DSpace Collection:https://dspace.lboro.ac.uk/2134/103912017-10-20T17:55:36Z2017-10-20T17:55:36ZColliding plane gravitational and fluid wavesAshby, Phillip C.https://dspace.lboro.ac.uk/2134/270262017-10-20T11:36:10Z1992-01-01T00:00:00ZTitle: Colliding plane gravitational and fluid waves
Authors: Ashby, Phillip C.
Abstract: This thesis describes the collision and subsequent interaction of
two waves which exhibit plane symmetry, according to the theory
of general relativity. The properties of plane waves are discussed
and the necessary field equations and boundary conditions describing
this situation are formulated. Techniques are introduced
by which exact solutions describing the collision of gravitational
waves with constant and aligned polarization may be generated.
By way of demonstrating these techniques, an explicit new solution
is obtained. A complete integral of a family of solutions
which are isomorphic to Gowdy cosmologies is derived, and another
general class of solutions which are the analogue of the
Weyl solutions for axisymmetric space-times is obtained. Exact
solutions are also described for the collision of gravitational waves
with arbitrary polarization when coupled with scalar fields or a
type of null fluid that forms a stiff perfect fluid on interaction. A
method for obtaining large families of solutions of this type from
existing vacuum solutions using either of two potential functions
is introduced, and examples of its application are given. The restriction
of these stiff fluid solutions to the case where the waves
have constant and aligned polarization allows the method to be
generalised.
Description: A Master's Thesis. Submitted in partial fulfilment of the requirements for the award of Master of Philosophy at Loughborough University.1992-01-01T00:00:00ZAn evaluation of the effectiveness of a computer-aided assessment system for mathematics and engineering studentsBroughton, Stephen J.https://dspace.lboro.ac.uk/2134/248302017-06-05T13:18:51Z2017-01-01T00:00:00ZTitle: An evaluation of the effectiveness of a computer-aided assessment system for mathematics and engineering students
Authors: Broughton, Stephen J.
Abstract: Computer-aided assessment is a means by which to assess many students quickly and
efficiently. Its popularity as a tool for assessing mathematics increased substantially in
the first decade of this millennium as computing and the Internet became more widely
available, and as cohort sizes grew.
This research sought to evaluate one such system that had been used at a higher education
institution for over ten years. However, the literature does not offer a clear or detailed
framework from which to perform an evaluation of this system.
Using cultural-historical activity theory, and cues from assessment literature, this research
presents a model for effective assessment. It provides a framework for judging
where an assessment is effective for individuals using the assessment and where it ceases
to be effective.
Case study analyses helped to identify where the assessment tool was no longer effective.
It identified that students struggled to construct new goals after the summative phase
of assessment. It also explained how and why the lecturers had diverse practices.
Description: A Thesis submitted in fulfilment of the requirements for the degree of Master of Philosophy.2017-01-01T00:00:00ZSigma form of the second Painleve hierarchyAndrew, Stuart J.https://dspace.lboro.ac.uk/2134/163552014-12-04T16:13:33Z2014-01-01T00:00:00ZTitle: Sigma form of the second Painleve hierarchy
Authors: Andrew, Stuart J.
Abstract: The second Painleve hierarchy is a sequence of non-linear differential equations that have the second classical Painleve equation as its first member. We construct the sigma forms of this hierarchy and use this to examine some natural applications.
Description: A Masters Thesis. Submitted in partial fulfilment of the requirements for the award of Master of Philosophy of Loughborough University.2014-01-01T00:00:00ZNumerical solution of the non-linear Schroedinger equation : the half-line problem and dynamical systems and bifurcations of vector fieldsZakynthinaki, Maria S.https://dspace.lboro.ac.uk/2134/141642014-02-17T15:08:51Z1997-01-01T00:00:00ZTitle: Numerical solution of the non-linear Schroedinger equation : the half-line problem and dynamical systems and bifurcations of vector fields
Authors: Zakynthinaki, Maria S.
Abstract: Solutions to the nonlinear Schrodinger equation with potential V(u) =
-λulul2 have been theoretically and numerically calculated, revealing the
formation of solitons. In this study the finite element method with linear
basis functions, distinguished for its simplicity and effective applicability,
is considered and a predictor-corrector scheme is applied to simulate the
propagation in time. Numerical experiments include the propagation of a
single soliton form, a two-soliton collision, as well as the formation of more
than one solitons from non-soliton initial data. The important problem of
boundary reflections has been successfully overcome by the implementation
of absorbing boundaries, a method that in practice achieves a gradual reduction
of the wave amplitude at the end of each time step.
The second part of this work deals with dynamical systems of the form [see file]. The dynamics of such systems near their equilibrium
point depends strongly on the adjustable parameter μ, as it is possible for the
system to lose its hyperbolicity and a bifurcation to occur. After reviewing
aspects of linearisation, the prospect of change in the equilibrium solutions
has been studied, both for flows and maps, in terms of the eigenvalues of
the linearised system. In the study of steady-state bifurcation, elements of
saddle-node, transcritical, pitchfork, as well as period-doubling bifurcation
are considered. Finally, the case when equilibrium solutions persist, known
as Hopf bifurcation, has also been included.
Description: A Master's Thesis. Submitted in partial fulfilment of the requirements for the award of Master of Philosophy of Loughborough University.1997-01-01T00:00:00Z