Monte-Carlo simulations for wall-bounded incompressible viscous fluid flows
Abstract
In this talk I will present several new stochastic representations for
solutions of the Navier-Stokes equations in a wall-bounded region,
in the spirit of mean field theory. These new representations are
obtained by using the duality of conditional laws associated with the Taylor diffusion family.
By using these representation, Monte-Carlo simulations for boundary fluid flows, including
boundary turbulence, may be implemented. Numerical experiments are given to demonstrate the usefulness of this approach.
Brownian excursions, conformal loop ensembles and critical Liouville quantum gravity
Abstract
It was recently shown by Aidekon and Da Silva how to construct a growth fragmentation process from a planar Brownian excursion. I will explain how this same growth fragmentation process arises in another setting: when one decorates a certain “critical Liouville quantum gravity random surface” with a conformal loop ensemble of parameter 4. This talk is based on joint work with Juhan Aru, Nina Holden and Xin Sun.
Lovers' Rock, romantic reggae put crudely, came to prominence in London in the 1970s, and has been a huge influence in the decades since, especially on R&B and hip-hop. One of film director Steve McQueen's recent Small Axe films was entitled Lovers Rock and featured this song, probably the best known of the genre.
Yesterday over 5000 applicants took the Mathematics Admissions Test, the entrance test used for undergraduate mathematics at Oxford, and other courses at Oxford and other universities. It's a two and a half hour exam. Here Dr James Munro gives you all the answers in 10 minutes or less.
The MAT is used by Oxford Mathematics to help us decide which candidates to invite for interview.