Welcome to the webpage of the Applied Mathematics Seminars of the University of St Andrews. Unless otherwise indicated, the seminars will be held in Lecture Theatre D, Mathematical Institute (MI). All interested are welcome to attend. Tea will be available afterwards in the Staff Common Room. External visitors are advised to confirm arrangements with the seminar organiser.

Martinmas Semester Programme 2020

Upcoming lectures

Previous lectures

  • Friday, October 23th 2020, 2:00pm
    Prof. Rachel Bearon, University of Liverpool

    Insights from mathematical models of spheroids for drug uptake & cancer spread

    Mathematical models can aid discovery in the life sciences, by providing predictive tools, and allowing efficient testing of ‘what-if’ scenarios. However, identifying the ‘right’ model, and suitably parameterizing it, is a challenging task which mathematicians are well-placed to contribute. I will discuss two projects based upon an experiments on 3D spheroid cell culture systems [1,2]. Cells cultured in such system have been shown to more closely resemble the functionality and morphology of cells in-vivo, and so there is increasing interest in using these systems for example in drug toxicity studies and for better understanding cancer metastasis. [1] Leedale, J. A., Kyffin, J., Harding, A., Colley, H., Murdoch, C., Sharma, P., Williams, D., Webb, S. & Bearon, R. (2020). Multiscale modelling of drug transport and metabolism in liver spheroids. Interface Focus, 10(2). doi:10.1098/rsfs.2019.0041 [2] Scott, M., Zychaluk, K. & Bearon, R. (submitted to Math. Med. & Biol.) A mathematical framework for modelling 3D cell motility; applications to Glioblastoma cell migration

  • Friday, October 16th 2020, 2:00pm
    Dr. Carina Dunlop, University of Surrey

    Cytoskeletal contractility in mechanosensing

    Cells have been demonstrated to be extremely sensitive to the physical properties of their external environments, changing behaviours as diverse as proliferation, differentiation and migration in response to physical stimuli. The molecular mechanism by which this mechanosensing is achieved is broadly understood. Molecular motors embedded within the cellular cytoskeletal network bring the network into tension with the degree of resistance broadly signalling information about the local external stiffness. Great strides have been made in understanding which molecular signalling mechanisms drive this behaviour, however the physical mechanisms that couple these molecular signals to the physical properties of the external environment are comparatively less clear. In this talk, I will present continuum elasticity models that capture these physical effects and which demonstrate a clear need to incorporate full spatially resolved models into experimental investigations of mechanotransduction.

  • Friday, October 9th 2020, 2:00pm
    Dr. Magda Carr, University of Newcastle

    Shoaling Internal Solitary Waves

    Internal solitary waves (ISWs) propagate along density interfaces in stably-stratified fluid systems. They occur frequently in geophysical settings such as estuaries, lakes, fjords, oceans, marginal seas and the atmosphere. They owe their existence to a balance between nonlinear wave steepening and linear wave dispersion. It is well know that large amplitude ISWs can induce currents and turbulence in the bottom boundary layer (BBL). There are several mechanisms by which the BBL can be energised and sediment resuspended. These dynamics are enhanced, when shoreward propagating ISWs shoal. The waves break during the process and loose energy to dissipation and turbulent mixing. Laboratory investigation and numerical simulation of the propagation of both mode-1 and mode-2 ISWs over a uniformly sloping, solid topographic boundary, will be presented. Mode-1 ISWs displace isopycnals in one direction only and can be waves of depression or elevation. Mode-2 ISWs on the other hand, displace isopycnals in opposite directions and can be convex or concave in form. The waves are generated by a lock-release method. In the mode-1 case, past literature is compared to recent work and the effect of stratification investigated. In the mode-2 case features of wave shoaling include (i) formation of an oscillatory tail, (ii) degeneration of the wave form, (iii) wave run up, (iv) boundary layer separation, (v) vortex formation and re-suspension at the bed and (vi) a reflected wave signal. In shallow slope cases, the wave form is destroyed by the shoaling process; the leading mode-2 ISW degenerates into a train of mode-1 waves of elevation and little boundary layer activity is seen. For steeper slopes, boundary layer separation, vortex formation and re-suspension at the bed are observed. The boundary layer dynamics is shown (numerically) to be dependent on the Reynolds number of the flow. Reference: Carr et al. J. Fluid Mech. (2019), vol. 879, pp. 604632.

  • Friday, September 25th 2020, 2:00pm
    Dr. Toms Eaves, University of Dundee

    Transition and equilibria in stratified shear flow

    Stratified shear flows control the degree of mixing of salt and heat occurring in the world's oceans. An understanding of the nonlinear flow structures which lead to, and mediate turbulent mixing in these flows is therefore vital in order to accurately model their effect on the Earth's energy balance. This talk will outline a constrained variational procedure which identifies nonlinear flow structures which are most likely to cause turbulence in stratified shear flows. We find that the inclusion of even small buoyancy effects in the flow significantly affects the sequence of events which trigger a turbulent mixing event. An important structure which mediates this transition sequence are edge states - exact, steady-state, unstable equilibria of the Navier-Stokes equations. We will examine these structures in closer detail, and investigate their dynamics over a large range of flow parameters, focussing in particular on the effect of the Prandtl number.

  • Friday, September 18th 2020, 2:00pm
    Dr. Angelika Manhart, University College London

    Aggregation without attraction: Analysing collective dynamics of swimmers and tethered obstacles.

    Aggregation phenomena in biology and beyond are often attributed to attraction between individuals. In this work we study how elastically tethered obstacles interacting with the swimmers impact the macroscopically created patterns. Simulations of an individual-based model reveal at least three distinct large-scale patterns: travelling bands, trails and moving clusters. This motivates the derivation of a macroscopic partial differential equations model, for which we assume large tether stiffness. The result is a coupled system of non-linear, non-local partial differential equations. We use linear stability analysis to predict pattern size from model parameters. Further analysis of the macroscopic equations reveal that, surprisingly, the obstacle interactions induce short-ranged swimmer aggregation, irrespective of whether obstacles and swimmers are attractive or repulsive.

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