Mathemateg a Ffiseg / Mathematics & Physics
http://hdl.handle.net/2160/14
Sat, 11 Jul 2020 15:47:26 GMT2020-07-11T15:47:26ZWhen is a surface foam-phobic or foam-philic?
http://hdl.handle.net/2160/46591
When is a surface foam-phobic or foam-philic?
Teixeira, Miguel A. C.; Arscott, Steve; Cox, Simon; Teixeira, Paulo I. C.
It is commonly assumed that the liquid making up a sessile bubble completely wets the surface upon which the bubble lies. However, this need not be so, and the degree of wetting will determine how well a collection of bubbles – a foam – sticks to a surface. As a preliminary to this difficult problem, we study the shape of a single vertical soap film spanning the gap between two flat, horizontal solid substrates of given wettabilities. For this simple geometry, the Young–Laplace equation can be solved (quasi-)analytically to yield the equilibrium shapes, under gravity, of the two-dimensional Plateau borders along which the film contacts the substrates. We thus show that these Plateau borders, where most of a foam’s liquid resides, can only exist if the values of the Bond number and of the liquid contact angle lie within certain domains in (\theta_c ,Bo) space: under these conditions the substrate is foam-philic. For values outside these domains, the substrate cannot support a soap film and it is foam-phobic. In other words, on a substrate of a given wettability, only Plateau borders of a certain range of sizes can form. For given (y c ,Bo), the top Plateau border can never have greater width or cross-sectional area than the bottom one. Moreover, the top Plateau border cannot exist in a steady state for contact angles above 901. Our conclusions are validated by comparison with both experimental and numerical (Surface Evolver) data. We conjecture that these results will hold, with slight modifications, for non-planar soap films and bubbles. Our results are also relevant to the motion of bubbles and foams in channels, where the friction force of the substrate on the Plateau borders plays an important role.
Soft Matter, 14: 5369-5382, 2018, DOI: 10.1039/C8SM00310F
Thu, 24 May 2018 00:00:00 GMThttp://hdl.handle.net/2160/465912018-05-24T00:00:00ZMathematics by the sea
http://hdl.handle.net/2160/44068
Mathematics by the sea
Fletcher, Colin R.
Foreword
E L Ellis in his definitive history of the University College of Wales, Aberystwyth, bemoans the fact that the natural title for his book had been pre-empted by the 1928 publication, The College by the Sea, that fascinating jumble of articles which so aptly conjured up life in this university outpost over the previous fifty years. The present book has no such predecessor and so the choice of title is not restricted. However, there was really only one possible title, using the 1928 volume with minimal alteration. The title almost from the first was to be Mathematics by the Sea.
The reason for this preamble is to apologize from the outset to those readers who will find this work a huge disappointment. This may be true especially of those present members of the Department of Mathematics and those recently retired, together with students of the modern era, for few of them are mentioned and their lives and works are unacknowledged. The truth is that the scope of this work has changed since the idea first formed in my mind. Initially I had the intention of compiling a history of the Department from the beginning until fairly recent times. But my interest was in people concerned, their background, their character, their lives at Aberystwyth, their relations with others, their subsequent careers if any, as well as their mathematical achievements. The book was not to be simply a list of names, theorems proved and papers published. And all this was possible up to a certain point, but that point did not extend anywhere near the present day if the work was to be kept within reasonable bounds. After much soul searching, that certain point was taken to be the move from the College by the sea to the College on the hill. In fact the span of years has been stretched somewhat. The three professors of mathematics, who led the move to the Physical Sciences building, foe one reason or another did not remain in post for long. The appointment of their successors has therefore been documented. And two members of staff who formed part of the move up the hill, only recently retired, have had their careers charted. Nevertheless, Mathematics by the Sea is an apt description of the contents of the present work. Its sequel, Mathematics on the Hill, will have to await a different hand.
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/2160/440682002-01-01T00:00:00ZTemperature and emission diagnostics of the solar corona: mapping plasma characteristics using multi-channel Extreme UltraViolet observations
http://hdl.handle.net/2160/43432
Temperature and emission diagnostics of the solar corona: mapping plasma characteristics using multi-channel Extreme UltraViolet observations
Leonard, Andrew
The solar corona is a hot, magnetised plasma of which several important aspects
remain poorly understood. The Atmospheric Imaging Assembly (AIA) provides
very high resolution images of the Sun in several extreme ultraviolet channels. AIA
offers a unique chance to improve our understanding of the corona - qualitatively
through detailed viewing of dynamic events and quantitatively through density and
temperature diagnostics.
This thesis presents a new software tool to quickly estimate coronal characteristics
using AIA data. The method creates high-resolution temperature and emission
measure maps of the whole solar disk within minutes. A slower but more thorough
version is also developed as a comparison, and complimentary to, the main method.
Both methods are tested extensively on synthetic data calculated from known temperature
distributions and are then applied to real data. A prototype method for
fast estimation of coronal line-of-sight emission distribution is also presented. A
broad study investigates the characteristics of various coronal regions. The results
are compared to previous works and found to be consistent, although the combination
of values produced by the two methods reveals material cooler than that found
by other studies, particularly at coronal hole boundaries. Another investigation applies
the fast method to two sets of flaring active regions. A weak correlation exists
between the flare size and mean temperature of the region for a small number of
flares in one set. In the other set each region’s temperature variability over time
is compared to a non-flaring region’s. The flaring regions’ mean temperatures are
found to vary more than the non-flaring region’s - significantly more in several cases.
This gives confidence in using such diagnostics as part of a future flare prediction
method. The fast temperature map method presented here offers a significant speed
advantage over similar methods, whilst maintaining robust results. This allows the
maximum exploitation of AIA’s fine spatial and temporal resolution for temperature
and emission measure studies.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/2160/434322016-01-01T00:00:00ZControl of open quantum systems
http://hdl.handle.net/2160/43312
Control of open quantum systems
Arenz, Christian
Known as decoherence, the unavoidable interaction of a quantum system with its
surrounding environment is usually considered to be detrimental for quantum information
processing. In this thesis the coherent, open loop control of such open
systems is studied. Concepts from quantum control theory and the theory of open
quantum system are adopted in order to fight decoherence and implement quantum
gates in a noiseless manner. In particular, Lie algebraic methods and numerical
optimization tools are used to investigate the control properties of a single spin interacting
with a spin environment. We show that, independent of the size of the
environment, every unitary transformation can be implemented on the system spin
through a single control field. We proceed by investigating dynamical decoupling,
a method to suppress the interactions with the environment, for finite- and for infinite
dimensional systems. We prove that every finite dimensional system can be
protected from decoherence, even if the environment is infinite dimensional, whereas
for noise described by a Lindblad master equation dynamical decoupling will never
succeed. This will lead to a new method to distinguish decoherence from intrinsic
noise terms. We further prove that not every infinite dimensional system can be
protected from decoherence through dynamical decoupling. Afterwards we investigate
dynamical decoupling of systems that are described by quadratic Hamiltonians,
showing that such interactions can always be suppressed with two simple operations.
In the last part we investigate the coherent control of a Lindblad master equation.
We show that a strong noise process exhibiting a decoherence free subspace can
substantially increase the number of unitary operations that can be implemented,
allowing us to fully control parts of the system. Afterwards we develop a scheme to
make Hamiltonians and Lindbladians commutative by adding an auxiliary system.
The old, possibly non-commutative dynamics, is recovered through a non-selective
measurement.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/2160/433122016-01-01T00:00:00Z