# JAMS

The JAMS is a weekly seminar with talks given by junior researchers on a topic in all areas in Mathematics. It is a great opportunity to share research, get feedback from other students and to become more confident in presenting work. We also provide drinks and snacks!

This year, there are two different types of talks:

Classic JAMS: Short talks, somewhat specialised and more focused on new results. A great opportunity to get know what fellow PhD students’ research is about.

Introductory JAMS: Longer talks, but more accessible and educational. These are meant to introduce you to the basic ideas of active research fields, and give you a broader picture of modern Applied Mathematics.

If you are interested in giving a talk (of either type) or have further questions, please email us at imperialsiam@gmail.com. You can also sign up to our Mailing List to receive regular updates on these events!

Venue: Huxley 130
Time: Wednesday 4pm-5pm

Upcoming Seminars

(21/03/18) Population dynamics in heterogeneous environments
Yong Sul Won
Abstract

We study a nonlinear reaction-diffusion system undergoing a logistic type competition. The diffusivity of species depends on the ratio of their population density and the resource distribution (nourishments). Such a feature provides us with not only a more realistic model of population dispersals but also interesting mathematical challenges. We will present some existence theorems together with a mollification strategy.

(21/03/18)The wonder of the Rado graph
Yibei Li
Abstract

The countable random graph, also referred to as the Rado graph, is a very interesting mathematical object as it appears in many different areas of Maths. It can be constructed using ideas from probability and number theory (more precisely the Dirichlet’s Theorem). It possesses nice properties in logic, group theory, the Ramsey theory and topological dynamics. We will touch upon all these areas to see why the Rado graph makes a fascinating structure.

Past Seminars

(24/01/18) Natural Language Processing with messy datasets
José Luis Ricón [Slides] Abstract

In this talk, I will introduce basic Natural Language Processing ideas and the machine learning approaches that are generally used for dealing with the problem of text classification. After this I will highlight the particular challenges posed by this particular project.

(07/02/18) The problem with turbulence: how can air travel be made more sustainable?
Eleanor Johnstone
Abstract

“When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first.”- Werner Heisenberg.

It is thought that one transatlantic flight can add as much to your carbon footprint as a typical year’s worth of driving. Why are planes so inefficient? Well, part of the reason is turbulence, which causes drag on the aircraft. Therefore one of the most important questions to ask is how can we control the flow so turbulence is less prevalent? Not only could this save the aerospace industry millions of pounds in fuel, but it would also have a huge impact on the sustainability of air travel, and help reduce the dependence on oil which is expected to run out within the next century.

This talk will cover a brief introduction to the equations governing fluid flows, and the emergence and structure of turbulence in basic boundary-layer flows. Specifically, the talk will cover what structures emerge in the transition from laminar to turbulent flow and how these can be described mathematically. These structures can help to provide an understanding of the underlying ‘scaffold’ of turbulence. This knowledge could be implemented to reduce their prevalence and therefore reduce turbulence/drag on an aircraft.

Keywords: fluid dynamics, turbulence, boundary layer, laminar flow control

(21/02/18) Numerical tsunami simulation using goal-oriented mesh adaptivity
Joe Wallwork
Abstract

A mesh adaptive shallow water solver is created for solving tsunami modelling problems. This builds upon previous work at Imperial College in the Firedrake and Thetis projects. The former project provides efficient, finite element solving software and the latter specialises this for coastal, estuarine and ocean modelling on unstructured meshes. An anisotropic mesh adaptivity library is created which is capable of adaption both to fields related to the flow (such as free surface displacement) and as guided by adjoint solution data. Applying mesh adaptivity to shallow water problems, enables the efficient generation of numerical solutions to tsunami wave propagation problems. The case study of the tsunami which struck Fukushima, Japan, in 2011 is considered, wherein leading tsunami waves reached the coast in just ten minutes. Numerical results indicate computational cost can be reduced, whilst retaining a sufficiently high accuracy, under mesh adaptivity. Through establishing a highly efficient approach to numerical tsunami simulation, sufficient warning could be provided in future scenarios, allowing for evacuation and damage mitigation in those coastal areas determined to be most at risk.

(28/02/18) Mode Interactions in Spherical Rayleigh-Bénard Convection
Paul Mannix
Abstract

The critical Rayleigh number $Ra_c$ for thermally convective instability depends on the wave-length of the disturbance.

In an annular spherical domain with separation d, there are degenerate points $(Ra_c , d _c )$ at which instability to two different sets of thermal-rolls occurs simultaneously.
This study provides a weakly non-linear analysis of the multiple-bifurcation problem, demonstrating that four distinct coupled amplitude equations govern the non-linear evolution of these interactions. The choice of which can be predicted from the inherent symmetry of the interacting modes. Considering a variety of $\ell:m$ mode interactions at different values of the Prandtl number $\sigma$, it is found that mixed mode solutions can exist only within certain regions of the parameter space. While for special resonant mode interactions a stable-period solution is found at low Prandtl number $\sigma$. In each case the weakly non-linear prediction is verified using direct numerical simulation.

(14/03/18)Long time behaviour and phase transitions for the McKean-Vlasov equation on the torus.
Rishabh Gvalani
Abstract

We study the McKean-Vlasov equation on the flat torus which is obtained as the mean field limit of a system of interacting diffusion processes enclosed in a periodic box. The system acts as a model for several real world phenomena from statistical mechanics, opinion dynamics, collective behaviour, and stellar dynamics.

After commenting on the well-posedness of the equation, we study its long time behaviour and convergence to equilibrium. We then focus our attention on the stationary problem – under certain assumptions on the interaction potential, we show that the system exhibits multiple equilibria which arise from the uniform state through continuous bifurcations. This relates closely with previous work on phase transitions for the Mckean-Vlasov equation (cf. Chayes and Panferov, J. Stat. Phys., 2010). Finally, we attempt to classify continuous and discontinuous transitions for this system and show how this work, in conjunction with previous studies of the system, can be used to recover classical results on phase transitions for the noisy Kuramoto model. This is joint work with José Carrillo, Greg Pavliotis, and André Schlichting.

(14/03/18)Finite element methods as geometric integrators
James Jackaman
Abstract

For long time accurate numerical integration, it is of paramount importance to preserve certain geometric structures
associated to the underlying system. This has been a key area of research in numerical analysis, known as geometric numerical integration, over the past few decades. In this talk we investigate the continuous Galerkin method as a geometric numerical integrator. We will also introduce a new discontinuous finite element method and discuss what geometric properties this method possesses.

Autumn 2017: [Archive]

Spring 2017: [Archive] Autumn 2016: [Archive]

Spring 2016: [Schedule] [Archive] Autumn 2015: [Schedule] [Archive]

Spring 2015: [Schedule] [Archive] Autumn 2014: [Schedule] [Archive]