Research Error. How I Came to be Where I am.

The text below reproduces, more or less, a talk I gave during the college’s Research Week in Spring 2003. Although the talk was scripted for the most part, there were a few improvised ‘passages’ – the major one occasioned by a latecomer’s tussle with the door, as I recall. Literally, ‘error’ means wandering and I used the word not just to create a link with William Carlos Williams’ unruly and roaming improvisation, Rome but also to signal my own sense of dissatisfaction, which was the goad for the talk in the first place. Dissatisfaction with the critical ‘voice’ in which I seemed to find myself ensnared after seventeen years purposeful writing and thinking in academia. A voice so clinical – or so it seemed to me – so anodyne and remote from the texts it was speaking about. The nature of these texts is very much to the point, since in working with ‘improvisations’ I was engaging with texts whose impetus and modus operandi fly in the face of many of the traditional pieties of academic discourse. Improvisations – those of Williams, at least – are not considered or consistent. They are often not finished, let alone polished. Subjectivity courses through them with an urgency that bursts syntax like a flash flood will snap a drain. So, should I rein back, refrain from engagements this kind of text altogether? As far as I know, only one other scholar has written in detail about Rome, although a published facsimile edition has been available now for over thirty years. What follows are my first real efforts to address the improvisations in a way that does not routinely betray their poetics but also traverses the communal space that is critical inquiry

Singularities of spacelike constant mean curvature surfaces in Lorentz-Minkowski space

We study singularities of spacelike, constant (non-zero) mean curvature (CMC) surfaces in the Lorentz-Minkowski 3-space $L^3$. We show how to solve the singular Bj\"orling problem for such surfaces, which is stated as follows: given a real analytic null-curve $f_0(x)$, and a real analytic null vector field $v(x)$ parallel to the tangent field of $f_0$, find a conformally parameterized (generalized) CMC $H$ surface in $L^3$ which contains this curve as a singular set and such that the partial derivatives $f_x$ and $f_y$ are given by \frac{\dd f_0}{\dd x} and $v$ along the curve. Within the class of generalized surfaces considered, the solution is unique and we give a formula for the generalized Weierstrass data for this surface. This gives a framework for studying the singularities of non-maximal CMC surfaces in $L^3$. We use this to find the Bj\"orling data -- and holomorphic potentials -- which characterize cuspidal edge, swallowtail and cross cap singularities.Comment: 28 pages, 2 figures. Version 2: Figure 2 adde

Contamination of optical surfaces

The effect of molecular contamination on Space Station optical surfaces is examined. In particular, contamination of solar voltaic power sources and optical solar reflectors for thermal control or solar dynamic power generation is addressed. The published Space Station requirements for molecular contamination accretion and for the monitoring of such accretion is discussed in the context of the historical performance of space systems. Specific reference is made to the results from the Spacecraft Charging at High Altitudes (SCATHA) ML12 experiment

UK Competition Policy and Shareholder Value: The Impact of Merger Inquiries

Some previous studies have suggested that competition re´gimes can destroy shareholder value. This study examines data on 50 mergers in the UK between 1989 and 2002. The study confirms the finding from earlier studies of greater gains to shareholders in target than bidding companies, but does not find evidence supporting overall loss of shareholder value to target company shareholders when a merger is prohibited. It finds evidence that when the regulatory re´gime is stable and well understood the capital market behaves efficiently in response to new information. However, for a subgroup of the mergers involving companies with a new regulatory re´gime, where the industry and the stock market had little or no experience with respect to mergers, the capital market operated less efficiently

Distributions generated by perturbation of symmetry with emphasis on a multivariate skew tt distribution

A fairly general procedure is studied to perturbate a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non-symmetric densities. The approach is general enough to encompass a number of recent proposals in the literature, variously related to the skew normal distribution. The special case of skew elliptical densities is examined in detail, establishing connections with existing similar work. The final part of the paper specializes further to a form of multivariate skew $t$ density. Likelihood inference for this distribution is examined, and it is illustrated with numerical examples.Comment: full-length version of the published paper, 31 pages with 9 figure

Nanoarrays for the generation of complex optical wave-forms

Light beams with unusual forms of wavefront offer a host of useful features to extend the repertoire of those developing new optical techniques. Complex, non-uniform wavefront structures offer a wide range of optomechanical applications, from microparticle rotation, traction and sorting, through to contactless microfluidic motors. Beams combining transverse nodal structures with orbital angular momentum, or vector beams with novel polarization profiles, also present new opportunities for imaging and the optical transmission of information, including quantum entanglement effects. Whilst there are numerous well-proven methods for generating light with complex wave-forms, most current methods work on the basis of modifying a conventional Hermite-Gaussian beam, by passage through suitably tailored optical elements. It has generally been considered impossible to directly generate wave-front structured beams either by spontaneous or stimulated emission from individual atoms, ions or molecules. However, newly emerged principles have shown that emitter arrays, cast in an appropriately specified geometry, can overcome the obstacles: one possibility is a construct based on the electronic excitation of nanofabricated circular arrays. Recent experimental work has extended this concept to a phase-imprinted ring of apertures holographically encoded in a diffractive mask, generated by a programmed spatial light modulator. These latest advances are potentially paving the way for creating new sources of structured light

Experimental measurement and theoretical modeling of microwave scattering and the structure of the sea surface influencing radar observations from space

The electromagnetic bias is an error present in radar altimetry of the ocean due to the non-uniform reflection from wave troughs and crests. A study of the electromagnetic bias became necessary to permit error reduction in mean sea level measurements of satellite radar altimeters. Satellite radar altimeters have been used to find the upper and lower bounds for the electromagnetic bias. This report will present a theory using physical optics scattering and an empirical model of the short wave modulation to predict the electromagnetic bias. The predicted electromagnetic bias will be compared to measurements at C and Ku bands

Polarisation structuring of broadband light

Spatial structuring of the intensity, phase and polarisation of light is useful in a wide variety of modern applications, from microscopy to optical communications. This shaping is most commonly achieved using liquid crystal spatial light modulators (LC-SLMs). However, the inherent chromatic dispersion of LC-SLMs when used as diffractive elements presents a challenge to the extension of such techniques from monochromatic to broadband light. In this work we demonstrate a method of generating broadband vector beams with dynamically tunable intensity, phase and polarisation over a bandwidth of 100 nm. We use our system to generate radially and azimuthally polarised vector vortex beams carrying orbital angular momentum, and beams whose polarisation states span the majority of the Poincaré sphere. We characterise these broadband vector beams using spatially and spectrally resolved Stokes measurements, and detail the technical and fundamental limitations of our technique, including beam generation fidelity and efficiency. The broadband vector beam shaper that we demonstrate here may find use in applications such as ultrafast beam shaping and white light microscopy

Technologies for aerobraking

Aerobraking is one of the largest contributors to making both lunar and Mars missions affordable. The use of aerobraking/aeroassist over all propulsive approaches saves as much as 60 percent of the initial mass required in low earth orbit (LEO); thus, the number and size of earth to orbit launch vehicles is reduced. Lunar transfer vehicles (LTV), which will be used to transport personnel and materials from LEO to lunar outpost, will aerobrake into earth's atmosphere at approximately 11 km/sec on return from the lunar surface. Current plans for both manned and robotic missions to Mars use aerocapture during arrival at Mars and at return to Earth. At Mars, the entry velocities will range from about 6 to 9.5 km/sec, and at Earth the return velocity will be about 12.5 to 14 km/sec. These entry velocities depend on trajectories, flight dates, and mission scenarios and bound the range of velocities required for the current studies. In order to successfully design aerobrakes to withstand the aerodynamic forces and heating associated with these entry velocities, as well as to make them efficient, several critical technologies must be developed. These are vehicle concepts and configurations, aerothermodynamics, thermal protection system materials, and guidance, navigation, and control systems. The status of each of these technologies are described, and what must be accomplished in each area to meet the requirements of the Space Exploration Initiative is outlined