Theoretical and numerical investigation of plasmon nanofocusing in metallic tapered rods and grooves

Effective focusing of electromagnetic (EM) energy to nanoscale regions is one of the major challenges in nano-photonics and plasmonics. The strong localization of the optical energy into regions much smaller than allowed by the diffraction limit, also called nanofocusing, offers promising applications in nano-sensor technology, nanofabrication, near-field optics or spectroscopy. One of the most promising solutions to the problem of efficient nanofocusing is related to surface plasmon propagation in metallic structures. Metallic tapered rods, commonly used as probes in near field microscopy and spectroscopy, are of a particular interest. They can provide very strong EM field enhancement at the tip due to surface plasmons (SP’s) propagating towards the tip of the tapered metal rod. A large number of studies have been devoted to the manufacturing process of tapered rods or tapered fibers coated by a metal film. On the other hand, structures such as metallic V-grooves or metal wedges can also provide strong electric field enhancements but manufacturing of these structures is still a challenge. It has been shown, however, that the attainable electric field enhancement at the apex in the V-groove is higher than at the tip of a metal tapered rod when the dissipation level in the metal is strong. Metallic V-grooves also have very promising characteristics as plasmonic waveguides. This thesis will present a thorough theoretical and numerical investigation of nanofocusing during plasmon propagation along a metal tapered rod and into a metallic V-groove. Optimal structural parameters including optimal taper angle, taper length and shape of the taper are determined in order to achieve maximum field enhancement factors at the tip of the nanofocusing structure. An analytical investigation of plasmon nanofocusing by metal tapered rods is carried out by means of the geometric optics approximation (GOA), which is also called adiabatic nanofocusing. However, GOA is applicable only for analysing tapered structures with small taper angles and without considering a terminating tip structure in order to neglect reflections. Rigorous numerical methods are employed for analysing non-adiabatic nanofocusing, by tapered rod and V-grooves with larger taper angles and with a rounded tip. These structures cannot be studied by analytical methods due to the presence of reflected waves from the taper section, the tip and also from (artificial) computational boundaries. A new method is introduced to combine the advantages of GOA and rigorous numerical methods in order to reduce significantly the use of computational resources and yet achieve accurate results for the analysis of large tapered structures, within reasonable calculation time. Detailed comparison between GOA and rigorous numerical methods will be carried out in order to find the critical taper angle of the tapered structures at which GOA is still applicable. It will be demonstrated that optimal taper angles, at which maximum field enhancements occur, coincide with the critical angles, at which GOA is still applicable. It will be shown that the applicability of GOA can be substantially expanded to include structures which could be analysed previously by numerical methods only. The influence of the rounded tip, the taper angle and the role of dissipation onto the plasmon field distribution along the tapered rod and near the tip will be analysed analytically and numerically in detail. It will be demonstrated that electric field enhancement factors of up to ~ 2500 within nanoscale regions are predicted. These are sufficient, for instance, to detect single molecules using surface enhanced Raman spectroscopy (SERS) with the tip of a tapered rod, an approach also known as tip enhanced Raman spectroscopy or TERS. The results obtained in this project will be important for applications for which strong local field enhancement factors are crucial for the performance of devices such as near field microscopes or spectroscopy. The optimal design of nanofocusing structures, at which the delivery of electromagnetic energy to the nanometer region is most efficient, will lead to new applications in near field sensors, near field measuring technology, or generation of nanometer sized energy sources. This includes: applications in tip enhanced Raman spectroscopy (TERS); manipulation of nanoparticles and molecules; efficient coupling of optical energy into and out of plasmonic circuits; second harmonic generation in non-linear optics; or delivery of energy to quantum dots, for instance, for quantum computations.

Inducing shades of meaning by matrix methods : a first step towards thematic analysis of opinion

This article explores two matrix methods to induce the ``shades of meaning" (SoM) of a word. A matrix representation of a word is computed from a corpus of traces based on the given word. Non-negative Matrix Factorisation (NMF) and Singular Value Decomposition (SVD) compute a set of vectors corresponding to a potential shade of meaning. The two methods were evaluated based on loss of conditional entropy with respect to two sets of manually tagged data. One set reflects concepts generally appearing in text, and the second set comprises words used for investigations into word sense disambiguation. Results show that for NMF consistently outperforms SVD for inducing both SoM of general concepts as well as word senses. The problem of inducing the shades of meaning of a word is more subtle than that of word sense induction and hence relevant to thematic analysis of opinion where nuances of opinion can arise.

How current pedagogy methods in games teaching in the UK, Australia and the US have been shaped by historical, socio cultural, environmental and political constraints

Crucial to enhancing the status and quality of games teaching in schools is a developed understanding of the teaching strategies adopted by practitioners. In this paper, we will demonstrate that contemporary games‟ teaching is a product of individual, task and environmental constraints (Newell, 1986). More specifically, we will show that current pedagogy in the U.K., Australia and the United States is strongly influenced by historical, socio-cultural environmental and political constraints. In summary, we will aim to answer the question „why do teachers teach games the way they do.‟ In answering this question, we conclude that teacher educators, who are trying to influence pedagogical practice, must understand these potential constraints and provide appropriate pre-service experiences to give future physical education teachers the knowledge, confidence and ability to adopt a range of teaching styles when they become fully fledged teachers. Essential to this process is the need to enable future practitioners to base their pedagogical practice on a sound understanding of contemporary learning theories of skill acquisition.

Krylov subspace methods for approximating functions of symmetric positive definite matrices with applications to applied statistics and anomalous diffusion

Matrix function approximation is a current focus of worldwide interest and finds application in a variety of areas of applied mathematics and statistics. In this thesis we focus on the approximation of A^(-α/2)b, where A ∈ ℝ^(n×n) is a large, sparse symmetric positive definite matrix and b ∈ ℝ^n is a vector. In particular, we will focus on matrix function techniques for sampling from Gaussian Markov random fields in applied statistics and the solution of fractional-in-space partial differential equations. Gaussian Markov random fields (GMRFs) are multivariate normal random variables characterised by a sparse precision (inverse covariance) matrix. GMRFs are popular models in computational spatial statistics as the sparse structure can be exploited, typically through the use of the sparse Cholesky decomposition, to construct fast sampling methods. It is well known, however, that for sufficiently large problems, iterative methods for solving linear systems outperform direct methods. Fractional-in-space partial differential equations arise in models of processes undergoing anomalous diffusion. Unfortunately, as the fractional Laplacian is a non-local operator, numerical methods based on the direct discretisation of these equations typically requires the solution of dense linear systems, which is impractical for fine discretisations. In this thesis, novel applications of Krylov subspace approximations to matrix functions for both of these problems are investigated. Matrix functions arise when sampling from a GMRF by noting that the Cholesky decomposition A = LL^T is, essentially, a `square root' of the precision matrix A. Therefore, we can replace the usual sampling method, which forms x = L^(-T)z, with x = A^(-1/2)z, where z is a vector of independent and identically distributed standard normal random variables. Similarly, the matrix transfer technique can be used to build solutions to the fractional Poisson equation of the form ϕn = A^(-α/2)b, where A is the finite difference approximation to the Laplacian. Hence both applications require the approximation of f(A)b, where f(t) = t^(-α/2) and A is sparse. In this thesis we will compare the Lanczos approximation, the shift-and-invert Lanczos approximation, the extended Krylov subspace method, rational approximations and the restarted Lanczos approximation for approximating matrix functions of this form. A number of new and novel results are presented in this thesis. Firstly, we prove the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and we give conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian. We then investigate a number of methods for approximating matrix functions of the form A^(-α/2)b and investigate stopping criteria for these methods. In particular, we derive a new method for restarting the Lanczos approximation to f(A)b. We then apply these techniques to the problem of sampling from a GMRF and construct a full suite of methods for sampling conditioned on linear constraints and approximating the likelihood. Finally, we consider the problem of sampling from a generalised Matern random field, which combines our techniques for solving fractional-in-space partial differential equations with our method for sampling from GMRFs.

Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term

In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moreover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Some numerical examples are given, and the results demonstrate the effectiveness of theoretical analysis.

Modified alternating direction methods for solving a two-dimensional non-continuous seepage flow with fractional derivatives

In this paper, a two-dimensional non-continuous seepage flow with fractional derivatives (2D-NCSF-FD) in uniform media is considered, which has modified the well known Darcy law. Using the relationship between Riemann-Liouville and Grunwald-Letnikov fractional derivatives, two modified alternating direction methods: a modified alternating direction implicit Euler method and a modified Peaceman-Rachford method, are proposed for solving the 2D-NCSF-FD in uniform media. The stability and consistency, thus convergence of the two methods in a bounded domain are discussed. Finally, numerical results are given.

Evolutionary optimisation methods with uncertainty for modern multidisciplinary design in aeronautical engineering

One of the new challenges in aeronautics is combining and accounting for multiple disciplines while considering uncertainties or variability in the design parameters or operating conditions. This paper describes a methodology for robust multidisciplinary design optimisation when there is uncertainty in the operating conditions. The methodology, which is based on canonical evolution algorithms, is enhanced by its coupling with an uncertainty analysis technique. The paper illustrates the use of this methodology on two practical test cases related to Unmanned Aerial Systems (UAS). These are the ideal candidates due to the multi-physics involved and the variability of missions to be performed. Results obtained from the optimisation show that the method is effective to find useful Pareto non-dominated solutions and demonstrate the use of robust design techniques.

Numerical methods for fractional partial differential equations with Riesz space fractional derivatives

In this paper, we consider the numerical solution of a fractional partial differential equation with Riesz space fractional derivatives (FPDE-RSFD) on a finite domain. Two types of FPDE-RSFD are considered: the Riesz fractional diffusion equation (RFDE) and the Riesz fractional advection–dispersion equation (RFADE). The RFDE is obtained from the standard diffusion equation by replacing the second-order space derivative with the Riesz fractional derivative of order αset membership, variant(1,2]. The RFADE is obtained from the standard advection–dispersion equation by replacing the first-order and second-order space derivatives with the Riesz fractional derivatives of order βset membership, variant(0,1) and of order αset membership, variant(1,2], respectively. Firstly, analytic solutions of both the RFDE and RFADE are derived. Secondly, three numerical methods are provided to deal with the Riesz space fractional derivatives, namely, the L1/L2-approximation method, the standard/shifted Grünwald method, and the matrix transform method (MTM). Thirdly, the RFDE and RFADE are transformed into a system of ordinary differential equations, which is then solved by the method of lines. Finally, numerical results are given, which demonstrate the effectiveness and convergence of the three numerical methods.

Measuring Visual Consistency in 3D Rendering Systems

One of the major challenges facing a present day game development company is the removal of bugs from such complex virtual environments. This work presents an approach for measuring the correctness of synthetic scenes generated by a rendering system of a 3D application, such as a computer game. Our approach builds a database of labelled point clouds representing the spatiotemporal colour distribution for the objects present in a sequence of bug-free frames. This is done by converting the position that the pixels take over time into the 3D equivalent points with associated colours. Once the space of labelled points is built, each new image produced from the same game by any rendering system can be analysed by measuring its visual inconsistency in terms of distance from the database. Objects within the scene can be relocated (manually or by the application engine); yet the algorithm is able to perform the image analysis in terms of the 3D structure and colour distribution of samples on the surface of the object. We applied our framework to the publicly available game RacingGame developed for Microsoft(R) Xna(R). Preliminary results show how this approach can be used to detect a variety of visual artifacts generated by the rendering system in a professional quality game engine.

Measurement properties of the Australian Women's Activity Survey

Purpose: The Australian Women’s Activity Survey (AWAS) was developed based on a systematic review and qualitative research on how to measure activity patterns of women with young children (WYC). AWAS assesses activity performed across five domains (planned activities, employment, childcare, domestic responsibilities and transport), and intensity levels (sitting, light-intensity, brisk walking, moderate-intensity and vigorous-intensity) in a typical week in the past month. The purpose of this study was to assess the test-retest reliability and criterion validity of the AWAS. Methods: WYC completed the AWAS on two occasions 7-d apart (test-retest reliability protocol) and/or wore an MTI ActiGraph accelerometer for 7-d in between (validity protocol). Forty WYC (mean age 35 ± 5yrs) completed the test-retest reliability protocol and 75 WYC (mean age 33 ± 5yrs) completed the validity protocol. Interclass Correlation Coefficients (ICC) between AWAS administrations and Spearman’s Correlation Coefficients (rs) between AWAS and MTI data were calculated. Results: AWAS showed good test-retest reliability (ICC=0.80 (0.65-0.89)) and acceptable criterion validity (rs= 0.28, p=0.01) for measuring weekly health-enhancing physical activity. AWAS also provided repeatable and valid estimates of sitting time (test-retest reliability ICC=0.42 (0.13-0.64), and criterion validity (rs= 0.32, p=0.006)). Conclusion: The measurement properties of the AWAS are comparable to those reported for existing self-report measures of physical activity. However, AWAS offers a more comprehensive and flexible alternative for accurately assessing different domains and intensities of activity relevant to WYC. Future research should investigate whether the AWAS is a suitable measure of intervention efficacy by examining its sensitivity to change.

The relationship between subjective appetite sensations, markers of inflammation and appetite in dialysis patients

Background: Poor appetite is a marker of morbidity and mortality in hemodialysis patients, making it an important area for research. Visual analog scales (VAS) can capture a range of subjective sensations related to appetite (such as hunger, desire to eat or fullness), but have not been commonly used to measure appetite in dialysis patients. The aim of this study was to explore the association between retrospective ratings of appetite using VAS and a range of clinical variables as well as biomarkers of appetite in hemodialysis patients.----- Methods: 28 hemodialysis patients (mean age 61±17y, 50% male, median dialysis vintage 19.5(4-101) months) rated their appetite using VAS for hunger, fullness and desire to eat and a 5-point categorical scale measuring general appetite. Blood levels of the appetite peptides leptin, ghrelin and peptide YY were also measured.----- Results: Hunger ratings measured by VAS were significantly (p<0.05) correlated with a range of clinical, nutritional and inflammatory markers: age (r=-0.376), co-morbidities, (r=-0.380) PG-SGA score (r=-0.451), weight (r=-0.375), fat-free mass (r=-0.435), C-Reactive Protein (CRP) (r=-0.383) and Intercellular adhesion molecule (sICAM-1) (r=-0.387). There was a consistent relationship between VAS and appetite on a 5-point categorical scale for questions of hunger, and a similar trend for desire to eat, but not for fullness. Neither method of measuring subjective appetite correlated with appetite peptides.----- Conclusions: Retrospective ratings of hunger on a VAS are associated with a range of clinical variables and further studies are warranted to support their use as a method of measuring appetite in dialysis patients.

Measuring CRM and SCM benefits : a preliminary measurement model

Organizations invest heavily in Customer Relationship Management (CRM) and Supply Chain Management (SCM) systems, and their related infrastructure, presumably expecting positive benefits to the organization. Assessing the benefits of such applications is an important aspect of managing such systems. Considering the salient differences between CRM and SCM applications with other intra-organizational applications, existing Information Systems benefits measurement models and frameworks are ill-suited to gauge benefits of inter-organizational systems. This paper reports the preliminary findings of a measurement model developed to assess benefits of CRM and SCM applications. The preliminary model, which reflects the characteristics of the Analytic Theory, is derived using a review of 55 academic studies and 44 papers from the practice. Six hundred and six identified benefits were then synthesized in to 74 non-overlapping benefits, arranged under six dimensions.

Linkage and heritability analysis of migraine symptom groupings: A comparison of three different clustering methods on twin data

Migraine is a painful disorder for which the etiology remains obscure. Diagnosis is largely based on International Headache Society criteria. However, no feature occurs in all patients who meet these criteria, and no single symptom is required for diagnosis. Consequently, this definition may not accurately reflect the phenotypic heterogeneity or genetic basis of the disorder. Such phenotypic uncertainty is typical for complex genetic disorders and has encouraged interest in multivariate statistical methods for classifying disease phenotypes. We applied three popular statistical phenotyping methods—latent class analysis, grade of membership and grade of membership “fuzzy” clustering (Fanny)—to migraine symptom data, and compared heritability and genome-wide linkage results obtained using each approach. Our results demonstrate that different methodologies produce different clustering structures and non-negligible differences in subsequent analyses. We therefore urge caution in the use of any single approach and suggest that multiple phenotyping methods be used.

Industrial playwriting : forms, strategies, and methods for creative production

This study, in its exploration of the attached play scripts and their method of development, evaluates the forms, strategies, and methods of an organised model of formalised playwriting. Through the examination, reflection and reaction to a perceived crisis in playwriting in the Australian theatre sector, the notion of Industrial Playwriting is arrived at: a practice whereby plays are designed and constructed, and where the process of writing becomes central to the efficient creation of new work and the improvement of the writer’s skill and knowledge base. Using a practice-led methodology and action research the study examines a system of play construction appropriate to and addressing the challenges of the contemporary Australian theatre sector. Specifically, using the action research methodology known as design-based research a conceptual framework was constructed to form the basis of the notion of Industrial Playwriting. From this two plays were constructed using a case study method and the process recorded and used to create a practical, step-by-step system of Industrial Playwriting. In the creative practice of manufacturing a single authored play, and then a group-devised play, Industrial Playwriting was tested and found to also offer a valid alternative approach to playwriting in the training of new and even emerging playwrights. Finally, it offered insight into how Industrial Playwriting could be used to greatly facilitate theatre companies’ ongoing need to have access to new writers and new Australian works, and how it might form the basis of a cost effective writer development model. This study of the methods of formalised writing as a means to confront some of the challenges of the Australian theatre sector, the practice of playwriting and the history associated with it, makes an original and important contribution to contemporary playwriting practice.

Numerical investigations of linear least squares methods for derivative estimation

The results of a numerical investigation into the errors for least squares estimates of function gradients are presented. The underlying algorithm is obtained by constructing a least squares problem using a truncated Taylor expansion. An error bound associated with this method contains in its numerator terms related to the Taylor series remainder, while its denominator contains the smallest singular value of the least squares matrix. Perhaps for this reason the error bounds are often found to be pessimistic by several orders of magnitude. The circumstance under which these poor estimates arise is elucidated and an empirical correction of the theoretical error bounds is conjectured and investigated numerically. This is followed by an indication of how the conjecture is supported by a rigorous argument.