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RECORDED TALKS

10 DECEMBER 

2pm to 3pm

Speaker: Sir Michael Berry (University of Bristol)

Title: Superoscillations in waves: old, new, common, uncommon

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Abstract:

In the mathematical phenomenon of superoscillations, bandlimited functions vary faster than their fastest Fourer components (‘faster than they should’). Superoscillations

• are associated with almost-destructive interference;

• occur near phase singularities in optics and on the world’s ocean tides;

• are a compact way to represent fractals;

• are rather common in light represented by scalar waves, and in many contexts in quantum physics; but in light represented by electric fields - and more so when magnetic fields are included - they are unexpectedly rare;

• are suppressed by differentiation;

• can be generalised, to quantum waves whose momentum (wavenumber) lies outside the classical range; 

• in red light, can escape as gamma radiation.

03 DECEMBER

2pm to 3pm

Speaker: Anotida Madzvamuse (University of Sussex)

Title: Theoretical and computational advances for bulk-surface PDEs

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Abstract:

In this talk, I will present recent theoretical and computational advances in modelling pattern formation and cell motility through the use of bulk-surface partial differential equations. In the first part of the talk, I will present generalisation of Turing diffusion-driven instability conditions for bulk-surface reaction-diffusion systems on stationary volumes. Analytical results will be validated through novel bulk-surface finite element methods with fractional step theta method for the time-discretisation. In the second part of the talk, I will present a bulk-surface model for wave pinning that allows to capture more faithfully the underlying physics of the biological problem. Numerical results using the bulk-surface finite element method on complex geometries reveals surprising, and yet to be confirmed experimentally, wave pinning patterning.

19 NOVEMBER

2pm to 3pm

Speaker: Marco Mazza (Loughborough University)

Title: Boundary-interior principle for microbial navigation in geometric confinement

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Abstract:

The motion of microbial cells has enormous impact: from swimming sperm cells to bacteria or microalgae colonizing new environments. Upon close observation, this motion often appears erratic, and yet the combination of nonequilibrium forces and confining surfaces can produce striking examples of organization in microbial systems. It remains elusive how

and at which length scale self-organization emerges in complex geometries.  In this talk, we will describe experiments and analytical and numerical calculations on the motion of motile cells under controlled microfluidic conditions.  We find that probability flux loops organize active motion, even at the level of a single cell exploring an isolated compartment of nontrivial geometry. By accounting for the interplay of activity and interfacial forces, we find that the boundary’s curvature determines the nonequilibrium probability fluxes of the motion. We theoretically predict a universal relation between fluxes and global geometric properties that is directly confirmed by experiments. Our findings open the possibility to decipher the most probable trajectories of motile cells and may enable the design of geometries guiding their time-averaged motion.

12 NOVEMBER

2pm to 3pm

Speaker: Dmitry Pelinovsky (McMaster University, Canada)

Title: Solitary waves in systems with intensity-dependent dispersion

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Abstract:

A continuous family of singular solitary waves exists in a prototypical

system with intensity-dependent dispersion. The family has a cusped

soliton as the limiting lowest energy state and is formed by the

solitary waves with bell-shaped heads of different lengths. We show that

this family can be obtained variationally by minimization of mass at

fixed energy and fixed length of the bell-shaped head. We develop a weak

formulation for the singular solitary waves and prove that they are

stable under perturbations which do not change the length of the

bell-shaped head. Numerical simulations confirm the stability of the

singular solitary waves. This is a joint work with P. G. Kevrekidis and

R.M. Ross (University of Massachusetts, Amherst).

22 OCTOBER

2pm to 3pm

Speaker: Alex Doak (University of Bath)

Title: Three-layer internal mode-2 solitary waves

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Abstract:

Internal waves occur in stratified fluids, such as the worlds oceans. They are responsible for the transport of momentum, heat, and organic material, as well as inducing turbulent mixing. Rather than attempting to model a continuously stratified fluid, a common simplification is to assume several homogenous layers of immiscible fluids, separated by infinitesimal interfaces. Two-layer flows have been explored extensively, and such models are used to predict wave properties of 'mode-1' waves. To explore higher modes, one needs additional interfaces. In this talk we shall discuss travelling wave solutions to a three-layer model. We will be presenting numerical solutions to both the full Euler system, and a reduced model called the Miyata-Choi-Camassa (MCC) equations. Mode-2 waves (typically) occur within the linear spectrum, and are hence associated with a resonant mode-1 oscillatory tail. However, as was found the MCC system by Barros et. al (2020), we will present numerical evidence that these oscillations can be found to have zero amplitude, resulting in a localised structure known as an embedded solitary wave. We also find mode-2 waves which travel faster than the maximum linear mode-1 wave speed, and are hence outside the linear spectrum. We relate large amplitude solutions to the so-called 'conjugate states' of the system, where the limiting solution of many of the solution branches is a 'tabletop soliton' connecting two conjugate states. 

Recorded Talks (Current Term): Schedule
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