Equations of motion for weakly compressible point vortices.

Equations of motion for compressible point vortices in the plane are obtained in the limit of small Mach number, , using a Rayleigh-Jansen expansion and the method of Matched Asymptotic Expansions. The solution in the region between vortices is matched to solutions around each vortex core. The motion of the vortices is modified over long time scales [Formula: see text] and [Formula: see text].

Stability Analysis of a Bulk-Surface Reaction Model for Membrane Protein Clustering.

Protein aggregation on the plasma membrane (PM) is of critical importance to many cellular processes such as cell adhesion, endocytosis, fibrillar conformation, and vesicle transport. Lateral diffusion of protein aggregates or clusters on the surface of the PM plays an important role in governing their heterogeneous surface distribution. However, the stability behavior of the surface distribution of protein aggregates remains poorly understood.

Numerical solution of scattering problems using a Riemann-Hilbert formulation.

A fast and accurate numerical method for the solution of scalar and matrix Wiener-Hopf (WH) problems is presented. The WH problems are formulated as Riemann-Hilbert problems on the real line, and a numerical approach developed for these problems is used. It is shown that the known far-field behaviour of the solutions can be exploited to construct numerical schemes providing spectrally accurate results.

Dynamics and transport properties of three surface quasigeostrophic point vortices.

The surface quasi-geostrophic (SQG) equations are a model for low-Rossby number geophysical flows in which the dynamics are governed by potential temperature dynamics on the boundary. We examine point vortex solutions to this model as well as the chaotic flows induced by three point vortices. The chaotic transport induced by these flows is investigated using techniques of Poincaré maps and the Finite Time Braiding Exponent (FTBE).

An Arabidopsis rhomboid protease has roles in the chloroplast and in flower development.

Increasing numbers of cellular pathways are now recognized to be regulated via proteolytic processing events. The rhomboid family of serine proteases plays a pivotal role in a diverse range of pathways, activating and releasing proteins via regulated intramembrane proteolysis. The prototype rhomboid protease, rhomboid-1 in Drosophila, is the key activator of epidermal growth factor (EGF) receptor pathway signalling in the fly and thus affects multiple aspects of development.

Wind gusts and plant aeroelasticity effects on the aerodynamics of pollen shedding: a hypothetical turbulence-initiated wind-pollination mechanism.

Plant reproduction depends on pollen dispersal. For anemophilous (wind-pollinated) species, such as grasses and many trees, shedding pollen from the anther must be accomplished by physical mechanisms. The unknown nature of this process has led to its description as the 'paradox of pollen liberation'.