top of page

ARCHIVE OF RECORDED TALKS

Year 2021

04 JUNE

2pm to 3pm

Speaker: Peter Galenko (Friedrich Schiller University, Germany)

Title: Cooperative atomic motion and crystal growth kinetics in glass-forming metallic systems

Abstract:

In the lecture, an analysis of experimental data and theoretical modelling of the microstructure of glass-forming alloys during their solidification is presented. A kinetic phase-field model is discussed with its solution to obtain the kinetic contribution into the whole balance of undercooling for the mesoscopic theory of dendritic growth. It is shown, how results of atomistic modelling and experimentally measured thermodynamic and kinetic properties of alloys may assist the development and interpretation of the theoretical modelling.

28 MAY

2pm to 3pm

Speaker: Svetlana Gurevich (University of Munster, Germany)

Title: Dynamics of spatio-temporal localized states in time-delayed systems

Abstract:

Time-delayed systems describe a large number of phenomena and exhibit a wealth of interesting dynamical regimes such as e.g., fronts, localized structures or chimera states. They naturally appear in situations where distant, pointwise, nonlinear nodes exchange information that propagates at a finite speed. In this talk, we review our recent theoretical results regarding the existence and the dynamics of temporal, spatial and spatio-temporal localized structures in the output of semiconductor mode-locked lasers. In particular, we discuss dispersive effects which are known to play a leading role in pattern formation. We show that they can appear naturally in delayed systems and we exemplify our result by studying the influence of high order dispersion in a system composed of coupled optical microcavities.

21 MAY

2pm to 3pm

Speaker: Kateryna Terletska (National Academy of Sciences of Ukraine, Ukraine)

Title: Classification of internal waves shoaling over slope-shelf topography

Abstract:

The shoaling of an internal solitary waves of depression in two layer fluid with an idealized slope-shelf topography is studied to classify the regimes of shoaling. Two mechanisms were assumed to be essential during wave shoaling: (i) wave breaking resulting in mixing and (ii) changing of the polarity of the initial wave of depression over the slope into wave of elevation on the shelf. Proposed three-dimensional 𝛼𝛽𝛾 classification diagram is based on three parameters: the slope angle 𝛾, the non-dimensional wave amplitude 𝛼 (wave amplitude normalized on the upper layer thickness) and the blocking parameter 𝛽 that is the ratio of the height of the bottom layer on the the shelf to the incident wave amplitude. Relations between the parameters 𝛼,𝛽,𝛾 for each regime were obtained using the empirical condition for wave breaking and weakly nonlinear theory for criterion of changing polarity of the wave. Four zones were separated in 𝛼𝛽𝛾 classification diagram: (I) Without changing polarity and wave breaking; (II) Changing polarity without breaking; (III) Wave breaking without changing polarity; (IV) Wave breaking with changing polarity. The results of field, laboratory and numerical experiments were compared with proposed classification and good agreement was found.

14 MAY

2pm to 3pm

Speaker: Dan Ratliff (Northumbria University)

Title: The Dynamics of Waves in the Neighbourhood of the Benjamin-Feir Instability.

Abstract:

The dynamics of dispersive nonlinear waves remains a problem that attracts significant interest, in part for their interesting stability properties. Arguably the most famous case is the Benjamin-Feir (BF) instability, where uniform wavetrains undergo a transition of stability due to a nonlinear frequency correction term ω2. This transition occurs precisely when ω0’’ ω2=0, where ω0 is the linear dispersion relation and primes denotes differentiation. There are several emergent behaviours, such as an increase in the wave’s wavelength (frequency downshifting) or resonant wave bursting, which have been observed but elude mathematical insight as to why they occur.


In order to understand these phenomena, we explore the wave dynamics of from the standpoint of Whitham modulation theory and phase dynamics, ultimately uncovering that each of the possible transitions (either ω0’’=0 or ω2=0) admits a different set of nonlinear dynamics governing the wave quantities whose solutions can be used to understand the wave behaviours near the BF threshold. Moreover, this work illustrates the role of mean flow is significant and is central to the emergence of permanent frequency downshifting and localised wave bursts one observes. We use this reasoning to explain, at least qualitatively, the experimental observations from wave-tank experiments in water waves and fluid conduits.

07 MAY

2pm to 3pm

Speaker: John Chapman (Keele University)

Title: Fractional power series and the method of dominant balances


Abstract:

In this talk I'll give a general treatment of the method of dominant balances for a single polynomial equation, in which an arbitrary number of parameters is to be scaled in such a way that the maximum possible number of terms in the equation is in balance at leading order.  This leads in general to a fractional power series (a `Puiseux series'), in which, surprisingly, there can be large and irregular gaps (lacunae) in the fractional powers actually occurring.


A complete theory is given to determine the gaps, requiring the notion of a Frobenius set from number theory, and its complement, a Sylvester set.  The starting point is the Newton polytope in arbitrarily many dimensions, and key tools for obtaining precise results are Faà di Bruno’s formula for the high derivatives of a composite function, and Bell polynomials.  Full account is taken of repeated roots, of arbitrary multiplicity, in the dominant balance which launches a Puiseux series.  The fractional powers in these series can have remarkably large denominators, even for a polynomial of modest degree, and the nature of Frobenius sets is such that it can take hundreds of terms for long-run regularity to emerge.


The talk is applied in outlook, as the method of dominant balances is widely used in physics and engineering, where it gives results of extraordinary accuracy, far beyond the expected range.  The work has been conducted in a collaboration begun at the Isaac Newton Institute, Cambridge, with H. P. Wynn (London School of Economics).  We believe the results are new.  Despite hundreds of years of use of Puiseux series (since 1676), we are not aware of any previous attempt to give a complete quantitative account of their gaps.


The talk may also be of interest to number theorists and algebraic geometers, especially to anyone interested in computational algebraic geometry - currently a booming area at the interface of algorithmic methods and pure mathematics.

30 APRIL

2pm to 3pm

Speaker: Silvia Gazzola (University of Bath)

Title: Iterative regularization methods for large-scale linear inverse problems.

Abstract: Inverse problems are ubiquitous in many areas of Science and Engineering and, once discretized, they lead to ill-conditioned linear systems, often of huge dimensions: regularization consists in replacing the original system by a nearby problem with better numerical properties, in order to find a meaningful approximation of its solution. After briefly surveying some standard regularization methods, both iterative (such as many Krylov methods) and direct (such as Tikhonov method), this talk will introduce a recent class of methods that merge an iterative and a direct approach to regularization. In particular, strategies for choosing the regularization parameter and the regularization matrix will be emphasized, eventually leading to the computation of approximate solutions of Tikhonov problems involving a regularization term expressed in a p-norm.

23 APRIL

2pm to 3pm

Speaker: Rohan Vernekar (University of Edinburgh, UK)

Title: Lattice Boltzmann simulations of particle growth and dissolution in flow.

Abstract: Particles at the small scales such as silica nano and micro particles have a wide rage of potential future applications from drug delivery to surface coatings. Control over the morphology, size distribution, porosity and dispersity of such particles is crucial for realizing their intended industrial applications. The physics and chemistry of growth of such particles under suspension flow conditions is not well understood, and is often a complex outcome of various effects and process time scales (e.g. advection, diffusion, reaction and deposition rates). Therefore predictive numerical simulation tools are crucial in order to realize industrial scale-up of particle growth processes.


I use a novel lattice Boltzmann (LB) algorithm that models growth of particles under particle-resolved flow conditions via chemical species deposition. This algorithm combines fluid LB for incompressible hydrodynamics, advection-diffusion LB for chemical species transport, resolved suspended particle dynamics through interface tracking and a mesoscale adsorption bundary condition for particle growth. The code can also be used for particle dissolution under flow, simply by reversing the surface reaction boundary condition at particle-fluid interface.


The algorithm is versatile enough to address a wide range of coupled problems such as particle growth under sheared suspension conditions, particle sedimentation coupled to reactive growth as well as particle dissolution under flow stirring. I shall present a selection of these problems demonstrating the capabilities of the solver, which enables the study of flow effects on particle growth/dissolution, morphology and size distribution of suspensions.

16 APRIL

2pm to 3pm

Speaker: László Gránásy (Wigner Research Centre for Physics, Hungary)

Title: Phase-field modeling of complex polycrystalline structures.

Abstract: 

Results from an orientation-field-based phase-field model will be reviewed. First I briefly present a phase-field model developed during the past decade that incorporates homogeneous and heterogeneous nucleation of growth centers, and several mechanisms for the formation of new grains at the perimeter of growing crystals, a phenomenon termed as growth front nucleation (GFN). This approach enables the modeling of complex polycrystalline structures including disordered ("dizzy") dendrites, crystal sheaves, spherulites, and fractal-like aggregates (Fig. 1). Possible control of solidification patterns via external fields, confined geometry, particle additives, scratching/piercing thin films, etc. via phase-field modeling will also be addressed. Microscopic aspects of GFN, quantitative simulations, and possible future directions will also be discussed briefly.


References:

1. Gránásy, L.; et al. Nat. Mater. 2004, 3, 645–650.

2. Gránásy, L.; et al. Metall. Mater. Trans. A 2014, 45, 1694–1719.

3. Gránásy, L.; et al. Prog. Mater. Sci. 2019, 106, 100569.

09 APRIL

2pm to 3pm

Speaker: Alexander Lykov (Lomonosov Moscow State University, Russia)

Title: Ergodic properties of many particle systems with random external collisions

Abstract: In the talk we will introduce Hamiltonian particle systems with quadratic potential in which only few degrees of freedom interact with external medium. This interaction is carried out by “collisions”. The meaning of “collision” is quite general in our framework. The main point is that the interaction occurs at random time moments t_1<t_2<… and the given degrees of freedom are transformed “randomly” by some nonlinear (in general) map. Particular cases are: velocity flip (change the momentum sign of the one degree of freedom), one-dimensional collision, two-dimensional collision, etc.. We will formulate several results about convergence to equilibrium for those models; discuss the main steps of the proof. The talk is based on the series of author’s papers (jointly with Malyshev V. ).

26 MARCH

2pm to 3pm

Speaker: Victor Shrira (Keele University)

Title: Why are gravity-capillary waves  skewed in the way they are? The physical mechanisms of front-back asymmetry

Abstract: 

In nature the wind waves of gravity-capillary range are noticeably skewed forward. The salient feature of such waves is a   characteristic pattern of capillary ripples on their crests. The   train of these 'parasitic capillaries' is not symmetric with respect   to the crest, it is localised on the front slope and decays towards   the trough. Although understanding the gravity-capillary waves   front-back asymmetry is important for remote sensing and,   potentially, for wave-wind interaction, the physical mechanisms   causing this asymmetry have not been identified. Here we address this gap by extensive numerical simulations of the Euler equations   employing the method of conformal mapping for two-dimensional potential flow and taking into account wave generation by wind and dissipation due to molecular viscosity. On examining the role of   various factors contributing to the wave profile front-back   asymmetry: wind forcing, viscous stresses, the Reynolds stresses   caused by ripples, we found in the absence of wave breaking the   latter to be by far the most important. It is the lop-sided ripple   distribution which leads to the noticeable fore-aft asymmetry of the   mean wave profile. We also found how the asymmetry depends on wavelength, steepness, wind, viscosity and surface tension. The results of the model are discussed in the context of the available   experimental data on asymmetry of gravity-capillary waves in both   breaking and non-breaking regimes. A reasonable agreement of the model with the data has been found for the regime without breaking or microbreaking.


The work was done jointly with A.Dosaev and Yu.Troitskaya.

19 MARCH

2pm to 3pm

Speaker: Gyula Toth (Loughborough University)

Title: Time-irreversibility in the classical many-body dynamics: Exact continuum equations in the macroscopic limit

Abstract: One of the unsolved fundamental problems in physics is the origin of the thermodynamic arrow of time provided by the second law of thermodynamics. In essence, while the solutions of the governing equations of matter operating on microscopic scales are time reversible, macroscopic-scale order is known to solely decay in spontaneous spatiotemporal processes. In 1876, Loschmidt argued that time reversibility of the solution is a property of a mathematical model which is independent of the number of degrees of freedom. Consequently, time irreversibility should not emerge in models providing time reversible solutions. This is called the Loschmidt’s paradox.


Loschmidt’s paradox has been puzzling physicists for 145 years. Despite the variety of approaches (ranging from the “illusion” of macroscopic irreversibility to the special initial conditions of the early Universe and the incompleteness of fundamental microscopic theories), the ultimate resolution of the problem is yet unknown. The main problem is that statistical physics, the only known mathematical bridge between microscopic and macroscopic models of matter, is flexible enough to bear such a contradiction on the practical level. In particular, irreversibility in statistical physics is manually added during the derivation of equations addressing macroscopic scales, and therefore the exact microscopic origin of elementary irreversible physical processes, the diffusion of mass and momentum, remains hidden.


In this talk I present exact continuum equations to the Hamiltonian many-body dynamics of pair interacting particles in the limit of infinitely many particles. The derivation relies on a mathematical transformation lacking the utilisation of statistical mechanics or other approximations. The only assumption made here is that the sum of infinitely many, infinitely small amplitude Dirac-delta distributions located infinitely closely to each other is a bounded function. It is shown that the emerging scale-free equations are time reversible and universal for a certain class of interaction potentials. The existence of thermodynamic equilibrium and non-equilibrium relaxation processes are studied in numerical simulations for smooth random field initial conditions. It is shown that these seemingly time irreversible processes are not diffusional, providing evidence for the lack of the second law of thermodynamics in the classical many-body problem. Further directions of the research will also be discussed.

12 MARCH

2pm to 3pm

Speaker: Richard Graham (School of Mathematical Sciences, University of Nottingham)

Title: Multiscale modelling of flow- induced crystallisation in polymers

Abstract: Applying flow to polymers can profoundly change how they crystallise. Flow enhances the crystal nucleation rate, often by orders of magnitude, and controls the shape and alignment of crystals. This externally driven, non-equilibrium phase transition is a key fundamental problem in polymer physics. It is also of great interest to the polymer processing industry. A quantitative understanding of flow-induced crystallisation would enable control of the properties of semi-crystalline products by tailoring flow conditions. However, simulating and modelling flow-induced crystallisation in polymers is notoriously difficult, due to the very wide spread of length and timescales. I will present results from a recent multiscale modelling project. Here, we used systematic multiscale modelling to integrate several different levels of modelling. This includes Molecular Dynamics simulations, highly coarse-grained kinetic Monte-Carlo simulations and continuum-level thermodynamic modelling. This results in a highly tractable model of flow-induced nucleation with deep-rooted molecular origins. Our model predicts that long chains are enriched in flow induced nucleation from polydisperse melts. In particular, the model shows that multiple chain lengths co-operate in non-trivial ways to create a critical nucleus. I will demonstrate quantitative support for this idea from both experiments and molecular dynamics simulations.

05 MARCH

2pm to 3pm

Speaker: Lev A. Ostrovsky (University of Colorado and University of North Carolina, USA, and Institute of Applied Physics, Russian Acad. Sci.)

Title: Nonlinear Waves of Envelopes: Glimpses of History

Abstract: The 1960-70s witnessed a fast development of the science of nonlinear waves. They can often be called modulated waves meaning that the parameters of “fast” oscillations in time and space, such as amplitude, frequency, and wavenumber, are slowly varying, and these variations can themselves propagate as nonlinear waves that can (albeit loosely) be called “waves of envelopes.” The applications have mostly related to two areas: the surface water waves and, after creation of a laser in 1960, the nonlinear optics. This presentation outlines some aspects of these early studies, having occurred in parallel in different groups, especially in Britain and Soviet Union.  It refers to such effects as self-phase modulation, self-steepening of an envelope, averaged variational principle, modulational instability, and envelope solitons.

Archive of Recorded Talks: Schedule

ARCHIVE OF RECORDED TALKS

Year 2020

18 DECEMBER

2pm to 3pm

Speaker: Chris Linton (Loughborough University)

Title: The mathematics of the rainbow

Abstract: The rainbow is an often observed yet striking phenomenon whose quantitative explanation requires a surprisingly high degree of mathematical sophistication. I will begin by providing a brief history of theories that were developed to explain this atmospheric phenomenon from the ancient Greeks to Newton, Young and Airy. It was in his efforts to provide a quantitative description of rainbow phenomena that Airy created what we know call the Airy function Ai(x).

I will then outline the full solution to the problem of electromagnetic scattering by a sphere and say a little about the difficulties that one encounters at high frequencies (as is the case in the light-raindrop problem).

Finally I will discuss one technique, the Watson transformation, that can be used to overcome some of these difficulties and describe an example of its application.

11 DECEMBER

2pm to 3pm

Speaker: Mark Blyth (University of East Anglia)

Title: Critical free-surface flow over topography 

Abstract: Two-dimensional free-surface flow over a localised bottom topography is examined with an emphasis on calculating steady, forced solitary-wave solutions. In particular we focus on the case of a Gaussian dip topography. Most of the focus is on the weakly-nonlinear limit where a forced KdV equation is applicable, and the problem essentially boils down to solving a forced nonlinear ODE with a single parameter that quantifies the amplitude of the topography. This equation has a rich solution space with a large (probably infinite) number of solution branches. Asymptotic analysis for small topography amplitude reveal some interesting features, for example an internal boundary layer which mediates a change from exponential to algebraic decay of the free-surface in the far-field. Traditional boundary-layer theory fails beyond the first two solution branches, where the surface profiles feature multiple waves trapped over the topography. The stability of the steady solutions will also be briefly discussed.

4 DECEMBER

2pm to 3pm

Speaker: Karima Khusnutdinova (Loughborough University

Title: Long surface and internal ring waves in stratified fluids with currents 

Abstract: There exists a linear modal decomposition (separation of variables) in the far-field set of Euler equations describing ring waves in a stratified fluid over a parallel shear flow, more complicated than the known decomposition for plane waves [1]. We used it to derive a 2+1D cylindrical Korteweg - de Vries (cKdV)-type model for the amplitudes of the waves [1,2], generalising R.S. Johnson's result for surface waves in a homogeneous fluid. Here, we consider a two-layered fluid with a rather general family of depth-dependent upper-layer currents (e.g. a river inflow, an exchange flow in a strait, or a wind-generated current). In the rigid-lid approximation, we analyse the set of modal equations and find the necessary singular solution of the nonlinear first-order ordinary differential equation responsible for the adjustment of the speed of the long interfacial ring waves in different directions (a 2D linear dispersion relation) in terms of the hypergeometric function [3]. This allows us to obtain an analytical description of the wavefronts and 2D modal functions. We will also discuss a ring waves' generalisation of L.V. Ovsyannikov's long-wave instability criterion for plane interfacial waves on a piecewise-constant current, which on physical level manifests itself in the counter-intuitive squeezing of the wavefront of the interfacial ring wave.


References:

1. K.R. Khusnutdinova, X. Zhang, Long ring waves in a stratified fluid over a shear flow, J. Fluid Mech., 794, 17-44 (2016).

2. K.R. Khusnutdinova, X. Zhang, Nonlinear ring waves in a two-layer fluid, Physica D, 333, 208-221 (2016).

3. K.R. Khusnutdinova, Long internal ring waves in a two-layer fluid with an upper-layer current, Russian J. Earth Sci. 20, ES4006 (2020). 

27 NOVEMBER

2pm to 3pm

Speaker: Anne Juel (The University of Manchester) 

Title: Viscous fingering: from suppression to disorder

Abstract: What links a baby?s first breath to adhesive debonding, enhanced oil recovery, filtration or multiphase microfluidics? These processes involve two-phase displacement flows in rigid or elastic confined vessels, which are prone to interfacial instabilities. The canonical viscous fingering instability, which occurs when air displaces a viscous fluid in the narrow gap between two parallel plates, provides a versatile test-bed for such phenomena. In this talk, I will use both experiments and numerical simulations of depth-averaged models to explore several aspects of viscous fingering. I will first show how the onset of fingering can be suppressed when replacing the upper plate of the vessel with an elastic sheet. Interfacial flows in narrow gaps can also exhibit considerable disorder, but they are rarely investigated from a dynamical systems perspective. I will show how compliance can promote rich multiplicity of front propagation modes in a channel, including disordered and therefore transient dynamics. I will then turn to exploring how organised transient dynamics of bubbles propagating in a rigid channel are orchestrated by weakly-unstable steady propagation modes, which can appear and disappear as the number of bubbles changes through bubble break-up and coalescence.

20 NOVEMBER

2pm to 3pm

Speaker: Roger Smith (Loughborough University)

Title: 52 years of computing fluid dynamics : A  personal perspective

Abstract: This talk will discuss a few research and consultancy projects involving computing and fluid dynamics that I have been involved over the years. There will be some mathematics in the talk but there will also be a few anecdotes. The aim will be to demonstrate via some personal examples how ever improving computing facilities have enabled bigger and bigger problems to be solved.

13 NOVEMBER

4pm to 5pm

Speaker: James Sprittles (The University of Warwick)

Title: Noisy Free Surface Nanoflows

Abstract: Understanding the behaviour of flows at the nanoscale holds the key to unlocking a myriad of emerging technologies.  However,  accurate experimental observation is complex due to the small spatio-temporal scales of interest and, consequently, mathematical modelling and computational simulation become key tools with which to probe such flows. 

At such scales, the classical Navier-Stokes paradigm no longer provides an accurate description of the flow physics; however, microscopic models such as molecular dynamics (MD) become computationally intractable for most flows of practical interest.  In this talk talk I will consider the influence of thermal fluctuations, which we will see are key to understanding counter-intuitive phenomena in nanoscale interfacial flows.   A `top down’ framework that incorporates thermal noise is provided by fluctuating hydrodynamics and we shall use this model to gain insight into interfacial nanoflows such as drop coalescence, jet breakup and thin film rupture, using MD as a benchmark.  

6 NOVEMBER

10am to 11am

Speaker: Yury Stepanyants (University of Southern Queensland, Australia)

Title: Asymptotic approach to the description of two-dimensional soliton patterns.

Abstract: An asymptotic approach is suggested for the description of interacting surface and internal oceanic solitary waves. This approach allows one to describe a stationary moving wave pattern consisting of two plane solitary waves moving at an angle to each other. The results obtained within the approximate asymptotic theory are validated by comparison with the exact two-soliton solutions of the Kadomtsev-Petviashvili equation. The suggested approach is equally applicable to a wide class of non-integrable equations. As an example, the asymptotic theory is applied to the description of wave patterns in the 2D Benjamin-Ono equation describing internal waves in the infinitely deep ocean.

Archive of Recorded Talks: Schedule
bottom of page