Applied Mathematics Seminars Summer 2019

Seminars (unless otherwise stated) will take place on Mondays at 2.00pm in Maths Room 505 - see the map for further details. There will be tea afterwards in Maths Room 606 (6th Floor, 25 Gordon Street) - see map for further details. If you require any more information on the Applied seminars please contact Prof Jean-Marc Vanden-Broeck (e-mail: j.vanden-broeck AT ucl.ac.uk or tel: 020-7679-2835) or Prof Ilia Kamotski (e-mail: i.kamotski AT ucl.ac.uk or tel: 020-7679-3937).

8 July 2019 at 2pm in Room 505

Speaker: Prof Vera Mikyoung Hur (University of Illinois at Urbana-Champaign, USA)

Title: Stokes waves in a constant vorticity flow: numerical computation

Stokes in the 1800s made formal but far-reaching considerations about periodic waves at the surface of water, under the influence of gravity, propagating a long distance at a practically constant velocity without change of form. For instance, he observed that the crests become sharper and the troughs flatter, and that the so-called wave of greatest height, or the wave of extreme form, is distinguished by a 120 degree's peaking at the crest. The irrotational flow assumption is justified in many situations, and facilitates rigorous analysis and numerical computation. But rotational effects are significant in many others. I will review recent progress in the constant vorticity setting. Numerical findings include folds and gaps in the wave speed vs. amplitude plane, and a profile enclosing multiple bubbles of fluids.

24 July 2019 at 3pm in Room 500

Speaker: Professor Janusz Mierczyński (Wrocław University of Science and Technology)

Title: Carrying Simplices for Competitive Maps:  A Survey

For a competitive map, a carrying simplex is an invariant unordered set towards which all nontrivial trajectories are attracted.  We will give a survey of known results (and their proofs) on the existence of carrying simplices.  In particular, emphasis will be laid on the smoothness and convexity of them.