Regularity Theory and Superalgebraic Solvers for Wire Antenna Problems

We consider the problem of evaluating the current distribution $J(z)$ that is induced on a straight wire antenna by a time-harmonic incident electromagnetic field. The scope of this paper is twofold. One of its main contributions is a regularity proof for a straight wire occupying the interval $[-1,1]$. In particular, for a smooth time-harmonic incident field this theorem implies that $J(z) = I(z)/\sqrt{1-z^2}$, where $I(z)$ is an infinitely differentiable function—the previous state of the art in this regard placed $I$ in the Sobolev space $W^{1,p}$, $p>1$. The second focus of this work is on numerics: we present three superalgebraically convergent algorithms for the solution of wire problems, two based on Hallén's integral equation and one based on the Pocklington integrodifferential equation. Both our proof and our algorithms are based on two main elements: (1) a new decomposition of the kernel of the form $G(z) = F_1(z) \ln\! |z| + F_2(z)$, where $F_1(z)$ and $F_2(z)$ are analytic functions on the real line; and (2) removal of the end-point square root singularities by means of a coordinate transformation. The Hallén- and Pocklington-based algorithms we propose converge superalgebraically: faster than $\mathcal{O}(N^{-m})$ and $\mathcal{O}(M^{-m})$ for any positive integer $m$, where $N$ and $M$ are the numbers of unknowns and the number of integration points required for construction of the discretized operator, respectively. In previous studies, at most the leading-order contribution to the logarithmic singular term was extracted from the kernel and treated analytically, the higher-order singular derivatives were left untreated, and the resulting integration methods for the kernel exhibit $\mathcal{O}(M^{-3})$ convergence at best. A rather comprehensive set of tests we consider shows that, in many cases, to achieve a given accuracy, the numbers $N$ of unknowns required by our codes are up to a factor of five times smaller than those required by the best solvers previously available; the required number $M$ of integration points, in turn, can be several orders of magnitude smaller than those required in previous methods. In particular, four-digit solutions were found in computational times of the order of four seconds and, in most cases, of the order of a fraction of a second on a contemporary personal computer; much higher accuracies result in very small additional computing times

How the emergency department four-hour target affects clinical outcomes for patients diagnosed with a personality disorder

The Emergency Department (ED) may already be an invalidating environment for those patients diagnosed with a personality disorder, with negative attitudes from staff perpetuating feelings of dismissal and rejection. Despite, however, personality disorder being more prevalent across health services including EDs, there is a lack of literature considering how achieving the target may take a priority over clinical need, leading to adverse outcomes for those patients diagnosed with a personality disorder. Expanding on Hardern’s application of the concept of Destructive Goal Pursuit to the four-hour target, existing literature is used to illustrate how pressures to meet the four-hour target may a lead to distortions of clinical priorities and to adverse clinical outcomes for this patient group. This paper challenges the concept of the target as being realistic and helpful to those patients specifically diagnosed with a personality disorder. Recommendations for practice include the use of short-stay units, where patients may be treated outside of the target wait time and the introduction of mental health triage in ED to improve the delivery of psychosocial assessments

Master of Science

thesisCarbon nanotubes (CNTs) exhibit extraordinary mechanical properties and display a high surface to volume ratio, which makes them a good filler material for polymer based composite materials. Their mechanical properties are most effectively utilized by aligning the tube axis in the direction of the applied loading. Several methods exist to align CNTs, including wet spinning, dry spinning, mechanical stretching, magnetic field alignment, and plasma enhanced chemical vapor deposition. However, the scalability of these methods is limited and, thus, they are only suited to align small amounts of CNTs. This work introduces a novel technique, based on bulk acoustic waves (BAWs), to align large amounts of CNTs quasi-instantaneously. This technique is employed to fabricate macroscale composite materials with aligned CNTs as filler material. CNTs are first dispersed in the liquid state of a thermoset resin and introduced into a reservoir where the alignment is performed by BAWs. The cross-linking of the resin fixates the aligned CNTs in the resin matrix and produces a composite material with aligned CNTs. Composite material specimens were produced using this technique with CNT loading rates up to 2 weight percent (wt%). The mechanical properties of these composites were evaluated experimentally and compared against specimens consisting of both randomly oriented CNTs and pure resin matrix material. Composite material specimens with aligned CNTs (0.15 wt %) displayed a 44% and 51% increase in elastic iv modulus compared to composite material specimens with randomly oriented CNTs and pure resin material specimens, respectively. However, due to insufficient dispersion of CNTs in the resin matrix a significant increase in elastic modulus and ultimate tensile strength with increasing CNT loading rate was not observed