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Forthcoming events in this series
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How Energy Escapes from a Tokamak: Orders of Magnitude Faster than Explained by Received Theory
Abstract
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From Individual to Collective Behaviour in Biological Systems:
The Bacterial Example
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A Delay Recruitment Model of the Cardiovascular Control System
Abstract
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Three dimensional travelling gravity-capillary water waves
Abstract
The classical gravity-capillary water-wave problem is the
study of the irrotational flow of a three-dimensional perfect
fluid bounded below by a flat, rigid bottom and above by a
free surface subject to the forces of gravity and surface
tension. In this lecture I will present a survey of currently
available existence theories for travelling-wave solutions of
this problem, that is, waves which move in a specific
direction with constant speed and without change of shape.
The talk will focus upon wave motions which are truly
three-dimensional, so that the free surface of the water
exhibits a two-dimensional pattern, and upon solutions of the
complete hydrodynamic equations for water waves rather than
model equations. Specific examples include (a) doubly
periodic surface waves; (b) wave patterns which have a
single- or multi-pulse profile in one distinguished
horizontal direction and are periodic in another; (c)
so-called 'fully-localised solitary waves' consisting of a
localised trough-like disturbance of the free surface which
decays to zero in all horizontal directions.
I will also sketch the mathematical techniques required to
prove the existence of the above waves. The key is a
formulation of the problem as a Hamiltonian system with
infinitely many degrees of freedom together with an
associated variational principle.
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Topology and Energy of Nematic Liquid Crystals in Polyhedral Cells
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Various Solutions to the Nonlinear Equations Describing the Motion of an Elastic String
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Complex Variable Approach for Water Entry Problems
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17:00
Mechanics of Toys<br>
<br>
A special lecture (complete with toys!) of interest to mathematicians at all levels, including unde
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Motion of singular sets
and
Why still bother with sonic booms?
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Localisation of waves in high contrast media via homogenisation and
photonic crystals
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Boundary Value Problems on Measure Chains
Abstract
When modelling a physical or biological system, it has to be decided
what framework best captures the underlying properties of the system
under investigation. Usually, either a continuous or a discrete
approach is adopted and the evolution of the system variables can then
be described by ordinary or partial differential equations or
difference equations, as appropriate. It is sometimes the case,
however, that the model variables evolve in space or time in a way
which involves both discrete and continuous elements. This is best
illustrated by a simple example. Suppose that the life span of a
species of insect is one time unit and at the end of its life span,
the insect mates, lays eggs and then dies. Suppose the eggs lie
dormant for a further 1 time unit before hatching. The `time-scale' on
which the insect population evolves is therefore best represented by a
set of continuous intervals separated by discrete gaps. This concept
of `time-scale' (or measure chain as it is referred to in a slightly
wider context) can be extended to sets consisting of almost arbitrary
combinations of intervals, discrete points and accumulation points,
and `time-scale analysis' defines a calculus, on such sets. The
standard `continuous' and `discrete' calculus then simply form special
cases of this more general time scale calculus.
In this talk, we will outline some of the basic properties of time
scales and time scale calculus before discussing some if the
technical problems that arise in deriving and analysing boundary
value problems on time scales.
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Stagnant-cap bubbles with both diffusion and adsorption rate-determining
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