Surrey Mathematics Research Blog

The blog on research in mathematics at the University of Surrey

Derks talk at Banff Workshop in Canada

Gianne Derks attended the Banff International Research Station in Canada the week of 4 November for a workshop on Analysis, Stability and Bifurcation in Modern Nonlinear Physical Systems. Her talk title was “Viscosity induced instability for Euler and averaged Euler equations in a circular domain” with abstract: We consider the infinite time behaviour of a family of stationary solutions of Euler’s equation, which can be described as constrained minima of energy on level sets of enstrophy. For free boundary conditions, this family shadows solutions of 2D Navier-Stokes equations. However, under the no-slip
and under the Navier-slip boundary conditions and in a circular domain, the infinite time Navier-Stokes evolution orbit of a starting point on the family of constrained minima has order 1 distance to the family, however small the viscosity is. The viscosity in the Navier-Stokes equations is a singular perturbation for Euler’s equation and one might suspect that the viscosity-induced instability is related to this singularity.  This is not the case: we show that the same phenomenon can be observed for the averaged Euler equations and second grade fluids with Navier-slip boundary conditions in a circular domain.

A video of Gianne’s talk is available here.

Pasquetti talk at Oxford

Sara Pasquetti gave a talk on Monday 19 November at the Mathematical Institute, Oxford. The talk was in the String Theory Seminar and the title was “Holomorphic blocks in three dimensions.”  An abstract follows: we show that sphere partition functions and indices of 3 dimensional, N = 2, gauge theories can be decomposed into a sum of products of a universal set of holomorphic blocks. The blocks count BPS states of a theory on R2 × S1 and are in one-to-one correspondence with the theory’s massive vacua. The blocks turn out to have a wealth of surprising properties such as a Stokes phenomenon and have interesting dual interpretations in analytically continued Chern-Simons theory and open topological strings.

Statistics project with FHMS

Karen Young is part of a team that has been awarded a grant to study the effect of vitamin D on paediatric patients with fatty liver disease (NAFLD).  In addition the project will also examine whether or not they have certain variants (known as polymorphisms) in genes that influence vitamin D status.   Furthermore, this project will also look, in vitro, at the effect vitamin D has on molecular events in the liver that may relate to disease progression.

The principal investigator is Dr J Bernadette Moore, Lecturer in Molecular Nutrition in FHMS.  Karen Young is the statistician on the project, Dr Kath Hart and Prof. Sue Lanham-New from Nutrition are co-investigators on the grant and the research includes clinical collaborators at King’s College Hospital Denmark Hill’s Paediatric Liver Clinic (Dr. Emer Fitzpatrick and Prof Anil Dhawan).

Visit of Alexei Ilyin from Moscow

Alexei Ilyin of the Keldysh Institute for Applied Mathematics and the Russian Academy of Sciences in Moscow visited the Department the week of 12 November.  His host was Sergey Zelik.  He gave a talk on Thursday in the Analysis seminar on “The Navier Stokes equations and spectral inequalities”.

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