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Events matching "T-duality and bulk-boundary correspondence"

A mathematical look at dripping honey
15:10 Fri 4 May, 2007 :: G08 Mathematics Building University of Adelaide :: Dr Yvonne Stokes :: University of Adelaide

Honey dripping from an upturned spoon is an everyday example of a flow that extends and breaks up into drops. Such flows have been of interest for over 300 years, attracting the attention of Plateau and Rayleigh among others. Theoretical understanding has, however, lagged behind experimental investigation, with major progress being made only in the last two decades, driven by industrial applications including ink-jet printing, spinning of polymer and glass fibres, blow-moulding of containers, light bulbs and glass tubing, and rheological measurement by fibre extension. Albeit, the exact details of the final stages of breakup are yet to be fully resolved. An aspect that is relatively unexplored is the evolution of drop and filament from some initial configuration, and the influence of initial conditions on the final breakup. We will consider a drop of very viscous fluid hanging beneath a solid boundary, similar to honey dripping from an upturned spoon, using methods that allow examination of development and behaviour from early time, when a drop and filament begin to form, out to large times when the bulk of the fluid forms a drop at the bottom of a long thin filament which connects it with the upper boundary. The roles of gravity, inertia and surface tension will be examined.
Similarity solutions for surface-tension driven flows
15:10 Fri 14 Mar, 2008 :: LG29 Napier Building University of Adelaide :: Prof John Lister :: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK

The breakup of a mass of fluid into drops is a ubiquitous phenomenon in daily life, the natural environment and technology, with common examples including a dripping tap, ocean spray and ink-jet printing. It is a feature of many generic industrial processes such as spraying, emulsification, aeration, mixing and atomisation, and is an undesirable feature in coating and fibre spinning. Surface-tension driven pinch-off and the subsequent recoil are examples of finite-time singularities in which the interfacial curvature becomes infinite at the point of disconnection. As a result, the flow near the point of disconnection becomes self-similar and independent of initial and far-field conditions. Similarity solutions will be presented for the cases of inviscid and very viscous flow, along with comparison to experiments. In each case, a boundary-integral representation can be used both to examine the time-dependent behaviour and as the basis of a modified Newton scheme for direct solution of the similarity equations.
The Mathematics of String Theory
15:10 Fri 2 May, 2008 :: LG29 Napier Building University of Adelaide :: Prof. Peter Bouwknegt :: Department of Mathematics, ANU

String Theory has had, and continues to have, a profound impact on many areas of mathematics and vice versa. In this talk I want to address some relatively recent developments. In particular I will argue, following Witten and others, that D-brane charges take values in the K-theory of spacetime, rather than in integral cohomology as one might have expected. I will also explore the mathematical consequences of a particular symmetry, called T-duality, in this context. I will give an intuitive introduction into D-branes and K-theory. No prior knowledge about either String Theory, D-branes or K-theory is required.
Free surface Stokes flows with surface tension
15:10 Fri 5 Sep, 2008 :: G03 Napier Building University of Adelaide :: Prof. Darren Crowdy :: Imperial College London

In this talk, we will survey a number of different free boundary problems involving slow viscous (Stokes) flows in which surface tension is active on the free boundary. Both steady and unsteady flows will be considered. Motivating applications range from industrial processes such as viscous sintering (where end-products are formed as a result of the surface-tension-driven densification of a compact of smaller particles that are heated in order that they coalesce) to biological phenomena such as understanding how organisms swim (i.e. propel themselves) at low Reynolds numbers. Common to our approach to all these problems will be an analytical/theoretical treatment of model problems via complex variable methods -- techniques well-known at infinite Reynolds numbers but used much less often in the Stokes regime. These model problems can give helpful insights into the behaviour of the true physical systems.
Oceanographic Research at the South Australian Research and Development Institute: opportunities for collaborative research
15:10 Fri 21 Nov, 2008 :: Napier G04 :: Associate Prof John Middleton :: South Australian Research and Development Institute

Increasing threats to S.A.'s fisheries and marine environment have underlined the increasing need for soundly based research into the ocean circulation and ecosystems (phyto/zooplankton) of the shelf and gulfs. With support of Marine Innovation SA, the Oceanography Program has within 2 years, grown to include 6 FTEs and a budget of over $4.8M. The program currently leads two major research projects, both of which involve numerical and applied mathematical modelling of oceanic flow and ecosystems as well as statistical techniques for the analysis of data. The first is the implementation of the Southern Australian Integrated Marine Observing System (SAIMOS) that is providing data to understand the dynamics of shelf boundary currents, monitor for climate change and understand the phyto/zooplankton ecosystems that under-pin SA's wild fisheries and aquaculture. SAIMOS involves the use of ship-based sampling, the deployment of underwater marine moorings, underwater gliders, HF Ocean RADAR, acoustic tracking of tagged fish and Autonomous Underwater vehicles.

The second major project involves measuring and modelling the ocean circulation and biological systems within Spencer Gulf and the impact on prawn larval dispersal and on the sustainability of existing and proposed aquaculture sites. The discussion will focus on opportunities for collaborative research with both faculty and students in this exciting growth area of S.A. science.

Impulsively generated drops
15:00 Fri 27 Feb, 2009 :: Napier LG29 :: Prof William Phillips :: Swinburne University of Technology

This talk is concerned with the evolution of an unbounded inviscid fluid-fluid interface subject to an axisymmetric impulse in pressure and how inertial, interfacial and gravitational forces affect that evolution. The construct was motivated by the occurrence of lung hemorrhage resulting from ultrasonic imaging and pursues the notion that bursts of ultrasound act to expel droplets that puncture the soft air-filled sacs in the lung plural surface allowing them to fill with blood. The evolution of the free surface is described by a boundary integral formulation which is integrated forward in time numerically. As the interface evolves, it is seen, depending upon the levels of gravity and surface tension, to form either axisymmetric surface jets, waves or droplets. Moreover the droplets may be spherical, inverted tear-shaped or pancake like. Also of interest is the finite time singularity which occurs when the drop pinches off; this is seen to be of the power law type with an exponent of 2/3.
Averaging reduction for stochastic PDEs
15:10 Fri 5 Jun, 2009 :: LG29 :: Dr Wei Wang :: University of Adelaide

In this talk, I introduce recent work on macroscopic reduction for stochastic PDEs by an averaging method. Furthermore by using a special coupling boundary conditions, a macroscopic discrete approximation model can be derived.
Nonlinear diffusion-driven flow in a stratified viscous fluid
15:00 Fri 26 Jun, 2009 :: Macbeth Lecture Theatre :: Associate Prof Michael Page :: Monash University

In 1970, two independent studies (by Wunsch and Phillips) of the behaviour of a linear density-stratified viscous fluid in a closed container demonstrated a slow flow can be generated simply due to the container having a sloping boundary surface This remarkable motion is generated as a result of the curvature of the lines of constant density near any sloping surface, which in turn enables a zero normal-flux condition on the density to be satisfied along that boundary. When the Rayleigh number is large (or equivalently Wunsch's parameter $R$ is small) this motion is concentrated in the near vicinity of the sloping surface, in a thin `buoyancy layer' that has many similarities to an Ekman layer in a rotating fluid.

A number of studies have since considered the consequences of this type of `diffusively-driven' flow in a semi-infinite domain, including in the deep ocean and with turbulent effects included. More recently, Page & Johnson (2008) described a steady linear theory for the broader-scale mass recirculation in a closed container and demonstrated that, unlike in previous studies, it is possible for the buoyancy layer to entrain fluid from that recirculation. That work has since been extended (Page & Johnson, 2009) to the nonlinear regime of the problem and some of the similarities to and differences from the linear case will be described in this talk. Simple and elegant analytical solutions in the limit as $R \to 0$ still exist in some situations, and they will be compared with numerical simulations in a tilted square container at small values of $R$. Further work on both the unsteady flow properties and the flow for other geometrical configurations will also be described.

Quantum Billiards
15:10 Fri 7 Aug, 2009 :: Badger labs G13 Macbeth Lecture Theatre :: Prof Andrew Hassell :: Australian National University

By a "billiard" I mean a bounded plane domain D, with smooth (enough) boundary. Quantum billiards is the study of properties of eigenfunctions of the Laplacian on D, i.e. solutions of $\Delta u = Eu$, where $u$ is a function on D vanishing at the boundary, $\Delta$ is the Laplacian on D and $E$ is a real number, in the limit as $E \to \infty$. This large-E limit is the "classical limit" in which eigenfunctions exhibit behaviour related to the classical billiard system (a billiard ball moving around inside D, bouncing elastically off the boundary). I will talk about Quantum Ergodicity, which is the property that "most of" the eigenfunctions become uniformly distributed in D, asymptotically as $E \to \infty$, i.e. they are the same size, on average, in all parts of the domain D; and the stronger property of Quantum Unique Ergodicity, which is the same property with the words "most of" deleted.
Stability of rotating boundary-layers
15:10 Wed 16 Sep, 2009 :: Napier LG29 :: Dr Christian Thomas :: University of Western Australia

Stable commutator length
13:40 Fri 25 Sep, 2009 :: Napier 102 :: Prof Danny Calegari :: California Institute of Technology

Stable commutator length answers the question: "what is the simplest surface in a given space with prescribed boundary?" where "simplest" is interpreted in topological terms. This topological definition is complemented by several equivalent definitions - in group theory, as a measure of non-commutativity of a group; and in linear programming, as the solution of a certain linear optimization problem. On the topological side, scl is concerned with questions such as computing the genus of a knot, or finding the simplest 4-manifold that bounds a given 3-manifold. On the linear programming side, scl is measured in terms of certain functions called quasimorphisms, which arise from hyperbolic geometry (negative curvature) and symplectic geometry (causal structures). In these talks we will discuss how scl in free and surface groups is connected to such diverse phenomena as the existence of closed surface subgroups in graphs of groups, rigidity and discreteness of symplectic representations, bounding immersed curves on a surface by immersed subsurfaces, and the theory of multi- dimensional continued fractions and Klein polyhedra. Danny Calegari is the Richard Merkin Professor of Mathematics at the California Institute of Technology, and is one of the recipients of the 2009 Clay Research Award for his work in geometric topology and geometric group theory. He received a B.A. in 1994 from the University of Melbourne, and a Ph.D. in 2000 from the University of California, Berkeley under the joint supervision of Andrew Casson and William Thurston. From 2000 to 2002 he was Benjamin Peirce Assistant Professor at Harvard University, after which he joined the Caltech faculty; he became Richard Merkin Professor in 2007.
Eigen-analysis of fluid-loaded compliant panels
15:10 Wed 9 Dec, 2009 :: Santos Lecture Theatre :: Prof Tony Lucey :: Curtin University of Technology

This presentation concerns the fluid-structure interaction (FSI) that occurs between a fluid flow and an arbitrarily deforming flexible boundary considered to be a flexible panel or a compliant coating that comprises the wetted surface of a marine vehicle. We develop and deploy an approach that is a hybrid of computational and theoretical techniques. The system studied is two-dimensional and linearised disturbances are assumed. Of particular novelty in the present work is the ability of our methods to extract a full set of fluid-structure eigenmodes for systems that have strong spatial inhomogeneity in the structure of the flexible wall.

We first present the approach and some results of the system in which an ideal, zero-pressure gradient, flow interacts with a flexible plate held at both its ends. We use a combination of boundary-element and finite-difference methods to express the FSI system as a single matrix equation in the interfacial variable. This is then couched in state-space form and standard methods used to extract the system eigenvalues. It is then shown how the incorporation of spatial inhomogeneity in the stiffness of the plate can be either stabilising or destabilising. We also show that adding a further restraint within the streamwise extent of a homogeneous panel can trigger an additional type of hydroelastic instability at low flow speeds. The mechanism for the fluid-to-structure energy transfer that underpins this instability can be explained in terms of the pressure-signal phase relative to that of the wall motion and the effect on this relationship of the added wall restraint.

We then show how the ideal-flow approach can be conceptually extended to include boundary-layer effects. The flow field is now modelled by the continuity equation and the linearised perturbation momentum equation written in velocity-velocity form. The near-wall flow field is spatially discretised into rectangular elements on an Eulerian grid and a variant of the discrete-vortex method is applied. The entire fluid-structure system can again be assembled as a linear system for a single set of unknowns - the flow-field vorticity and the wall displacements - that admits the extraction of eigenvalues. We then show how stability diagrams for the fully-coupled finite flow-structure system can be assembled, in doing so identifying classes of wall-based or fluid-based and spatio-temporal wave behaviour.

Some unusual uses of usual symmetries and some usual uses of unusual symmetries
12:10 Wed 10 Mar, 2010 :: School board room :: Prof Phil Broadbridge :: La Trobe University

Ever since Sophus Lie around 1880, continuous groups of invariance transformations have been used to reduce variables and to construct special solutions of PDEs. I will outline the general ideas, then show some variations on the usual reduction algorithm that I have used to solve some practical nonlinear boundary value problems. Applications include soil-water flow, metal surface evolution and population genetics.
Compound and constrained regression analyses for EIV models
15:05 Fri 27 Aug, 2010 :: Napier LG28 :: Prof Wei Zhu :: State University of New York at Stony Brook

In linear regression analysis, randomness often exists in the independent variables and the resulting models are referred to errors-in-variables (EIV) models. The existing general EIV modeling framework, the structural model approach, is parametric and dependent on the usually unknown underlying distributions. In this work, we introduce a general non-parametric EIV modeling framework, the compound regression analysis, featuring an intuitive geometric representation and a 1-1 correspondence to the structural model. Properties, examples and further generalizations of this new modeling approach are discussed in this talk.
Hugs not drugs
15:10 Mon 20 Sep, 2010 :: Ingkarni Wardli B17 :: Dr Scott McCue :: Queensland University of Technology

I will discuss a model for drug diffusion that involves a Stefan problem with a "kinetic undercooling". I like Stefan problems, so I like this model. I like drugs too, but only legal ones of course. Anyway, it turns out that in some parameter regimes, this sophisticated moving boundary problem hardly works better than a simple linear undergraduate model (there's a lesson here for mathematical modelling). On the other hand, for certain polymer capsules, the results are interesting and suggest new means for controlled drug delivery. If time permits, I may discuss certain asymptotic limits that are of interest from a Stefan problem perspective. Finally, I won't bring any drugs with me to the seminar, but I'm willing to provide hugs if necessary.
Principal Component Analysis Revisited
15:10 Fri 15 Oct, 2010 :: Napier G04 :: Assoc. Prof Inge Koch :: University of Adelaide

Since the beginning of the 20th century, Principal Component Analysis (PCA) has been an important tool in the analysis of multivariate data. The principal components summarise data in fewer than the original number of variables without losing essential information, and thus allow a split of the data into signal and noise components. PCA is a linear method, based on elegant mathematical theory. The increasing complexity of data together with the emergence of fast computers in the later parts of the 20th century has led to a renaissance of PCA. The growing numbers of variables (in particular, high-dimensional low sample size problems), non-Gaussian data, and functional data (where the data are curves) are posing exciting challenges to statisticians, and have resulted in new research which extends the classical theory. I begin with the classical PCA methodology and illustrate the challenges presented by the complex data that we are now able to collect. The main part of the talk focuses on extensions of PCA: the duality of PCA and the Principal Coordinates of Multidimensional Scaling, Sparse PCA, and consistency results relating to principal components, as the dimension grows. We will also look at newer developments such as Principal Component Regression and Supervised PCA, nonlinear PCA and Functional PCA.
Slippery issues in nano- and microscale fluid flows
11:10 Tue 30 Nov, 2010 :: Innova teaching suite B21 :: Dr Shaun C. Hendy :: Victoria University of Wellington

The no-slip boundary condition was considered to have been experimentally established for the flow of simple liquids over solid surfaces in the early 20th century. Nonetheless the refinement of a number of measurement techniques has recently led to the observation of nano- and microscale violations of the no-slip boundary condition by simple fluids flowing over non-wetting surfaces. However it is important to distinguish between intrinsic slip, which arises solely from the chemical interaction between the liquid and a homogeneous, atomically flat surface and effective slip, typically measured in macroscopic experiments, which emerges from the interaction of microscopic chemical heterogeneity, roughness and contaminants. Here we consider the role of both intrinsic and effective slip boundary conditions in nanoscale and microscale fluid flows using a theoretical approach, complemented by molecular dynamics simulations, and experimental evidence where available. Firstly, we consider nanoscale flows in small capillaries, including carbon nanotubes, where we have developed and solved a generalised Lucas-Washburn equation that incorporates slip to describe the uptake of droplets. We then consider the general problem of relating effective slip to microscopic intrinsic slip and roughness, and discuss several cases where we have been able to solve this problem analytically. Finally, we look at applications of these results to carbon nanotube growth, self-cleaning surfaces, catalysis, and putting insulation in your roof.
Heat transfer scaling and emergence of three-dimensional flow in horizontal convection
15:10 Fri 25 Feb, 2011 :: Conference Room Level 7 Ingkarni Wardli :: Dr Greg Sheard :: Monash University

Horizontal convecton refers to flows driven by uneven heating on a horizontal forcing boundary. Flows exhibiting these characteristics are prevalent in nature, and include the North-South Hadley circulation within the atmosphere between warmer and more temperate latitudes, as well as ocean currents driven by non-uniform heating via solar radiation.

Here a model for these generic convection flows is established featuring a rectangular enclosure, insulated on the side and top walls, and driven by a linear temperature gradient applied along the bottom wall. Rayleigh number dependence of heat transfer through the forcing boundary is computed and compared with theory. Attention is given to transitions in the flow, including the development of unsteady flow and three-dimensional flow: the effect of these transitions on the Nusselt-Rayleigh number scaling exponents is described.

The Extended-Domain-Eigenfunction Method: making old mathematics work for new problems
15:10 Fri 13 May, 2011 :: 7.15 Ingkarni Wardli :: Prof Stan Miklavcic :: University of South Australia

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Standard analytical solutions to elliptic boundary value problems on asymmetric domains are rarely, if ever, obtainable. Several years ago I proposed a solution technique to cope with such complicated domains. It involves the embedding of the original domain into one with simple boundaries where the classical eigenfunction solution approach can be used. The solution in the larger domain, when restricted to the original domain is then the solution of the original boundary value problem. In this talk I will present supporting theory for this idea, some numerical results for the particular case of the Laplace equation and the Stokes flow equations in two-dimensions and discuss advantages and limitations of the proposal.
Probability density estimation by diffusion
15:10 Fri 10 Jun, 2011 :: 7.15 Ingkarni Wardli :: Prof Dirk Kroese :: University of Queensland

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One of the beautiful aspects of Mathematics is that seemingly disparate areas can often have deep connections. This talk is about the fundamental connection between probability density estimation, diffusion processes, and partial differential equations. Specifically, we show how to obtain efficient probability density estimators by solving partial differential equations related to diffusion processes. This new perspective leads, in combination with Fast Fourier techniques, to very fast and accurate algorithms for density estimation. Moreover, the diffusion formulation unifies most of the existing adaptive smoothing algorithms and provides a natural solution to the boundary bias of classical kernel density estimators. This talk covers topics in Statistics, Probability, Applied Mathematics, and Numerical Mathematics, with a surprise appearance of the theta function. This is joint work with Zdravko Botev and Joe Grotowski.
Stochastic models of reaction diffusion
15:10 Fri 17 Jun, 2011 :: 7.15 Ingkarni Wardli :: Prof Jon Chapman :: Oxford University

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We consider two different position jump processes: (i) a random walk on a lattice (ii) the Euler scheme for the Smoluchowski differential equation. Both of these reduce to the diffusion equation as the time step and size of the jump tend to zero. We consider the problem of adding chemical reactions to these processes, both at a surface and in the bulk. We show how the "microscopic" parameters should be chosen to achieve the correct "macroscopic" reaction rate. This choice is found to depend on which stochastic model for diffusion is used.
AustMS/AMSI Mahler Lecture: Chaos, quantum mechanics and number theory
18:00 Tue 9 Aug, 2011 :: Napier 102 :: Prof Peter Sarnak :: Institute for Advanced Study, Princeton

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The correspondence principle in quantum mechanics is concerned with the relation between a mechanical system and its quantization. When the mechanical system are relatively orderly ("integrable"), then this relation is well understood. However when the system is chaotic much less is understood. The key features already appear and are well illustrated in the simplest systems which we will review. For chaotic systems defined number-theoretically, much more is understood and the basic problems are connected with central questions in number theory. The Mahler lectures are a biennial activity organised by the Australian Mathematical Society with the assistance of the Australian Mathematical Sciences Institute.
Laplace's equation on multiply-connected domains
12:10 Mon 29 Aug, 2011 :: 5.57 Ingkarni Wardli :: Mr Hayden Tronnolone :: University of Adelaide

Various physical processes take place on multiply-connected domains (domains with some number of 'holes'), such as the stirring of a fluid with paddles or the extrusion of material from a die. These systems may be described by partial differential equations (PDEs). However, standard numerical methods for solving PDEs are not well-suited to such examples: finite difference methods are difficult to implement on multiply-connected domains, especially when the boundaries are irregular or moving, while finite element methods are computationally expensive. In this talk I will describe a fast and accurate numerical method for solving certain PDEs on two-dimensional multiply-connected domains, considering Laplace's equation as an example. This method takes advantage of complex variable techniques which allow the solution to be found with spectral accuracy provided the boundary data is smooth. Other advantages over traditional numerical methods will also be discussed.
T-duality via bundle gerbes I
13:10 Fri 23 Sep, 2011 :: B.19 Ingkarni Wardli :: Dr Raymond Vozzo :: University of Adelaide

In physics T-duality is a phenomenon which relates certain types of string theories to one another. From a topological point of view, one can view string theory as a duality between line bundles carrying a degree three cohomology class (the H-flux). In this talk we will use bundle gerbes to give a geometric realisation of the H-flux and explain how to construct the T-dual of a line bundle together with its T-dual bundle gerbe.
T-duality via bundle gerbes II
13:10 Fri 21 Oct, 2011 :: B.19 Ingkarni Wardli :: Dr Raymond Vozzo :: University of Adelaide

In physics T-duality is a phenomenon which relates certain types of string theories to one another. From a topological point of view, one can view string theory as a duality between line bundles carrying a degree three cohomology class (the H-flux). In this talk we will use bundle gerbes to give a geometric realisation of the H-flux and explain how to construct the T-dual of a line bundle together with its T-dual bundle gerbe.
Collision and instability in a rotating fluid-filled torus
15:10 Mon 12 Dec, 2011 :: Benham Lecture Theatre :: Dr Richard Clarke :: The University of Auckland

The simple experiment discussed in this talk, first conceived by Madden and Mullin (JFM, 1994) as part of their investigations into the non-uniqueness of decaying turbulent flow, consists of a fluid-filled torus which is rotated in an horizontal plane. Turbulence within the contained flow is triggered through a rapid change in its rotation rate. The flow instabilities which transition the flow to this turbulent state, however, are truly fascinating in their own right, and form the subject of this presentation. Flow features observed in both UK- and Auckland-based experiments will be highlighted, and explained through both boundary-layer analysis and full DNS. In concluding we argue that this flow regime, with its compact geometry and lack of cumbersome flow entry effects, presents an ideal regime in which to study many prototype flow behaviours, very much in the same spirit as Taylor-Couette flow.
Embedding circle domains into the affine plane C^2
13:10 Fri 10 Feb, 2012 :: B.20 Ingkarni Wardli :: Prof Franc Forstneric :: University of Ljubljana

We prove that every circle domain in the Riemann sphere admits a proper holomorphic embedding into the affine plane C^2. By a circle domain we mean a domain obtained by removing from the Riemann sphere a finite or countable family of pairwise disjoint closed round discs. Our proof also applies to some circle domains with punctures. The uniformization theorem of He and Schramm (1996) says that every domain in the Riemann sphere with at most countably many boundary components is conformally equivalent to a circle domain, so our theorem embeds all such domains properly holomorphically in C^2. (Joint work with Erlend F. Wold.)
Plurisubharmonic subextensions as envelopes of disc functionals
13:10 Fri 2 Mar, 2012 :: B.20 Ingkarni Wardli :: A/Prof Finnur Larusson :: University of Adelaide

I will describe new joint work with Evgeny Poletsky. We prove a disc formula for the largest plurisubharmonic subextension of an upper semicontinuous function on a domain $W$ in a Stein manifold to a larger domain $X$ under suitable conditions on $W$ and $X$. We introduce a related equivalence relation on the space of analytic discs in $X$ with boundary in $W$. The quotient is a complex manifold with a local biholomorphism to $X$, except it need not be Hausdorff. We use our disc formula to generalise Kiselman's minimum principle. We show that his infimum function is an example of a plurisubharmonic subextension.
The entropy of an overlapping dynamical system
15:10 Fri 23 Mar, 2012 :: Napier G03 :: Prof Michael Barnsley :: Australian National University

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The term "overlapping" refers to a certain fairly simple type of piecewise continuous function from the unit interval to itself and also to a fairly simple type of iterated function system (IFS) on the unit interval. A correspondence between these two classes of objects is used to: 1. find a necessary and sufficient condition for a fractal transformation from the attractor of one overlapping IFS to the attractor of another overlapping IFS to be a homeomorphism and 2. find a formula for the topological entropy of the dynamical system associated with an overlapping function. These results suggest a new method for analysing clocks, weather systems and prime numbers.
The mechanics of plant root growth
15:10 Fri 30 Mar, 2012 :: B.21 Ingkarni Wardli :: Dr Rosemary Dyson :: University of Birmingham

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Growing plant cells undergo rapid axial elongation with negligible radial expansion: high internal turgor pressure causes viscous stretching of the cell wall. We represent the cell wall as a thin fibre-reinforced viscous sheet, providing insight into the geometric and biomechanical parameters underlying bulk quantities such as wall extensibility and showing how either dynamical changes in material properties, achieved through changes in the cell-wall microstructure, or passive fibre reorientation may suppress cell elongation. We then investigate how the action of enzymes on the cell wall microstructure can lead to the required dynamic changes in macroscale wall material properties, and thus demonstrate a mechanism by which hormones may regulate plant growth.
Index type invariants for twisted signature complexes
13:10 Fri 11 May, 2012 :: Napier LG28 :: Prof Mathai Varghese :: University of Adelaide

Atiyah-Patodi-Singer proved an index theorem for non-local boundary conditions in the 1970's that has been widely used in mathematics and mathematical physics. A key application of their theory gives the index theorem for signature operators on oriented manifolds with boundary. As a consequence, they defined certain secondary invariants that were metric independent. I will discuss some recent work with Benameur where we extend the APS theory to signature operators twisted by an odd degree closed differential form, and study the corresponding secondary invariants.
A brief introduction to Support Vector Machines
12:30 Mon 4 Jun, 2012 :: 5.57 Ingkarni Wardli :: Mr Tyman Stanford :: University of Adelaide

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Support Vector Machines (SVMs) are used in a variety of contexts for a range of purposes including regression, feature selection and classification. To convey the basic principles of SVMs, this presentation will focus on the application of SVMs to classification. Classification (or discrimination), in a statistical sense, is supervised model creation for the purpose of assigning future observations to a group or class. An example might be determining healthy or diseased labels to patients from p characteristics obtained from a blood sample. While SVMs are widely used, they are most successful when the data have one or more of the following properties: The data are not consistent with a standard probability distribution. The number of observations, n, used to create the model is less than the number of predictive features, p. (The so-called small-n, big-p problem.) The decision boundary between the classes is likely to be non-linear in the feature space. I will present a short overview of how SVMs are constructed, keeping in mind their purpose. As this presentation is part of a double post-grad seminar, I will keep it to a maximum of 15 minutes.
Boundary-layer transition and separation over asymmetrically textured spherical surfaces
12:30 Mon 27 Aug, 2012 :: B.21 Ingkarni Wardli :: Mr Adam Tunney :: University of Adelaide

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The game of cricket is unique among ball sports by the ignorant exploitation of \thetitle in the practice of swing bowling, often referred to as a "mysterious art". I will talk a bit about the Magnus effect exploited in inferior sports, the properties of a cricket ball that allow swing bowling, and the explanation of three modes of swing (conventional, contrast and reverse). Following that there will be some discussion on how I plan to use mathematics to turn this "art" into science.
The boundary conditions for macroscale modelling of a discrete diffusion system with periodic diffusivity
12:10 Mon 29 Apr, 2013 :: B.19 Ingkarni Wardli :: Chen Chen :: University of Adelaide

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Many mathematical and engineering problems have a multiscale nature. There are a vast of theories supporting multiscale modelling on infinite domain, such as homogenization theory and centre manifold theory. To date, there are little consideration of the correct boundary conditions to be used at the edge of macroscale model. In this seminar, I will present how to derive macroscale boundary conditions for the diffusion system.
Multiscale modelling couples patches of wave-like simulations
12:10 Mon 27 May, 2013 :: B.19 Ingkarni Wardli :: Meng Cao :: University of Adelaide

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A multiscale model is proposed to significantly reduce the expensive numerical simulations of complicated waves over large spatial domains. The multiscale model is built from given microscale simulations of complicated physical processes such as sea ice or turbulent shallow water. Our long term aim is to enable macroscale simulations obtained by coupling small patches of simulations together over large physical distances. This initial work explores the coupling of patch simulations of wave-like pdes. With the line of development being to water waves we discuss the dynamics of two complementary fields called the 'depth' h and 'velocity' u. A staggered grid is used for the microscale simulation of the depth h and velocity u. We introduce a macroscale staggered grid to couple the microscale patches. Linear or quadratic interpolation provides boundary conditions on the field in each patch. Linear analysis of the whole coupled multiscale system establishes that the resultant macroscale dynamics is appropriate. Numerical simulations support the linear analysis. This multiscale method should empower the feasible computation of large scale simulations of wave-like dynamics with complicated underlying physics.
A strong Oka principle for proper immersions of finitely connected planar domains into CxC*
12:10 Fri 31 May, 2013 :: Ingkarni Wardli B19 :: Dr Tyson Ritter :: University of Adelaide

Gromov, in his seminal 1989 paper on the Oka principle, proved that every continuous map from a Stein manifold into an elliptic manifold is homotopic to a holomorphic map. In previous work we showed that, given a continuous map from X to the elliptic manifold CxC*, where X is a finitely connected planar domain without isolated boundary points, a stronger Oka property holds whereby the map is homotopic to a proper holomorphic embedding. If the planar domain is additionally permitted to have isolated boundary points the problem becomes more difficult, and it is not yet clear whether a strong Oka property for embeddings into CxC* continues to hold. We will discuss recent results showing that every continuous map from a finitely connected planar domain into CxC* is homotopic to a proper immersion that, in most cases, identifies at most finitely many pairs of distinct points. This is joint work with Finnur Larusson.
The Einstein equations with torsion, reduction and duality
12:10 Fri 23 Aug, 2013 :: Ingkarni Wardli B19 :: Dr David Baraglia :: University of Adelaide

We consider the Einstein equations for connections with skew torsion. After some general remarks we look at these equations on principal G-bundles, making contact with string structures and heterotic string theory in the process. When G is a torus the equations are shown to possess a symmetry not shared by the usual Einstein equations - T-duality. This is joint work with Pedram Hekmati.
Group meeting
15:10 Fri 25 Oct, 2013 :: 5.58 (Ingkarni Wardli) :: Dr Ben Binder and Mr David Wilke :: University of Adelaide

Dr Ben Binder :: 'An inverse approach for solutions to free-surface flow problems' :: Abstract: Surface water waves are familiar to most people, for example, the wave pattern generated at the stern of a ship. The boundary or interface between the air and water is called the free-surface. When determining a solution to a free-surface flow problem it is commonplace for the forcing (eg. shape of ship or waterbed topography) that creates the surface waves to be prescribed, with the free-surface coming as part of the solution. Alternatively, one can choose to prescribe the shape of the free-surface and find the forcing inversely. In this talk I will discuss my ongoing work using an inverse approach to discover new types of solutions to free-surface flow problems in two and three dimensions, and how the predictions of the method might be verified with experiments. :: Mr David Wilke:: 'A Computational Fluid Dynamic Study of Blood Flow Within the Coiled Umbilical Arteries':: Abstract: The umbilical cord is the lifeline of the fetus throughout gestation. In a normal pregnancy it facilitates the supply of oxygen and nutrients from the placenta via a single vein, in addition to the return of deoxygenated blood from the developing embryo or fetus via two umbilical arteries. Despite the major role it plays in the growth of the fetus, pathologies of the umbilical cord are poorly understood. In particular, variations in the cord geometry, which typically forms a helical arrangement, have been correlated with adverse outcomes in pregnancy. Cords exhibiting either abnormally low or high levels of coiling have been associated with pathological results including growth-restriction and fetal demise. Despite this, the methodology currently employed by clinicians to characterise umbilical pathologies can misdiagnose cords and is prone to error. In this talk a computational model of blood flow within rigid three-dimensional structures representative of the umbilical arteries will be presented. This study determined that the current characterization was unable to differentiate between cords which exhibited clinically distinguishable flow properties, including the cord pressure drop, which provides a measure of the loading on the fetal heart.
A gentle introduction to bubble evolution in Hele-Shaw flows
15:10 Fri 22 Nov, 2013 :: 5.58 (Ingkarni Wardli) :: Dr Scott McCue :: QUT

A Hele-Shaw cell is easy to make and serves as a fun toy for an applied mathematician to play with. If we inject air into a Hele-Shaw cell that is otherwise filled with viscous fluid, we can observe a bubble of air growing in size. The process is highly unstable, and the bubble boundary expands in an uneven fashion, leading to striking fingering patterns (look up Hele-Shaw cell or Saffman-Taylor instability on YouTube). From a mathematical perspective, modelling these Hele-Shaw flows is interesting because the governing equations are sufficiently ``simple'' that a considerable amount of analytical progress is possible. Indeed, there is no other context in which (genuinely) two-dimensional moving boundary problems are so tractable. More generally, Hele-Shaw flows are important as they serve as prototypes for more complicated (and important) physical processes such as crystal growth and diffusion limited aggregation. I will give an introduction to some of the main ideas and summarise some of my present research in this area.
Semiclassical restriction estimates
12:10 Fri 4 Apr, 2014 :: Ingkarni Wardli B20 :: Melissa Tacy :: University of Adelaide

Eigenfunctions of Hamiltonians arise naturally in the theory of quantum mechanics as stationary states of quantum systems. Their eigenvalues have an interpretation as the square root of E, where E is the energy of the system. We wish to better understand the high energy limit which defines the boundary between quantum and classical mechanics. In this talk I will focus on results regarding the restriction of eigenfunctions to lower dimensional subspaces, in particular to hypersurfaces. A convenient way to study such problems is to reframe them as problems in semiclassical analysis.
Flow barriers and flux in unsteady flows
15:10 Fri 4 Apr, 2014 :: B.21 Ingkarni Wardli :: Dr Sanjeeva Balasuriya :: The University of Adelaide

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How does one define the boundary of the ozone hole, an oceanic eddy, or Jupiter's Great Red Spot? These occur in flows which are unsteady (nonautonomous), that is, which change with time, and therefore any boundary must as well. In steady (autonomous) flows, defining flow boundaries is straightforward: one first finds fixed points of the flow, and then determines entities in space which are attracted to or repelled from these points as time progresses. These are respectively the stable and unstable manifolds of the fixed points, and can be shown to partition space into regions of different types of flow. This talk will focus on the required modifications to this idea for determining flow barriers in the more realistic unsteady context. An application to maximising mixing in microfluidic devices will also be presented.
T-Duality and its Generalizations
12:10 Fri 11 Apr, 2014 :: Ingkarni Wardli B20 :: Jarah Evslin :: Theoretical Physics Center for Science Facilities, CAS

Given a manifold M with a torus action and a choice of integral 3-cocycle H, T-duality yields another manifold with a torus action and integral 3-cocyle. It induces a number of surprising automorphisms between structures on these manifolds. In this talk I will review T-duality and describe some work on two generalizations which are realized in string theory: NS5-branes and heterotic strings. These respectively correspond to non-closed 3-classes H and to principal bundles fibered over M.
Estimates for eigenfunctions of the Laplacian on compact Riemannian manifolds
12:10 Fri 1 Aug, 2014 :: Ingkarni Wardli B20 :: Andrew Hassell :: Australian National University

I am interested in estimates on eigenfunctions, accurate in the high-eigenvalue limit. I will discuss estimates on the size (as measured by L^p norms) of eigenfunctions, on the whole Riemannian manifold, at the boundary, or at an interior hypersurface. The link between high-eigenvalue estimates, geometry, and the dynamics of geodesic flow will be emphasized.
Fast computation of eigenvalues and eigenfunctions on bounded plane domains
15:10 Fri 1 Aug, 2014 :: B.18 Ingkarni Wardli :: Professor Andrew Hassell :: Australian National University

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I will describe a new method for numerically computing eigenfunctions and eigenvalues on certain plane domains, derived from the so-called "scaling method" of Vergini and Saraceno. It is based on properties of the Dirichlet-to-Neumann map on the domain, which relates a function f on the boundary of the domain to the normal derivative (at the boundary) of the eigenfunction with boundary data f. This is a topic of independent interest in pure mathematics. In my talk I will try to emphasize the inteplay between theory and applications, which is very rich in this situation. This is joint work with numerical analyst Alex Barnett (Dartmouth).
The Dirichlet problem for the prescribed Ricci curvature equation
12:10 Fri 15 Aug, 2014 :: Ingkarni Wardli B20 :: Artem Pulemotov :: University of Queensland

We will discuss the following question: is it possible to find a Riemannian metric whose Ricci curvature is equal to a given tensor on a manifold M? To answer this question, one must analyze a weakly elliptic second-order geometric PDE. In the first part of the talk, we will review the history of the subject and state several classical theorems. After that, our focus will be on new results concerning the case where M has nonempty boundary.
Boundary-value problems for the Ricci flow
15:10 Fri 15 Aug, 2014 :: B.18 Ingkarni Wardli :: Dr Artem Pulemotov :: The University of Queensland

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The Ricci flow is a differential equation describing the evolution of a Riemannian manifold (i.e., a "curved" geometric object) into an Einstein manifold (i.e., an object with a "constant" curvature). This equation is particularly famous for its key role in the proof of the Poincare Conjecture. Understanding the Ricci flow on manifolds with boundary is a difficult problem with applications to a variety of fields, such as topology and mathematical physics. The talk will survey the current progress towards the resolution of this problem. In particular, we will discuss new results concerning spaces with symmetries.
T-duality and the chiral de Rham complex
12:10 Fri 22 Aug, 2014 :: Ingkarni Wardli B20 :: Andrew Linshaw :: University of Denver

The chiral de Rham complex of Malikov, Schechtman, and Vaintrob is a sheaf of vertex algebras that exists on any smooth manifold M. It has a square-zero differential D, and contains the algebra of differential forms on M as a subcomplex. In this talk, I'll give an introduction to vertex algebras and sketch this construction. Finally, I'll discuss a notion of T-duality in this setting. This is based on joint work in progress with V. Mathai.
Spherical T-duality
01:10 Mon 25 Aug, 2014 :: Ingkarni Wardli B18 :: Mathai Varghese :: University of Adelaide

I will talk on a new variant of T-duality, called spherical T-duality, which relates pairs of the form (P,H) consisting of a principal SU(2)-bundle P --> M and a 7-cocycle H on P. Intuitively spherical T-duality exchanges H with the second Chern class c_2(P). This is precisely true when M is compact oriented and dim(M) is at most 4. When M is higher dimensional, not all pairs (P,H) admit spherical T-duals and even when they exist, the spherical T-duals are not always unique. We will try and explain this phenomenon. Nonetheless, we prove that all spherical T-dualities induce a degree-shifting isomorphism on the 7-twisted cohomologies of the bundles and, when dim(M) is at most 7, also their integral twisted cohomologies and, when dim(M) is at most 4, even their 7-twisted K-theories. While the complete physical relevance of spherical T-duality is still being explored, it does provide an identification between conserved charges in certain distinct IIB supergravity and string compactifications. This is joint work with Peter Bouwknegt and Jarah Evslin.
Fractal substitution tilings
11:10 Wed 17 Dec, 2014 :: Ingkarni Wardli B17 :: Mike Whittaker :: University of Wollongong

Starting with a substitution tiling, I will demonstrate a method for constructing infinitely many new substitution tilings. Each of these new tilings is derived from a graph iterated function system and the tiles typically have fractal boundary. As an application, we construct an odd spectral triple on a C*-algebra associated with an aperiodic substitution tiling. No knowledge of tilings, C*-algebras, or spectral triples will be assumed. This is joint work with Natalie Frank, Michael Mampusti, and Sam Webster.
Boundary behaviour of Hitchin and hypo flows with left-invariant initial data
12:10 Fri 27 Feb, 2015 :: Ingkarni Wardli B20 :: Vicente Cortes :: University of Hamburg

Hitchin and hypo flows constitute a system of first order pdes for the construction of Ricci-flat Riemannian mertrics of special holonomy in dimensions 6, 7 and 8. Assuming that the initial geometric structure is left-invariant, we study whether the resulting Ricci-flat manifolds can be extended in a natural way to complete Ricci-flat manifolds. This talk is based on joint work with Florin Belgun, Marco Freibert and Oliver Goertsches, see arXiv:1405.1866 (math.DG).
Tannaka duality for stacks
12:10 Fri 6 Mar, 2015 :: Ingkarni Wardli B20 :: Jack Hall :: Australian National University

Traditionally, Tannaka duality is used to reconstruct a group from its representations. I will describe a reformulation of this duality for stacks, which is due to Lurie, and briefly touch on some applications.
On the analyticity of CR-diffeomorphisms
12:10 Fri 13 Mar, 2015 :: Engineering North N132 :: Ilya Kossivskiy :: University of Vienna

One of the fundamental objects in several complex variables is CR-mappings. CR-mappings naturally occur in complex analysis as boundary values of mappings between domains, and as restrictions of holomorphic mappings onto real submanifolds. It was already observed by Cartan that smooth CR-diffeomorphisms between CR-submanifolds in C^N tend to be very regular, i.e., they are restrictions of holomorphic maps. However, in general smooth CR-mappings form a more restrictive class of mappings. Thus, since the inception of CR-geometry, the following general question has been of fundamental importance for the field: Are CR-equivalent real-analytic CR-structures also equivalent holomorphically? In joint work with Lamel, we answer this question in the negative, in any positive CR-dimension and CR-codimension. Our construction is based on a recent dynamical technique in CR-geometry, developed in my earlier work with Shafikov.
Singular Pfaffian systems in dimension 6
12:10 Fri 20 Mar, 2015 :: Napier 144 :: Pawel Nurowski :: Center for Theoretical Physics, Polish Academy of Sciences

We consider a pair of rank 3 distributions in dimension 6 with some remarkable properties. They define an analog of the celebrated nearly-Kahler structure on the 6 sphere, with the exceptional simple Lie group G2 as a group of symmetries. In our case the metric associated with the structure is pseudo-Riemannian, of split signature. The 6 manifold has a 5-dimensional boundary with interesting induced geometry. This structure on the boundary has no analog in the Riemannian case.
Higher rank discrete Nahm equations for SU(N) monopoles in hyperbolic space
11:10 Wed 8 Apr, 2015 :: Engineering & Maths EM213 :: Joseph Chan :: University of Melbourne

Braam and Austin in 1990, proved that SU(2) magnetic monopoles in hyperbolic space H^3 are the same as solutions of the discrete Nahm equations. I apply equivariant K-theory to the ADHM construction of instantons/holomorphic bundles to extend the Braam-Austin result from SU(2) to SU(N). During its evolution, the matrices of the higher rank discrete Nahm equations jump in dimensions and this behaviour has not been observed in discrete evolution equations before. A secondary result is that the monopole field at the boundary of H^3 determines the monopole.
Spherical T-duality: the non-principal case
12:10 Fri 1 May, 2015 :: Napier 144 :: Mathai Varghese :: University of Adelaide

Spherical T-duality is related to M-theory and was introduced in recent joint work with Bouwknegt and Evslin. I will begin by briefly reviewing the case of principal SU(2)-bundles with degree 7 flux, and then focus on the non-principal case for most of the talk, ending with the relation to SUGRA/M-theory.
An Engineer-Mathematician Duality Approach to Finite Element Methods
12:10 Mon 18 May, 2015 :: Napier LG29 :: Jordan Belperio :: University of Adelaide

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The finite element method has been a prominently used numerical technique for engineers solving solid mechanics, electro-magnetic and heat transfer problems for over 30 years. More recently the finite element method has been used to solve fluid mechanics problems, a field where finite difference methods are more commonly used. In this talk, I will introduce the basic mathematics behind the finite element method, the similarity between the finite element method and finite difference method and comparing how engineers and mathematicians use finite element methods. I will then demonstrate two solutions to the wave equation using the finite element method.
T-duality and bulk-boundary correspondence
12:10 Fri 11 Sep, 2015 :: Ingkarni Wardli B17 :: Guo Chuan Thiang :: The University of Adelaide

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Bulk-boundary correspondences in physics can be modelled as topological boundary homomorphisms in K-theory, associated to an extension of a "bulk algebra" by a "boundary algebra". In joint work with V. Mathai, such bulk-boundary maps are shown to T-dualize into simple restriction maps in a large number of cases, generalizing what the Fourier transform does for ordinary functions. I will give examples, involving both complex and real K-theory, and explain how these results may be used to study topological phases of matter and D-brane charges in string theory.
Real Lie Groups and Complex Flag Manifolds
12:10 Fri 9 Oct, 2015 :: Ingkarni Wardli B17 :: Joseph A. Wolf :: University of California, Berkeley

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Let G be a complex simple direct limit group. Let G_R be a real form of G that corresponds to an hermitian symmetric space. I'll describe the corresponding bounded symmetric domain in the context of the Borel embedding, Cayley transforms, and the Bergman-Shilov boundary. Let Q be a parabolic subgroup of G. In finite dimensions this means that G/Q is a complex projective variety, or equivalently has a Kaehler metric invariant under a maximal compact subgroup of G. Then I'll show just how the bounded symmetric domains describe cycle spaces for open G_R orbits on G/Q. These cycle spaces include the complex bounded symmetric domains. In finite dimensions they are tightly related to moduli spaces for compact Kaehler manifolds and to representations of semisimple Lie groups; in infinite dimensions there are more problems than answers. Finally, time permitting, I'll indicate how some of this goes over to real and to quaternionic bounded symmetric domains.
Ocean dynamics of Gulf St Vincent: a numerical study
12:10 Mon 2 Nov, 2015 :: Benham Labs G10 :: Henry Ellis :: University of Adelaide

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The aim of this research is to determine the physical dynamics of ocean circulation within Gulf St. Vincent, South Australia, and the exchange of momentum, nutrients, heat, salt and other water properties between the gulf and shelf via Investigator Strait and Backstairs Passage. The project aims to achieve this through the creation of high-resolution numerical models, combined with new and historical observations from a moored instrument package, satellite data, and shipboard surveys. The quasi-realistic high-resolution models are forced using boundary conditions generated by existing larger scale ROMS models, which in turn are forced at the boundary by a global model, creating a global to regional to local model network. Climatological forcing is done using European Centres for Medium range Weather Forecasting (ECMWF) data sets and is consistent over the regional and local models. A series of conceptual models are used to investigate the relative importance of separate physical processes in addition to fully forced quasi-realistic models. An outline of the research to be undertaken is given: • Connectivity of Gulf St. Vincent with shelf waters including seasonal variation due to wind and thermoclinic patterns; • The role of winter time cooling and formation of eddies in flushing the gulf; • The formation of a temperature front within the gulf during summer time; and • The connectivity and importance of nutrient rich, cool, water upwelling from the Bonney Coast with the gulf via Backstairs Passage during summer time.
T-duality for elliptic curve orientifolds
12:10 Fri 4 Mar, 2016 :: Ingkarni Wardli B17 :: Jonathan Rosenberg :: University of Maryland

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Orientifold string theories are quantum field theories based on the geometry of a space with an involution. T-dualities are certain relationships between such theories that look different on the surface but give rise to the same observable physics. In this talk I will not assume any knowledge of physics but will concentrate on the associated geometry, in the case where the underlying space is a (complex) elliptic curve and the involution is either holomorphic or anti-holomorphic. The results blend algebraic topology and algebraic geometry. This is mostly joint work with Chuck Doran and Stefan Mendez-Diez.
Harmonic Analysis in Rough Contexts
15:10 Fri 13 May, 2016 :: Engineering South S112 :: Dr Pierre Portal :: Australian National University

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In recent years, perspectives on what constitutes the ``natural" framework within which to conduct various forms of mathematical analysis have shifted substantially. The common theme of these shifts can be described as a move towards roughness, i.e. the elimination of smoothness assumptions that had previously been considered fundamental. Examples include partial differential equations on domains with a boundary that is merely Lipschitz continuous, geometric analysis on metric measure spaces that do not have a smooth structure, and stochastic analysis of dynamical systems that have nowhere differentiable trajectories. In this talk, aimed at a general mathematical audience, I describe some of these shifts towards roughness, placing an emphasis on harmonic analysis, and on my own contributions. This includes the development of heat kernel methods in situations where such a kernel is merely a distribution, and applications to deterministic and stochastic partial differential equations.
Some free boundary value problems in mean curvature flow and fully nonlinear curvature flows
12:10 Fri 27 May, 2016 :: Eng & Maths EM205 :: Valentina Wheeler :: University of Wollongong

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In this talk we present an overview of the current research in mean curvature flow and fully nonlinear curvature flows with free boundaries, with particular focus on our own results. Firstly we consider the scenario of a mean curvature flow solution with a ninety-degree angle condition on a fixed hypersurface in Euclidean space, that we call the contact hypersurface. We prove that under restrictions on either the initial hypersurface (such as rotational symmetry) or restrictions on the contact hypersurface the flow exists for all times and converges to a self-similar solution. We also discuss the possibility of a curvature singularity appearing on the free boundary contained in the contact hypersurface. We extend some of these results to the setting of a hypersurface evolving in its normal direction with speed given by a fully nonlinear functional of the principal curvatures.
Multi-scale modeling in biofluids and particle aggregation
15:10 Fri 17 Jun, 2016 :: B17 Ingkarni Wardli :: Dr Sarthok Sircar :: University of Adelaide

In today's seminar I will give 2 examples in mathematical biology which describes the multi-scale organization at 2 levels: the meso/micro level and the continuum/macro level. I will then detail suitable tools in statistical mechanics to link these different scales. The first problem arises in mathematical physiology: swelling-de-swelling mechanism of mucus, an ionic gel. Mucus is packaged inside cells at high concentration (volume fraction) and when released into the extracellular environment, it expands in volume by two orders of magnitude in a matter of seconds. This rapid expansion is due to the rapid exchange of calcium and sodium that changes the cross-linked structure of the mucus polymers, thereby causing it to swell. Modeling this problem involves a two-phase, polymer/solvent mixture theory (in the continuum level description), together with the chemistry of the polymer, its nearest neighbor interaction and its binding with the dissolved ionic species (in the micro-scale description). The problem is posed as a free-boundary problem, with the boundary conditions derived from a combination of variational principle and perturbation analysis. The dynamics of neutral gels and the equilibrium-states of the ionic gels are analyzed. In the second example, we numerically study the adhesion fragmentation dynamics of rigid, round particles clusters subject to a homogeneous shear flow. In the macro level we describe the dynamics of the number density of these cluster. The description in the micro-scale includes (a) binding/unbinding of the bonds attached on the particle surface, (b) bond torsion, (c) surface potential due to ionic medium, and (d) flow hydrodynamics due to shear flow.
Chern-Simons invariants of Seifert manifolds via Loop spaces
14:10 Tue 28 Jun, 2016 :: Ingkarni Wardli B17 :: Ryan Mickler :: Northeastern University

Over the past 30 years the Chern-Simons functional for connections on G-bundles over three-manfolds has lead to a deep understanding of the geometry of three-manfiolds, as well as knot invariants such as the Jones polynomial. Here we study this functional for three-manfolds that are topologically given as the total space of a principal circle bundle over a compact Riemann surface base, which are known as Seifert manifolds. We show that on such manifolds the Chern-Simons functional reduces to a particular gauge-theoretic functional on the 2d base, that describes a gauge theory of connections on an infinite dimensional bundle over this base with structure group given by the level-k affine central extension of the loop group LG. We show that this formulation gives a new understanding of results of Beasley-Witten on the computability of quantum Chern-Simons invariants of these manifolds as well as knot invariants for knots that wrap a single fiber of the circle bundle. A central tool in our analysis is the Caloron correspondence of Murray-Stevenson-Vozzo.
Etale ideas in topological and algebraic dynamical systems
12:10 Fri 5 Aug, 2016 :: Ingkarni Wardli B18 :: Tuyen Truong :: University of Adelaide

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In etale topology, instead of considering open subsets of a space, we consider etale neighbourhoods lying over these open subsets. In this talk, I define an etale analog of dynamical systems: to understand a dynamical system f:(X,\Omega )->(X,\Omega ), we consider other dynamical systems lying over it. I then propose to use this to resolve the following two questions: Question 1: What should be the topological entropy of a dynamical system (f,X,\Omega ) when (X,\Omega ) is not a compact space? Question 2: What is the relation between topological entropy of a rational map or correspondence (over a field of arbitrary characteristic) to the pullback on cohomology groups and algebraic cycles?
Toroidal Soap Bubbles: Constant Mean Curvature Tori in S ^ 3 and R ^3
12:10 Fri 28 Oct, 2016 :: Ingkarni Wardli B18 :: Emma Carberry :: University of Sydney

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Constant mean curvature (CMC) tori in S ^ 3, R ^ 3 or H ^ 3 are in bijective correspondence with spectral curve data, consisting of a hyperelliptic curve, a line bundle on this curve and some additional data, which in particular determines the relevant space form. This point of view is particularly relevant for considering moduli-space questions, such as the prevalence of tori amongst CMC planes and whether tori can be deformed. I will address these questions for the spherical and Euclidean cases, using Whitham deformations.
Segregation of particles in incompressible flows due to streamline topology and particle-boundary interaction
15:10 Fri 2 Dec, 2016 :: Ingkarni Wardli 5.57 :: Professor Hendrik C. Kuhlmann :: Institute of Fluid Mechanics and Heat Transfer, TU Wien, Vienna, Austria

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The incompressible flow in a number of classical benchmark problems (e.g. lid-driven cavity, liquid bridge) undergoes an instability from a two-dimensional steady to a periodic three-dimensional flow, which is steady or in form of a traveling wave, if the Reynolds number is increased. In the supercritical regime chaotic as well as regular (quasi-periodic) streamlines can coexist for a range of Reynolds numbers. The spatial structures of the regular regions in three-dimensional Navier-Stokes flows has received relatively little attention, partly because of the high numerical effort required for resolving these structures. Particles whose density does not differ much from that of the liquid approximately follow the chaotic or regular streamlines in the bulk. Near the boundaries, however, their trajectories strongly deviate from the streamlines, in particular if the boundary (wall or free surface) is moving tangentially. As a result of this particle-boundary interaction particles can rapidly segregate and be attracted to periodic or quasi-periodic orbits, yielding particle accumulation structures (PAS). The mechanism of PAS will be explained and results from experiments and numerical modelling will be presented to demonstrate the generic character of the phenomenon.
Diffeomorphisms of discs, harmonic spinors and positive scalar curvature
11:10 Fri 17 Mar, 2017 :: Engineering Nth N218 :: Diarmuid Crowley :: University of Melbourne

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Let Diff(D^k) be the space of diffeomorphisms of the k-disc fixing the boundary point wise. In this talk I will show for k > 5, that the homotopy groups \pi_*Diff(D^k) have non-zero 8-periodic 2-torsion detected in real K-theory. I will then discuss applications for spin manifolds M of dimension 6 or greater: 1) Our results input to arguments of Hitchin which now show that M admits a metric with a harmonic spinor. 2) If non-empty, space of positive scalar curvature metrics on M has non-zero 8-periodic 2-torsion in its homotopy groups which is detected in real K-theory. This is part of joint work with Thomas Schick and Wolfgang Steimle.
Minimal surfaces and complex analysis
12:10 Fri 24 Mar, 2017 :: Napier 209 :: Antonio Alarcon :: University of Granada

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A surface in the Euclidean space R^3 is said to be minimal if it is locally area-minimizing, meaning that every point in the surface admits a compact neighborhood with the least area among all the surfaces with the same boundary. Although the origin of minimal surfaces is in physics, since they can be realized locally as soap films, this family of surfaces lies in the intersection of many fields of mathematics. In particular, complex analysis in one and several variables plays a fundamental role in the theory. In this lecture we will discuss the influence of complex analysis in the study of minimal surfaces.
Poisson-Lie T-duality and integrability
11:10 Thu 13 Apr, 2017 :: Engineering & Math EM213 :: Ctirad Klimcik :: Aix-Marseille University, Marseille

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The Poisson-Lie T-duality relates sigma-models with target spaces symmetric with respect to mutually dual Poisson-Lie groups. In the special case if the Poisson-Lie symmetry reduces to the standard non-Abelian symmetry one of the corresponding mutually dual sigma-models is the standard principal chiral model which is known to enjoy the property of integrability. A natural question whether this non-Abelian integrability can be lifted to integrability of sigma model dualizable with respect to the general Poisson-Lie symmetry has been answered in the affirmative by myself in 2008. The corresponding Poisson-Lie symmetric and integrable model is a one-parameter deformation of the principal chiral model and features a remarkable explicit appearance of the standard Yang-Baxter operator in the target space geometry. Several distinct integrable deformations of the Yang-Baxter sigma model have been then subsequently uncovered which turn out to be related by the Poisson-Lie T-duality to the so called lambda-deformed sigma models. My talk gives a review of these developments some of which found applications in string theory in the framework of the AdS/CFT correspondence.
Geometric limits of knot complements
12:10 Fri 28 Apr, 2017 :: Napier 209 :: Jessica Purcell :: Monash University

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The complement of a knot often admits a hyperbolic metric: a metric with constant curvature -1. In this talk, we will investigate sequences of hyperbolic knots, and the possible spaces they converge to as a geometric limit. In particular, we show that there exist hyperbolic knots in the 3-sphere such that the set of points of large injectivity radius in the complement take up the bulk of the volume. This is joint work with Autumn Kent.
Exact coherent structures in high speed flows
15:10 Fri 28 Jul, 2017 :: Ingkarni Wardli B17 :: Prof Philip Hall :: Monash University

In recent years, there has been much interest in the relevance of nonlinear solutions of the Navier-Stokes equations to fully turbulent flows. The solutions must be calculated numerically at moderate Reynolds numbers but in the limit of high Reynolds numbers asymptotic methods can be used to greatly simplify the computational task and to uncover the key physical processes sustaining the nonlinear states. In particular, in confined flows exact coherent structures defining the boundary between the laminar and turbulent attractors can be constructed. In addition, structures which capture the essential physical properties of fully turbulent flows can be found. The extension of the ideas to boundary layer flows and current work attempting to explain the law of the wall will be discussed.
Time-reversal symmetric topology from physics
12:10 Fri 25 Aug, 2017 :: Engineering Sth S111 :: Guo Chuan Thiang :: University of Adelaide

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Time-reversal plays a crucial role in experimentally discovered topological insulators (2008) and semimetals (2015). This is mathematically interesting because one is forced to use "Quaternionic" characteristic classes and differential topology --- a previously ill-motivated generalisation. Guided by physical intuition, an equivariant Poincare-Lefschetz duality, Euler structures, and a new type of monopole with torsion charge, will be introduced.
End-periodic K-homology and spin bordism
12:10 Fri 20 Oct, 2017 :: Engineering Sth S111 :: Michael Hallam :: University of Adelaide

This talk introduces new "end-periodic" variants of geometric K-homology and spin bordism theories that are tailored to a recent index theorem for even-dimensional manifolds with periodic ends. This index theorem, due to Mrowka, Ruberman and Saveliev, is a generalisation of the Atiyah-Patodi-Singer index theorem for manifolds with odd-dimensional boundary. As in the APS index theorem, there is an (end-periodic) eta invariant that appears as a correction term for the periodic end. Invariance properties of the standard relative eta invariants are elegantly expressed using K-homology and spin bordism, and this continues to hold in the end-periodic case. In fact, there are natural isomorphisms between the standard K-homology/bordism theories and their end-periodic versions, and moreover these isomorphisms preserve relative eta invariants. The study is motivated by results on positive scalar curvature, namely obstructions and distinct path components of the moduli space of PSC metrics. Our isomorphisms provide a systematic method for transferring certain results on PSC from the odd-dimensional case to the even-dimensional case. This work is joint with Mathai Varghese.
Springer correspondence for symmetric spaces
12:10 Fri 17 Nov, 2017 :: Engineering Sth S111 :: Ting Xue :: University of Melbourne

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The Springer theory for reductive algebraic groups plays an important role in representation theory. It relates nilpotent orbits in the Lie algebra to irreducible representations of the Weyl group. We develop a Springer theory in the case of symmetric spaces using Fourier transform, which relates nilpotent orbits in this setting to irreducible representations of Hecke algebras of various Coxeter groups with specified parameters. This in turn gives rise to character sheaves on symmetric spaces, which we describe explicitly in the case of classical symmetric spaces. A key ingredient in the construction is the nearby cycle sheaves associated to the adjoint quotient map. The talk is based on joint work with Kari Vilonen and partly based on joint work with Misha Grinberg and Kari Vilonen.
A Hecke module structure on the KK-theory of arithmetic groups
13:10 Fri 2 Mar, 2018 :: Barr Smith South Polygon Lecture theatre :: Bram Mesland :: University of Bonn

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Let $G$ be a locally compact group, $\Gamma$ a discrete subgroup and $C_{G}(\Gamma)$ the commensurator of $\Gamma$ in $G$. The cohomology of $\Gamma$ is a module over the Shimura Hecke ring of the pair $(\Gamma,C_G(\Gamma))$. This construction recovers the action of the Hecke operators on modular forms for $SL(2,\mathbb{Z})$ as a particular case. In this talk I will discuss how the Shimura Hecke ring of a pair $(\Gamma, C_{G}(\Gamma))$ maps into the $KK$-ring associated to an arbitrary $\Gamma$-C*-algebra. From this we obtain a variety of $K$-theoretic Hecke modules. In the case of manifolds the Chern character provides a Hecke equivariant transformation into cohomology, which is an isomorphism in low dimensions. We discuss Hecke equivariant exact sequences arising from possibly noncommutative compactifications of $\Gamma$-spaces. Examples include the Borel-Serre and geodesic compactifications of the universal cover of an arithmetic manifold, and the totally disconnected boundary of the Bruhat-Tits tree of $SL(2,\mathbb{Z})$. This is joint work with M.H. Sengun (Sheffield).
Stability Through a Geometric Lens
15:10 Fri 18 May, 2018 :: Horace Lamb 1022 :: Dr Robby Marangell :: University of Sydney

Focussing on the example of the Fisher/KPP equation, I will show how geometric information can be used to establish (in)stability results in some partial differential equations (PDEs). Viewing standing and travelling waves as fixed points of a flow in an infinite dimensional system, leads to a reduction of the linearised stability problem to a boundary value problem in a linear non-autonomous ordinary differential equation (ODE). Next, by exploiting the linearity of the system, one can use geometric ideas to reveal additional structure underlying the determination of stability. I will show how the Riccati equation can be used to produce a reasonably computable detector of eigenvalues and how such a detector is related to another, well-known eigenvalue detector, the Evans function. If there is time, I will try to expand on how to generalise these ideas to systems of PDEs.
The topology and geometry of spaces of Yang-Mills-Higgs flow lines
11:10 Fri 27 Jul, 2018 :: Barr Smith South Polygon Lecture theatre :: Graeme Wilkin :: National University of Singapore

Given a smooth complex vector bundle over a compact Riemann surface, one can define the space of Higgs bundles and an energy functional on this space: the Yang-Mills-Higgs functional. The gradient flow of this functional resembles a nonlinear heat equation, and the limit of the flow detects information about the algebraic structure of the initial Higgs bundle (e.g. whether or not it is semistable). In this talk I will explain my work to classify ancient solutions of the Yang-Mills-Higgs flow in terms of their algebraic structure, which leads to an algebro-geometric classification of Yang-Mills-Higgs flow lines. Critical points connected by flow lines can then be interpreted in terms of the Hecke correspondence, which appears in Witten’s recent work on Geometric Langlands. This classification also gives a geometric description of spaces of unbroken flow lines in terms of secant varieties of the underlying Riemann surface, and in the remaining time I will describe work in progress to relate the (analytic) Morse compactification of these spaces by broken flow lines to an algebro-geometric compactification by iterated blowups of secant varieties.
Discrete fluxes and duality in gauge theory
11:10 Fri 24 Aug, 2018 :: Barr Smith South Polygon Lecture theatre :: Siye Wu :: National Tsinghua University

We explore the notions of discrete electric and magnetic fluxes introduced by 't Hooft in the late 1970s. After explaining their physics origin, we consider the description in mathematical terminology. We finally study their role in duality.
An Introduction to Ricci Flow
11:10 Fri 19 Oct, 2018 :: Barr Smith South Polygon Lecture theatre :: Miles Simon :: University of Magdeburg

In these three talks we give an introduction to Ricci flow and present some applications thereof. After introducing the Ricci flow we present some theorems and arguments from the theory of linear and non-linear parabolic equations. We explain why this theory guarantees that there is always a solution to the Ricci flow for a short time for any given smooth initial metric on a compact manifold without boundary. We calculate evolution equations for certain geometric quantities, and present some examples of maximum principle type arguments. In the last lecture we present some geometric results which are derived with the help of the Ricci flow.
Local Ricci flow and limits of non-collapsed regions whose Ricci curvature is bounded from below
11:10 Fri 26 Oct, 2018 :: Barr Smith South Polygon Lecture theatre :: Miles Simon :: University of Magdeburg

We use a local Ricci flow to obtain a bi-Holder correspondence between non-collapsed (possibly non-complete) 3-manifolds with Ricci curvature bounded from below and Gromov-Hausdorff limits of sequences thereof. This is joint work with Peter Topping and the proofs build on results and ideas from recent papers of Hochard and Topping+Simon.

News matching "T-duality and bulk-boundary correspondence"

Australian Research Council Discovery Project Successes

Congratulations to the following members of the School for their success in the ARC Discovery Grants which were announced recently.

  • A/Prof M Roughan; Prof H Shen $315K Network Management in a World of Secrets
  • Prof AJ Roberts; Dr D Strunin $315K Effective and accurate model dynamics, deterministic and stochastic, across multiple space and time scales
  • A/Prof J Denier; Prof AP Bassom $180K A novel approach to controlling boundary-layer separation
Posted Wed 17 Sep 08.
ARC Grant successes
The School of Mathematical Sciences has again had outstanding success in the ARC Discovery and Linkage Projects schemes. Congratulations to the following staff for their success in the Discovery Project scheme: Prof Nigel Bean, Dr Josh Ross, Prof Phil Pollett, Prof Peter Taylor, New methods for improving active adaptive management in biological systems, $255,000 over 3 years; Dr Josh Ross, New methods for integrating population structure and stochasticity into models of disease dynamics, $248,000 over three years; A/Prof Matt Roughan, Dr Walter Willinger, Internet traffic-matrix synthesis, $290,000 over three years; Prof Patricia Solomon, A/Prof John Moran, Statistical methods for the analysis of critical care data, with application to the Australian and New Zealand Intensive Care Database, $310,000 over 3 years; Prof Mathai Varghese, Prof Peter Bouwknegt, Supersymmetric quantum field theory, topology and duality, $375,000 over 3 years; Prof Peter Taylor, Prof Nigel Bean, Dr Sophie Hautphenne, Dr Mark Fackrell, Dr Malgorzata O'Reilly, Prof Guy Latouche, Advanced matrix-analytic methods with applications, $600,000 over 3 years. Congratulations to the following staff for their success in the Linkage Project scheme: Prof Simon Beecham, Prof Lee White, A/Prof John Boland, Prof Phil Howlett, Dr Yvonne Stokes, Mr John Wells, Paving the way: an experimental approach to the mathematical modelling and design of permeable pavements, $370,000 over 3 years; Dr Amie Albrecht, Prof Phil Howlett, Dr Andrew Metcalfe, Dr Peter Pudney, Prof Roderick Smith, Saving energy on trains - demonstration, evaluation, integration, $540,000 over 3 years Posted Fri 29 Oct 10.

Publications matching "T-duality and bulk-boundary correspondence"

Publications
Non-commutative correspondences, duality and D-branes in bivariant K-theory
Brodzki, J; Varghese, Mathai; Rosenberg, J; Szabo, R, Advances in Theoretical and Mathematical Physics 13 (497–552) 2009
T-duality as a duality of loop group bundles
Bouwknegt, Pier; Varghese, Mathai, Journal of Physics A: Mathematical and Theoretical (Print Edition) 42 (162001-1–162001-8) 2009
Boundary-Layer Separation and Vortex generations in a Suddenly Blocked Pipe
Denier, James; Jewell, Nathaniel, XXII ICTAM 2008, Adelaide 25/08/08
Boundary-layer breakdown in a rotating, fluid-filled torus
Clarke, Richard; Hewitt, R; del Pino, C; Denier, James; Mullin, T, XXII International Congress of Theoretical and Applied Mechanics, Adelaide 24/08/08
On penalty approaches for navier-slip and other boundary conditions in vicous flow
Stokes, Yvonne; Carey, G, XXII International Congress of Theoretical and Applied Mechanics, Adelaide 24/08/08
Spation-temporal stability of mixed forced-free convection boundary layers
Mureithi, E; Denier, James, XXII International Congress of Theoretical and Applied Mechanics, Adelaide 24/08/08
D-branes, KK-theory and duality on noncommutative spaces
Brodzki, J; Varghese, Mathai; Rosenberg, J; Szabo, R, Journal of Physics: Conference Series (Print Edition) 103 (1–13) 2008
D-branes, RR-fields and duality on noncommutative manifolds
Brodzki, J; Varghese, Mathai; Rosenberg, J; Szabo, R, Communications in Mathematical Physics 277 (643–706) 2008
Nonlinear transient heat conduction problems for a class of inhomogeneous anisotropic materials by BEM
Azis, Mohammad; Clements, David, Engineering Analysis With Boundary Elements 32 (1054–1060) 2008
A hypersingular boundary integral equation for a class of problems conderning infiltration from periodic channels
Clements, David; Lobo, Maria; Widana, N, Electronic Journal of Boundary Elements 5 (1–16) 2007
T-Duality in type II string theory via noncommutative geometry and beyond
Varghese, Mathai, Progress of Theoretical Physics Supplement 171 (237–257) 2007
General tooth boundary conditions for equation free modeling
Roberts, Anthony John; Kevrekidis, I, Siam Journal on Scientific Computing 29 (1495–1510) 2007
The solution of a free boundary problem related to environmental management systems
Elliott, Robert; Filinkov, Alexei, Stochastic Analysis and Applications 25 (1189–1202) 2007
On mysteriously missing T-duals, H-flux and the T-duality Group
Varghese, Mathai; Rosenberg, J, chapter in Differential geometry and physics (World Scientific Publishing) 350–358, 2006
Duality symmetry and the form fields of M-theory
Sati, Hicham, The Journal of High Energy Physics (Print Edition) 6 (0–10) 2006
Flux compactifications on projective spaces and the S-duality puzzle
Bouwknegt, Pier; Evslin, J; Jurco, B; Varghese, Mathai; Sati, Hicham, Advances in Theoretical and Mathematical Physics 10 (345–394) 2006
Nonassociative Tori and Applications to T-Duality
Bouwknegt, Pier; Hannabuss, K; Varghese, Mathai, Communications in Mathematical Physics 264 (41–69) 2006
On the indentation of an inhomogeneous anisotropic elastic material by multiple straight rigid punches
Clements, David; Ang, W, Engineering Analysis With Boundary Elements 30 (284–291) 2006
T-duality for torus bundles with H-fluxes via noncommutative topology, II: the high-dimensional case and the T-duality group
Varghese, Mathai; Rosenberg, J, Advances in Theoretical and Mathematical Physics 10 (123–158) 2006
The development (and suppression) of very short-scale instabilities in buoyant boundary layers
Denier, James; Duck, P; Li, J, 21st International Congress of Theoretical and Applied Mechanics, Warsaw, Poland 12/08/04
Boundary element methods for infiltration from irrigation channels
Lobo, Maria; Clements, David, The International Conference on Boundary Element Techniques VI, Montreal, Canada 27/07/05
On the growth (and suppression) of very short-scale disturbances in mixed forced-free convection boundary layers
Denier, James; Duck, P; Li, J-M, Journal of Fluid Mechanics 526 (147–170) 2005
Ramaswami's duality and probabilistic algorithms for determining the rate matrix for a structured GI/M/1 Markov chain
Hunt, Emma, The ANZIAM Journal 46 (485–493) 2005
Self-similar "stagnation point" boundary layer flows with suction or injection
King, J; Cox, Stephen, Studies in Applied Mathematics 115 (73–107) 2005
T-duality for principal torus bundles and dimensionally reduced Gysin sequences
Bouwknegt, Pier; Hannabuss, K; Varghese, Mathai, Advances in Theoretical and Mathematical Physics 9 (1–25) 2005
T-duality for torus bundles with H-fluxes via noncommutative topology
Varghese, Mathai; Rosenberg, J, Communications in Mathematical Physics 253 (705–721) 2005
Type IIB string theory, S-duality, and generalized cohomology
Kriz, I; Sati, Hicham, Nuclear Physics B 715 (639–664) 2005
Optimal nose shaping for delayed boundary-layer separation in laminar plane-symmetric and axisymmetric flow
Mattner, Trent; Tuck, Ernest; Denier, James, ANZIAM Applied Mathematics Conference (41st: 2005: Hawke's Bay, N.Z.), Napier, New Zealand 31/01/05
A boundary integral formulation for the indentation of an anisotropic bi-layered elastic slab
Ang, W; Sridhar, I; Clements, David, ICCM 2004, Singapore 15/12/04
Optimal nose shaping for delayed boundary-layer separation in laminar plane-symmetric and axisymmetric flow
Mattner, Trent; Tuck, Ernest; Denier, James, 15th Australasian Fluid Mechanics Conference 2004, Sydney, Australia 13/12/04
Asymptotic matching constraints for a boundary-layer flow of a power-law fluid
Denier, James; Hewitt, R, Journal of Fluid Mechanics 518 (261–279) 2004
On the boundary-layer equations for power-law fluids
Denier, James; Dabrowski, Paul, Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 460 (3143–3158) 2004
T-duality for principal torus bundles
Bouwknegt, Pier; Hannabuss, K; Varghese, Mathai, The Journal of High Energy Physics (Online Editions) 3 (WWW 1–WWW 10) 2004
T-duality: Topology change from H-flux
Bouwknegt, Pier; Evslin, J; Varghese, Mathai, Communications in Mathematical Physics 249 (383–415) 2004
Diffusive mass transfer and its effect upon boundary-layer flows
Halatchev, Iordan; Denier, James, Computational Fluid Dynamics 2002, Sydney, Australia 15/07/03
A boundary element method for steady infiltration from periodic channels
Azis, Mohammad; Clements, David; Lobo, Maria, The ANZIAM Journal 44 (C61–C68) 2003
A boundary element method for the numerical solution of a class of elliptic boundary value problems for anisotropic inhomogeneous media
Azis, Mohammad; Clements, David; Budhi, W, The ANZIAM Journal 44 (C79–C95) 2003
A dual-reciprocity boundary element method for a class of elliptic boundary value problems for non-homogenous anisotropic media
Ang, W; Clements, David; Vahdati, N, Engineering Analysis With Boundary Elements 27 (49–55) 2003
The nonparallel evolution of nonlinear short waves in buoyant boundary layers
Denier, James; Bassom, A, Studies in Applied Mathematics 110 (139–156) 2003
The stability of boundary-layer flows under conditions of intense interfacial mass transfer: the effect of interfacial coupling
Halatchev, Iordan; Denier, James, International Journal of Heat and Mass Transfer 46 (3881–3895) 2003
Derive boundary conditions for holistic discretisations of Burgers' equation
Roberts, Anthony John, The ANZIAM Journal 44 (C664–C686) 2003
The stability of boundary layers on curved heated plates
Stott, Jillian; Denier, James, The ANZIAM Journal 43 (333–358) 2002
Blowing-induced boundary-layer separation of shear-thinning fluids
Dabrowski, Paul; Denier, James, The Fourteenth Australasian Fluid Mechanics Conference, Adelaide, Australia 09/12/01
The effect of diffusive mass transfer on boundary-layer stability
Halatchev, Iordan; Denier, James, The Fourteenth Australasian Fluid Mechanics Conference, Adelaide, Australia 09/12/01
A boundary element method for anisotropic inhomogeneous elasticity
Azis, Mohammad; Clements, David, International Journal of Solids and Structures 38 (5747–5763) 2001
Three-dimensional inviscid waves in buoyant boundary layer flows
Denier, James; Stott, Jillian; Bassom, A, Fluid Dynamics Research 28 (89–109) 2001
Topological duality in humanoid robot dynamics
Ivancevic, V; Pearce, Charles, The ANZIAM Journal 43 (183–194) 2001
Hamiltonian quantization of fermions on an odd dimensional manifold with boundary
Carey, Alan; Mickelsson, J, chapter in Proceedings of the International Symposium Quantum Theory and Symmetries (World Scientific Publishing) 46–51, 2000
A gerbe obstruction to quantization of fermions on odd-dimensional manifolds with boundary
Carey, Alan; Mickelsson, J, Letters in Mathematical Physics 51 (145–160) 2000
A note on a boundary element method for the numerical solution of boundary value problems in isotropic inhomogeneous elasticity
Clements, David; Azis, Mohammad, Journal of the Chinese Institute of Engineers 23 (261–268) 2000

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