Research topics

Smith, W. R. & Wang, Q. X. 2022 A tractable mathematical model for rectified diffusion. Journal of Fluid Mechanics 951, 25, A12.

The growth of a bubble subject to an acoustic rectification over 6 million cycles of oscillation. Our theory using matched asymptotic expansions in space and multi-scales in time correlates with experiments (cicles). This is the first rational model that predicts the development of ultrasound cavitation development. This milestone development will have long, wide and important impact in research and applications of ultrasound cavitation.

 saturated fusion systems defined on maximal class p-groups. In a slightly different direction, in joint work with Jason Semeraro, Chris has developed computational methods to work with fusion systems using computers.

Wang, Q. X., Liu, W.K., Corbett, C. and Smith, W. R. 2022 Microbubble dynamics in a viscous compressible liquid subject to ultrasound. Physics of Fluids 34, 012105

Bubble oscillates subject to an acoustic wave. This is the only available numerical model that agrees excellently with experiment images for non-spherical bubbles in dozen cycles of oscillations.

You, Y. Cui, J.,Smith, W. R. and Wang, Q. X. Computational and experimental study for bubble dynamics near a rigid boundary for a Reynolds number of O(10-100)

We show that a vortex ring associated with a toroidal bubble is not generated instantaneously as the liquid jet penetrates the bubble, as assumed for over a half of century, but develops within the bubble gas before that.