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**Applied Mathematics Seminars**- Previous Applied Seminars
- Applied Mathematics Seminars Autumn 2017
- Applied Mathematics Seminars Summer 2017
- Applied Mathematics Seminars Spring 2017
- Applied Mathematics Seminars Autumn 2016
- Applied Mathematics Seminars Summer 2016
- Applied Mathematics Seminars Spring 2016
- Applied Mathematics Seminars Autumn 2015
- Applied Mathematics Seminars Summer 2015
- Applied Mathematics Seminars Spring 2015
- Applied Mathematics Seminars Autumn 2014
- Applied Mathematics Seminars Summer 2014
- Applied Mathematics Seminars Spring 2014
- Applied Mathematics Seminars Autumn 2013
- Applied Mathematics Seminars Spring 2013
- Applied Mathematics Seminars Autumn 2012
- Applied Mathematics Seminars Summer 2012
- Applied Mathematics Seminars Spring 2012
- Applied Mathematics Seminars Autumn 2011
- Applied Mathematics Seminars Spring 2011
- Applied Mathematics Seminars Autumn 2010
- Applied Mathematics Seminars Spring 2010
- Applied Mathematics Seminars Autumn 2009
- Applied Mathematics Seminars Spring 2009
- Applied Mathematics Seminars Autumn 2008
- Applied Mathematics Seminars Spring 2008
- Applied Mathematics Seminars Autumn 2007

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## Applied Mathematics Seminars

### Spring 2017

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

#### Speaker: Dr Sheehan Olver (Imperial College)

###### Title: Sparse spectral methods for PDEs on triangles with multivariate orthogonal polynomials

**Abstract: **Univariate orthogonal polynomials have a long
history in applied and computational mathematics, playing a fundamental role in
quadrature, spectral theory and solving differential equations with spectral
methods. Unfortunately, while numerous theoretical results concerning
multivariate orthogonal polynomials exist, they have an unfair reputation of
being unwieldy on non-tensor product domains, and their use in applications has
been limited. In reality, many of the powerful computational aspects of
univariate orthogonal polynomials translate naturally to multivariate
orthogonal polynomials, including the existence of Jacobi operators, fast
evaluation of expansions using Clenshaw’s algorithm and the ability to
construct sparse partial differential operators, a la the ultrapsherical
spectral method [Olver & Townsend 2012]. We demonstrate these computational
aspects using multivariate orthogonal polynomials on a triangle, including the
fast solution of general partial differential equations.

### 06 March 2018

##### Please see the Departmental Colloquia webpage

### 13 March 2018

#### Speaker: Dr Mark Blyth (University of East Anglia)

###### Title: Critical free-surface flow over localised topography

**Abstract: **Two-dimensional free-surface flow over a
localised bottom topography at critical Froude number (F=1) is examined with an
emphasis on calculating steady, forced solitary-wave solutions. In particular
we focus on the case of a Gaussian topography. We study the flow in the
weakly-nonlinear limit by way of the forced KdV equation, but also compute some
fully nonlinear solutions using a conformal mapping method. Boundary-layer
theory is used to construct asymptotic solutions in appropriate limits. One
point of interest here is an internal boundary layer which mediates a change
from an initial exponential decay of the free-surface to algebraic decay in the
far-field. (Algebraic far-field decay is a characteristic feature of steady
critical flow solutions.) Many solution branches are identified including
branches with multiple waves trapped over the main part of the topography,
which cannot be described by boundary-layer theory. Solutions on the first few
branches are also found for the fully nonlinear problem. The stability of the
steady solutions is also considered.

### 20 March 2018

#### Speaker: Prof Pierre Degond from Imperial College

###### 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.