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**Applied Mathematics Seminars**- Previous Applied Seminars
- 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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2014 results
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*EPSRC award offers new PhD opportunities in pure mathematics* - PhD Open Afternoon, Wednesday 2 December 2015 - Registration
- Helen Wilson and Adam Townsend publish a paper on 'The Physics of Chocolate Fountains'

## Applied Mathematics Seminars

### Autumn 2015

All seminars (unless otherwise stated) will take place on **Tuesdays at
3.00pm in ****Room 505 in the Mathematics Department **(25 Gordon Street). See see how to find us for further details. There will be tea afterwards in Mathematics Room 606. If
you require any more information on the Applied seminars please
contact Prof Slava Kurylev e-mail: y.kurylev AT ucl.ac.uk or
tel:
020-7679-7896.

### 29 September 2015, 3pm

Dr Anatasia Kisil, University of Cambridge

###### Title: Approximate matrix Wiener-Hopf factorisation and applications to problems in acoustics

**Abstract:** This talk will introduce a technique for solving
a class of PDEs called the Wiener-Hopf method. It is an elegant method which
extends the separation of variables technique used to investigate PDEs. After
introducing the topic I will talk about my work on the approximate matrix
Wiener-Hopf factorisation and stability analysis. This is then applied to the
scattering of a sound wave by an infinite periodic grating composed of rigid
plates (joint work with I. D. Abrahams).

### 6 October 2015, 3pm

Dr Yue-Kin Tsang, University of Exeter

###### Title: Advection-condensation of water vapour in a stochastic model with coherent stirring

**Abstract:** Atmospheric water vapour is an important greenhouse gas and has
a strong impact on climate. Observations show that large-scale moisture
dynamics can be captured by kinematic models in which water vapour is treated
as a passive scalar advected by a prescribed flow and reacts through
condensation. Condensation acts as a sink that maintains specific humidity
below a prescribed, spatially dependent saturation value. Models of this type
have previously been studied using spatially decorrelated Brownian motion as a
crude approximation to turbulent motion. In this work we examine the effect of
a coherent flow represented by a single vortex which adds a deterministic
component to the random motion of fluid parcels. We consider two problems: (i)
the drying of a water-vapour anomaly released in the flow at an initial time,
and (ii) the steady-state water-vapour distribution achieved in the presence of
a moisture source at a boundary. In the strong vortex limit, we solve the
governing stochastic differential equations and derive the distribution of
specific humidity. Monte Carlo simulations are used to verify these theoretical
results and to explore the system beyond the strong vortex limit.

### 13 October 2015, 4pm

Prof Paul Houston, School of Mathematical Sciences, University of Nottingham, UK

###### Title: Adaptive Finite Element Methods for PDEs Posed on Complicated Domains.

**Abstract:** In this talk we consider high-order/hp-version
interior penalty discontinuous Galerkin methods for the discretization of second-order elliptic partial differential equations
on general computational meshes consisting of polygonal/polyhedral elements. By admitting such general meshes, this class of methods allows for the
approximation of problems posed on computational domains which may contain a huge number of local geometrical features, or micro-structures. While standard numerical methods can be devised for such problems, the computational effort may be extremely high, as the minimal number of elements needed to represent the underlying domain can be very large. In contrast, the
minimal dimension of the underlying (composite) finite element space based on general polytopic meshes is independent of the number of geometric features. Here we consider both the a priori and a posteriori error analysis of this class of methods, as well as their application within Schwarz-type
domain decomposition preconditioners.

### 20 October 2015, 4-5pm

Dr Garth Wells, University of Cambridge

Location of Seminar: Harry-Massey Lecture Theatre

###### Title: High-performance differential equation solvers made easy

**Abstract:** There is typically a disconnect between the
tools used by domain scientists and research engineers exploring
scientific problems through simulation, and the leading edge of
high-performance solver technology. Bridging this gap is important to
accelerate the exploitation of new computational and mathematical tools
for enabling new scientific investigations and new engineering design. In
the context of the FEniCS Project (<http://fenicsproject.org>), we have been successful
in making the creation of new, performant finite element-based solvers
compact and expressive, and accessible and straightforward for domain
scientists. A natural step to is to place a wide range of high-performance
solvers at the fingertips of researchers, allowing them explore the
parameter space of sophisticated solvers for advanced applications with
ease, with the objective of finding scalable, parallel solvers for new
and changing models. I will present a number of examples of how this can be
made easy, from elliptic problems with over 10 billion degrees of freedom,
to multi-field equations, to some of the largest practical engineering
simulations performed.

### 27 October 2015, 3pm

Prof Yury Stepanyants, University of Southern Queensland, Australia

###### Title: Analysis of modulational stability of quasi-harmonic wave trains in media with double dispersion (with S P Nikitenkova, N N Singh)

**Abstract:** The problem of modulation stability of quasi-monochromatic long waves
propagating in a medium with the double dispersion is revised. The nonlinear
Schrödinger equation which describes the evolution of narrow-band wave-trains
is derived from the primitive set of shallow-water equations for the rotating
fluid in the Boussinesq approximation. The regions of stability and instability
in the spectral space are obtained for various signs of dispersion
coefficients. Application of results to concrete physical systems (water waves,
plasma waves, waves in solids, etc.) is discussed.

### 3 November 2015 - Colloquium Talk

Prof John Willis - DAMTP, University of Cambridge

###### - please see the Departmental Colloquia webpage

### 10 November 2015 - No Seminar (Reading Week)

### 17 November 2015, 3pm

Dr Rodolphe Sepulchre, University of Cambridge, Department of Engineering

###### Title: Differentially positive system

**Abstract:** Differentially positive systems are
systems whose linearization along an arbitrary trajectory is positive. The geometric picture is that a given cone field is
infinitesimally contracted along the flow. This property induces a (conal) order that strongly
constrains the asymptotic behavior
of solutions.

The talk will introduce the concept on simple examples and motivate its relevance for the analysis of nonlinear behaviors in engineering. The results illustrate that behaviors constrained by local order properties extend beyond the well-studied class of linear positive systems and monotone systems, which both require a constant cone field and a linear state space. In particular, differential positivity suggests a novel approach to analyze limit cycles in possibly high-dimensional systems.

Joint work with Fulvio Forni. Preprint on arxiv: http://arxiv.org/abs/1405.6298

### 24 November 2015, 3pm

Dr H Salman, University of East Anglia

###### Title: Long-range Ordering and Negative Temperature States of Quantized Vortices in a Two-dimensional Superfluid

**Abstract: **We study the relaxation of a 2D superfluid from a non-equilibrium initial
state consisting of vortices with positive and negative circulation in
experimentally realizable square and rectangular traps. We focus on how
like-signed quantized vortices can form clusters and show that such clustering
can be understood in terms of negative temperature states of a vortex gas. Using
a mean field approximation for the vortex gas, we identify an order parameter
that is related to the formation of long-range correlations between the
vortices. It turns out that the order parameter corresponds to the stream function
of a 2D flow field that is governed by a Boltzmann-Poisson equation. It is, therefore, associated with the emergence
of a mean rotational hydrodynamic flow with a nonzero coarse-grained vorticity
field. Solutions of the Boltzmann-Poisson equation in a square domain reveal that maximum entropy states of the vortex
gas correspond to a large scale monopole flow field. A striking feature of this
mean flow, is the spontaneous acquisition of angular momentum by a superfluid flow with a neutral vortex charge. These mean-field
predictions are verified through direct simulations of a point vortex gas and
2D simulations of the Gross-Pitaevskii equation. Due to the long-range nature
of the Coulomb-like interactions in point vortex flows, the negative temperature
states strongly depend on the shape of the geometry. By modifying the domain to
a rectangular region, we identify a geometry induced phase transition of the
most probable mean flow field which our numerical simulations
reproduce

### 1 December 2015, 3-4pm

Dr Peter Stewart, School of Mathematics and Statistics, University of Glasgow

###### Title: Microstructural effects in aqueous foam fracture

**Abstract:** We
examine the fracture of a quasi two-dimensional aqueous foam under an applied
driving pressure, using a network modelling approach developed for metallic
foams . In agreement with experiments, we observe two distinct mechanisms of
failure analogous to those observed in a crystalline solid: a slow ductile mode
when the driving pressure is applied slowly, where the void propagates as
bubbles interchange neighbours through the T1 process, and a rapid brittle mode
for faster application of pressures, where the void advances by successive
rupture of liquid films driven by Rayleigh--Taylor instability.

This is joint work with Prof S Hilgenfeldt, Mechanical Sciences and Engineering, University of Illinois, Urbana-Champaign, IL

### 8 December 2015, 3pm

Dr Ory Schnitzer, Imperial College London

###### Title: Singular asymptotics of surface-plasmon resonance

**Abstract:** Surface plasmons are collective
electron-density oscillations at a metal-dielectric interface. In particular,
surface-plasmon modes of nano-metallic structures with narrow gaps, which
enable a tuneable resonance frequency and a giant near-field enhancement, are
at the heart of numerous nanophotonics applications. In this work, we elucidate
the singular near-contact asymptotics of such structures. In the classical
regime, valid for gap widths > 1nm, we find a generic scaling describing the
drastic redshift of the resonance frequency as the gap width is reduced, and in
several prototypical dimer configurations derive explicit expressions for the
plasmonic eigenvalues and eigenmodes using matched asymptotics; we also derive
expressions describing the resonant excitation of such modes by light based on
a weak-dissipation limit. In the sub-nanometric ``nonlocal’’ regime, we show
intuitively and by systematic analysis of the hydrodynamic Drude model that
nonlocality manifests itself as a potential discontinuity, and in the
near-contact limit equivalently as a widening of the gap. We thereby find the
near-contact asymptotics as a renormalisation of the local asymptotics, and in
particular a lower bound on plasmon frequency, scaling with the 1/4 power of
the Fermi wavelength. Joint work with Vincenzo Giannini, Richard V. Craster and Stefan
A. Maier

### 15 December 2015

TBC

###### Title: TBC

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