Generalising unitary time evolution

In this third Quantum Interaction (QI) meeting it is time to examine our failures. One of the weakest elements of QI as a field, arises in its continuing lack of models displaying proper evolutionary dynamics. This paper presents an overview of the modern generalised approach to the derivation of time evolution equations in physics, showing how the notion of symmetry is essential to the extraction of operators in quantum theory. The form that symmetry might take in non-physical models is explored, with a number of viable avenues identified.

Modelling of some biological materials using continuum mechanics

Continuum mechanics provides a mathematical framework for modelling the physical stresses experienced by a material. Recent studies show that physical stresses play an important role in a wide variety of biological processes, including dermal wound healing, soft tissue growth and morphogenesis. Thus, continuum mechanics is a useful mathematical tool for modelling a range of biological phenomena. Unfortunately, classical continuum mechanics is of limited use in biomechanical problems. As cells refashion the �bres that make up a soft tissue, they sometimes alter the tissue's fundamental mechanical structure. Advanced mathematical techniques are needed in order to accurately describe this sort of biological `plasticity'. A number of such techniques have been proposed by previous researchers. However, models that incorporate biological plasticity tend to be very complicated. Furthermore, these models are often di�cult to apply and/or interpret, making them of limited practical use. One alternative approach is to ignore biological plasticity and use classical continuum mechanics. For example, most mechanochemical models of dermal wound healing assume that the skin behaves as a linear viscoelastic solid. Our analysis indicates that this assumption leads to physically unrealistic results. In this thesis we present a novel and practical approach to modelling biological plasticity. Our principal aim is to combine the simplicity of classical linear models with the sophistication of plasticity theory. To achieve this, we perform a careful mathematical analysis of the concept of a `zero stress state'. This leads us to a formal de�nition of strain that is appropriate for materials that undergo internal remodelling. Next, we consider the evolution of the zero stress state over time. We develop a novel theory of `morphoelasticity' that can be used to describe how the zero stress state changes in response to growth and remodelling. Importantly, our work yields an intuitive and internally consistent way of modelling anisotropic growth. Furthermore, we are able to use our theory of morphoelasticity to develop evolution equations for elastic strain. We also present some applications of our theory. For example, we show that morphoelasticity can be used to obtain a constitutive law for a Maxwell viscoelastic uid that is valid at large deformation gradients. Similarly, we analyse a morphoelastic model of the stress-dependent growth of a tumour spheroid. This work leads to the prediction that a tumour spheroid will always be in a state of radial compression and circumferential tension. Finally, we conclude by presenting a novel mechanochemical model of dermal wound healing that takes into account the plasticity of the healing skin.

New exact solutions for Hele-Shaw flow in doubly connected regions

Radial Hele-Shaw flows are treated analytically using conformal mapping techniques. The geometry of interest has a doubly-connected annular region of viscous fluid surrounding an inviscid bubble that is either expanding or contracting due to a pressure difference caused by injection or suction of the inviscid fluid. The zero-surface-tension problem is ill-posed for both bubble expansion and contraction, as both scenarios involve viscous fluid displacing inviscid fluid. Exact solutions are derived by tracking the location of singularities and critical points in the analytic continuation of the mapping function. We show that by treating the critical points, it is easy to observe finite-time blow-up, and the evolution equations may be written in exact form using complex residues. We present solutions that start with cusps on one interface and end with cusps on the other, as well as solutions that have the bubble contracting to a point. For the latter solutions, the bubble approaches an ellipse in shape at extinction.

Effective Cell-Centred Time-Domain Maxwell's Equations Numerical Solvers

This research work analyses techniques for implementing a cell-centred finite-volume time-domain (ccFV-TD) computational methodology for the purpose of studying microwave heating. Various state-of-the-art spatial and temporal discretisation methods employed to solve Maxwell's equations on multidimensional structured grid networks are investigated, and the dispersive and dissipative errors inherent in those techniques examined. Both staggered and unstaggered grid approaches are considered. Upwind schemes using a Riemann solver and intensity vector splitting are studied and evaluated. Staggered and unstaggered Leapfrog and Runge-Kutta time integration methods are analysed in terms of phase and amplitude error to identify which method is the most accurate and efficient for simulating microwave heating processes. The implementation and migration of typical electromagnetic boundary conditions. from staggered in space to cell-centred approaches also is deliberated. In particular, an existing perfectly matched layer absorbing boundary methodology is adapted to formulate a new cell-centred boundary implementation for the ccFV-TD solvers. Finally for microwave heating purposes, a comparison of analytical and numerical results for standard case studies in rectangular waveguides allows the accuracy of the developed methods to be assessed.

Investigation of RuO2/Ta2O5 thin film evolution by thermogravimetry combined with mass spectrometry

The thermal evolution process of RuO2–Ta2O5/Ti coatings with varying noble metal content has been investigated under in situ conditions by thermogravimetry combined with mass spectrometry. The gel-like films prepared from alcoholic solutions of the precursor salts (RuCl3·3H2O, TaCl5) onto titanium metal support were heated in an atmosphere containing 20% O2 and 80% Ar up to 600 °C. The evolution of the mixed oxide coatings was followed by the mass spectrometric ion intensity curves. The cracking of retained solvent and the combustion of organic surface species formed were also followed by the mass spectrometric curves. The formation of carbonyl- and carboxylate-type surface species connected to the noble metal was identified by Fourier transform infrared emission spectroscopy. These secondary processes–catalyzed by the noble metal–may play an important role in the development of surface morphology and electrochemical properties. The evolution of the two oxide phases does not take place independently, and the effect of the noble metal as a combustion catalyst was proved.

Some Remarks on the Approximation of Transitional Density in Stochastic Differential Equations

Aijt-Sahalia (2002) introduced a method to estimate transitional probability densities of di®usion processes by means of Hermite expansions with coe±cients determined by means of Taylor series. This note describes a numerical procedure to ¯nd these coe±cients based on the calculation of moments. One advantage of this procedure is that it can be used e®ectively when the mathematical operations required to ¯nd closed-form expressions for these coe±cients are otherwise infeasible.

Constructive development of the solutions of linear equations in introductory ordinary differential equations

The solution of linear ordinary differential equations (ODEs) is commonly taught in first year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognising what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced studies in mathematics. In this study we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery based approach where students employ their existing skills as a framework for constructing the solutions of first and second order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first year undergraduate class. Finally we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.

ASERA : an uncontroversial evolution

The Australasian Science Education Research Association Ltd. (ASERA) is the oldest educational research association in Australasia. Starting as an informal meeting of science educators at Monash University in May 1970, it has evolved progressively without major controversy into a formally constituted limited company that promotes science education at all levels and contexts. There are no revelations of fractures within the association, and no accounts of major controversy, other than reference to a few grumbles here and there when changes were proposed. So, has the ASERA experience been positive and uplifting for all? Are there unspoken controversies? Can the uncontroversial be made controversial?

Multi-level order, friction and contradiction : the evolution of Australian film industry policy

Cultural policy studies have previously highlighted the importance of multiple logics, friction and contradiction in cultural policy. Recent developments in institutional theory provide a framework for analysing change in cultural policy which explores movement between these multiple and sometimes contradictory logics. This paper analyses the role of friction in the evolution of Australian film industry policy and in particular the tension between competing logics regarding nationalism, commercialism and the state. The paper is suggestive of the relevance of institutional theory as a framework for understanding cultural policy evolution.

Defining an Identity : The Evolution of Science Education

Research in science education is now an international activity. This book asks for the first time, Does this research activity have an identity?-It uses the significant studies of more than 75 researchers in 15 countries to see to what extent they provide evidence for an identity as a distinctive field of research.-It considers trends in the research over time, and looks particularly at what progression in the research entails.-It provides insight into how researchers influence each other and how involvement in research affects the being of the researcher as a person.-It addresses the relation between research and practice in a manner that sees teaching and learning in the science classroom as interdependent with national policies and curriculum traditions about science. It gives graduate students and other early researchers an unusual overview of their research area as a whole. Established researchers will be interested in, and challenged by, the identity the author ascribes to the research and by the plea he makes for the science content itself to be seen as problematic.