AIMS Seminars 2022-2023 Schedule

Semester 1

2022

Odd dynamics of living chiral crystals

AS

(note PHT away)

Scott McCue

(QUT)

Fluid-boundary interaction: confinement effects, stratification and transport  

No talk

The volume of ice stored in glaciers and ice sheets is the primary control on Earth’s sea level, so the question of how it responds to the changing climate is of profound interest.  Fundamental to addressing this question is the fluid-like creep of the ice, and the rate at which it can slip over the underlying ‘bed'.  In this talk we will first discuss basic mathematical models of ice-sheet volume and evolution, and how these are coupled to the climate.  Secondly, we’ll consider the detailed problem of how slip at the ice-bed interface is facilitated by the formation of water-filled cavities, which results in a very interesting free-boundary problem.  Finally, we’ll look at a simplified model for marine ice-sheet dynamics when a Coulomb-like plastic law is assumed for the slip.

Ananyo Maitra

(CY Cergy Paris Universite)

Chiral molecules form a plethora of liquid-crystalline phases, even in equilibrium. However, while chirality is important for understanding the microstructure of these phases, it is cloaked in the long-time, large-scale properties of these passive states. Activity allows chirality to reveal its full dynamic potential. For instance, while the long-wavelength elastic and hydrodynamic properties of passive chiral layered and columnar states are equivalent to their achiral counterparts, activity leads to unique forms of odd elastic behaviours in active cholesteric and chiral columnar phases. The interplay of chirality and activity also leads to liquid-crystalline phases without any passive analogue, such as time liquid crystals. In this talk, I will summarise my work on chiral active liquid crystals, highlighting how the interplay of chirality and activity allows the former to mould the dynamic and static properties of ordered states, in direct contrast to passive matter.

AS

(Note PHT away)

In this talk I will introduce a higher-dimensional generalization of the NLS equation, known as the Karpman equation. These equations describe the behaviour of optical solitary waves that are used to describe laser behaviour. I will show that the waves present in solutions to this equation are generically "nanoptera", or nonlocal solitary waves with exponentially small oscillatory tails, whenever the equation parameter is positive.

I will then consider the same equation after a finite-difference discretization has been applied in time and space. I will show that the same oscillations are present, but only when the oscillation parameter exceeds 1/4. The act of discretizing this equation changes the value at which the bifurcation occurs. Finally, I will show how the two behaviours can be connected together by increasing the order of the discretization. This is joint work with Aaron Moston-Duggan (Macquarie University) and Mason Porter (UCLA).

Alan Champneys (Bristol)

Many beyond-all-orders problems arise in the unfolding of bifurcation points in four-dimensional phase space 
that involve homoclinic or heteroclinic orbits. Such problems naturally arise in the theory of small amplitude bifurcation of localised patterns,  or solitary waves in a wide number of contexts, where an infinite spatial coordinate plays the role of time. Examples include so-called embedded solitons within families of generalised solitary waves, the birth of localised patterns through so-called homoclinic snaking, and the small amplitude birth of chaotic attractors from a saddle-node Hopf bifurcation. 

In this talk I shall aim to give an informal overview of how to understand these problems in terms of the geometric
theory of dynamical systems. The common feature in each case is that the normal form of the bifurcation in question
is integrable or has a symmetry that means the intersections between stable and unstable manifolds are degenerate. Any generic perturbation will break this degeneracy and lead to transverse intersections. However the normal form computation can be carried out to all algebraic orders, which means that the perturbations that break the degenerate intersections must be beyond all orders. In turn, this tends to lead to phenomena occurring within exponentially thin regions of parameter space. 

Binary Synchronization of noise-coupled oscillators

Synchronisation of non-locally coupled oscillators has been extensively studied since Kuramoto’s model of oscillators was proposed in 1975. From fireflies to pedestrians on a bridge, this model is widely applicable in modelling the collective behaviour of large groups of individuals. This and other traditional models of synchronisation are predicated on deterministic forcing between individuals. Intrinsic randomness of oscillators has been incorporated into the Kuramoto model but this invariably causes a decrease in synchronization. In this talk we will show that, while noise usually creates disorder, systems can reach order through randomness. We propose and analyse a model that reproduces many of the common features of the Kuramoto model around the incoherent state but exhibits binary phase locking instead of full coherence. Using recently developed methods we are able to find exact solutions for the stationary, synchronized state. We also find approximate low dimensional dynamics for this model which qualitatively describes the full system of oscillators.

Geometric non-conservative fluid dynamics: an introduction and a case-study of viscous barotropic fluids

Geometric mechanics is a modern formulation of classical mechanics in the language of differential geometry. A geometric viewpoint highlights the underlying structure of equations of motion. Moreover, the general formulation on arbitrary manifolds allows to translate the equations into different coordinate systems.

As is well known, Hamilton's principle is only applicable for conservative systems. By restoring the time-symmetry, Galley formulated a type of action principle for non-conservative systems, inspired by Hamilton's principle.

Mariia Dvoriashyna

(Oxford)

Gibin Powathil 

(Swansea)

Dr Finn Box, Manchester: finn.box@manchester.ac.uk
Experimentalist working on elasticity & fluid structure interactions, https://personalpages.manchester.ac.uk/staff/finn.box/index.html 

Dr Adam Lowe, Aston: a.lowe3@aston.ac.uk
Theorist (a physicist, but in a Maths Dept.)  working on information measures applied to quantum systems

Dr Jonathan Skipp, Aston: j.skipp@aston.ac.uk
Theorist working on wave turbulence in, e.g. Nonlinear Shroedinger

Dr Joseph Pollard: joseph.pollard@durham.ac.uk
Theorist working on yield stress fluids with Suzanne Fielding, and liquid crystal topology. 

Dr Carl Whitfield: carl.whitfield@manchester.ac.uk
Theorist working on applying tools from network science to respiratory (e.g. lung) networks. 

1D Faraday Wave-Droplet Dynamics

Eileen Russell

A millimetric droplet of silicon oil will bounce periodically on a suitably vibrating bath. Increasing the amplitude of the vibrations, the droplet walks across the surface and as the amplitude increases further the droplet's motion becomes chaotic. This system is of interest to many mathematicians and physicists as it bears resemblance to the quantum realm. Indeed, the droplet has both a mass and a wavefield which is compared to quantum mechanic's wave-particle duality hypothesis. Many physicists have succeeded in creating analogues between this system and common features of quantum mechanics such as tunnelling, diffraction, interference, and quantised orbits.