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Congratulations to Professor of Mathematical Sciences, Yvonne Stokes, on being awarded the 2018 EO Tuck Medal for outstanding research and distinguished service to the field of Applied Mathematics. She is pictured with Professor Peter Taylor from the University of Melbourne.

More information: http://www.anziam.org.au/The+EO+Tuck+Medal

Photo: Mark McGuinness

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Seminar:

When: Friday, 16 /2/18
Ingkarni Wardli 5.57 3:10-4pm
Speaker: Dr Guillermo Gomez, Centre for Cancer Biology, Uni SA
Title: Active mechanical relaxation of adherens junctions in the vicinity of apoptotic cells facilitates cell extrusion by promoting epithelial topological transitions.

Abstract: Cell extrusion allows the elimination of minorities of cells from the epithelium. Although this process entails active events that occur within the extruding cell, much less is known on the role of its neighbouring cells. Using apoptotic cell extrusion as a model, we found that as cell extrusion completes, the junctions on neighbouring cells, elongate and form multicellular junctions or “rosettes”. Computational modelling and experimentation show that active mechanical softening of junctions plays a key role during these junctional rearrangements that have all the characteristic of a topological transition. Junctional mechanotransduction is essential for epithelial topological transitions during extrusion as tension-sensitive junctional accumulation of cofilin-1 activates SFKs that are required for active junctional softening. We therefore propose that softening of the tissue plays a key role facilitating the topological transitions that favours extrusion.

Seminar:

When: Thursday, 22/2/18
Ingkarni Wardli 5.57 3:10-4pm
Speaker: Ms Lisa Reischmann, University of Augsberg
Title: A multiscale approximation of a Cahn-Larche system with phase separation on the microscale
Abstract:

We consider the process of phase separation of a binary system under the influence of mechanical deformation and we derive a mathematical multiscale model, which describes the evolving microstructure taking into account the elastic properties of the involved materials.

Motivated by phase-separation processes observed in lipid monolayers in film-balance experiments, the starting point of the model is the Cahn-Hilliard equation coupled with the equations of linear elasticity, the so-called Cahn-Larche system.

Owing to the fact that the mechanical deformation takes place on a macrosopic scale whereas the phase separation happens on a microscopic level, a multiscale approach is imperative.

We assume the pattern of the evolving microstructure to have an intrinsic length scale associated with it, which, after nondimensionalisation, leads to a scaled model involving a small parameter epsilon>0, which is suitable for periodic-homogenisation techniques.

For the full nonlinear problem the so-called homogenised problem is then obtained by letting epsilon tend to zero using the method of asymptotic expansion.

Furthermore, we present a linearised Cahn-Larche system and use the method of two-scale convergence to obtain the associated limit problem, which turns out to have the same structure as in the nonlinear case, in a mathematically rigorous way. Properties of the limit model will be discussed.

Seminar:

When: Friday 20 April

3:10pm, IW 5.58

Speaker: Dr Joe Giddings, University of Adelaide

Title: One Dimensional Models for Slugging in Channel Flow

Abstract:Gas-liquid pipe flows are extremely important in many industries, one of which is the oil/gas industry which is where the motivation for this work comes from. In subsea natural gas pipelines the gas is compressed before being pumped through the pipe at high pressure. As it flows through the pipe some of the gas condenses into a low density mixture of hydrocarbon liquids. When gas and liquid flow together there are several possible flow regimes that can occur depending on the velocity of the gas and liquid, one of which is slug flow where the liquid forms a series of plugs (slugs) separated by relatively large gas pockets. The occurrence of slug flow is a major concern in the oil and gas industry due to the difficulty of dealing with large changes in the oil and gas flow rates at the exit of the pipe.

We develop a hydraulic theory to describe the occurrence and structure of slugging in two-layer-gas-liquid flow generated by prescribed, constant, upstream flow rates in each layer. We will investigate how small-amplitude disturbances affect the flow in order to study the stability of spatially uniform solutions. We will then consider the existence of periodic travelling wave solutions numerically in order to investigate the influencing factors that may lead to a transition from stratified flow to slug flow. We then solve the governing equations numerically as an initial value problem in order to improve our understanding of how and why slugs form and are able to compare our solutions to those predicted by the periodic travelling wave theory.

Finally, we investigate the effects of non-horizontal channels with small, slowly varying inclination on the development of slug flow by re-writing our equations in terms of a curvilinear co-ordinate system.From this we find that the height of the layer of liquid increases with the angle of the channel and our solutions are significantly different to those in the horizontal case.

Seminar:

Title: Obstructions to smooth group actions on 4-manifolds from families Seiberg-Witten theory
When: Friday, 25 May 2018 at 1:10pm in Barr Smith South Polygon Lec theatre
Speaker: David Baraglia (University of Adelaide)

Abstract: Let X be a smooth, compact, oriented 4-manifold and consider the following problem. Let G be a group which acts on the second cohomology of X preserving the intersection form. Can this action of G on H^2(X) be lifted to an action of G on X by diffeomorphisms? We study a parametrised version of Seiberg-Witten theory for smooth families of 4-manifolds and obtain obstructions to the existence of such lifts. For example, we construct compact simply-connected 4-manifolds X and involutions on H^2(X) that can be realised by a continuous involution on X, or by a diffeomorphism, but not by an involutive diffeomorphism for any smooth structure on X.

Seminar:

Title: The mass of Riemannian manifolds
When: Friday, 1 June 2018 at 1:10pm in Barr Smith South Polygon Lec theatre
Speaker: Matthias Ludewig (MPIM Bonn)

Abstract: We will define the mass of differential operators L on compact Riemannian manifolds. In odd dimensions, if L is a conformally covariant differential operator, then its mass is also conformally covariant, while in even dimensions, one has a more complicated transformation rule. In the special case that L is the Yamabe operator, its mass is related to  the ADM mass of an associated asymptotically flat spacetime. In particular, one expects positive mass theorems in various settings. Here we highlight some recent results.

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Mark Girolami Chair of Statistics, Imperial College London, and The Alan Turing Institute presents: Stochastic Modelling of Urban Structure

When: Monday 20 November, 11:10am

Where: Engineering North N132

Abstract:
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Urban systems are complex in nature and comprise of a large number of individuals that act according to utility, a measure of net benefit pertaining to preferences. The actions of individuals give rise to an emergent behaviour, creating the so-called urban structure that we observe. In this talk, I develop a stochastic model of urban structure to formally account for uncertainty arising from the complex behaviour. We further use this stochastic model to infer the components of a utility function from observed urban structure. This is a more powerful modelling framework in comparison to the ubiquitous discrete choice models that are of limited use for complex systems, in which the overall preferences of individuals are difficult to ascertain. We model urban structure as a realization of a Boltzmann distribution that is the invariant distribution of a related stochastic differential equation (SDE) that describes the dynamics of the urban system. Our specification of Boltzmann distribution assigns higher probability to stable configurations, in the sense that consumer surplus (demand) is balanced with running costs (supply), as characterized by a potential function. We specify a Bayesian hierarchical model to infer the components of a utility function from observed structure. Our model is doubly-intractable and poses significant computational challenges that we overcome using recent advances in Markov chain Monte Carlo (MCMC) methods. We demonstrate our methodology with case studies on the London retail system and airports in England.
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When:Friday 27 Oct Where: Ingkarni Wardli B17 Presented by Dr Sophie Hautphenne, University of Melbourne Abstract: Markovian binary trees form a general and tractable class of continuous-time branching processes, which makes them well-suited for real-world applications. Thanks to their appealing probabilistic and computational features, these processes have proven to be an excellent modelling tool for […]

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Friday 13 October Ingkarni Wardli B17 Professor Mat Simpson, Queensland University of Technology Abstract: Scald burns from accidental exposure to hot liquids are the most common cause of burn injury in children. Over 2000 children are treated for accidental burn injuries in Australia each year. Despite the frequency of these injuries, basic questions about the […]

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This Friday, 11 August, we have a School Colloquium with Dr Robyn Araujo from Queensland University of Technology. The talk is in Ingkarni Wardli B17 at 15:10. Mathematics is Biology’s Next Microscope (Only Better!) Abstract: While mathematics has long been considered “an essential tool for physics”, the foundations of biology and the life sciences have […]

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The School of Mathematical Sciences has a long history of achievement in research and postgraduate education, and a reputation for providing a stimulating and supportive environment. The School is highly respected internationally for its research strengths in geometry, statistics, stochastic modelling and operations research, and dynamics, modelling and computation. Please see our Research pages, for […]

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This Friday, 28 July, we have a School Colloquium with Prof Philip Hall from Monash University. The talk is in Ingkarni Wardli B17 at 15:10. Abstract: 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 […]

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Elder Professor of Mathematics in the School of Mathematical Sciences, has been awarded an Australian Laureate Fellowship worth $1.64 million to advance Index Theory and its applications. The project is expected to enhance Australia’s position at the forefront of international research in geometric analysis. To find out more visit: http://www.arc.gov.au/2017-laureate-profile-professor-mathai-varghese

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Offering a range of engaging talks, informative displays and tours of world-class teaching and research facilities, the Faculty of ECMS presents an overview of study areas and career prospects in these dynamic disciplines. All schools within the faculty will be showcasing their programs in the Ingkarni Wardli atrium, with academics and current university students available […]

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