DSpace Community:https://dspace.lboro.ac.uk/2134/892019-05-21T03:12:53Z2019-05-21T03:12:53ZRemarkable charged particle dynamics near magnetic field null linesNeishtadt, AnatolyArtemyev, A.V.Turaev, Dmitryhttps://dspace.lboro.ac.uk/2134/377222019-05-09T10:02:08Z2019-01-01T00:00:00ZTitle: Remarkable charged particle dynamics near magnetic field null lines
Authors: Neishtadt, Anatoly; Artemyev, A.V.; Turaev, Dmitry
Abstract: The study of charged-particle motion in electromagnetic fields is a rich source of problems, models, and new
phenomena for nonlinear dynamics. The case of a strong magnetic field is well studied in the framework of
a guiding center theory, which is based on conservation of an adiabatic invariant – the magnetic moment. This theory ceases to work near a line on which the magnetic field vanishes – the magnetic field null line. In this paper we show that the existence of these lines leads to remarkable phenomena which are new both for nonlinear dynamics in general and for the theory of charged-particle motion. We consider the planar motion of a charged particle in a strong stationary perpendicular magnetic field with a null line and a strong electric field. We show that particle dynamics switch between a slow guiding center motion and the fast traverse along a segment of the magnetic field null line. This segment is the same (in the principal approximation) for all particles with the same total energy. During the phase of a guiding center motion, the magnetic moment of particle’s Larmor rotation stays approximately constant, i.e., it is an adiabatic invariant. However, upon each traversing of the null-line, the magnetic moment changes in a random fashion, causing the particle choose a new trajectory of the guiding center motion. This results in a stationary distribution of the magnetic moment, which only depends on the particle’s total energy. The jumps in the adiabatic invariant are described by Painleve II equation.
Description: This paper is closed access until it is published.2019-01-01T00:00:00ZComputer enhanced learning for mathematics in MalawiNgwale, Matthews A.https://dspace.lboro.ac.uk/2134/377002019-05-03T14:00:57Z1987-01-01T00:00:00ZTitle: Computer enhanced learning for mathematics in Malawi
Authors: Ngwale, Matthews A.
Abstract: Mathematics is a dreaded subject all over the world more so in
third world countries. Results in Malawian examination papers
clearly show a higher failure rate in mathematics than other
subjects. New teaching methods are needed to revolutionalise
pupils' perspective of mathematical concepts and help them see
mathematics as a doing subject independently or as a service
discipline. The new teaching methods must be seen to make
mathematical experience accessible to pupils which will in turn
promote pupils' enjoyment of mathematics.
Lack of student active participation in present mathematics
teaching methods and abstraction in some topics puts off weaker
or slow learning students and develops in such students a sense
of defeat and demotivation towards the subject. In Britain and
other developed countries, syllabuses and teaching methods are
constantly under review. In some cases new syllabuses are adopted
without prior training for teachers causing additional problems,
e.g. the new GCSE syllabus in U.K. which is new in methodology,
content and assessment methods.
This research, carried out for Malawi, particularly for the
Polytechnic, looks at how this massive percentage of under
achievement can be reduced. It also exposes the instructional
ineffectiveness and inefficiency at learning tasks. The
importance of in-service training for secondary and primary
school mathematics teachers is also highlighted.
Computers can be a key to realising educational goals such as
promoting pupil-directed inquiry, enhancing the development of
scientific and mathematical concepts and addressing more
efficiently the learning needs of individual children in mixed
ability and overcrowded classrooms. An assessment of Computer
Enhanced Learning for the improvement and reinforcement of
present teaching methods is therefore made.
Finally, a set of recommendations for the improvement of
mathematics education in Malawi is suggested to the Ministry
of Education and Culture through the Polytechnic for
implementation.
Description: A Masters Thesis. Submitted in partial fulfilment of the requirements for the award of Master of Philosophy of Loughborough University.1987-01-01T00:00:00ZDeterministic fibre tracking improved by diffusion tensor similarityYe, LeiZhou, DiweiHunsicker, EugenieLi, Baihuahttps://dspace.lboro.ac.uk/2134/376892019-05-08T23:02:49Z2019-01-01T00:00:00ZTitle: Deterministic fibre tracking improved by diffusion tensor similarity
Authors: Ye, Lei; Zhou, Diwei; Hunsicker, Eugenie; Li, Baihua
Abstract: Fibre tracking is a non-invasive technique based on Diffusion
Tensor Imaging (DTI) that provides useful information about biological
anatomy and connectivity. In this paper, we propose a new tractography
algorithm, named TAS (Tracking by Angle and Similarity), which is able
to overcome the shortfalls of existing algorithms by considering not only
the main diffusion directions, but also the similarity of diffusion tensors.
The algorithm achieved better tracking results in simulation experiments.
Fibre tracking from a real brain dataset is presented.
Description: This paper is in closed access until 12 months after publication.2019-01-01T00:00:00ZBinding potentials for vapour nanobubbles on surfaces using density functional theory.Yin, HanyuSibley, David N.Archer, Andrew J.https://dspace.lboro.ac.uk/2134/376782019-04-30T08:23:08Z2019-01-01T00:00:00ZTitle: Binding potentials for vapour nanobubbles on surfaces using density functional theory.
Authors: Yin, Hanyu; Sibley, David N.; Archer, Andrew J.
Abstract: We calculate one-body density profiles of a simple model fluid in contact with a planar surface using density functional theory (DFT), in particular for the case where there is a vapour layer intruding between the wall and the bulk liquid. We apply the method of Hughes \emph{et al.}\ [J.\ Chem.\ Phys.\ {\bf 142}, 074702 (2015)] to calculate the density profiles for varying (specified) amounts of the vapour adsorbed at the wall. This is equivalent to varying the thickness $h$ of the vapour at the surface. From the resulting sequence of density profiles we calculate the thermodynamic grand potential as $h$ is varied and thereby determine the binding potential as a function of $h$. The binding potential obtained via this coarse-graining approach allows us to determine the disjoining pressure in the film and also to predict the shape of vapour nano-bubbles on the surface. Our microscopic DFT based approach captures information from length scales much smaller than some commonly used models in continuum mechanics.
Description: This paper is in closed access until 12th April 2020.2019-01-01T00:00:00Z