Dr Martin Winter receives the award for his paper:

"Rigidity, Tensegrity and Reconstruction of Polytopes under Metric ConstraintsLink opens in a new window"

in International Mathematics Research Notices.

Citation:

Polytopes are higher dimensional analogues of the cubes, pyramids and other solid shapes that one often sees in classrooms. They appear frequently in mathematics and computer science, especially in linear programming problems. In this article Winter discusses how to reconstruct polytopes from limited information and he solves the problem in several important cases. To do so he introduces unexpected tools from spectral graph theory as well as high-dimensional geometry. In particular, he uses the Wachspress coordinates that have appeared in what look like completely unconnected contexts.

Dr Kawa Manmi receives the award for his paper:

"Oscillation of an ultrasonically driven gas bubble in an asymmetric confined domainLink opens in a new window"

in International Journal of Mechanical Sciences, joint with Bapir, Saeed and Dadvand.

Citation:

The article considers modelling and analysis of a gas bubble which moves in a confined domain, guided by ultrasounds. This problem is relevant for applications such as cleaning and decontamination, as well as removing of kidney stones – this is because the high pressure that can develop in these bubbles as they collapse can generate flow movement that is violent enough to erode adjacent material. The paper develops advanced numerical techniques which tackle challenges present in the literature (for example, the new mesh and algorithm proposed here preserves volume and does not create unphysical gas phases which were issues in previous papers) and the results are validated against analytical solutions and experiments (with excellent agreement).

Congratulations to both winners!