
THE
FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

Fields
Institute Applied Mathematics Colloquium/Seminar
201415


Organizing
Committee
Jim
Colliander (U
of Toronto)
Walter Craig (McMaster)
Catherine Sulem (U of Toronto)

Robert
McCann (U of Toronto)
Adrian Nachman (U of Toronto)
Mary Pugh (U of Toronto)
Huaxiong
Huang (York) 



The Fields Institute Colloquium/Seminar in Applied Mathematics
is a monthly colloquium series for mathematicians in the areas of
applied mathematics and analysis. The series alternates between
colloquium talks by internationally recognized experts in the field,
and less formal, more specialized seminars. In recent years, the
series has featured applications to diverse areas of science and
technology; examples include superconductivity, nonlinear wave
propagation, optical fiber communications, and financial modeling.
The intent of the series is to bring together the applied mathematics
community on a regular basis, to present current results in the
field, and to strengthen the potential for communication and collaboration
between researchers with common interests. We meet for one session
per month during the academic year. The organizers welcome suggestions
for speakers and topics.
Tuesday
June 16, 2015
Stewart Library
coming
Talks 2015 
Chris Budd (University of Bath, UK)  2:00 p.m. Mesh
generation using optimal transport
When numerically solving a PDE in three dimensions , it is often
necessary to generate a mesh on which to discretize the solution.
Often this can be expensive to do. However, by using ideas from optimal
transport it is possible both to construct a mesh quickly and cheaply,
and also to prove that it has the necessary regularity properties
to allow an accurate approximation of the solution of the PDE. In
this talk I will describe these methods, prove results about their
regularity and then apply them to some problems in meteorology.

Friday May 8, 2015
Stewart Library

Roderick S. C. Wong (City University of Hong Kong)  11:00
a.m.
Asymptotics and Orthogonal Polynomials
In this talk, we review some of the methods that are now available
in asymptotics, and show how they can be applied to classical and
nonclassical orthogonal polynomials. These include methods in asymptotic
evaluation of integrals and asymptotic theory for ordinary differential
equations. Also included are two newer methods, namely, the RiemannHilbert
method and asymptotics for linear recurrences.

Tuesday May 5, 2015
Stewart Library

Jerome Neufeld (University of Cambridge)  2:00 p.m.
Dynamics of fluiddriven fracturing
Fluiddriven delamination or fracturing occurs in a host of materials
with applications to the damage of biological tissues, the deformation
of engineered materials and the fracture and deformation of the Earth’s
crust. In direct analogy with the physical and mathematical complexities
faced at the contact line of a spreading capillary drop, we show that
bending and inplane tension within the sheet play particularly crucial
roles near the delaminating tip of an elastic blister. Matching a
quasistatic interior blister to the dynamics as the peeling or pulling
tip thereby determining the evolution of a fluid blisters beneath
thin elastic sheets.
The macroscopic manifestation of the contact line are highlighted
by a new experimental system, elastic magnetic sheets, in which the
magnetic attraction which provides a repeatable laboratory analogue
in which to study fluiddriven fracturing. This experimental system
exhibits transitions from static to dynamicallydriven fluid fracturing
in both the bending and tensional regimes, and therefore provides
a new laboratory analogue in which to repeatably study the dynamics
of fluid driven fracturing of elastica.
Lister, J.R., Peng, G.G., Neufeld, J.A. (2013). Viscous control of
peeling an elastic sheet by bending and pulling. Phys. Rev. Lett.,
111, 1–5.

Wednesday April 8, 2015
Stewart Library

Hiro Oh (University of Edinburgh)  10:3011:30 am
Invariant Gibbs measures for Hamiltonian PDEs
In this talk, I will talk about different aspects of invariant Gibbs
measures for Hamiltonian PDEs. We first go over the construction of
invariant Gibbs measures for Hamiltonian PDEs on the circle due to
Bourgain '94. Then, we move onto the real line case. If time permits,
I will mention the higher dimensional situation (at least in the periodic
setting.)
Oana Pocovnicu (Princeton University)  12:001:00 pm
A modulated twosoliton with transient turbulent regime for a focusing
cubic nonlinear halfwave equation on the real line
In this talk we discuss work in progress regarding a nonlocal focusing
cubic halfwave equation on the real line. Evolution problems with
nonlocal dispersion naturally arise in physical settings which include
models for weak turbulence, continuum limits of lattice systems, and
gravitational collapse. The goal of the present work is to construct
an asymptotic globalintime modulated twosoliton solution of small
mass, which exhibits the following two regimes: (i) a turbulent regime
characterized by an explicit growth of high Sobolev norms on a finite
time interval, followed by (ii) a stabilized regime in which the high
Sobolev norms remain stationary large forever in time. This talk is
based on joint work with P. Gerard (Orsay, France), E. Lenzmann (Basel,
Switzerland), and P. Raphael (Nice, France).

February 24, 2015
2:00 pm
Stewart Library

Peter Perry (University of Kentucky, Lexington)
The DaveyStewartson Equation: A Case Study of the Completely Integrable
Method in Two Space Dimensions
The DaveyStewartson II equation is a completely integrable, nonlinear
dispersive equation in two space and one time dimensions which describes
the amplitude of weakly nonlinear waves in shallow water. We'll discuss
recent work on both the defocussing and focussing case which uses
the completely integrable method to obtain global wellposedness,
and largetime asymptotics (defocussing case) and spectral instability
of soliton solutions (focussing case). This work builds on the pioneering
work of AblowitzFokas, BealsCoifman, and others. The technical core
of this work is a careful study of a $\overline{\partial}$problem
where the spacetime parameters enter through an oscillatory phase.
Yaushu Wong (University of Alberta)
This is a joint work with Kun Wang & Jian Deng
Pollution  free Difference Schemes for Helmholtz Equation in Polar
and Spherical Coordinates
The Helmholtz equation arises in many problems related to wave propagations,
such as acoustic, electromagnetic wave scattering and models in geophysical
applications. Developing efficient and highly accurate numerical schemes
to solve the Helmholtz equation at large wave numbers is a very challenging
scientific problem and it has attracted a great deal of attention
for a long time. The foremost difficulty in solving the Helmholtz
equation is to eliminate or minimize the pollution effect which could
lead to a serious problem as the wave number increases. Let k, h,
and n denote the wave number, the grid size and the order of a finite
difference or finite element approximations, we could show that the
relative error is bounded by where or 1 for a finite difference or
finite element method. Recently, new finite difference schemes are
developed for onedimensional Helmholtz equation with constant wave
numbers, and it is shown that error estimate is bounded by and the
convergence is independent of the wave number k even when kh>1.
In this talk, we extend the idea on constructing the pollution free
difference schemes to multidimensional Helmholtz equation in the
polar and spherical coordinates. The superior performances of the
new schemes are validated by comparing the numerical solutions with
those obtained by the standard finite difference and the fourthorder
compact schemes.

October
28, 2014
3:30 pm 
Peter
Howell (Mathematical Institute  University of Oxford)
Deterministic and stochastic modelling of lithiation/delithiation in
a Lithiumion battery electrode
Two mathematical models will be presented for the lithiation/delithiation
of a single nanoparticle in a Lithiumion battery electrode. The first
is a deterministic ODE model that describes quasiequilibrium and
outofequilibrium lithiation/delithiation under voltage control.
The dynamics of a single particle can be reduced to rapid switching
between an ‘empty’ state and a ‘full’ state. Using
asymptotic analysis, the critical voltage at which the switch occurs
is identified under both static and dynamic conditions.
The second model is based on a probabilistic description of the discrete
number of Lithium ions in a single particle. Starting from the chemical
master equations, a discretetocontinuum model is derived for the
probability distribution during dynamic charging/discharging. Distinct
asymptotic regimes are identified in which either discreteness and
thermal noise are important or the dynamics is well captured by the
continuous deterministic model.

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