The mechanism for the generation of vorticity at a viscous free surface is described This is a free surface analogue of Lighthill s strategy for determining the vorticity ux at solid boundaries In this method the zero shear stress and pressure boundary conditions are transformed into a boundary integral formulation suitable for the velocity vorticity description of the ow A vortex sheet along t...

In many dispersed multiphase flows bubbles, droplets, and particles move and disappear due to a phase change. Practical examples include vapour bubbles condensing in subcooled liquids, fuel droplets evaporating in a hot gas and ice crystals melting in water. After these 'bodies' have disappeared, they leave behind a remnant 'ghost' vortex as an expression of momentum conservation. A general fra...

We show that one-dimensional nonlocal flow models in PDE form with Lighthill-Whitham-Richards flux supplemented appropriate in- and out-flow terms can be spatially discretized a finite volume scheme to obtain formally kinetic physically meaningful reaction graph structure. This allows the utilization of theory chemical networks, as demonstrated here via stability analysis model circular topolog...

We derive and analyze two equivalent integral formulations for the time-harmonic electromagnetic scattering by a dielectric object. One is a volume integral equation (VIE) with a strongly singular kernel and the other one is a coupled surface-volume system of integral equations with weakly singular kernels. The analysis of the coupled system is based on standard Fredholm integral equations, and...

The swimming of a micro-organism by the propagation of helical waves on a long slender flagellum is analysed. The model developed by Higdon (1979) is used to study the motion of an organism with a spherical cell body (radius A ) propelled by a cylindrical flagellum (radius a, length L). The average swimming speed and power consumption are calculated for helical waves (amplitude a, wavenumber k)...