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Applied Mathematics Seminars 

Spring 2023

Seminars (unless otherwise stated) usually take place online on Tuesdays at 3.00pm on Zoom via the link https://ucl.zoom.us/j/99614222402. 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).

Tuesday 17 January 2023

Speaker: Jean-Luc Thiffeault (University of Wisconsin - Madison)

Title: The mathematics of burger flipping

Abstract:
Ever since the dawn of time people have (literally) asked the question -- what is the most effective way to grill food? Timing is everything, since only one surface is exposed to heat at a given time. Should we flip only once, or many times?  I will show a simple model of cooking by flipping, and some interesting mathematics will emerge. The rate of cooking depends on the spectrum of a linear operator, and on the fixed point of a map.  If the system is symmetric, the rate of cooking becomes independent of the sequence of flips, as long as the last point to be cooked is the midpoint.  This toy problem has some characteristics reminiscent of more realistic scenarios, such as thermal convection and heat exchangers.

Tuesday 24 January 2023

Speaker: Jean-Marc Vanden-Broeck (UCL)

Title: Capillary waves, interfacial waves and waves with vorticity

Abstract:
Water waves have been studied for over 200 years and many important results have been obtained. However there are still open questions for nonlinear waves. In this talk we will follow branches of solutions and focus on the limiting configurations (i.e. the waves of maximum amplitude which can be reached on each branch). We shall assume the fluids to be incompressible and inviscid. We will include various effects in the dynamic boundary condition and show how the limiting configurations differ for capillary waves, gravity waves interfacial waves (i.e. waves travelling at the interface between two layers of fluid of different constant densities) and waves with constant vorticity. These problems are mathematically difficult because of the nonlineartity and the presence of free surfaces. They are solved by a combination of analytical and numerical methods. These include boundary integral equation methods and series truncation methods. Both periodic and solitary waves are considered in frames of reference moving with the waves. New branches of solutions for interfacial waves will be presented. They usually emerge as branches bifurcating from known branches but they do not have an equivalent in the classical problem of pure gravity surface waves. Some unexpected connections between capillary waves and waves with constant vorticity will also be explored in the talk. As time permits asymmetric waves and other types of waves will be discussed. Some of these recent works are joint with Xin Guan, Zhan Wang, Vera Hur, Frédéric Dias, Tao Gao and Alex Doak.

Tuesday 31 January 2023

Speaker: Gunnar Peng (Imperial College)

Title: weakly nonlinear dynamics of self-propelling active particles 

Abstract:
A submerged isotropic active particle (or droplet) that emits/consumes a chemical and interacts with it to drive flow via diffusio-osmotic slip (or Marangoni effects) can exhibit symmetry-breaking spontaneous motion. We derive a reduced-order model for the slow dynamics of the particle near the threshold for spontaneous motion using a weakly nonlinear expansion, which involves matching a quasi-steady particle-scale solution to an unsteady diffusive remote region. The resulting amplitude equation for the particle velocity includes a term representing the interaction of the particle with its own wake in the remote region, which can be expressed as a time integral over the history of the particle motion, allowing theoretical analysis and efficient numerical simulation of fully three-dimensional problems. We study various cases, including the particle interacting with a force, a wall, other particles and/or other weak perturbations, resulting in linear motion, circular motion, and more exotic dynamics.

Tuesday 07 February 2023

Speaker: Frédéric Dias (Centre Borelli, ENS-Saclay, France)

Title: On extreme ocean waves

Abstract:
The study of extreme ocean waves is a rapidly expanding area of research worldwide. Although much work in this area is based on modelling and experiments in controlled wave tanks, the starting point of all studies is wave observation in the natural world. During this talk, we will provide some evidence of extreme wave events, describe the main mechanisms for their generation and conclude with what we believe makes ocean waves go rogue in the real world.

Tuesday 14 February 2023

READING WEEK - NO SEMINAR

 

Tuesday 21 February 2023

Speaker: TBC

Title: TBC

Abstract:
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Tuesday 28 February 2023

Speaker: TBC

Title: TBC

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Tuesday 07 March 2023

Speaker: Alessandro Manacorda (Universite du Luxembourg)

Title: TBC

Abstract:
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Tuesday 14 March 2023

Speaker: Sasha Korobkin (University of East Anglia)

Title: TBC

Abstract:
TBC

Tuesday 21 March 2023

Speaker: Bernhard Scheichl (Technische Universitat Wien, Vienna, Austria)

Title: TBC

Abstract:
TBC