A survey in mathematics for industry: Two-timing and matched asymptotic expansions for singular perturbation problems

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383-410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations. © 2011 Cambridge University Press.

A Combined Renormalization Group-Multiple Scale Method for Singularly Perturbed Problems

This paper introduces a straightforward method to asymptotically solve a variety of initial and boundary value problems for singularly perturbed ordinary differential equations whose solution structure can be anticipated. The approach is simpler than conventional methods, including those based on asymptotic matching or on eliminating secular terms. © 2010 by the Massachusetts Institute of Technology.

Amplitude equations and asymptotic expansions for multi-scale problems

In this paper we introduce a new technique to obtain the slow-motion dynamics in nonequilibrium and singularly perturbed problems characterized by multiple scales. Our method is based on a straightforward asymptotic reduction of the order of the governing differential equation and leads to amplitude equations that describe the slowly-varying envelope variation of a uniformly valid asymptotic expansion. This may constitute a simpler and in certain cases a more general approach toward the derivation of asymptotic expansions, compared to other mainstream methods such as the method of Multiple Scales or Matched Asymptotic expansions because of its relation with the Renormalization Group. We illustrate our method with a number of singularly perturbed problems for ordinary and partial differential equations and recover certain results from the literature as special cases. © 2010 - IOS Press and the authors. All rights reserved.

Methods for sociological inquiry on emotion in educational settings

Sociological approaches to inquiry on emotion in educational settings are growing. Despite a long tradition of research and theory in disciplines such as psychology and sociology, the methods and approaches for naturalistic investigation of emotion are in a developmental phase in educational settings. In this article, recent empirical studies on emotion in educational contexts are canvassed. The discussion focuses on the use of multiple methods within research conducted in high school and university classrooms highlighting recent methodological progress. The methods discussed include facial expression analysis, verbal and non-verbal conduct, and self-report methods. Analyses drawn from different studies, informed by perspectives from microsociology, highlight the strengths and limitations of any one method. The power and limitations of multi-method approaches is discussed.

Part 2. MOO methods for multidisciplinary design using parallel evolutionary algorithms, game theory and hierarchical topology. (Part 2.) Numerical aspects and implementation of model test cases

These lecture notes describe the use and implementation of a framework in which mathematical as well as engineering optimisation problems can be analysed. The foundations of the framework and algorithms described -Hierarchical Asynchronous Parallel Evolutionary Algorithms (HAPEAs) - lie upon traditional evolution strategies and incorporate the concepts of a multi-objective optimisation, hierarchical topology, asynchronous evaluation of candidate solutions , parallel computing and game strategies. In a step by step approach, the numerical implementation of EAs and HAPEAs for solving multi criteria optimisation problems is conducted providing the reader with the knowledge to reproduce these hand on training in his – her- academic or industrial environment.

Part 3. MOO methods for multidisciplinary design using parallel evolutionary algorithms, game theory and hierarchical topology. (Part 3.) Practical application to the design and optimisation of UAV systems

These lecture notes highlight some of the recent applications of multi-objective and multidisciplinary design optimisation in aeronautical design using the framework and methodology described in References 8, 23, 24 and in Part 1 and 2 of the notes. A summary of the methodology is described and the treatment of uncertainties in flight conditions parameters by the HAPEAs software and game strategies is introduced. Several test cases dealing with detailed design and computed with the software are presented and results discussed in section 4 of these notes.

Self-interaction of magnetoplasma surface waves at a plasma-metal boundary

We investigate nonlinear self-interacting magnetoplasma surface waves (SW) propagating perpendicular to an external magnetic field at a plasma-metal boundary. We obtain the nonlinear dispersion equation and nonlinear Schroedinger equation for the envelope field of the SW. The solution to this equation is studied with regard to stability relative to longitudinal and transverse perturbations.

Nanostructured copper oxide semiconductors : a perspective on materials, synthesis methods and applications

The oxides of copper (CuxO) are fascinating materials due to their remarkable optical, electrical, thermal and magnetic properties. Nanostructuring of CuxO can further enhance the performance of this important functional material and provide it with unique properties that do not exist in its bulk form. Three distinctly different phases of CuxO, mainly CuO, Cu2O and Cu4O3, can be prepared by numerous synthesis techniques including, vapour deposition and liquid phase chemical methods. In this article, we present a review of nanostructured CuxO focusing on their material properties, methods of synthesis and an overview of various applications that have been associated with nanostructured CuxO.

Resonant generation of the second harmonic of a surface wave on a plasma-metal boundary

The process of resonant generation of the second harmonic of the surface wave, propagating along the external magnetic field at the plasma-metal boundary is considered. The periodic process of the energy exchange between the first and the second harmonics of the wave is investigated as well. It is shown that the process under study is periodic one. The analytical expressions are obtained and numerical estimations are presented for characteristic time of nonlinear energy exchange. The self-action effect of main frequency wave is account for harmonics interaction. It is shown that the effect leads to nonlinear phenomena attenuation, which expresses in narrowing possible value interval of harmonics amplitudes during energy exchange process and in increasing the nonlinear interaction time.

Corner and finger formation in Hele-Shaw flow with kinetic undercooling regularisation

We examine the effect of a kinetic undercooling condition on the evolution of a free boundary in Hele--Shaw flow, in both bubble and channel geometries. We present analytical and numerical evidence that the bubble boundary is unstable and may develop one or more corners in finite time, for both expansion and contraction cases. This loss of regularity is interesting because it occurs regardless of whether the less viscous fluid is displacing the more viscous fluid, or vice versa. We show that small contracting bubbles are described to leading order by a well-studied geometric flow rule. Exact solutions to this asymptotic problem continue past the corner formation until the bubble contracts to a point as a slit in the limit. Lastly, we consider the evolving boundary with kinetic undercooling in a Saffman--Taylor channel geometry. The boundary may either form corners in finite time, or evolve to a single long finger travelling at constant speed, depending on the strength of kinetic undercooling. We demonstrate these two different behaviours numerically. For the travelling finger, we present results of a numerical solution method similar to that used to demonstrate the selection of discrete fingers by surface tension. With kinetic undercooling, a continuum of corner-free travelling fingers exists for any finger width above a critical value, which goes to zero as the kinetic undercooling vanishes. We have not been able to compute the discrete family of analytic solutions, predicted by previous asymptotic analysis, because the numerical scheme cannot distinguish between solutions characterised by analytic fingers and those which are corner-free but non-analytic.

Boundary swaying

This practice-led research is positioned within my ongoing enquiry into the dancer’s experience and role within the creative process. Gins and Arakawa (1997) and Keane (2007) speak to the unsatisfactory reliance on discipline boundaries, to describe the dynamic lived-experience of interaction. This theorising is of application to this project, which examines creative agency through the lens of Arakawa and Gins’ language prompt, boundary-swaying. In this project the boundaries of movement creator, performer and director overlap and blur through the use of improvisation and multiple cameras. All contributors are invested creatively and compositionally in the ensuing dynamic collaboration, wearing many hats, ‘conceiver, creative thinker, teacher and learner’ (McKechnie 2005, 93; Stevens & McKechnie 2005, 250). This project asked the question, how can the work of Arakawa and Gins to agitate, disrupt, and transform the modus operandi of creative practice between choreographer and practice, dancer and practice and choreographer and dancer? The use of Arakawa and Gins’ philosophy and language prompts within this project stimulated and positively influenced the established creative relationship of researcher and choreographer/artist in the following ways: • Foregrounded the dancers tacit knowledge, first-hand experience, know-how and embodied savviness; • Promoted artistic collaboration, illuminating new creative possibilities, choices and innovation; • Facilitated the distribution of creative authority and agency. This creative work was presented as part of the AG3 ONLINE: the Third International Arakawa and Gins - Architecture and Philosophy Conference. The work was vetted for inclusion by an international panel of examiners.

Using enterprise information architecture methods to model wicked problems in information systems design research

Design Science is the process of solving ‘wicked problems’ through designing, developing, instantiating, and evaluating novel solutions (Hevner, March, Park and Ram, 2004). Wicked problems are described as agent finitude in combination with problem complexity and normative constraint (Farrell and Hooker, 2013). In Information Systems Design Science, determining that problems are ‘wicked’ differentiates Design Science research from Solutions Engineering (Winter, 2008) and is a necessary part of proving the relevance to Information Systems Design Science research (Hevner, 2007; Iivari, 2007). Problem complexity is characterised as many problem components with nested, dependent and co-dependent relationships interacting through multiple feedback and feed-forward loops. Farrell and Hooker (2013) specifically state for wicked problems “it will often be impossible to disentangle the consequences of specific actions from those of other co-occurring interactions”. This paper discusses the application of an Enterprise Information Architecture modelling technique to disentangle the wicked problem complexity for one case. It proposes that such a modelling technique can be applied to other wicked problems and can lay the foundations for proving relevancy to DSR, provide solution pathways for artefact development, and aid to substantiate those elements required to produce Design Theory.

Space within the surface : the patterned surfaces of Florence Broadhurst and Jim Thompson

The Woods Bagot 2007 refurbishment of the Qantas and British Airways Bangkok Business lounge in the Survarnabhumi Airport features wall finishes designed by wallpaper designer, Florence Broadhurst (1899-1977) and Thai Silk trader, Jim Thompson (1906-1967). This distinctive selection, which is proclaimed on the airport’s website, of patterned wall surfaces side by side draws attention to their striking similarities and their defining differences . Thompson and Broadhurst would appear to be worlds apart, but here in the airport their work brings them together. Thompson, the son of a wealthy cotton family in America, worked as an architect before joining the army. He moved to Bangkok to start The Thai Silk Company in 1948. Broadhurst was born on a farm in Mt. Perry, Queensland. She began her career as a performance artist, as part of an Australian troupe in Shanghai, moving onto pursue a career in fashion design, catering to the middle and upper classes in London. Upon her return to Australia, Broadhurst started a print design company in 1959. Both Broadhurst and Thompson pursued multiple careers, lived many lives, and died under mysterious circumstances. Broadhurst was murdered in 1977 at her Sydney print warehouse, which remains an unsolved crime. Thompson disappeared in Malaysia in 1967 and his body has never been found. This chapter investigates the parallels between Thompson and Broadhurst and what lead them to design such popular patterns for wall surfaces towards the end of their careers. While neither designer was a household name, their work is familiar to most, seen in the costume and set design of films, on the walls of restaurants and cafes and even in family homes. The reason for the popularity of their patterns has not previously been analysed. However, this chapter suggests that the patterns are intriguing because they contain something of their designers’ identities. It suggests that the coloured surface provides a way of camouflaging and hiding its subjects’ histories, such that Broadhurst and Thompson, consciously or unconsciously, used the patterned surface as a plane in which their past lives could be buried. The revealing nature of the stark white wall, compared with the forgiveness provided by the pattern in which to hide, is elaborated by painter and advocate for polychromatic architecture, Fernand Léger in his essay, “The Wall, The Architect, The Painter (1965).” Léger writes that, “the modern architect has gone too far in his magnificent attempts to cleanse through emptiness,” and that the resultant white walls of modernity create ‘an impalpability of air, of slick, brilliant new surfaces where nothing can be hidden any longer …even shadows don’t dare to enter’. To counter the exposure produced by the white wall, Thompson and Broadhurst designed patterned surfaces that could harbour their personal histories. Broadhurst and Thompson’s works share a number of commonalities in their design production, even though their work in print design commenced a decade apart. Both designers opted to work more with traditional methods of pattern making. Broadhurst used hand-operated screens, and Thompson outsourced work to local weavers and refrained from operating out of a factory. Despite humble beginnings, Broadhurst and Thompson enjoyed international success with their wall patterns being featured in a number of renowned international hotels in Bahrain, Singapore, Sydney, and London in the 1970s and 1980s. Their patterns were also transferred to fabric for soft furnishings and clothing. Thompson’s patterns were used for costumes in films including the King and I and Ben Hur. Broadhurst’s patterns were also widely used by fashion designers and artists, such as Akira Isogowa‘s costume design for Salome, a 1998 production by the Sydney Dance Company. Most recently her print designs have been used by skin illustrator Emma Hack, in a series of works painting female bodies into Broadhurst’s patterns. Hack’s works camouflage the models’ bodies into the patterned surface, assimilating subject and surface, hinting at there being something living within the patterned wall. More than four decades after Broadhurst’s murder and five decades since Thompson’s disappearance, their print designs persist as more than just a legacy. They are applied as surface finishes with the same fervour as when the designs were first released. This chapter argues that the reason for the ongoing celebration of their work is that there is the impalpable presence of the creator in the patterns. It suggests that the patterns blur the boundary between subject and surface.

Computational strategies for surface fitting using thin plate spline finite element methods

Thin plate spline finite element methods are used to fit a surface to an irregularly scattered dataset [S. Roberts, M. Hegland, and I. Altas. Approximation of a Thin Plate Spline Smoother using Continuous Piecewise Polynomial Functions. SIAM, 1:208--234, 2003]. The computational bottleneck for this algorithm is the solution of large, ill-conditioned systems of linear equations at each step of a generalised cross validation algorithm. Preconditioning techniques are investigated to accelerate the convergence of the solution of these systems using Krylov subspace methods. The preconditioners under consideration are block diagonal, block triangular and constraint preconditioners [M. Benzi, G. H. Golub, and J. Liesen. Numerical solution of saddle point problems. Acta Numer., 14:1--137, 2005]. The effectiveness of each of these preconditioners is examined on a sample dataset taken from a known surface. From our numerical investigation, constraint preconditioners appear to provide improved convergence for this surface fitting problem compared to block preconditioners.

Assessment of cone beam CT registration for prostate radiation therapy : fiducial marker and soft tissue methods

Introduction This investigation aimed to assess the consistency and accuracy of radiation therapists (RTs) performing cone beam computed tomography (CBCT) alignment to fiducial markers (FMs) (CBCTFM) and the soft tissue prostate (CBCTST). Methods Six patients receiving prostate radiation therapy underwent daily CBCTs. Manual alignment of CBCTFM and CBCTST was performed by three RTs. Inter-observer agreement was assessed using a modified Bland–Altman analysis for each alignment method. Clinically acceptable 95% limits of agreement with the mean (LoAmean) were defined as ±2.0 mm for CBCTFM and ±3.0 mm for CBCTST. Differences between CBCTST alignment and the observer-averaged CBCTFM (AvCBCTFM) alignment were analysed. Clinically acceptable 95% LoA were defined as ±3.0 mm for the comparison of CBCTST and AvCBCTFM. Results CBCTFM and CBCTST alignments were performed for 185 images. The CBCTFM 95% LoAmean were within ±2.0 mm in all planes. CBCTST 95% LoAmean were within ±3.0 mm in all planes. Comparison of CBCTST with AvCBCTFM resulted in 95% LoA of −4.9 to 2.6, −1.6 to 2.5 and −4.7 to 1.9 mm in the superior–inferior, left–right and anterior–posterior planes, respectively. Conclusions Significant differences were found between soft tissue alignment and the predicted FM position. FMs are useful in reducing inter-observer variability compared with soft tissue alignment. Consideration needs to be given to margin design when using soft tissue matching due to increased inter-observer variability. This study highlights some of the complexities of soft tissue guidance for prostate radiation therapy.