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Seminars
Applied mathematics/general seminars
Speaker: Dr. Joel Moitsheki, School of Computational and Applied Mathematics, University of the Witwatersrand Johannesburg, South Africa
Title: Some exact solutions of the steady state fin problem with a power law temperature-dependent thermal conductivity
Day: 2 Oct 2009
Location: Rm 15.113
Time: 3.30 pm
Abstract: This study investigates the exact solutions of nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient. Both the conduction and the heat transfer terms are given by the same power law in one case and the distinct power law in the other. Classical Lie symmetry techniques are employed to construct the exact solutions which satisfy the realistic boundary conditions. The effects of the physical applicable parameters such as thermo-geometric fin parameter and the fin efficiency are analyzed
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Speaker: Dr Ha Hoang, Nanyang Technological University, Singapore
Title: Analytical and Numerical Effective Medium Theory for Heterogeneous Media
Day: 1 Oct 2009
Location: Rm 15.113
Time: 11.30 am
Abstract: Heterogeneous media are encountered in many real world situations: natural composite materials (earth, wood, bone, ...), man made materials (carbon fibre reinforced composites), subsurface flow, etc. ... Due to the rapid variation of the media's physical properties, conventional analytical and numerical approaches are not capable of solving the partial differential equations that govern the physical processes in these media. The effective medium and homogenization theories have play crucial roles in treating these problems. This seminar will review the basic concepts of these theories together with an introduction to the speaker's current research.
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Speaker: Prof. Jim Greenberg, Carnegie Mellon University, Pittsburgh
Title: A new Lagrangian shallow water circulation model
Day: 18 Sept 2009
Location: Rm 15.113
Time: 2.30 pm
Abstract: [not supplied]
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Speaker: Dr. Susanne Griebsch from UTS
Title: A Stochastic Approach to the Valuation of Barrier Options in Heston's Stochastic Volatility Model
Day: 7 Sept 2009
Location: Rm 15.113
Time: 11.30 am
Abstract: In this study we derive (semi-)analytical solutions for the value of continuous barrier options in the presence of stochastic volatility. First we focus on the case where the underlying asset price evolves according to Heston's stochastic volatility model and restrict the interest rate spread as well as the correlation to be equal to zero. In the second part we show how approximation formulas for barrier options in the Heston model with an interest rate spread unequal to zero and specific correlation structures can be obtained. We compare our approach with other numerical pricing techniques.
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Speaker: Professor Jeong-Hoon KIM, Yonsei University, Korea
Title: Pricing and Hedging for a Stochastic Elasticity of Variance Model
Day: 20 August 2009
Location: Rm 15.111
Time: 11.30 am
Abstract: A new generalized risky asset pricing model is proposed in such a way that constant elasticity of the CEV model is extended to stochastic elasticity. Option pricing and hedging theory is developed based upon the proposed model. We assume that volatility's elasticity is given by a function of the Ornstein-Uhlenbeck process with fast mean reversion. We obtain a Kolmogorov PDE with a nonlocal diffusion coefficient satisfied by the option price. Using some asymptotic analysis we derive the pricing PDEs for the leading order and the first correction terms. The well-known Black-Scholes and CEV models are identified as special cases of our model in context of pricing theory. Also, a corrected hedging strategy is developed for our model.
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Speaker: Associate Professor Geoff Mercer, National Centre for Epidemiology and Population Health, Australian National University
Title: Maritime surveillance route planning and dengue fever modeling
Day: 21 May 2009
Location: Rm 67.104
Time: 3.30 pm
Abstract: Airborne maritime surveillance operations are part of Australia's national security. The determination of optimal routes for such surveillance operations is a complex variation on the classical Travelling Salesman Problem from Operations Research. Of particular interest is how the route varies to take account of moving targets (ships), and variations in both the detection and classification ranges. Constraints on the route such as fuel usage, total flying time and crew considerations are also investigated. Computational runtime for the algorithms is kept to a minimum enabling these methods to be used in real time onboard an aircraft. Substantial improvements over the current practices have been found.
Dengue fever is a serious and increasing issue in northern Australia with the 2008/09 season having a particularly severe outbreak. Recently it has been demonstrated that dengue fever can be transmitted in blood transfusions which has potentially dramatic consequences to Australia's blood supply. Dr Mercer is in the process of developing various dengue spread models that can be used to evaluate the risk to the blood supply and assess intervention measures such as mosquito eradication programs. Also of interest is how climate change will affect the range of the mosquito vector and hence the distribution of dengue in Australia.
Dr Mercer is a Fellow in Infectious Disease Modelling at the National Centre for Epidemiology and Population Health, ANU and a Visiting Fellow, Applied and Industrial Mathematics Research Group, School of Physical, Environmental and Mathematical Sciences, UNSW at ADFA.
Dr Mercer is a guest of the SMART Infrastructure Facility.
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Speaker: Dr Elizabeth Winstanley, School of Mathematics and Statistics, The University of Sheffield, UK
Title: Furry black holes
Day: 12 March 2009
Location: Rm 15.113
Time: 11.30-12.30
Abstract: Black hole solutions of the Einstein equations of general relativity have been studied for over 90 years. Traditionally, the simplest types of black hole solutions have been studied, but over the past 20 years there has been an explosion of interest in more complicated black holes which arise when the Einstein equations are coupled to different types of matter field. These more complicated black holes are known as "hairy" black holes. In this talk we describe some black hole solutions of the Einstein equation with a particular type of matter (a Yang-Mills gauge field), in which the black hole solutions can have unlimited amounts of "hair", which we call "furry" black holes.
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Speaker: Andrew Holder, UoW
Title: Smooth approximation of the maximum function
Day: 23 February 2009
Location: Rm 15.113
Time: 2.30 pm
Abstract: A report on Andrew's work in his summer vacation scholarship.
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Speaker: Dr. Shijun LIAO, from Shanghai Jiao Tong University
Title: Beyond Perturbation - Homotopy Analysis Methods and Its Applications for Nonlinear Problems
Day: Wednesday 6 August 2008
Location: Rm 15.113
Time: 11.30-12.30 pm
Abstract: The basic ideas of a general analytic method for highly nonlinear problems, namely the homotopy analysis method (HAM), are described briefly. This method is based on homotopy in topology. Different from widely applied perturbation techniques, this method does not depend upon any small/large physical parameters, and therefore can be used to solve nonlinear problems with strong non-linearity. As a result, most of limitations of perturbation methods are overcome by this method. Besides, it logically contains other non-perturbation techniques, such as Lyapunov’s artificial small parameter method, Adomian’s decomposition method, 
-expansion method and so on, and thus is rather general. Some examples in mechanics, physics, biology and finance are given to show the validity, generality and flexibility of this new method for nonlinear problems in science, engineering and finance. A few new solutions of well-known nonlinear problems are reported, which are difficult to find even by means of numerical techniques. Some new concepts are provided. Especially, we show that the HAM provides us with much larger freedom and flexibility to solve nonlinear problems: for example, a 2nd-order nonlinear PDE can be replaced by an infinite number of 4th-order linear ODEs, and it is much easier to get accurate result.
Dr. Shijun LIAO got his Ph.D degree in 1992, Shanghai Jiao Tong University. Then, he works in School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, as lecturer (1992), associate professor (1993), professor (1996) and Chung Kong chair professor (2001). He studied three years in Germany (1989-1992), visited University of Hong Kong from 1995 to 1996, and University of Hawaii from 1999 to 2000. Dr. Liao published one book “Beyond Perturbation: Introduction to the homotopy analysis method” via Chapman & Hall/CRC, USA, and about 70 international journal papers in mechanics and applied mathematics. Dr. Liao is associate editor of Differential Equation and Nonlinear Mechanics.
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Speaker: Dr Shaun Hendy from Industrial Research Ltd, New Zealand
Title: Modelling Nanofluidics
Day: Wednesday 7 May 2008
Location: Rm 15.113
Time: 3.30-4.30 pm
Abstract: At the nanoscale, interfacial effects such as slip and surface tension can dominate the bulk behaviours of liquids, presenting new challenges and opportunities for nanotechnologists. In this talk I will use both mathematical modelling and molecular dynamics to look at several problems in nanofluidics. We consider flows of simple liquids over chemically heterogeneous surfaces and derive expressions for effective slip lengths in certain limits. These results are used to reconcile apparent inconsistencies in experimental measurements of slip that appear in the literature. We consider the uptake of non-wetting liquid droplets by carbon nanotubes and find a generalisation of the Lucas-Washburn law for the capillary rise in the nanotube. We argue that results have implications for the growth of carbon nanotubes by metal catalyst particles. Finally, we analyse the flow of a small droplet on a surface with switchable wettability, and show that it is possible to beat the scaling laws that occur in pressure driven flows in microfluidics.
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Speaker: Dr Shaun Hendy from Industrial Research Ltd, New Zealand
Title: Modelling Nanoparticles
Day: Tuesday 6 May 2008
Location: Rm 15.113
Time: 10.30-11.30 am
Abstract: Metal nanoparticles are one of the key building blocks of nanotechnology. They can be deposited on surfaces to fabricate nanowires, and play an important role as catalysts for the growth of carbon nanotubes. In this talk we use mathematical modelling and atomistic simulations to study the properties of metal nanoparticles. In the first part of the talk I discuss the melting of metal nanoparticles, examining the role of the excess surface energy and the interfacial thickness of the solid-liquid interface. In the second part of the talk, I will discuss the self-assembly of vacuum-deposited nanoparticles which involves a variety of complex physical processes including the mechanics of particle reflection and adhesion so a substrate, and particle-particle coalescence.
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Speaker: Dr. Joachim Mai, from ac3
Title: ac3 supercomputing
Day: Thursday, 20 March 2008
Location: Rm 15.206
Time: 12.30-1.30 pm
Abstract: [not available] The talk will be suitable for new and existing users of the ac3 supercomputing facility.
Speaker: Ed Heffern (U.S. Bureau of Land Management in Cheyenne, Wyoming, USA)
Title: Modern and Ancient Coal Fires in the Powder River Basin, Wyoming and Montana
Day: Tuesday, 12 March 2008
Location: Rm 15.113
Time: 12.00 noon
Abstract: The Powder River Basin (PRB) of northeast Wyoming and southeast Montana produces over a third of the coal mined today in the United States. Hundreds of coal fires, mostly small, burn today in the PRB. Some consume coal in abandoned underground mines or burn in highwalls and spoil piles at active surface mines. But they are only part of the picture. Natural coal fires caused by lightning strikes, range and forest fires, and spontaneous combustion have left a record of clinker on hilltops and ridges throughout the landscape. The reddish, brick- to lava-like clinker rock formed when fires in coal outcrops burned back into hillsides and baked and melted the overlying sandstone and shale. Clinker outcrops cover 1600 square miles (4100 square kilometers) of the basin and represent natural burning of tens of billions of tons of coal. Isotopic ages of zircon grains in baked sandstones reveal that coal has burned to form clinker throughout the past few million years.