## Spring 2018

All seminars (unless otherwise stated) will take place on **Tuesdays at 3.00pm in ****Room ****500 **(25 Gordon Street). See the map for further details. There will be tea afterwards in Mathematics Room 606 (25 Gordon Street). If you require any more information on the Applied seminars please contact Prof Jean-Marc Vanden-Broeck (e-mail: j.vanden-broeck AT ucl.ac.uk or tel: 020-7679-2835) or Prof ilia Kamotski (e-mail: i.kamotski AT ucl.ac.uk or tel: 020-7679-3937).

## 09 January 2018

### NO SEMINAR

## 16 January 2018

### Speaker: Dr Carlos Antonio Galeano Rios (Bath University)

##### Title: Modelling bouncing droplets from first principles: A kinematic matching approach

**Abstract: **Within a certain parameter regime, a small droplet can be made to bounce on the surface of a vibrating bath for an indefinitely long time. More surprisingly, if the shaking amplitude is greater than a certain threshold value, the bouncing motion becomes unstable to lateral perturbations. The droplet then becomes a moving source of waves whose trajectory is affected by the wave field at each impact point. We model the droplet as a perfectly hydrophobic rigid sphere and impose the natural geometric and kinematic constraints during contact. We obtain an impact model that is free of parametrisations which yields detailed predictions of the evolution of the contact area and the interfacial pressure during impacts. We obtain walking droplets superposing a series of translations of axisymmetric impacts on the existing surface waves. The resulting simulations are in remarkably good agreement with bouncing droplet experiments.

## 23 January 2018

### Speaker: Dr Sante Carloni (University of Lisbon, Portugal)

##### Title: Dynamical systems, Cosmology and the Dark Universe: the joys and toils of cosmological phase spaces.

**Abstract: **The discovery of the phenomenon of cosmic acceleration has changed dramatically our understanding of the dynamics of the universe. In this talk I will firstly review a general algorithm that allows to use dynamical systems techniques to analyze a relativistic cosmological model. I will then use this algorithm to evaluate some recently proposed frameworks for the theoretical understanding of cosmic acceleration. Special emphasis will be given to some subtle mathematical issues related the structure of the algorithm and their resolution, when available.

## 30 January 2018

### Speaker: Professor Peter G. Baines (University of Malbourne, Australia)

##### Title: Stratified Flow and Rossby Wave Hydraulics: upstream influence due to flow over obstacles and through contractions.

**Abstract: **Quantifying the "upstream influence" of the flow of uniformly stratified fluid over an obstacle (which can lead to blocking flow) has been recognised as a significant unsolved problem for the past 60 years. Here I present a mathematical approach to this problem which provides amplitudes of upstream modes that can produce upstream blocking. The same equations (suitably scaled) also apply to Rossby waves in an east-west channel, and an application to flow through the Drake Passage will be presented.

## 06 February 2018

### Speaker: Dr Stephen Baigent (UCL)

##### Title: Invariant manifolds of monotone dynamical systems: Existence, Geometry and Applications

**Abstract: **Monotone dynamical systems preserve the ordering of points in phase space. As a consequence they possess two special types of invariant manifolds: connecting orbits between fixed points where all points can be ordered, and invariant hypersurfaces where no points can be ordered. I will show how the graph transform can be used to study the existence of these manifolds. I will also show how the bending of hyperplanes under the flow can be used to determine when the invariant hypersurfaces are convex or concave. Throughout the talk the main ideas will be illustrated through models of population dynamics.

## 13 February 2018

### NO SEMINAR (READING WEEK)

## 20 February 2018

### Speaker: Professor Gunnar Martinsson (Oxford)

##### Title: Randomised algorithms for accelerating matrix computations

**Abstract: **Low-rank matrix approximations, such as partial spectral decompositions or principal component analysis (PCA), play a central role in data analysis and scientific computing. The talk will describe a set of randomized algorithms for efficiently computing such approximations. These techniques exploit modern computational architectures more fully than classical methods and enable certain computations involving massive data sets. The algorithms described are supported by a rigorous mathematical analysis that exploits recent work in random matrix theory. The talk will briefly review some of the key theoretical results.

## 27 February 2018

### SEMINAR CANCELLED

## 06 March 2018

#### Please see the Departmental Colloquia webpage

## 13 March 2018

### SEMINAR CANCELLED

## 20 March 2018

### Speaker: Professor Pierre Degond (Imperial College London)

##### Title: Coarse-graining of collective dynamics models

**Abstract: **In this talk, we will report on some new individual-based models of collective dynamics and their coarse-graining into continuum models. The applications span from collective cell dynamics (such as social bacteria or sperm) to flocking of birds or fish. Models of social behavior are best set up at the individual scale where behavioral rules can be easily introduced and tested. However, the complexity of individual-based models increases rapidly with the number of individuals and their calibration or control can hardly be implemented at this level. To overcome this limitation, one often uses continuum model that describe the system through average quantities such as densities or mean orientation. But the downside of most models in the literature is that the link between the rules at the individual behavior and the coefficients in the macroscopic model are not known exactly and are at best extrapolated from heuristic consideration. Here, we propose a systematic and mathematical rigorous way to derive continuum models from collective dynamics models. It relies on the introduction of a new concept, the 'generalized collision invariants', which permit to overcome the lack of physical invariance in most systems undergoing collective dynamics. In this talk, we will review some recent developments of these concepts and how they can be used to model systems of practical scientific importance.