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.

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.

Discrete dislocation plasticity analysis of crack-tip fields in polycrystalline materials

Small scale yielding around a mode I crack is analysed using polycrystalline discrete dislocation plasticity. Plane strain analyses are carried out with the dislocations all of edge character and modelled as line singularities in a linear elastic material. The lattice resistance to dislocation motion, nucleation, interaction with obstacles and annihilation are incorporated through a set of constitutive rules. Grain boundaries are modelled as impenetrable to dislocations. The polycrystalline material is taken to consist of two types of square grains, one of which has a bcc-like orientation and the other an fcc-like orientation. For both orientations there are three active slip systems. Alternating rows, alternating columns and a checker-board-like arrangement of the grains is used to construct the polycrystalline materials. Consistent with the increasing yield strength of the polycrystalline material with decreasing grain size, the calculations predict a decrease in both the plastic zone size and the crack-tip opening displacement for a given applied mode I stress intensity factor. Furthermore, slip-band and kink-band formation is inhibited by all grain arrangements and, with decreasing grain size, the stress and strain distributions more closely resemble the HRR fields with the crack-tip opening approximately inversely proportional to the yield strength of the polycrystalline materials. The calculations predict a reduction in fracture toughness with decreasing grain size associated with the grain boundaries acting as effective barriers to dislocation motion.

Photonics and lasing in liquid crystal materials

Owing to fundamental reasons of symmetry, liquid crystals are soft materials. This softness allows long length-scales, large susceptibilities and the existence of modulated phases, which respond readily to external fields. Liquid crystals with such phases are tunable, self-assembled, photonic band gap materials; they offer exciting opportunities both in basic science and in technology. Since the density of photon states is suppressed in the stop band and is enhanced at the band edges, these materials may be used as switchable filters or as mirrorless lasers. Disordered periodic liquid crystal structures can show random lasing. We highlight recent advances in this rapidly growing area, and discuss future prospects in emerging liquid crystal materials. Liquid crystal elastomers and orientationally ordered nanoparticle assemblies are of particular interest. © 2006 The Royal Society.

Characterization of nano-composite M-2411/Y-123 thin films by electron backscatter diffraction and in-field critical current measurements

Thin films of nano-composite Y-Ba-Cu-O (YBCO) superconductors containing nano-sized, non-superconducting particles of Y2Ba 4CuMOx (M-2411 with M = Ag and Nb) have been prepared by the PLD technique. Electron backscatter diffraction (EBSD) has been used to analyze the crystallographic orientation of nano-particles embedded in the film microstructure. The superconducting YBa2Cu3O7 (Y-123) phase matrix is textured with a dominant (001) orientation for all samples, whereas the M-2411 phase exhibits a random orientation. Angular critical current measurements at various temperature (T) and applied magnetic field (B) have been performed on thin films containing different concentration of the M-2411 second phase. An increase in critical current density J c at T < 77 K and B < 6 T is observed for samples with low concentration of the second phase (2 mol % M-2411). Films containing 5 mol % Ag-2411 exhibit lower Jc than pure Y-123 thin films at all fields and temperatures. Samples with 5 mol % Nb-2411 show higher Jc(B) than phase pure Y-123 thin films for T < 77 K. © 2010 IOP Publishing Ltd.

The Ic behavior of 2G YBCO tapes under DC/AC magnetic fields at various temperatures

In order to design a High Temperature Superconducting (HTS) machine that is able to operate safely and reliably, studies on the characterization of Second Generation (2G) HTS tapes are of paramount importance. This paper presents an experimental setup to measure critical current of 2G HTS tapes in high DC magnetic fields (up to 5 Tesla) with an AC current ripple superimposed, as well as various temperatures ranging from 25 K to 77 K. The 2G tape measured is the SGS12050 coated conductor made by SuperPower. The critical current is measured by a flux vector with reference to the widest sample face from 0 to 90 degrees in 10 degree steps. Smaller steps are required close to 0 . A Variable Temperature Insert (VTI) is utilized to control temperature change. © 2010 IEEE.

Methods of patterning magnetic fields using bulk superconductors

High Temperature superconductors are able to carry very high current densities, and thereby sustain very high magnetic fields. There are many projects which use the first property and these have concentrated on power generation, transmission and utilization, however there are relatively few which are currently exploiting the ability to sustain high magnetic fields. There are two main reasons for this: high field wound magnets can and have been made from both BSCCO and YBCO but currently their cost is much higher than the alternative provided by low Tc materials such as Nb3Sn and NbTi. An alternative form of the material is the bulk form which can be magnetized to high fields and using flux pumping this can be done in situ. This paper explores some of the applications of bulk superconductors and describes methods of producing field patterns using the highly uniform magnetic fields required for MRI and accelerator magnets as the frame of reference. The patterns are not limited to uniform fields and it is entirely possible to produce a field varying sinusoidally in space such as would be required for a motor or a generator. The scheme described in this paper describes a dipole magnet such as is found in an accelerator magnet. The tunnel is 30 × 50 × 1000 mm and we achieve a uniformity of better than 200 ppm over the 1000 mm length and better than 1 ppm over the central 500 mm region. The paper presents results for both the overall uniformity and the integrated uniformity which is 302 ppm over the 1000 mm length. © 2010 IEEE.