C4

A solid object placed at a liquid-gas interface causes the formation of a meniscus around it. In the case of a vertical circular cylinder, the final state of the static meniscus is well understood, from both experimental and theoretical viewpoints. Experimental investigations suggest the presence of two different power laws in the growth of the meniscus. In this talk I will introduce a theoretical model for the dynamics and show that the early-time growth of the meniscus is self-similar, in agreement with one of the experimental predictions. I will also discuss the use of a numerical solution to investigate the validity of the second power law.

Pluripotency is a key feature of embryonic stem cells (ESCs), and is defined as the ability to give rise to all cell lineages in the adult body. Currently, there is a good understanding of the signals required to maintain ESCs in the pluripotent state and the transcription factors that comprise their gene regulatory network. However, little is known about how ESCs exit the pluripotent state and begin the process of differentiation. We aim to understand the molecular events associated with this process via an experiment-model cycle.

It is often difficult to include sufficient biological detail when modelling cell population growth to make models with real predictive power. Continuum models often fail to capture physical and chemical processes happening at the level of individual cells and discrete cell-based models are often very computationally expensive to solve. In the first part of this talk, I will describe a phenomenological continuum model of cell aggregate growth in a specific perfusion bioreactor cell culture system, and the results of numerical simulations of the model to determine the effects of the bioreactor operating conditions and cell seeding on the growth. In the second part of the talk, I will introduce a modelling approach used to derive continuum models for cell population growth from discrete cell-based models, and consider possible extensions to this framework.

JH: Water filtration systems typically involve flow along a channel with permeable walls and suction applied across the wall. In this ``cross-flow'' arrangement, clean water leaves the channel while impurities remain within it. A limiting factor for the operation of cross-flow devices is the build-up of a high concentration of particles near the wall due to the induced flow. Termed concentration polarization (CP), this effect ultimately leads to the blocking of pores within the permeable wall and the deposition of a ``cake'' on the wall surface. Here we show that, through strategic choices in the spatial variations of the channel-wall permeability, we may reduce the effects of CP by allowing diffusion to smear out any build up of particles that may occur. We demonstrate that, for certain classes of variable permeability, there exist optimal choices that maximize the flux of clean water out of a device.

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IvG: TBC

Berz used the Hahn-Banach Theorem over Q to prove that the graph of a measurable subadditive function that is non-negatively Q-homogeneous consists of two lines through the origin. I will give a proof using the density topology and Steinhaus’ Sum-set Theorem. This dualizes to a much simpler category version: a `Baire-Berz Theorem’. I will give the broader picture of this using F. Burton Jones’ analysis of additivity versus linearity. Shift-compactness and special subsets of R will be an inevitable ingredient. The talk draws on recent work with Nick Bingham and separately with Harry I. Miller.

Data assimilation is a particular form of state estimation. That's partly the "what". We'll also look at the how's, the why's, some who's and some where's.