Past Junior Applied Mathematics Seminar

17 May 2016
12:45
Arnold Mathijssen
Abstract

Interactions between micro-swimmers and their complex flow environments are important in many biological systems, such as sperm cells swimming in cervical mucus or bacteria in biofilm initiation areas. We present a theoretical model describing the dynamics of micro-organisms swimming in a plane Poiseuille flow of a viscoelastic fluid, accounting for hydrodynamic interactions and biological noise. General non-Newtonian effects are investigated, including shear-thinning and normal stress differences that lead to migration of the organisms across the streamlines of the background flow. We show that micro-swimmers are driven towards the centre-line of the channel, even if countered by hydrodynamic interactions with the channel walls that typically lead to boundary accumulation. Furthermore, we demonstrate that the normal stress differences reorient the swimmers at the centre-line in the direction against the flow so that they swim upstream. This suggests a natural sorting mechanism to select swimmers with a given swimming speed larger than the tunable Poiseuille flow velocity. This framework is then extended to study trapping and colony formation of pathogens near surfaces, in corners and crevices. 

  • Junior Applied Mathematics Seminar
3 May 2016
13:00
Abstract

We consider the motion of a thin liquid drop on a smooth substrate as the drop evaporates into an inert gas. Many experiments suggest that, at times close to the drop’s extinction, the drop radius scales as the square root of the time remaining until extinction. However, other experiments observe slightly different scaling laws. We use the method of matched asymptotic expansions to investigate whether this different behaviour is systematic or an artefact of experiment.

  • Junior Applied Mathematics Seminar
17 June 2014
13:15
Marya Bazzi
Abstract

Networks provide a convenient way to represent complex systems of interacting entities. Many networks contain "communities" of nodes that are more strongly connected to each other than to nodes in the rest of the network. Most methods for detecting communities are designed for static networks. However, in many applications, entities and/or interactions between entities evolve in time. To incorporate temporal variation into the detection of a network's community structure, two main approaches have been adopted. The first approach entails aggregating different snapshots of a network over time to form a static network and then using static techniques on the resulting network. The second approach entails using static techniques on a sequence of snapshots or aggregations over time, and then tracking the temporal evolution of communities across the sequence in some ad hoc manner. We represent a temporal network as a multilayer network (a sequence of coupled snapshots), and discuss  a method that can find communities that extend across time. 

  • Junior Applied Mathematics Seminar
3 June 2014
13:00
Paul Taylor and Mark Gilbert
Abstract
Position jump models of diffusion are a valuable tool in biology, but stochastic simulations can be very computationally intensive, especially when the number of particles involved grows large. It will be seen that time-savings can be made by allowing particles to jump with a range of distances and rates, rather than being restricted to moving to adjacent boxes on the lattice. Since diffusive systems can often be described with a PDE in the diffusive limit when particle numbers are large, we also discuss the derivation of equivalent boundary conditions for the discrete, non-local system, as well as variations on the basic scheme such as biased jumping and hybrid systems.
  • Junior Applied Mathematics Seminar
13 May 2014
13:00
to
14 May 2014
14:00
Yves-Lauren Kom Samo
Abstract

Cox processes arise as a natural extension of inhomogeneous Poisson Processes, when the intensity function itself is taken to be stochastic. In multiple applications one is often concerned with characterizing the posterior distribution over the intensity process (given some observed data). Markov Chain Monte Carlo methods have historically been successful at such tasks. However, direct methods are doubly intractable, especially when the intensity process takes values in a space of continuous functions.

In this talk I'll be presenting a method to overcome this intractability that is based on the idea of "thinning" and that does not resort to approximations.

  • Junior Applied Mathematics Seminar

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