Colloquium

Colloquium

Colloquium

The Departmental Colloquia are held on Friday afternoons, from 3:00 to 4:00pm, during the teaching semesters and are followed by refreshments.

2018 Series...

Session 2, Week  13 - 09 November

Date: Friday, 09 November 2018
Speaker: Prof Michael Small (University of Western Australia)

Venue:  E7B 146 ACE room

Title: Transportation on complex networks

Abstract: 

Over the last couple of decades, complex networks have attracted the interest of physicists largely because they are described by simple generative processes and exhibit a host of unexpected emergent properties. Applications have been more sporadic - the friendship paradox (that your Facebook friends have more friends than you do) has been proposed as an improved method for distribution of limited vaccines, and my own work has helped to understand dynamical systems, measured from time series, via the topology of an associated graph. One interesting class of problems is those related to transport on complex networks and in this talk I will review two specific examples which we have looked at - on-field interaction among players of an (AFL) football team (the object of transport here is the ball), and water distribution networks. In both cases we are interested in failure of transport - either because the ball is intercepted, or the water network fails. We show that properties of the network are informative and helpful in understanding the underlying dynamics of these systems and even have practical implications. If time permits, I will also briefly mention a separate class of problems currently percolating through the physics literature - where one is searching on a complex network for a moving target.

Session 2, Week  12 - 02 November

Date: Friday, 02 November 2018
Speaker: Dr Jennifer Flegg (University of Melbourne)

Venue:  E7B 146 ACE room

Title: Mathematical modelling of the emergence and spread of antimalarial drug resistance

Abstract:

Malaria parasites have repeatedly evolved resistance to antimalarial drugs, thwarting efforts to eliminate the disease and contributing to an increase in mortality. In this talk, I will introduce several statistical and mathematical models for monitoring the emergence and spread of antimalarial drug resistance. For example, results will be presented from Bayesian geostatistical models that have quantified the space-time trends in drug resistance in Africa and Southeast Asia. I will discuss how the results of these models have been used to update public health policy.

Session 2, Week  11 - 26 October

Date: Friday, 26 October 2018
Speaker: Dr Edward Green (University of Adelaide)

Venue:  E7B 146 ACE room

Title: Quantification and modelling of biological patterns

Abstract: 

Tissue growth requires cells of various types to organise themselves into the appropriate patterns and structures to produce viable, functional tissue. Similar processes occur in tissue repair (e.g. wound healing) or in biofilms (communities of bacteria or yeast cells). Understanding how this organisation is coordinated is therefore an important basic problem in biology, and mathematicians have made important contributions, such as Alan Turing's seminal work on 'The chemical basis of morphogenesis'.

I will present a brief overview of continuum and individual-cell based approaches to modelling pattern formation in biological systems, and discuss how we have applied them in recent work on pattern formation in biofilms, and in interacting cell populations. A particular focus of our work has been on using image processing methods and spatial statistics (such as pair-correlation functions) to quantify experimental data, to allow more precise comparisons with our model results

Session 2, Week  10 - 19 October

Date: Friday, 19 October 2018
Speaker: Prof Matthew Simpson (Queensland University of Technology)

Venue:  E7B 146 ACE room

Title: Challenges in parameterising mathematical models of cell migration and cell proliferation

Abstract:

In this presentation, I will give an overview of some of the challenges we face when attempting to quantitatively calibrate mathematical models of cell migration and cell proliferation to match experimental data. Two different experimental scenarios will be considered. First, we will deal with very simple observations of cell migration and cell proliferation on a two-dimensional substrate, called a cell proliferation assay. I will present an off lattice model of cell migration, cell proliferation and crowding effects, and explore how to parameterise the computational model using approximate Bayesian computation. Second, we will deal with a much more complicated experimental situation where we observe three-dimensional spreading and invasion of malignant melanoma cells within human tissues, called a human melanoma skin equivalent assay. I will present a typical continuum model of cell invasion and explain how to use a Bayesian learning approach, with an exact likelihood, to calibrate the model. In both example problems there are no accepted protocols for connecting mathematical models with experimental data. Therefore, both approaches I present are novel, and I hope that the presentation will stimulate discussion about how these methods can be improved and adapted to other situations.

Session 2, Week 9 - 12 October

Date: Friday, 12 October 2018
Speaker: Prof Billy Todd (Swinburne University of Technology)

Venue:  E7B 146 ACE room

Title: Towards an extended Navier-Stokes hydrodynamics at the nanoscale

Abstract:

In this presentation, both theoretical and simulation studies are highlighted that clearly demonstrate the importance of several non-classical phenomena fundamental to the extension of Navier-Stokes hydrodynamics for highly confined fluids. These are: (1) the prevalence of slip, (2) the strong coupling of molecular spin to linear translational momentum, and (3) the non-locality of viscous transport at the nanoscale. In the first of these, we utilize a newly developed equilibrium based model to accurately predict the slip velocity and slip lengths of systems such as water or methane flowing in graphene nanochannels and carbon nanotubes. We demonstrate that traditional molecular dynamics simulations of such systems are far less efficient and accurate than the easily implemented model we propose. Next, we show that ignoring the coupling of spin angular momentum to linear translational motion of a highly confined fluid can lead to significant over-estimation of the predicted flow rates using conventional Navier-Stokes treatments. By including spin-coupling into the extended Navier-Stokes equations, hydrodynamic prediction is seen to be very accurate down to length scales of a few atomic diameters. We also demonstrate how this knowledge, coupled with our knowledge of slip, can be used to pump molecular fluids such as water via non-intrusive application of a rotating electric field. Finally, we show that a complete generalisation of Navier-Stokes hydrodynamics comes about in the realisation that at the nanoscale viscous transport is fundamentally non-local in nature. We explore this theme for homogeneous systems and discuss the ramifications and problems yet to overcome for nanofluidic applications.

Session 2, Week 8 -  05 October

Date: Friday, 05 October 2018
Speaker: Dr David Harvey (University of New South Wales)

Venue:  E7B 146 ACE room

Title: Integer multiplication and the truncated product problem

Abstract:

It is now over a decade since the appearance of Fürer's breakthrough result on the asymptotic complexity of integer multiplication. Over the past few years, several authors, building on Fürer's ideas, have proposed improved and simplified algorithms for this problem. I will give an overview of the current status of research in this area. I will also discuss recent progress on the problem of computing a truncated integer product, i.e., computing only the top half (or bottom half) of the product of two integers.

Session 2, Week 7 - 14 September

Date: Friday, 14 September 2018
Speaker: Prof Mason Porter (University of California Los Angeles, USA)

Venue:  E7B 146 ACE room

Title: Multilayer networks

Abstract:

Networks arise pervasively in biology, physics, technology, social science, and myriad other areas. Traditionally, a network is modelled as a graph and consists of a time-independent collection of entities (the nodes) that interact with each other via a single type of edge. However, most networks include multiple types of connections (which could represent, for example, different modes of transportation), multiple subsystems, and nodes and/or edges that change in time. The study of "multilayer networks", which is one of the most popular areas of network science, allows one to investigate networks with such complexities. In this talk, I'll give an introduction to multilayer networks and their applications.

Session 2, Week 6 - 07 September

Date: Friday, 07 September 2018
Speaker: A/Prof Linda Stals (Australian National University)

Venue:  E7B 146 ACE room

Title: Multigrid methods applied to the thin-plate spline saddle point problem

Abstract: 

Data fitting is an integral part of a number of applications including data mining, 3D reconstruction of geometric models, image warping and medical image analysis. A commonly used method for fitting functions to data is the thin-plate spline method. This method is popular because it is not sensitive to noise in the data. We have developed a discrete thin-plate spline approximation technique that uses local basis functions. With this approach the system of equations is sparse and its size depends only on the number of points in the discrete grid, not the number of data points. Nevertheless the resulting system is a saddle point problem that can be ill-conditioned for certain choices of parameters. In this talk I will present a multigrid based preconditioner that works with a wide choice of parameters.

Session 2, Week 5 - 31 August

Date: Friday, 31 August 2018
Speaker: Dr Geoffrey Vasil (University of Sydney)

Venue:  E7B 146 ACE room

Title: Flexible, accurate, efficient, and automatic numerical computations

Abstract: 

In this talk I will discuss the latest developments from the Dedalus project. This will describe an effort to create genuinely flexible and automatic solvers for a wide range of applied partial differential equations. Creating software that operates with minimal human intervention requires mastering some pretty interesting abstract mathematics. I will discus some of the latest results in this regard. I will also give an overview of several application areas that we can now better model. These include example from geophysical and astrophysical fluid dynamics, fluid-solid interactions, actively driven bio-fluids, quantum graph networks, and pattern formation.

Session 2, Week 4 - 24 August

Date: Friday, 24 August 2018
Speaker: A/Prof Jessica Purcell (Monash University)

Venue:  E7B 146 ACE room

Title: Cusp shape and tunnel number

Abstract:

Throughout their history, 3-manifolds have been studied by investigating surfaces embedded within them. In the last 50 years, the geometry of manifolds and surfaces have played an increasingly important role. However, there are still many open questions concerning which surfaces with which geometries embed isometrically in geometric 3-manifolds. In this talk, I will discuss one such question. Associated to a cusped hyperbolic 3-manifold, such as a knot complement, is a cusp shape, which is a Euclidean structure on the torus and therefore determines a point in Teichmuller space. It is natural to ask which points arise. In the 1990s, Nimmersheim showed that the cusp shapes of finite volume hyperbolic 3-manifolds, which form a countable set, are dense in Teichmuller space. However, the 3-manifolds constructed in that theorem are very complicated topologically. Restrict instead to simpler manifolds. For example, every 3-manifold has a Heegaard splitting. If we restrict to simple Heegaard splittings, of bounded genus g, which cusp shapes arise? In this talk, we will give background on hyperbolic geometry and Heegaard splittings, and show that for fixed genus g, cusp shapes of finite volume 3-manifolds of genus g are still dense in Teichmuller space.

Session 2, Week 3 - 17 August

Date: Friday, 17 August 2018
Speaker: Prof Troy Farrell (Queensland University of Technology)

Venue:  E7B 146 ACE room

Title: From bagasse to biofuel: the modelling of a cellulosic biomaterial

Abstract: 

Sugar cane is harvested in Australia over a six month period (generally June to December). Bagasse is the fibrous residue produced in sugar mills in large quantities when the cane is crushed. The energy balance in raw sugar factories has traditionally been configured such that little surplus bagasse remains at the end of the crushing season. However, over the past decade a number of factories have reduced their energy consumption in order to produce surplus bagasse for conversion to bioenergy products.

Support for such conversion processes requires significant bagasse storage capability so that surplus bagasse produced is available to maintain the utilisation of bioenergy conversion processes beyond the milling season. This surplus bagasse is stored in large stockpiles, typically of the order of 8m high, 20m wide, 100m long, however, a wide variety of local conditions and requirements means that in practice the sizes and shapes of bagasse stockpiles vary between locations. Some are covered with tarpaulins and others are uncovered, allowing infiltration of water during rainfall, and the degree of compaction can vary significantly between stockpiles. The bagasse that is stockpiled has a water content of up to 55% by weight and an initial temperature of approximately 50 degrees Celsius. The oxidation processes that occur within stockpiles can, under certain conditions, lead to spontaneous combustion and a potential total loss of feedstock. In the first part of this talk we will present a comprehensive, one-dimensional mathematical model for the heat and mass transfer within large-scale bagasse stockpiles with the aim of understanding the transport dynamics that take place within large stockpiles and analysing some of the important parameters that govern the predicted stockpile dynamics.

Bagasse is also a promising feedstock for the production of bioethanol, whereby the cellulosic material within bagasse is hydrolysed by enzymes to produce glucose, which is subsequently fermented to produce bioethanol. Hemicellulose within the bagasse fibres forms a monolayer coating around cellulose that inhibits the enzymatic saccharification process. Acid pre-treatment is a method of removing the hemicellulose, which allows enzymes greater access to the cellulose. Ensuring the efficiency of acid pre-treatment improves the overall cost-effectiveness of bioethanol production. In the second part of this talk, I will present a fibre-scale model that marries the chain length dependency of population balance equations with “hard-to-hydrolyse” kinetics. The model also accounts for the diffusion of species from within the fibre into the surrounding hydrolysate and allows for the material to vary temporally and spatially. The model predictions will be compared with experimentally obtained oligomer yield profiles.

Session 2, Week 2 - 10 August

Date: Friday, 10 August 2018
Speaker: Dr Anja Slim (Monash University)

Venue:  E7B 146 ACE room

Title: Gravity currents and similarity solutions of the shallow-water equations

Abstract:

Gravity currents occur whenever fluid of one density flows predominantly horizontally into fluid of a different density. A common example is the sea breeze, where cooler, denser air above the ocean displaces hotter, less dense air above land. Such flows can be accurately modeled by the shallow-water equations with a particular frontal boundary condition. At long times, solutions of this model are typically self-similar. Transforming to the appropriate similarity variable, the governing pdes become a pair of autonomous odes on the surface of a torus. Finding similarity solutions then corresponds to finding the integral curve connecting the phase-plane point representing the frontal boundary condition and a phase-plane equilibrium particular to the problem geometry. I will present several example solutions, illustrating the connection with characteristic solutions of Riemann problems, showing that anticipated similarity variables are not always correct, and finding a similarity solution of the second kind, where the similarity exponent is obtained from an eigenvalue problem.

Session 2, Week 1 - 03 August

Date: Friday, 03 August 2018
Speaker: Dr Joanne Hall (Royal Melbourne Institute of Technology)

Venue:  E7B 146 ACE room

Title: Skolem circles

Abstract:

A Skolem sequence on m symbols is a sequence of 2m symbols from the symbol set {1,2,...,m} with each symbol appearing twice, such that the distance between any pair of that same symbol is that symbols value in integers. For example, 41134232 is a Skolem sequence on 4 symbols. We investigate wrapping a Skolem sequence around a circle. A Skolem circle is a circular configuration of 2m cells which can be filled with the symbol set {1,2,...,m} with each symbol appearing twice, such that the distance between any pair of that same symbol is that symbols value in integers. There are some Skolem circles which cannot be unwrapped into a Skolem sequence. Joint work with James Bubear, QUT.

27 July 2018

Date: Friday, 27 July 2018
Speaker: Dr Ross Moore (Macquarie University)

Venue:  E7B 146 ACE room

Title: Authoring accessible tagged PDF documents using LaTeX

Abstract:

Several ISO standards have emerged for what should be contained in PDF documents, to support applications such as 'archivability' (PDF/A) and 'accessibility' (PDF/UA). These involve the concept of 'tagging', both of content and structure, so that smart reader/browser-like software can adjust the view presented to a human reader, perhaps afflicted with some physical disability. In this talk we will look at a range of documents which are fully conformant with these modern standards, mostly containing at least some mathematical content, created directly in LaTeX. The examples are available on my website (http://web.science.mq.edu.au/~ross/TaggedPDF/).

The desirability – both morally and legally – of producing documents this way will discussed, along with aspects of how much extra work is required of the author.

Also on the above website is a 'five-year plan' proposal how to modify the production of LaTeX-based scientific publications to adopt such methods. This will involve cooperation between academic publishers and a TeX Users Group (TUG) working group. The proposal PDF document (http://web.science.mq.edu.au/~ross/TaggedPDF/PDF-standards-v2.pdf) is itself produced to be fully accessible, complying with both PDF/UA-1 and PDF/A-2a standards.

For past seminars, please go to our archive.

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