Conference Programme
Abstract Book
Nonlinearity plays an important role in many fields of Science, Engineering and Technology. The aim of this conference is to bring together researchers working on aspects of nonlinear phenomena and to encourage interaction between experts from different areas such as Applied Mathematics, Mathematical Analysis, Fluid Dynamics, Engineering and Physics. Recent theoretical developments, new computational methods and experimental findings will be presented and discussed. We plan to avoid parallel sessions and foster as much as possible communication across the different communities.
Please note all talks will be recorded and available shortly after the event for everyone who had paid and registered for the conference and will be available for one month after.
This Conference has been organised in cooperation with the Society for Industrial and Applied Mathematics (SIAM).
Conference topics
- Integrable systems and soliton theory
- Nonlinear waves and nonlinear evolution equations
- Dispersive hydrodynamics
- Rogue waves and extreme wave phenomena
- Instabilities in nonlinear media
- Coherent structures and turbulence
- Nonlinear phenomena in physical and biological sciences
- Phenomena at the interface of nonlinear waves and machine learning
Invited Speakers
Professor Tamara Grava (University of Bristol, UK and SISSA, Italy)
Professor Vera Hur (University of Illinois at Urbana-Champaign, USA)
Professor David Lannes (University of Bordeaux, France)
Professor Demetrios Papageorgiou (Imperial College, UK)
Professor Emilian Părău (University of East Anglia, UK)
Talk Titles and Abstracts
Professor Tamara Grava (University of Bristol, UK and SISSA, Italy) – Gibbs ensemble for the Ablowitz-Ladik lattice, circular beta-ensemble and double confluent Heun equation
We consider the discrete defocusing nonlinear Schrodinger equation in its integrable version, that is called Ablowitz Ladik lattice. We consider the Generalized Gibbs ensemble for the Ablowitz Ladik lattice. In this setting the random Lax matrix of the Ablowitz Ladik is related to the circulant beta-ensemble at high temperature. We obtain the free energy of the Ablowitz-Ladik lattice and the density of tates of the random Lax matrix by establishing a mapping to the one-dimensional log-gas. The density of states is obtained via a particular solution of the double-confluent Heun equation. Joint work with Guido Mazzuca.
Professor Vera Hur (University of Illinois at Urbana-Champaign, USA) – Unstable water waves: a new Evans function approach
I will discuss a new periodic Evans function approach for cylindrical domains, and its application to the spectral instability of Stokes waves in the finite depth. Numerical evidence suggests instability whenever the unperturbed wave is ‘resonant’ with its infinitesimal perturbation waves. This has not been studied analytically except the Benjamin-Feir instability, near the origin of the spectral plane, when (wave number)x(depth)>1.3627…. I will discuss an alternative proof of the Benjamin-Feir instability and, also, the first proof of spectral instability away from the origin, when 0.86430…<(wave number)x(depth)<1.00804…, elucidating the numerical findings. I will discuss capillary-gravity waves and Stokes waves in constant vorticity flows.
Professor David Lannes (University of Bordeaux, France) – Modelling and numerical simulation of a floating object
We present here how the standard Boussinesq equations frequently used to describe the propagation of nonlinear dispersive water waves can be used to model wave-structure interactions. We show that in order to describe these interactions, it is sufficient to solve a transmission problem for the Boussinesq equations, coupled with a set of nonlinear forced ODEs. We propose a second order numerical scheme to solve these equations and validate this simulations with some explicit solutions that can be computed in particular configurations.
Professor Demetrios Papageorgiou (Imperial College, UK) – Nonlinear interfacial waves on the microscale
As system size goes down, physical effects that can be safely ignored in classical wave studies (e.g. viscosity or surface tension) must be brought back in, and indeed can dominate the dynamics. Recent technological applications include microfluidics and other micro-engineering processes, where the main concern is to either identify and harness naturally occurring instabilities, or drive the system out of equilibrium using external forces, in order to facilitate goals such as mixing, heat and mass transfer, and liquid fragmentation, for example. The result is a rich multiphysics environment to be modelled mathematically and understood via analysis and computations.
This talk will provide an overview of nonlinear interfacial instabilities in microscale flows where inertia may be absent or moderate. Several problems involving single-, two- and three-fluid multilayer flows will be discussed and the nonlinear coherent structures that can emerge will be illustrated. In addition, a brief overview of the effect of additives (surfactants) and external fields (e.g. electric fields) will be given with emphasis on the potential of achieving feedback and optimal control of nonlinear interfacial problems.
Professor Emilian Părău (University of East Anglia, UK) – Flexural-gravity waves generated by moving loads on ice plates
Three-dimensional waves generated by moving loads on top of floating ice plates are investigated. The ice plates are modelled using the thin plate theory. Different viscoelastic models for the ice will be presented and wave patterns will be calculated. Nonlinear steady waves will be computed using boundary integral methods. Fully dispersive weakly nonlinear equations will also be derived and comparisons of solutions with field observations will be provided. Other related flows will be discussed.
Call For Abstracts
Our Call for Abstracts is now closed.
Registration
Registration for this event is now closed.
Please note all talks will be recorded and available shortly after the event for everyone who had paid and registered for the conference and will be available for one month after.
Fees
Online Conference Fee – Non IMA Member – £105
Online Conference Fee- IMA/SIAM Member – £75
Online Conference Fee- Non IMA Student Member – £45
Online Conference Fee- IMA/SIAM Student -£30
Online Day rate available for £40 each day – Please contact the IMA Team at conferences@ima.org.uk if you want to attend one day only.
The fees go towards covering staff costs, and the cost of software licence fees required to run the conference.
Scientific Committee
Dr Karima Khusnutdinova (Loughborough University) ‐ Chair
Professor Sara Lombardo (Loughborough University) (Deputy Chair)
Professor Peter Clarkson (University of Kent) – SIAM representative
Professor Gennady El (Northumbria University)
Professor Paul Milewski (University of Bath)
Professor Demetrios Papageorgiou (Imperial College London)
Professor Emilian Părău (University of East Anglia)
Dr Matteo Sommacal (Northumbria University)
Professor Jean‐Marc Vanden‐Broeck (University College London)
Local Organising Committee
Professor Evgeny Ferapontov (Loughborough University)
Dr Karima Khusnutdinova (Loughborough University)
Professor Sara Lombardo (Loughborough University)
Contact information
For scientific queries please contact: Dr. Karima Khusnutdinova (Loughborough University) – K.Khusnutdinova@lboro.ac.uk
For general conference queries please contact the Conference Department – conferences@ima.org.uk Tel: +44 (0) 1702 354 020
