MIMS EPrints
Not a member yet
2151 research outputs found
Sort by
On the diffraction of acoustic waves by a quarter-plane
Get PDFThis paper follows the work of A.V. Shanin on diffraction by an ideal quarter-plane. Shanin�s theory, based on embedding formulae, the acoustic uniqueness theorem and spherical edge Green�s functions, leads to three modified Smyshlyaev formulae, which partially solve the far-field problem of scattering of an incident plane wave by a quarter-plane in the Dirichlet case. In this paper, we present similar formulae in the Neumann case, and describe a numerical method allowing a fast computation of the diffraction coefficient using Shanin�s third modified Smyshlyaev formula. The method requires knowledge of the eigenvalues of the Laplace�Beltrami operator on the unit sphere with a cut, and we also describe a way of computing these eigenvalues. Numerical results are given for different directions of incident plane wave in the Dirichlet and the Neumann cases, emphasising the superiority of the third modified Smyshlyaev formula over the other two
The Hurewicz image of the family
Get PDFWe consider the problem of detecting Mahowald's
family H_* \Omega_0^{2^{i+1} - 8 + k}S^{2^i-2}0 \leq k \leq 6ARH_* Q_0S^0$
Algorithms for Matrix Polynomials and Structured Matrix Problems
No full textIn this thesis we focus on algorithms for matrix polynomials and structured matrix problems.
We begin by presenting a general purpose eigensolver for dense quadratic eigenvalue problems,
which incorporates recent contributions on the numerical solution of
polynomial eigenvalue problems, namely a scaling of
the eigenvalue parameter prior to the computation,
and a choice of linearization with favourable
conditioning and backward stability properties.
Our algorithm includes a preprocessing step
that
reveals the zero and infinite eigenvalues contributed by singular
leading and trailing matrix coefficients and
deflates them.
Numerical experiments are presented, comparing the performance of this algorithm on a collection of test problems, in terms of accuracy and stability.
We then describe structure preserving transformations for quadratic matrix polynomials.
Given a pair of distinct eigenvalues s (\l_1,\l_2) of an n-by-n quadratic matrix polynomial Q(\l)=\l^2 A_2+\l A_1 +A_0
with a nonsingular leading coefficient and their corresponding eigenvectors,
we show how to transform Q(\l) into a quadratic of the form
\mmtwobytwomatrix{\Qd(\l)}{0}{0}{q(\l)} having the same eigenvalues as Q(\l), with
\Qd(\l) an quadratic matrix polynomial and
q(\l) a scalar quadratic polynomial with roots \l_1 and \l_2
Involutions in Fischer�s sporadic groups
No full textFor each of Fischer�s sporadic simple groups and their automorphism groups, we catalogue the suborbits of the conjugation action on each of the involution conjugacy classes. Representative elements for the suborbits are provided, where possible as words in the standard generators and elsewhere they are given electronically as base images. Additionally we use this data to determine the structure of the commuting involution graphs on the two largest involution classes in Fi24
Classifying weighted projective spaces
Get PDFWe obtain two classifications of complex weighted projective spaces, up to homeomorphism and up to homotopy equivalence. The first turns out to coincide with Al Amrani's classification up to isomorphism of algebraic varieties, and
the second follows from our proof that the Mislin genus of any weighted projective space is rigid
Investigating the Performance of Asynchronous Jacobi's Method for Solving Systems of Linear Equations
Get PDFEver-increasing core counts create the need to develop parallel algorithms that avoid closely-coupled execution across cores. In this paper we present two case studies investigating the performance of several parallel asynchronous implementations of Jacobi's method for solving systems of linear equations. Although conditions for the convergence of asynchronous Jacobi are well known, what drives its rate of convergence is less well understood. The first case study investigates the algorithm's performance when executed on large numbers of processors on a Cray XE6, while the second explores the effect of varying the number of synchronous and asynchronous processors. We observe that the performance of parallel asynchronous Jacobi is highly implementation, problem and architecture-dependent
The Determination of a Dynamic Cut-Off Grade for the Mining Industry
Get PDFPrior to extraction from a mine, a pit is usually divided up into 3-D `blocks' which contain varying levels of estimated ore-grades. From these, the order (or `pathway') of extraction is decided, and this order of extraction can remain unchanged for several years. However, because commodity prices are uncertain, once each block is extracted from the mine, the company must decide in real-time whether the ore grade is high enough to warrant processing the block further in readiness for sale, or simply to waste the block. This paper first shows how the optimal cut-off ore grade—the level below which a block should be wasted—is not simply a function of the current commodity price and the ore grade, but also a function of the ore-grades of subsequent blocks, the costs of processing, and the bounds on the rates of processing and extraction. Secondly, the paper applies a stochastic price uncertainty, and shows how to derive an efficient mathematical algorithm to calculate and operate a dynamic optimal cut-off grade criterion throughout the extraction process, allowing the mine operator to respond to future market movements. The model is applied to a real mine composed of some 60,000 blocks, and shows that an extra 10% of value can be created by implementing such an optimal regime
Local Fusion Graphs of Finite Groups
Get PDFLet G be a group, with X a G-conjugacy class of involutions. The local fusion graph F(G,X) has X as its vertex set, with vertices x,y in X joined by an edge if, and only if, x and y are not equal and the order of the product xy is odd. In this thesis we study these, and other related graphs, for a variety of finite groups, paying particular attention to the cases when G is a finite simple group. We also present a computational algorithm regarding centralisers of involutions, which makes use of local fusion graphs
Homogenization Methods to Approximate the Effective Response of Random Fibre-reinforced Composites
Get PDFIn this article a fibre-reinforced composite material is modelled via an approach employing a Representative Volume Element with periodic boundary conditions. The effective elastic moduli of the material are thus derived. In particular, the method of asymptotic homogenization is used where a finite number of fibres are randomly distributed within the representative periodic cell. The study focuses on the efficacy of such an approach in representing a macroscopically random (hence transversely isotropic) material. Of particular importance is the sensitivity of the method to cell shape, and how this choice affects the resulting (configurationally averaged) elastic moduli. The averaging method is shown to yield results that lie within the Hashin-Shtrikman variational bounds for fibre-reinforced media and compares well with the multiple scattering and (classical) self-consistent approximations with a deviation from the latter in the larger volume fraction cases. Results also compare favourably with well-known experimental data from the literature