Academic Year 2011/2012
Fri 7 Oct (2pm, Lecture Theatre D)
:
Dr Gunnar Hornig (Division of Mathematics, Dundee)
How to unbraid a magnetic field
Abstract:
Using the example of a turbulent relaxation of a braided magnetic field we
look into the question of how a fluid system with very low dissipation can
reach lower energy states. This leads us to questions of hidden topological
invariants of the relaxation process and we will explore various analogies
with vortex dynamics on the way.
Fri 18 Nov (2pm, Lecture Theatre D)
:
Dr Mikael Vejdemo-Johansson (School of Mathematics and Statistics, St Andrews)
Topological Data Analysis
Abstract:
In the past two decades, the mathematical discipline of algebraic
topology has opened up to applications through a dedicated development of
methods to handle point cloud data with topological tools. It turns out that
while geometric methods are quite adept at handling _quantitative_ aspects,
topological methods tend to capture _qualitative_ aspects of data, and to do
so with a degree of robustness that can be hard to achieve otherwise.
In this seminar, we shall display some of the basic definitions of the field
of topological data analysis, and demonstrate some applications from
biomedicine, robotics, sensor networks and data analysis.
Fri 9 Dec (2pm, Lecture Theatre D)
:
Dr Natalia Tronko (Centre for Fusion, Space and Astrophysics, Warwick)
Higher Order Guiding Center Theory
Abstract:
Fri 3 Feb (2pm, Lecture Theatre D)
:
Prof Chris Jones (Department of Applied Mathematics, Leeds)
Zonal flow generation and bursting in rotating convecting systems
Abstract:
Fast zonal flows, east-west wind systems, are found in the atmospheres
of giant planets. It has been proposed that banded zonal flows,
alternating in direction as the latitude increases, can be created
by the interaction of convection and rotation in rapidly rotating
systems.
The talk is divided into two main sections. In the first, the results
of direct numerical simulations (DNS) of rotating convection in
compressible shells are presented. Both Boussinesq and anelastic convection
simulations have been performed. Anelastic models take the large density
variation between the interiors and the atmospheres of gas giants into
account. Banded zonal flows are found in these models, provided the
boundaries are stress-free. The zonal flows found are rather z-independent,
as might be expected from the Proudman-Taylor theorem.
Banded zonal flows are only seen at very low Ekman number, that is the
viscous terms must be very small compared to the Coriolis terms.
Unfortunately, this is a very expensive limit for three-dimensional
DNS simulations. In the second part of the talk, a simplified
geostrophic model of convection, the Busse annulus, is used to explore the very
low
Ekman number regime. Multiple jets with bands whose width is in accord
with the Rhines scaling are found. In another regime, bursting
convection
is found. In this state, the system remains mostly quiescent, but
the zonal
flow is driven by occasional bursts of convective activity. The
causes
of this bursting phenomenon have been investigated, and we show for
the first time that not only does the zonal flow suppress the
convection,
overshoot of the mean temperature gradient plays a key role.
Fri 2 Mar (2pm, Lecture Theatre D)
:
Prof Mark Chaplain (Division of Mathematics, Dundee)
Mathematical modelling of intracellular negative feedback systems
Abstract:
There are many intracellular signalling pathways where the spatial
distribution of the molecular species cannot be neglected. These pathways
often contain negative feedback loops and can exhibit oscillatory dynamics
in space and time. Two such pathways are those involving Hes1 and p53-Mdm2,
both of which are implicated in cancer.
In this talk we present the results from recent mathematical models which
have been used to study the spatio-temporal dynamics of such intracellular
molecular systems. The models are systems of coupled nonlinear PDEs,
including transport terms and reaction kinetics. The transport is assumed to
be both random (diffusion) and active - proteins are convected in the
cytoplasm toward the nucleus, modelling transport along microtubules.
Internal structures such as ribosomes and the nuclear membrane are also
modelled explicitly.
Through numerical simulations we find ranges of values for the model
parameters such that sustained oscillatory dynamics occur, consistent with
available experimental measurements. In order to bridge the gap between in
vivo and in silico experiments we investigate more realistic cell geometries
by using an imported image of a real cell as our computational domain. For
the extended p53-Mdm2 model, we consider the effect of
microtubule-disrupting drugs and proteasome inhibitor drugs, obtaining
results that are in agreement with experimental studies. Applications to
other important intracellular systems such as NFkB are also discussed.
Fri 20 Apr (2pm, Lecture Theatre D)
:
Prof Nicholas Kevlahan (Department of Mathematics and Statistics, McMaster)
Controlling the dual cascade of two-dimensional turbulence
Abstract:
The Kraichnan--Leith-Batchelor (KLB) theory of statistically stationary
forced homogeneous isotropic 2-D turbulence predicts the existence of
two inertial ranges: an energy inertial range with an energy spectrum
scaling of $k^{-5/3}$, and an enstrophy inertial range with an energy
spectrum scaling of $k^{-3}$. However, unlike the analogous Kolmogorov
theory for 3-D turbulence, the scaling of the enstrophy range in 2-D
turbulence seems to be Reynolds number dependent: numerical simulations
have shown that as Reynolds number tends to infinity the enstrophy range
of the energy spectrum converges to the KLB prediction, i.e. $E\sim k^{-3}$.
The present paper uses a novel optimal control approach to find a forcing
that does produce the KLB scaling of the energy spectrum in a moderate
Reynolds number flow. We show that the time-space structure of the
forcing can significantly alter the scaling of the energy spectrum over
inertial ranges. A careful analysis of the optimal forcing suggests that
it is unlikely to be realized in nature, or by a simple numerical model.
Fri 11 May (2pm, Lecture Theatre D)
:
Prof Bruce Sutherland (Departments of Physics and of Earth and Atmospheric
Sciences, Alberta)
(What's the Story) Internal Solitary Waves?
Abstract:
Seminars are currently being organised by Dr Chuong Tran, who may be
contacted at
chuong@mcs.st-and.ac.uk.
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