| Monday 22nd October 2001 |
2.00pm | Room MI1 |
Gero Friesecke (Warwick) |
Symmetries of atoms according to the periodic table
versus symmetries derivable from quantum mechanics
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| Monday 29th October 2001 |
12.00 | Room 123 |
Nicola Sottocornola (INLN) |
Robust heteroclinic cycles in 4 dimensions
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| Monday 29th October 2001 |
2.00pm | Room MI1 |
Ian Melbourne (Surrey) |
Central limit theorems and approximation by Brownian motion for
partially hyperbolic dynamical systems
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| Abstract:
The dynamical and probabilistic properties of uniformly hyperbolic (Axiom A) systems have been much studied Recently, there has been a great deal of interest in dynamical systems that are partially hyperbolic. Perhaps the simples examples of partially hyperbolic systems are provided by time-one maps of hyperbolic flows, and by Lie group extensions of hyperbolic
dynamical systems.
In systems with continuous symmetry, hyperbolicity is automatically violated, so Lie group extensions of hyperbolic dynamical systems are the natural generalisation of Axiom A systems.
I will describe recent results on dynamical properties (stable transitivity) and probabilistic properties (decay of correlations, central limit theorems, approximation by Brownian motion) for Lie group extensions and time-one maps of hyperbolic dynamical systems.
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| Monday 5th November 2001 |
2.00pm | Room MI1 |
No seminar because of MIR@W Day on |
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| Wednesday 7th November 2001 |
2.00 | Room 26 |
Florian Theil (Warwick) |
Propagation of spatial oscillations in certain nonlinear
wave equations
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| Monday 12th November 2001 |
2.00pm | Room MI1 |
Tadashi Tokieda (Montréal) |
Dancing vortices
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| Abstract:
The hamiltonian theory of point vortices in a planar ideal fluid is classical (from the 19th century). On surfaces other than the plane, not much is known. In recent years Montaldi, Roberts, et al. have developed a geometric perturbation theory for symmetric hamiltonian systems, and used it to study relative equilibria of vortices on a sphere. The next step would be to apply the theory to relative periodic orbits on general surfaces. But whereas examples abound for planar vortices, in the case of surfaces we did not know any nontrivial example of a periodic orbit (other than relative equilibria on a sphere). This talk will describe an infinite family of periodic orbits for vortices on spheres, ellipsoids, tori, and many other surfaces, as well as some of their features that smell like theorems.
Partly joint work with J. Montaldi.
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| Monday 19th November 2001 |
2.00pm | Room MI1 |
TBA |
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| Monday 26th November 2001 |
2.00pm | Room MI1 |
No seminar because of MIR@W Day on |
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| Monday 3rd December 2001 |
2.00pm | Room MI1 |
Gert van der Heijden (UCL) |
Constrained rods: from drill strings to DNA supercoils
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| Abstract:
I will discuss recent work on rods (quasi-statically) deforming in
the presence of constraining surfaces.
First the case of a rod in permanent contact with a cylindrical
surface will be considered. This provides a simple model for a drill
string confined to a narrow borehole and also turns out to be
relevant for DNA supercoiling and textile yarn spinning. The
remarkably subtle process of ply formation in an end-loaded clamped
rod will be illustrated.
Then more recent work on variational formulations for problems
with one- or two-sided constraints will be discussed and applied
to rods on or inside arbitrary surfaces, allowing for touch-down
and lift-off. These formulations extend the impetus-striction method
of Maddocks & Dichmann for turning a Lagrangian problem with
constraints into an unconstrained Hamiltonian problem in which the
constraints are manifested as integrals of motion (roughly the dual
to Dirac's method of constraints). Due to lack of convexity,
inextensible rods, as opposed to extensible ones, are found to
require a 'higher-order' version of the method.
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| Wednesday 5th December 2001 |
2.00pm | Room 26 |
Renzo Ricca (UCL) |
From vortex knots to complex systems
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| Abstract:
In this talk we review some recent developments in topological
fluid mechanics in the light of modern applications
of knot theory to fluid flows. In particular we present some results
on vortex knots and links and discuss recent work on complex systems
of vortex tangles.
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