Overview of the programme
Early Career Mathematicians “Icebreaker”. Organised and run by the IMA (separate registration via the IMA)
Professor Alan Champneys
University of Bristol
Beyond Kuramoto: Synchronisation and the wisdom of the crowd
This talk shall begin with the beautiful and highly influential theory of phase-coupled oscillators due to Yoshiki Kuramoto, which has led to much understanding of emergent synchronisation among incoherent autonomous agents. Although never the main theme of my research, I shall introduce a number of problems in applied maths I have worked on over the years that involve the concept of synchronisation. In each case, it turns out that one needs to go beyond Kuramoto. Problems addressed include stability of the national grid, how courting mosquitoes synchronise harmonics of their wing beat frequencies, and, within neurophysiology, ongoing work on modelling circadian rhythms and synchronous bursting activity of neurons responsible for dopamine secretion. The main example though will be recent published work in which we busted the popular myth that the lateral pedestrian-induced instability of the London Millennium Bridge is a text-book example of Kuramoto-style synchronisation. It transpires that there is a simpler theory, fully consistent with observations on many bridges. Simply put; when walking on moving ground, pedestrians try not to fall over. As I shall show, its slightly more subtle than that. But the main point is that, irrespective of their gait frequency, pedestrians provide positive feedback, or negative damping, on average. Thus, as has been understood by engineers for a while, pedestrian-induced bridge instability is a simple Hopf bifurcation, not due to resonance but to a positive feedback mechanism, akin to flutter in fluid-structure interaction problems. I shall conclude by finding other examples that suggest this other kind of synchronisation may be more prevalent than previously thought, where incoherent agents provide positive feedback on average leading to the onset of and entrainment to a single exogenous oscillation frequency.
Professor William Parnell
University of Manchester
The QJMAM Lecture
The Mathematics of Waves and (Meta)Materials
The last two decades have seen a rapid advance in the science of advanced composites and metamaterials, i.e. media that have properties that surpass those exhibited by materials available from natural sources. Applied mathematics has played a key role in this progress, ranging from developments in transformation theory to yield the required properties of cloaks and metamaterials, to advances in dynamic homogenisation techniques to predict effective properties for specific microstructures in order to try to realise those metamaterials. It was also understood that the Willis-Milton-Briane equations, first introduced by Willis in 1981, could model the effective dynamic behaviour of complex inhomogeneous media with microstructural asymmetries, by employing non-standard elastodynamic constitutive equations. A range of topics will be described in this talk, covering much of the work that our group has carried out over the last 5-6 years and in particular in the areas of wave propagation in complex media, metamaterials, and the modelling and design of advanced composites. We will highlight the benefits that can be realised by working at the interface of mathematics and materials characterisation, imaging and state-of-the-art experimentation and the impact that this can have on applied mathematics. In the first half of the talk we will cover some concepts associated with wave propagation in complex media and the notion of effective properties of inhomogeneous materials. We will introduce transformation theory and describe how this can act as one approach to metamaterial and advanced composites design. We will describe slow sound, and acoustic cloaks, as well as elastic cloaks in both the static and dynamic regimes. Much of acoustics is focused on tuning the impedance of a medium in order to control sound and vibration. We will discuss one such application for a specific type of composite foam, describing its constitutive behaviour with reference to a broad range of mathematical techniques including nonlinear viscoelasticity and constrained buckling. Under load, the medium in question undergoes strong nonlinearity and we describe how modelling has been integrated with experimentation and characterisation to better understand the behaviour of these foams, whilst also pointing to surrogate modelling techniques that can be exploited to optimise the material’s response in future designs. The second half of the talk will cover some very recent work associated with elastodynamic metamaterials. We introduce some new concepts for enhanced elastodynamic resonators and discuss how they can be employed to tune scattered fields and metamaterial properties. Following this, we describe a novel microstructural configuration with asymmetry that leads to directional-dependent properties that do not break (physical) reciprocity arguments. The effective response of these materials must be described by elastodynamic constitutive laws with a non-zero Willis coupling coefficient. These materials and their associated dynamic constitutive laws pave the way for new materials that can control, tune and redirect acoustic and elastic waves in novel and exciting ways.
Professor Catherine Sulem FRSC
University of Toronto
Stewartson Memorial Lecture
Normal form transformations and the Dysthe’s equation for the nonlinear modulation of deep-water gravity waves
Modulation theory has been an effective tool for the asymptotic modeling and analysis of surface gravity waves in a weakly nonlinear scaling regime. Two limiting regimes of interest are the shallow-water regime where waves are viewed as mild modulations of the uniform mean flow, and the deep-water regime where approximate solutions are sought in the form of mild modulations of monochromatic waves. The present talk is focused on the latter case where a modulational Ansatz makes it possible to derive reduced models for the wave envelope such as the nonlinear Schrödinger equation which is a canonical model for nonlinear dispersive waves. Another example is the Davey–Stewartson system which describes wave modulation on finite depth in three dimensions. A higher-order approximation was proposed by Dysthe (1979) for deep water using the perturbative method of multiple scales and was later extended to several other settings. The Dysthe equation and its variants have been widely used in the water wave community due to their efficiency at describing realistic waves, in particular waves with moderately large steepness. However, unlike the Nonlinear Schrödinger equation, earlier versions of the Dysthe equation are not Hamiltonian while the original water wave system has a Hamiltonian structure. Using the method of normal form transformations near the equilibrium state, I will present a new derivation of the Dysthe equation that preserves the Hamiltonian character of the water wave problem. A precise calculation of the third-order normal form allows for a refined reconstruction of the free surface. This modulation approximation is tested against direct numerical simulations of the full Euler system and against predictions from the classical Dysthe equation in various physical settings.
Professor Helen Wilson
University College London
IMA Lighthill Lecture
Modelling Complex Suspensions
Materials made from a mixture of liquid and solid are, instinctively, very obviously complex. From dilatancy (the reason wet sand becomes dry when you step on it) to extreme shear-thinning (quicksand) or shear-thickening (cornflour oobleck) there is a wide range of behaviours to explain and predict. I’ll discuss the seemingly simple case of solid spheres suspended in a Newtonian fluid, which still has plenty of surprises up its sleeve.
Professor Julia Yeomans FRS
University of Oxford
Active Matter: “Evading the decay to equilibrium”
In his 1944 book, “”What is Life? The Physical Aspect of the Living Cell””, Erwin Schrödinger wrote living matter evades the decay to equilibrium.
Active matter theories, which describe persistent non-equilibrium behaviour, are being increasingly applied to biological processes. Dense active matter shows complex collective behaviour, and mesoscale turbulence, the emergence of chaotic flow structures characterised by high vorticity and self-propelled topological defects. I shall discuss how the ideas of active matter are suggesting new ways of interpreting cell motility and morphogenesis.
“Mathematics: Enabling Innovation in Sport”
Dr Peter Husemeyer, Co-Founder and CTO of Sportable Sportable Technologies Ltd is a UK-based Sports Data company. They recently launched the world’s first commercially available ‘smart’ rugby ball in partnership with Gilbert. Sportable is an innovative, forward thinking tech start-up that is revolutionising how we view, understand and interact with live sport. With rugby as a primary focus, they are working with a number of top teams and manufacturers, creating and developing state of the art hardware and wearable devices that enable sport specific data to be collated in real time to deliver an enhanced spectator experience, and elevated fan engagement. Peter holds Bachelor and Master’s degrees from the University of Cape Town, and a PhD in Nuclear Engineering from the University of Cambridge. Prior to founding Sportable, Peter worked at the NASA Marshall Space Flight Center, investigating the feasibility of an advanced rocket engine concept. In 2016, Peter co-founded Sportable, and as its Chief Technology Officer leads on product development and innovation related activities.
Professor Mike Caine, Professor of Sports Technology and Innovation and Associate Pro Vice-Chancellor for Sport. Professor Caine has collaborated with many of the world’s leading sporting goods brands, developing and commercialising new products.
Dr Varuna De Silva – Senior Lecturer in Artificial Intelligence, specifically multi-agent reinforcement learning, multimodal computer vision, and simulation models in Sport, and other application domains.
Dr Lauren Burch – Senior Lecturer in Sport Business with research interests in digital and social media communication and marketing within the Sports industry.
Professor Nick Jennings – Vice-Chancellor and President of Loughborough University. Professor Nick Jennings is an internationally-recognised authority in the areas of AI, autonomous systems, cyber-security and agent-based computing.
Advances and challenges in the modelling of multiscale, complex, and heterogeneous materials
Dr Ariel Ramírez Torres and Dr Raimondo Penta
Applied Algebra and Geometry
Dr Emilie Dufresne, Dr Dimitra Kosta and Dr Nelly Villamizar
At the interface between analytical methods and high performance computing in fluid mechanics
Radu Cimpeanu and Matthew Moore
Decision making under uncertainty
Eric Hall and Abdul-Lateef Haji-Ali
Deep Learning and Inverse Problems
Margaret Duff and Matthias J. Ehrhardt
Dispersive hydrodynamics and applications
Daniel Ratliff and Thibault Congy
Ethics in Mathematics
Dr Timothy Johnson
Inflammation and the Immune Response
Martin R. Nelson and Joanne L. Dunster
Mathematical Modelling in the Social Sciences
Ben Goddard and Greg Pavliotis
Mathematical modelling of biological oscillations
Anne Skeldon and Kyle Wedgwood
Mathematical models of plant-soil interactions
Matthias Mimault, Mariya Ptashnyk and Lionel Dupuy
Mathematics in microbiology
Sara Jabbari and John Ward
Mathematics in single-cell biology
Aden Forrow and Bianca Dumitrascu
Mathematics of the eye
Dr Jennifer Tweedy
Modelling the respiratory transmission of Covid-19
Nonlinear Surface and Internal Waves
Dr Emiliano Renzi and Dr Alberto Alberello
Nonlinear Waves and Jets
Dr Emiliano Renzi
Nonreversible processes: analysis and computations
Hong Duong and Nikolas Nüsken
Reservoir Computing and Dynamical Systems
Jonathan Dawes and Andrea Ceni
Smectic Fluids: Reduced Dimensionality/Increased Complexity
Tyler Shendruk and Marco Mazza
Wave Problems in Complex Continua
Further programme information to follow