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Applied Mathematics Seminars

For Further Information, please contact :

Dr. Sergey Suslov

David Richards

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Previous Seminar Listing

Seminar 1: February 16, 2009

Title:
Using CAS to Enhance Tertiary Students' Learning in Mathematics
Speaker:
Dr Robyn Pierce, University of Melbourne
Abstract:

The use of mathematical analysis software, such as computer algebra systems, offers pedagogical opportunities at the level of the tasks set, classroom expectations and interactions and the way a mathematical subject is approached.

In this seminar I will share both findings from international reports and my own research on teaching with CAS and my experience (until 2006) of using CAS in teaching first year undergraduate mathematics students at the University of Ballarat. At the University of Ballarat, Computer Algebra Systems (CAS) has been used since 1990 in the teaching of first year undergraduate mathematics.

Initially CAS was used chiefly to support students' algebra skills as they solved problems which did not have quick and neat solutions and to offer students access to graphical as well as algebraic solutions. In many ways students saw learning to use CAS as an additional, not integral, part of learning mathematics. From 1996 CAS was used to support students' learning of mathematics as well as their doing of mathematics. The results of our research clearly indicate that the use of CAS for learning mathematics is not trivial for either staff or students. If students are to come to use CAS effectively then they must be: assisted to overcome technological hurdles; convinced the use of CAS has institutional value; and guided into both pedagogical and functional use of the software.

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Seminar 2: March 6, 2009

Title:
Impulsively generated drops
Speaker:
Professor William R.C. Phillips, SUT
Abstract:

This talk is concerned with the evolution of an unbounded inviscid fluid-fluidinterface 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.

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Seminar 3: March 13, 2009

Title:
Minimal realizations of transfer functions in connection with the problem of designing superoptimal robust feedback controller
Speaker:
Prof. Victor V. Peller (Michigan State University, USA)
Abstract:

I am going to discuss the problem of robust stabilization. In other words, given a linear system, we are looking for a feedback controller that stabilizes not only the system itself, but also all systems that are sufficiently close to it. Moreover, we are interested in superoptimal robust stabilization. This means that we optimise robustness with respect not only to the worst direction of uncertainty (in the space of transfer functions), but also to other directions. If the initial (multiple-input-multiple-output) system admits a finite-dimensional realization, the superoptimal robust controller also admits a finite-dimensional realization. In a recent joint paper with Vasyunin we have solved a problem that was open for over 15 years.

The problem is to estimate the dimension of the space of minimal realization.

It is very important in control theory.

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Seminar 4: March 27, 2009

Title:
Non-Gaussian properties of random directional wave fields: laboratory experiments and numerical simulations
Speaker:
Dr Alessandro Toffoli (Postdoctoral Fellow, FEIS, SUT)
Abstract:

A comparison between laboratory experiments in a three dimensional basin and numerical simulations has been carried out to investigate the effect of the directional energy distribution on the statistical properties of surface gravity waves. In particular, different degrees of directionality have been considered in order to achieve a complete description of the transition region between the strongly non--Gaussian behavior of long crested waves and the weakly non--Gaussian statistics of short crested waves. The observed statistical properties have been reconstructed by simulating many random repetitions of the temporal evolution of the surface elevation, including the contribution of both bound and free waves. Third-order nonlinearity is accounted for. Simulations are based on two different approaches: numerical integration of a modified nonlinear Schr\"odinger equation and numerical integration of the Euler equations using a higher order spectral method. Whereas the former assumes a weakly nonlinear narrow banded approximation (both in frequency and direction), the latter is free from any bandwidth constrains.

Results show a very good agreement between the laboratory experiments and both numerical approaches, confirming the robustness of the transition between strongly and weakly non-Gaussian statistics.

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Seminar 5: April 24, 2009

Title:
Finite amplitude two-layer flow past topography
Speaker:
Simon Clarke, School of Mathematical Sciences, Monash University
Abstract:

We consider the problem of large-amplitude waves forced by the flow of a two layer fluid of finite depth past topography, such as would arise in exchange flows in geophysical fluid dynamics. Of particular interest is the long wave dynamics for this problem, which are governed by the Camassa--Choi (CC) equations. In the hydraulic limit these reduce to the two-layer shallow water (SW) equations, while for weakly nonlinear, near-resonant flows the limiting dynamics are governed by the forced extended Korteweg--de Vries (feKdV) equation. The phenomenology of the steady SW equations are then considered, which raises the fundamental question of what asymptotic solution results from a given initial--value problem, for example, the trivial initial condition. Numerical solutions of the finite-amplitude SW and CC equations are presented which demonstrate the evolution to hydraulic states. However, these cannot be efficiently used to determine the asymptotics for the full parameter space. Rather an alternative approach is outlined, where in the weakly nonlinear limit the hydraulic regimes must match with the regimes which result from the feKdV equation. Thus we consider in detail the weakly dispersive limit of the feKdV equation and from this outline the hydraulic regimes which must result.

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Seminar 6: May 1, 2009

Title:
Generalizing the 'Kelly' betting strategy to allow for multiple payouts.
Speaker:
Dr Tristan Barnett, Victoria University
Abstract:

The 'Kelly' strategy for calculating the optimal bet size for a single payout is well established. By formulating a theorem and proof, this talk provides a generalization of the 'Kelly' strategy for when multiple payouts exist. Interestingly, using this generalized 'Kelly' theorem, it can be shown that it is not always optimal to maximize the expected payout in order to maximize the long-term growth of the bankroll. Examples of where this methodology can be applied are given from video poker, blackjack, spread betting, decision theory and game theory.

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Seminar 7: May 8, 2009

Title:
Operating mechanism and dynamics of motor proteins: Intrinsic fluctuation, dynamic correlations and allosteric cooperativity.
Speaker:
Dr Ming Liu, ICT, SUT
Abstract:

Molecular motors are naturally occurring or hybrid biomolecular complexes that exert forces and motions in living cells. Molecular motors produce mechanics while fulfilling various biological functions. They are normally powered by hydrolysis/synthesis of nucleotides such as ATP, and/or by the photon or proton-motivated drives, and thus provide great potential for emerging bio-nanotechnology. However, operating mechanism and dynamics of molecular motors largely remain unknown at molecular level. To achieve a better understanding and control of molecular motors, we tackle dynamics problems of motor proteins by multi-scale molecular dynamics simulations. While taking ATP synthase and kinase as templates and in conjunction with structural and dynamic experiments, essential dynamics issues such as (a) mechanochemical transduction from the nucleotide reaction to the rotational/translational motion; (b) complex and interactive cooperativity between different catalysis sites; (c) structural transitions, flexibility, collective motion and dynamic correlations of active subunits; (d) large-scale allosteric communications etc, are revealed with an atomistic resolution. These investigations are extendable for mechanochemistry and dynamics properties of general proteins.

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Seminar 8: May 22, 2009

Title:
Bifurcations and State Changes in the Human Alpha Rhythm
Speaker:
A/Prof. David Liley, Brain Sciences Institute, SUT
Abstract:

Despite many decades investigating scalp recordable 8-13 Hz (alpha) electroencephalographic activity, no consensus has yet emerged regarding its physiological origins nor its functional role in cognition. Here we outline a detailed, physiologically meaningful, theory for the genesis of this rhythm that may provide important clues to its functional role. In particular we find that electroencephalographically plausible model dynamics, obtained with physiological admissible parameterisations, reveals a cortex perched on the brink of stability, which, when perturbed, gives rise to a range of unanticipated complex dynamics that include 40-Hz (gamma) activity. Preliminary experimental evidence, involving the detection of weak nonlinearity in resting EEG using an extension of the well-known surrogate data method, suggests that nonlinear (deterministic) dynamics are more likely to be associated with weakly damped alpha activity. Thus rather than the "alpha rhythm" being an idling rhythm it may be more profitable to conceive it as a readiness rhythm.

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Seminar 9: Jul 21, 2009

Title:
Ocean's 16: Dynamical, evolutionary and molecular origins of Redfield ratio N : P = 16 in oceans.
Speaker:
Dr Irakli Loladze, University of Nebraska-Lincoln, USA.
Abstract:

Among the biosphere's largest patterns is atomic nitrogen: phosphorus ratio (N : P) = 16 found throughout deep ocean; though N : P of individual phytoplankton species ranges from 6 to 60, the average N : P of plankton is also 16. Discovered empirically by Redfield over 70 years ago, this pattern is crucial to carbon sequestration, climate change and biogeochemical cycling models. However, the rationale behind N : P = 16 is not known. Here, we show that N : P = 16 is the result of biogeochemical homeostasis that originates on a molecular scale while evolutionary forcing and feedback of upwelling amplify the pattern to the global scale. First, we show that when nutrients are replete, Redfield ratio stems from five fundamental molecular values, including N in amino acids, N and P in nucleotides. Next, we construct a dynamical model that considers RNA:protein ratio as an evolutionary trait; it shows that when nutrients are limiting, an evolutionary stable strategy is for N : P of plankton to deviate toward N : P of the inflow. Finally, we show that upwelling of nutrients in our model provides a feedback that results in the convergence of N : P of plankton to Redfield ratio over geological times.

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Seminar 10: Aug 20, 2009

Title:
Error bounds and Stokes' phenomenon in the theory of divergent expansions
Speaker:
Prof. Vladimir P. Gurarii, Mathematics, Swinburne University of Technology
Abstract:
We consider classes of functions uniquely determined by coefficients of their divergent expansions. Approximating a function from such a class by partial sums of its expansion, we study how the accuracy changes when we move within a region of the complex plane. Analysis of these changes allows us to propose a theory of divergent expansions, which includes Stokes phenomenon as its essential part. This in turns enables us to formulate the necessary and sufficient conditions for an individual divergent expansion to encounter Stokes` phenomenon. We show explicit expressions for exponentially small terms which appear upon crossing Stokes lines and which lead to improvement of accuracy. The main features of the theory will be illustrated using classical divergent expansions. Even for these well known expansions our approach reveals properties which have not been known previously:
  • Euler factorial series 1/z-1!/z^2+2!/z^3-...;
  • Stirling expansion for z!;
  • Divergent expansions for Airy and Bessel functions.
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Seminar 11: September 10, 2009

Title:
Why I need mathematicians?!
Speaker:
Chris Berndt, Director, IRIS, Swinburne University of Technology
Abstract:

My research life in coatings technologies involves dealing with apparently random processes that produce highly variable products. Indeed, it is somewhat surprising that these coatings actually work and have some form of functionality. It is not the intent of this talk to present a highly polished package of R&D. The intent is to present the scientific and engineering problems that I need to consider. It could be that there is someone at Swinburne who can help me find solutions to these problems?

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Seminar 12: September 17, 2009

Title:
Thermo-magnetic convection in ferro-nanofluids
Speaker:
Dr Sergey Suslov, Mathematics, Swinburne University of Technology
Abstract:
Common magnetic fluids consist of magnetite colloids which contain single-domain ferro-magnetic nano-particles suspended in a carrier liquid. Their industrial production became possible in 1960 and since then the areas of their practical application have been continuously growing: magnetic sealing of gaps and joints, targeted medication delivery, tumor treatment, cooling of high-power loud speakers to name a few. One of the important future applications of ferrofluids is as a heat carrier in cooling devices operating in reduced gravity conditions on orbital stations where heat removal by natural gravitational convection cannot be achieved. In this talk the major properties of common ferro-fluids and the major physical mechanisms determining their flow characteristics (thermo-magnetic convection in particular) will be discussed. Both comprehensive experimental and theoretical magneto-convection analyses will be presented. It will be shown how the results obtained using various rigorous analytical and computational methods explain what is observed experimentally and guide further exprimental investigation and practical applications of ferro-colloids.
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Seminar 13: October 1, 2009

Title:
Nonlinear diffusion-driven flow in a stratified viscous fluid
Speaker:
A/Prof. Michael Page, School of Mathematical Sciences, Monash University
Abstract:
In 1970, two independent studies (by Wunsch and Phillips) of the behaviour of a linear density-stratified viscous fluid in a closed container demonstrated that a slow uphil) 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 vicinit of the sloping surface, in a thin `buoyancy layer'. A number of studies have since considered 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, the buoyancy layer can entrain fluid from that recirculation. That work has since been extended (Page & Johnson, 2009) to the nonlinear regime of the problem. Simple and elegant analytical solutions can be found in the limit as R -> 0 and in this talk they will be compared with numerical simulations in a tilted square container at small values of R. Further work will also be described.
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Seminar 14: October 15, 2009

Title:
Understanding global stability and transient growth in physiological-type flows
Speaker:
A/Prof. Hugh Blackburn (Mechanical & Aerospace Engineering, Monash University)
Abstract:
This talk outlines time-stepper based direct methods for computing linear flow global instability and transient growth in arbitrary geometry flows. The main area of applications discussed is to idealized physiological-type flows in circular and constricted tubes. It is observed that when flow separation is present, maximum transient growth energy scales exponentially with Reynolds number as opposed to the square of Reynolds number as observed in parallel shear flows. For pulsatile stenotic flows with comparatively large peak flow Reynolds numbers as found in the larger arteries of the human arterial tree, this sensitivity to Reynolds numbers leads to localized bypass transition to turbulence.
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Seminar 15: October 22, 2009

Title:
Problems of representational consistency and physical solutions and their significance for studies of brain functional activity
Speaker:
Dr Burzin Bhavnagri, SUT, Wantirna Campus.
Abstract:
Information in databases or computers is represented by characters that are mapped to numbers. For example, in ASCII coding A is represented by 65, B by 66, and so on. The question arises whether it is possible to consistently represent the information about biological and other systems in a similar way. Unfortunately, simultaneous monomorphisms of a set with some structure can combine in such a way that this structure is lost, which is a form of data representation inconsistency. In particular, finite sets of numbers suffer from this problem. To avoid it we have to know what types of structures the data systems contain and what their physical meaning is. The existence theorem for sets with structures having data representation consistency is known in terms of an action principle. We show that symmetric spaces violate its conditions while non-symmetric Lens spaces satisfy them. This turns out to have a clear geometric interpretation that offers an insight into the geometric process resulting in representational consistency. Some properties of Hilbert space of Spin 1/2n published in relation to Bell non-locality are intriguing. We propose to apply them to describe the observed correlation between blood oxygenation level and functional activity of brain. We then proceed towards posing the problem of finding physical solutions of the action principle using quantum chemistry methods for solving Shrodinger equation.
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Seminar 16: October 29, 2009

Title:
Prediction of plume generation and movement from dredging operations in Port Phillip Bay
Speaker:
David Provis, Cardno Lawson Treloar
Abstract:
This talk will describe the calibration, validation and application of numerical models to assess the spreading, dispersion and settling of the material put into suspension during the Channel Deepening Project in Port Phillip Bay. The models were set-up and validated using field data collected during a Trial Dredging Program undertaken as part of investigations for the Supplementary Environment Effects Statement. A brief discussion of the Trial and some of the data collected will be included. A range of dredging scenarios consisting of varying wind and tide conditions and different dredging configurations were simulated. The full dredging program, spanning about 18 months, was modelled and, in addition, more than one operational scenario was considered so that a very large modelling effort was undertaken. The talk will discuss the techniques and methods used to present the data in forms which allowed an assessment of, in the first instance, the potential ecological impact of the project, and, during the project, a means of comparing the model predictions with measured data. Some of the results obtained during the dredging project will be discussed including the quantitative comparisons of model predictions and measured data. These comparisons allowed an on-going assessment of the validity of the environmental impact assessments. Since the environmental impact assessment depended very much on the modelled predictions of turbidity, the comparisons provide a process whereby deviations can be identified and, if necessary, the operational procedures revised.
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Seminar 17: March 12, 2010

Title:
Numerical solution of 2D equations for potential flow with a free surface
Speaker:
Professor Dmitry Chalikov, Chief Scientist, Institute of Oceanography of the Russian Academy of Sciences and Research Professor, Swinburne’s Centre for Sustainable Infrastructure
Abstract:
A numerical model for long-term simulation of gravity surface waves is described. The method is based on a nonstationary conformal surface-following coordinate transformation; this approach reduces the principal equations of potential waves to two simple evolution equations for the elevation and the velocity potential of the surface. The numerical scheme is based on a Fourier transform method. High accuracy was confirmed by control of integral invariants and by validation of the nonstationary model against known solutions. The scheme allows reproduction of the propagation of steep Stokes waves for thousands of periods with very high accuracy. The model is designed for investigation of nonlinear wave~s dynamics and as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between ocean and atmosphere. The method developed here is applied to simulation of the evolution of wave fields with large number of modes for many periods of the dominant waves. The wave-number/frequency spectrum, statistical properties of nonlinear wave, mechanics of extreme waves (freak waves) generation and their statistics have been investigated. Model is coupled with that of the boundary layer above, based on Reynolds equations. Subsequently, the dynamics of wind-wave coupling has been investigated. The perspectives of further development are outlined: a 3-D models of potential flow with a free surface, a model for generation of vorticity and turbulence in potential waves, and a LES model of boundary layer.
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Seminar 18: Friday April 9, 2010

Title:
A new design technique for optical links: Theory and Application
Speaker:
Dr Kerry Hinton, ARC Special Centre for Ultra-Broadband Information Networks at the University of Melbourne
Abstract:
A new optical link design tool is described. This tool provides an accurate measure of link performance. It can include a wide range of linear path degradations without requiring computer simulations of the link. An example of using this tool in optical label switched networks is given. Due to the nature of traffic in these networks, traditional optical performance monitoring methods will not work. Using the link design tool, we show that payload error rate monitoring in these networks requires asynchronous sampling of the payload at the payload bit rate. This has a significant impact on the engineering viability of these networks.
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Seminar 19: Friday May 21, 2010

Title:
Evaluating global climate model simulations
Speaker:
Professor David Karoly, School of Earth Sciences, University of Melbourne
Abstract:
How good (or bad) are global climate models at simulating climate variability and climate change at global and regional scales? This question will be answered using several different diagnostic analyses of the multi-model data archive available through the WCRP Climate Model Intercomparison Project (CMIP) 3. The answer depends on the space and time scale being considered, as well as the specific climate variable.

The analyses will focus on surface temperature variations, as models generally simulate its large-scale variability quite well. In contrast, some limitations of model simulations of rainfall will be discussed.
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Seminar 20: Thursday July 29, 2010

Title:
A brief tour through some of the basic ideas of queueing theory
Speaker:
Dr Yoni Nazarathy, Faculty of Engineering & Industrial Sciences, SUT
Abstract:
The purpose of this talk is to take a broad scientific audience for a quick flight over queueing theory. The basic notions, ideas, nomenclature, models and results are introduced. No prior knowledge of stochastic processes is assumed except for a basic understanding of discrete and continuous probability distributions. After quickly motivating the need to evaluate queue length distributions and waiting times, we begin a tour of some of the key results of the past century.

First, we systematically present the basic ideas of simple queues represented by Markov processes introduced in the beginning of the 20'th century. The basic M/M/1 result is derived. We then continue to present the M/G/1 embedded Markov chain (1950's) and the Pollaczek - Khinchine formula. Further, we highlight the difficulty of extending this result for explicitly solving slightly more complex models such as the M/G/2 queue and the GI/G/1 queue. This motivates the use of heavy traffic diffusion approximations for these systems.

Touching on complex queueing networks, we introduce the notion of Jackson networks and their product form stationary distributions. We then highlight some of the modern stability results of non-Markovian networks. We conclude with a brief touch of computational models such as quasi-birth-death Markov chains.

Our tour ends with a look ahead, presenting some future challenges, applications and research directions.
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Seminar 21: Wednesday August 25, 2010

Title:
Fixed point iterative processes
Speaker:
Dr Walter Kozlowski, UNSW/Telstra Corporation
Date:
2:30 - 3:30pm, Wednesday August 25, 2010
Room:
BA806
Abstract:
In 2008, Kirk and Xu proved the fixed point existence for the asymptotic pointwise nonexpansive mappings T : C --> C,

i.e. mappings such that ||Tn(x) -Tn(y)|| < an(x) ||x-y||, where lim sup an(x)<1, n-->infinity for all x,y in C, where C is a nonempty, closed, bounded and convex subset of a uniformly convex Banach space X.

We will present this result against the historical background of the fixed point theory for nonexpansive mappings with the particular focus on the convergence of some iterative algorithms for the construction of fixed points for such mappings.
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Seminar 22: Wednesday September 8, 2010

Title:
New postgraduate internship scheme
Speaker:
Prof. Geoff Prince, AMSI, Director
Date:
2:30 - 3:30pm, Wednesday September 8, 2010
Room:
BA806
Abstract:
This presentation will discuss the new postgraduate internship scheme which has just been announced with the Commonwealth’s Enterprise Connect agency. Internships are available for mathematics, statistics and cognate disciplines such as computer science, bioinformatics, physics and engineering.

It will also give a briefing on AMSI’s latest business plan and the expansion of its scientific and higher education programs. These changes significantly increase opportunity for AMSI members including undergraduates, postgraduates and researchers.
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Seminar 23: Wednesday September 15, 2010

Title:
E-learning? Technology enhanced teaching and learning in symbol-based disciplines
Speaker:
Dr Bitgit Loch, Swinburne University of Technology
Date:
2:30 - 3:30pm, Wednesday September 15, 2010
Room:
BA806
Abstract:
In this presentation I will give an overview of how tablet and related technologies can be used effectively for teaching and learning in symbol based disciplines such as mathematics, statistics, physics and engineering: face-to-face and in e-learning.

I will talk about technologies I have trialed. These include tablet PCs, graphics tablets, digital note pens, e-book readers, pen-enabled screens, but also mini-tablet PCs for students.

Software packages like Jing, Camtasia Studio or Camtasia Relay are used to produce lecture recordings or short screencasts to support students, and may be played back on portable devices such as iPods or mobile phones. For students not attending traditional classes, online tutorials are offered using Windows Live Messenger and its inking capability, or web conferencing software (Elluminate).

I will give examples of an Operations Research subject where screencasts have been embedded in the study material, and describe a current government funded project to create primary/high school mathematics teacher support material with embedded screencasts.

I will also mention a project trialling tablet PCs across disciplines, and how lecturers engaged with this technology.
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Seminar 24: Wednesday October 6, 2010

Title:
Dimension reduction in regression and an example robustness study of inverse response plot estimation
Speaker:
Dr Luke Prendergast, La Trobe University
Date:
2:30 - 3:30pm, Wednesday October 6, 2010
Room:
BA806
Abstract:
This talk consists of two parts. Firstly, I will briefly introduce some modern dimension reduction methods in the regression setting and highlight how such approaches can be useful in determining perhaps complex regression structure that can be otherwise difficult to find.

In the second part of the talk I will focus on inverse response plot estimation (Cook & Weisberg, 1994) - in particular with respect to response transformation estimation for linearization following dimension reduction. Here I will show that the influence function (a tool for understanding the sensitivity of an estimator) can be very insightful, helping to explain unexpected behaviour with respect to estimation of the response transformation.

For example, often the dimension reduction can be carried out poorly yet reasonable estimates of the response transformation can still be found. I will also show that a simple robust procedure can often greatly improve results with respect to both the dimension reduction and the subsequent estimation of the response transformation.

This second part of the talk is based on joint work with Professor Simon Sheather from Texas A&M University.
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Seminar 25: Wednesday October 20, 2010

Title:
A numerical study of an influenza epidemic model with vaccination and diffusion
Speaker:
MD Samsuzzoha, PhD candidate, Swinburne University of Technology
Date:
2:30 - 3:00pm, Wednesday October 20, 2010
Room:
BA806
Abstract:
A vaccinated diffusive compartmental epidemic model is developed to explore the impact of vaccination as well as diffusion on the transmission dynamics of influenza.
The basic reproduction numbers with and without vaccination are obtained. Stability analysis of the points of equilibrium has been performed. Using the combined effect of the vaccine efficacy and vaccination rate, the model is analysed to determine criteria for control of influenza epidemic.
The roles of vaccine efficacy and vaccination rate are compared. It is shown that higher levels of vaccine efficacy and vaccination rate lead to a decrease in the epidemic size.
It is also demonstrated that an accurate estimation of the efficiency of vaccine is necessary to control the spread of influenza and thus vaccination strategy needs to be implemented carefully.
Title:
Nonlinear instability of wavy shear flow
Speaker:
Daniel Hayes, PhD Candidate, Swinburne University of Technology
Date:
3:00 - 3:30pm, Wednesday October 20, 2010
Room:
BA806
Abstract:
I will present an asymptotic analysis of Langmuir circulation in shallow water, in the long wave limit. Langmuir circulations are wind aligned rolls in the upper ocean that can grow to the size of sports stadiums and are critical to mixing the upper ocean. Of interest is the Rayleigh number and the corresponding spacing between cells for the case of onset of instability.

I will extend the perturbation analysis from Cox and Leibovich who used uniform distributions of shear and drift, to non uniform distributions. I do so using a power series expansion for each and obtain an exact analytical result for the Rayleigh number; the spacing then follows. They find that Neumann boundary conditions lead to physically unrealistic results for the spacing between cells at onset but using Cauchy boundary conditions do lead to physically realistic results for the spacing at onset, and we concur.

I will show how the Rayleigh number and corresponding spacing between cells for the case of onset of instability varies when we use nonuniform distributions for drift and shear. Then I compare these results with those of Cox and Leibovich.
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Title:
Study of an Early Stage Interaction of Oxygen with Aluminium
Speaker:
Behrooz Fateh, PhD candidate, Swinburne University of Technology
Date:
2:30 - 3:00pm, Wednesday October 27, 2010
Room:
BA806
Abstract:
Aluminium is among the metals with the greatest affinity for oxygen.
Aluminium oxidation is a process which occurs easily and rapidly in order of milliseconds. Even at elevated temperatures, the interaction rate increases. Study of initial oxidation is very important as it concerns the first step of a metal?s oxidation and corrosion behaviour.

Characteristics of the kinetics of early-stage oxidation are believed to have an important influence on the later steady-state growth.

Furthermore, there are many aspects of Al melt handling and cast process that results in oxidation of Al and dross formation. Modern sophisticated experimental studies such as scanning tunnelling microscopy (STM), X-ray photo-electron Spectroscopy (XPS), low energy electron diffractions (LEED), combining ellipsometry and auger electron microscopy and etc, have almost clarified the details of initial stage of both oxygen chemisorptions and oxidation kinetics of Al. However, must of the experimental data are not consistent and reproducible.

Furthermore, the dynamics of absorption and oxidation process are much less understood. This presentation reviews the methods, techniques and the challenges of Al initial stage oxidation process measurements and also introduces a new method for studying the oxide layer formation upon solid and molten aluminium, following ablation of the surface with an ultra-fast laser beam and a fast imaging techniques.
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Title:
Production of High Purity Magnesium from Silicothermic Processes
Speaker:
Winny Wulandari, PhD candidate, Swinburne University of Technology
Date:
3:00 - 3:30pm, Wednesday October 27, 2010
Room:
BA806
Abstract:
Magnesium is an important metal used in automotive industry for car weight reduction. The widely used method for obtaining magnesium is the Pidgeon process which is small batchwise procedure based on silicothermic reduction of dolomite. This project is concerned with the fundamental physical chemistry associated with producing high-purity magnesium via silicothermic processes.

The study focuses on thermodynamic modelling of processes using Gibbs Energy Minimisation methods to determine the degree of purity that can be achieved for a range of process configurations and operating conditions. The study extends to kinetic analysis of the solid-solid reaction to provide insight into the process tand determine the limiting magnesium recovery.

High temperature apparatus has been developed and experimental study has been carried out to determine the distribution of impurities in magnesium extraction via silicothermic reduction.
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Title:
Origin of our Solar system: new ideas gleaned from the Cassini-Huygens mission to Saturn and Titan and the MESSENGER mission to Mercury.
Speaker:
Dr Andrew Prentice, Monash University
Date:
2:30 - 3:30pm, Wednesday November 3, 2010
Room:
BA806
Abstract:
The mechanism by which our planetary system and the regular satellite systems of Jupiter and Saturn were formed is not properly understood, despite the great wealth of information about those systems that has been gathered by interplanetary space probes and Earth-based measurements.

This is especially the case for the Saturn system. Exactly 30 years have now elapsed since the visits of the Voyager 1 and 2 spacecraft to Saturn. Today, the Cassini-Huygens Mission to Saturn and Titan is slowly unravelling the mysteries of Saturn and its remarkable satellite system. Saturn’s largest satellite Titan is more like a planet than a moon. Its mass is nearly 60 times larger than that of the second largest moon Saturnian Rhea and its physical size exceeds that of iron-rich Mercury. Titan is also unique because of its thick atmosphere which is 4 times denser than that of the Earth at its surface.

A surprising feature of Titan is its slightly oblate shape, as revealed by the Cassini radar experiment (Zebker et al. 2009). Such a shape lends support to the idea that Titan originally condensed as a secondary embryo in the gas ring that was shed by contracting protosolar cloud (hereafter PSC and see the graphic below) at Saturn’s orbital distance from the Sun (Prentice, 1980 JPL Publication 80-80; 1984 Earth, Moon and Planets 30 209). By forming in a free orbit about the PSC, Titan’s shape would have initially been oblate, like the asteroid Ceres.
Its bulk chemical composition is predicted to be anhydrous rock (mass fraction 0.4925), water ice (0.4739) and graphite (0.0336). It is suggested that Titan’s capture by the proto-Saturnian system was secured by collision with one or both of 2 volatile-rich native moons of Saturn that once existed at 17RSat and 24RSat, where RSat is Saturn’s equatorial radius (Prentice 2006 PASA 23 1). It is the NH3 and CH4 ices of those lost moons which are the source of Titan’s N2–CH4 atmosphere.

In this talk I discuss the formation of the planetary system and the satellite system of Saturn within the context of the author’s ‘Modern Laplacian Theory’ of solar system origin. According to this model, the planets condensed form an orbiting family of gas rings that had been shed by the gravitationally contracting PSC, some 4.6 billion years ago. The gas rings are shed at the equator of the rotating cloud as a means for disposing of excess spin angular momentum.

Very strong thermal convection within the cloud provides the mechanism for the shedding of discrete gas rings, rather than a continuous nebula. The temperatures Tn of the gas rings vary with mean orbital radius Rn according as Tn = 670 (AU/Rn)0.9 K, where AU is the astronomical unit. The chemical condensation sequence for the planets Mercury through Saturn is shown here.

Mercury consists mostly of Fe-Ni (67% by mass) and has a concentration of Th & U that is 4.3 times the terrestrial value. This allows us to explain why the outer core of the planet is still molten: the blisteringly hot ceramic mantle inhibits the escape of heat from the interior. A partly molten interior has been deduced from the large librations of the Mercurian crust and the existence of the planet’s large dipole magnetic field. Titan condensed in a solar orbit and was initially spinning rapidly, with a highly oblate shape.

If Titan’s outer ice mantle was still warm at the time of capture, then its shape would soon relax via tidal dissipation to that demanded by the moon’s new orbit about Saturn. The shape of the cold inner core might, however, retain its oblate shape. Titan’s shape today is thus the outcome of an amazing and complex dynamical past. I present numerical models for Titan’s radiogenic evolution to solar age which show that the central core has remained cold to solar age.
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