Projective Limit Random Probabilities on Polish Spaces

A pivotal problem in Bayesian nonparametrics is the construction of prior distributions on the space M(V) of probability measures on a given domain V. In principle, such distributions on the infinite-dimensional space M(V) can be constructed from their finite-dimensional marginals---the most prominent example being the construction of the Dirichlet process from finite-dimensional Dirichlet distributions. This approach is both intuitive and applicable to the construction of arbitrary distributions on M(V), but also hamstrung by a number of technical difficulties. We show how these difficulties can be resolved if the domain V is a Polish topological space, and give a representation theorem directly applicable to the construction of any probability distribution on M(V) whose first moment measure is well-defined. The proof draws on a projective limit theorem of Bochner, and on properties of set functions on Polish spaces to establish countable additivity of the resulting random probabilities.

Characterisation of carbon nano-onions using Raman spectroscopy

Characteristics of the Raman spectrum from carbon onions have been identified in terms of the position of the G peak and appearance of the transverse optic phonon peaks. Five new peaks were observed in the low wavenumber region, at about 1100, 861, 700, 450 and 250 cm(-1). The origins of these peaks are discussed in terms of the phonon density of states (PDOS) and phonon dispersion curves of graphite. The curvature of the graphene planes is invoked to explain the relaxation of the Raman selection rules and the appearance of the new peaks. The Raman spectrum of carbon onions is compared with that of highly oriented pyrolytic graphite (HOPG). The strain of graphene planes due to curvature has been estimated analytically and is used to account for the downward shift of the G peak. (C) 2003 Elsevier Science B.V. All rights reserved.

Critical current anisotropy in high temperature superconductors

After nearly 15 years of research effort, High Temperature Superconductors (HTS) are finding a wide range of practical applications. A clear understanding of the factors controlling the current carrying capacity of these materials is a prerequisite to their successful technological development. The critical current density (Jc) in HTS is directly dependent on the structure and pinning of the Flux Line Lattice (FLL) in these materials. This thesis presents an investigation of the Jc anisotropy in HTS. The use of thin films grown on off c-axis (vicinal) substrates allowed the effect of current directions outside the cuprate planes to be studied. With this experimental geometry Berghuis, et al. (Phys. Rev. Lett. 79, 12, pg. 2332) observed a striking flux channelling effect in vicinal YBa2Cu3O7-δ (YBCO) films. By confirming, and extending, this observation, it is demonstrated that this is an intrinsic effect. The results obtained, appear to fit well with the predictions of a field angle dependent cross-over from a three dimensional rectilinear FLL to a kinked lattice of strings and pancakes. The pinning force density for movement of strings inside the cuprate planes is considerably less than that on vortex pancake elements. When the FLL is entirely string-like this reduced pinning leads to the observed channelling minima. It is observed that anti-phase boundaries enhance the Jc in vicinal YBCO films by strongly pinning vortex strings. The effect on the FLL structure cross-over of increasing anisotropy has been elucidated using de-oxygenated vicinal YBCO films. Intriguingly, the counter intuitive prediction that the range of applied field angle for which the kinked lattice is fully developed reduces with increasing anisotropy, appears to be confirmed. Although vortex channelling cannot be observed in c-axis YBCO films, the pinning force density for vortex string channelling has been extracted by observing string dragging. By studying the effect of rotating the applied field at a constant angle to the cuprate planes, it is possible to observe the cross-over into the string pancake regime in c-axis films. In the 3D region, the observed behaviour is well explained by the anisotropic Ginzburg-Landau model. Measurements were also made on thin films of the much more anisotropic Bi 2Sr2CaCu2O8+x material, grown on vicinal substrates. The absence of any flux channelling effect and clear adherence to the expected Kes-Law behaviour in the observed Jc characteristics does not provide evidence for the existence of the predicted ‘crossing lattice’ in Bi 2Sr2CaCu2O8+x .

Direct observation of the structural component of the metal-insulator phase transition and growth habits of epitaxially grown VO2 nanowires.

We have grown epitaxially orientation-controlled monoclinic VO2 nanowires without employing catalysts by a vapor-phase transport process. Electron microscopy results reveal that single crystalline VO2 nanowires having a [100] growth direction grow laterally on the basal c plane and out of the basal r and a planes of sapphire, exhibiting triangular and rectangular cross sections, respectively. In addition, we have directly observed the structural phase transition of single crystalline VO2 nanowires between the monoclinic and tetragonal phases which exhibit insulating and metallic properties, respectively, and clearly analyzed their corresponding relationships using in situ transmission electron microscopy.

Development of non-weak link bulk YBCO grain boundaries for high magnetic field eegimeering applications

A non-weak link joining technique has been developed for YBCO pseudo-crystals fabricated by seeded peritectic solidification based on the formation of a liquid phase which segregates from the platelet boundaries at temperatures above = 920 °C. Electrical and magnetic measurements on these boundaries suggest that their irreversibility field can be as high as 7 T at 77 K in fully oxygenated pseudo-crystals joined along their crystallographic ab-planes which is comparable to the irreversibility behaviour of the adjacent YBCO grains. © 1999 IEEE.

Behavior of bulk melt-textured YBCO single domains subjected to crossed magnetic fields

We have experimentally investigated the crossed magnetic field effects on bulk melt-processed YBCO single domains. The samples were first permanently magnetized along their c-axis and then subjected to several cycles of a transverse magnetic field parallel to the ab planes. The magnetic properties along the c and ab directions were simultaneously measured using a couple of orthogonal pick-up coils as well as a Hall probe placed against the sample surface. The effects of both sweep amplitude and polarity were investigated. Field sweeps of alternate polarities are shown to affect the decay of the c-axis magnetization much more strongly than field sweeps of unique polarity do. However, the c-axis magnetization does not show any saturation even after a large number of field sweeps. Next, a micro-Hall probe scanning system was used to measure the distribution of magnetic induction over the top surface of the single domain subjected to the same combination of magnetic fields. The results are shown to be consistent with those determined with the sensing coils and bring out the role played by geometric effects.

Low Molar Mass Organosiloxane Liquid Crystalline Dyes for Dye Guest Host Ferroelectric Display Devices

In low molar mass organosiloxane liquid-crystal materials the siloxane moieties micro-separate and aggregate in planes that could be regarded as an effective or virtual two-dimensional polymer backbone. We show that if a siloxane moiety is attached to a dichroic dye molecule, the micro-segregation of the siloxane moieties makes it possible to include a high concentration of the guest dye (more than 50%) in a host organosiloxane solution. This effect, combined with the temperature independent tilt angles achievable with ferroelectric organosiloxane liquid crystals, provide an ideal material for high-contrast surface-stabilised ferroelectric display devices. We present dyed ferroelectric materials with a temperature independent tilt angle greater than 42 degrees, a wide (room temperature to over 100°C) mesomorphic temperature range and a response time shorter than 500μs in the dye guest host mode.

A procedure for automatically estimating model parameters in optical motion capture

Model-based optical motion capture systems require knowledge of the position of the markers relative to the underlying skeleton, the lengths of the skeleton's limbs, and which limb each marker is attached to. These model parameters are typically assumed and entered into the system manually, although techniques exist for calculating some of them, such as the position of the markers relative to the skeleton's joints. We present a fully automatic procedure for determining these model parameters. It tracks the 2D positions of the markers on the cameras' image planes and determines which markers lie on each limb before calculating the position of the underlying skeleton. The only assumption is that the skeleton consists of rigid limbs connected with ball joints. The proposed system is demonstrated on a number of real data examples and is shown to calculate good estimates of the model parameters in each. © 2004 Elsevier B.V. All rights reserved.