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Dynamics, Modelling and Computation Group Seminars: Semester 1

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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