Time-parallel iterative solvers for parabolic evolution equations

We present original time-parallel algorithms for the solution of the implicit Euler discretization of general linear parabolic evolution equations with time-dependent self-adjoint spatial operators. Motivated by the inf-sup theory of parabolic problems, we show that the standard nonsymmetric time-global system can be equivalently reformulated as an original symmetric saddle-point system that remains inf-sup stable with respect to the same natural parabolic norms. We then propose and analyse an efficient and readily implementable parallel-in-time preconditioner to be used with an inexact Uzawa method. The proposed preconditioner is non-intrusive and easy to implement in practice, and also features the key theoretical advantages of robust spectral bounds, leading to convergence rates that are independent of the number of time-steps, final time, or spatial mesh sizes, and also a theoretical parallel complexity that grows only logarithmically with respect to the number of time-steps. Numerical experiments with large-scale parallel computations show the effectiveness of the method, along with its good weak and strong scaling properties

A permanent formula for the Jones polynomial

The permanent of a square matrix is defined in a way similar to the determinant, but without using signs. The exact computation of the permanent is hard, but there are Monte-Carlo algorithms that can estimate general permanents. Given a planar diagram of a link L with $n$ crossings, we define a 7n by 7n matrix whose permanent equals to the Jones polynomial of L. This result accompanied with recent work of Freedman, Kitaev, Larson and Wang provides a Monte-Carlo algorithm to any decision problem belonging to the class BQP, i.e. such that it can be computed with bounded error in polynomial time using quantum resources.Comment: To appear in Advances in Applied Mathematic

High index top layer for multimaterial coatings

For application in future cryogenically cooled gravitational wave detectors, the thermal noise of low absorbing mirror coatings has to be reduced. The development of low mechanical and optical loss materials is challenging, but thermal noise reduction can be significantly supported by using a multimaterial coating design. We analyze the possible improvement of the total (optical and mechanical) loss of a three-material based coating obtained by optimizing the properties of the top layer of the coating stack. A top-layer material with sufficiently high refractive index could have a significantly higher optical and mechanical loss than currently used tantala, while still enabling reduction of the total coating loss. Restrictions on possible top-layer material properties are made, and the option of a crystalline top layer is discussed

Factors affecting the success of Information Systems projects

This thesis looks at how accurately project managers can pre-predict what problems may arise during an Information Systems project they are about to commence based on their experience of previous projects. The second part investigates what actions a project manager is likely to take to expedite a troubled project. Both of these questions are investigated and it is found that while project managers can confidently predict which problems could arise, and how to take actions to rectify such actions when they occur, these problems still arise

Turning up the lights - fabrication of brighter SERRS nanotags

Brighter SERRS nanotags ideal for improved SERRS imaging were prepared by the controlled addition of electrolyte producing a dimer enriched solution, which was incubated with a Raman reporter before being stabilised by a polyethylene glycol (PEG) shell

Polyterthiophenes incorporating 3,4-difluorothiophene units : application in organic field-effect transistors

Two terthiophenes bearing core fluorinated thienyl units have been synthesised as potential semiconductor materials for organic field-effect transistors. Polymerisation of these compounds has been achieved using conventional iron(III) chloride oxidative coupling methods and by electrochemical oxidation. Characterisation of the fluorinated materials has been achieved by absorption spectroscopy and cyclic voltammetry. A soluble hexyl-functionalised polymer (poly8b) was used in an OFET device; hole mobilities were measured up to 3 × 10−3 cm2 · V−1 · s−1, and the device had an on/off ratio of 105 and a turn-on voltage of +4 V