $ρ$ and $Z$ are smooth outside $\maS$ and $Z$ is smooth in polar coordinates around each singular point. Let us denote by $Λ$ the periodicity lattice and set $\TT := \RR^3/ Λ$. In the first paper of this series \cite{HLNU1}, we obtained regularity results in weighted Sobolev space for the eigenfunctions of the Schrödinger-type operator $H = -Δ+ V$ acting on $L^2(\TT)$, as well as for the induced $\vt k$--Hamiltonians $\Hk$ obtained by resticting the action of $H$ to Bloch waves. In this paper we present two related applications: one to the Finite Element approximation of the solution of $(L+\Hk) v = f$ and one to the numerical approximation of the eigenvalues, $λ$, and eigenfunctions, $u$, of $\Hk$. We give optimal, higher order convergence results for approximation spaces defined piecewise polynomials. Our numerical tests are in good agreement with the theoretical results.

Steff Farley, Jo E. A. Hodgkinson, Oliver M. Gordon et al.

A wide range of techniques can be considered for segmentation of images of nanostructured surfaces. Manually segmenting these images is time-consuming and results in a user-dependent segmentation bias, while there is currently no consensus on the best automated segmentation methods for particular techniques, image classes, and samples. Any image segmentation approach must minimise the noise in the images to ensure accurate and meaningful statistical analysis can be carried out. Here we develop protocols for the segmentation of images of 2D assemblies of gold nanoparticles formed on silicon surfaces via deposition from an organic solvent. The evaporation of the solvent drives far-from-equilibrium self-organisation of the particles, producing a wide variety of nano- and micro-structured patterns. We show that a segmentation strategy using the U-Net convolutional neural network outperforms traditional automated approaches and has particular potential in the processing of images of nanostructured systems.

Angelika Skarysz, Dahlia Salman, Michael Eddleston et al.

Volatile organic compounds (VOCs) in human breath can reveal a large spectrum of health conditions and can be used for fast, accurate and non-invasive diagnostics. Gas chromatography-mass spectrometry (GC-MS) is used to measure VOCs, but its application is limited by expert-driven data analysis that is time-consuming, subjective and may introduce errors. We propose a system to perform GC-MS data analysis that exploits deep learning pattern recognition ability to learn and automatically detect VOCs directly from raw data, thus bypassing expert-led processing. The new proposed approach showed to outperform the expert-led analysis by detecting a significantly higher number of VOCs in just a fraction of time while maintaining high specificity. These results suggest that the proposed method can help the large-scale deployment of breath-based diagnosis by reducing time and cost, and increasing accuracy and consistency.

Charles E. Dickerson, Michael K. Wilkinson, Eugenie Hunsicker et al.

Architecture Definition, which is central to system design, is one of the two most used technical processes in the practice of model-based systems engineering. In this paper a fundamental approach to architecture definition is presented and demonstrated. The success of its application to engineering problems depends on a precise but practical definition of the term architecture. In the standard for Architecture Description, ISO/IEC/IEEE 42010:2011, a definition was adopted that has been subsumed into later standards. In 2018 the working group JTC1/SC7/WG42 on System Architecture began a review of the adopted definition, holding sessions late in the year. This paper extends and complements a position paper submitted during the meetings; in which Tarski model theory and ISO/IEC 24707:2018 (logic-based languages) were used to better understand relationships between system models and concepts related to architecture. Independent from the working group, it now contributes intuitive fundamental definitions of the terms architecture and system that are used to specify a mathematically based technical process for architecture definition. The engineering utility and benefits to complex system design are demonstrated in a diesel engine emissions reduction case study.