Exotic Statistics for Strings in 4d BF Theory

After a review of exotic statistics for point particles in 3d BF theory, and especially 3d quantum gravity, we show that string-like defects in 4d BF theory obey exotic statistics governed by the 'loop braid group'. This group has a set of generators that switch two strings just as one would normally switch point particles, but also a set of generators that switch two strings by passing one through the other. The first set generates a copy of the symmetric group, while the second generates a copy of the braid group. Thanks to recent work of Xiao-Song Lin, we can give a presentation of the whole loop braid group, which turns out to be isomorphic to the 'braid permutation group' of Fenn, Rimanyi and Rourke. In the context 4d BF theory this group naturally acts on the moduli space of flat G-bundles on the complement of a collection of unlinked unknotted circles in R^3. When G is unimodular, this gives a unitary representation of the loop braid group. We also discuss 'quandle field theory', in which the gauge group G is replaced by a quandle.Comment: 41 pages, many figures. New version has minor corrections and clarifications, and some added reference

Production of superconductor/carbon bicomponent fibers

Certain materials are unable to be drawn or spun into fiber form due to their improper melting characteristics or brittleness. However, fibrous samples of such materials are often necessary for the fabrication of intricate shapes and composites. In response to this problem, a unique process, referred to as the piggyback process, was developed to prepare fibrous samples of a variety of nonspinnable ceramics. In this technique, specially produced C shaped carbon fibers serve as micromolds to hold the desired materials prior to sintering. Depending on the sintering atmosphere used, bicomponent or single component fibers result. While much has been shown worldwide concerning the YBa2Cu3O(7-x) superconductor, fabrication into unique forms has proven quite difficult. However, a variety of intricate shapes are necessary for rapid commercialization of the superconducting materials. The potential for producing fibrous samples of the YBa2Cu3O(7-x) compound by the piggyback process is being studied. Various organic and acrylic materials were studied to determine suspending ability, reactivity with the YBa2Cu3O(7-x) compound during long term storage, and burn out characteristics. While many questions were answered with respect to the interfacial reactions between YBa2Cu3O(7-x) and carbon, much work is still necessary to improve the quality of the sintered material if the fibers produced are to be incorporated into useful composite or cables

Production of superconductor/carbon bicomponent fibers

Certain materials are unable to be drawn or spun into fiber form due to their improper melting characteristics or brittleness. However, fibrous samples of such materials are often necessary for the fabrication of intricate shapes and composites. In response to this problem, a unique process, referred to as the piggyback process, was developed to prepare fibrous samples of a variety of nonspinnable ceramics. In this technique, specially produced C-shaped carbon fibers serve as micromolds to hold the desired materials prior to sintering. Depending on the sintering atmosphere used, bicomponent or single component fibers result. While much has been demonstrated worldwide concerning the YBa2Cu3O(7-x) superconductor, fabrication into unique forms has proven quite difficult. However, a variety of intricate shapes are necessary for rapid commercialization of the superconducting materials. The potential for producing fibrous samples of the YBa2Cu3O(7-x) compound by the piggyback process is being investigated. Various organic and acrylic materials were investigated to determine suspending ability, reactivity with the YBa2Cu3O(7-x) compound during long term storage, and burn out characteristics. While many questions were answered with respect to the interfacial reactions between YBa2Cu3O(7-x) and carbon, much work is still necessary to improve the quality of the sintered material if the fibers produced are to be incorporated into useful composites or cables. Additional research is necessary to evaluate quality of the barrier layer during long soakings at the peak temperature; adjust the firing schedule to avoid microcracking and improve densification; and increase the solids loading in the superconductive suspension to decrease porosity

Spontaneously generated X-shaped light bullets

We observe the formation of an intense optical wavepacket fully localized in all dimensions, i.e. both longitudinally (in time) and in the transverse plane, with an extension of a few tens of fsec and microns, respectively. Our measurements show that the self-trapped wave is a X-shaped light bullet spontaneously generated from a standard laser wavepacket via the nonlinear material response (i.e., second-harmonic generation), which extend the soliton concept to a new realm, where the main hump coexists with conical tails which reflect the symmetry of linear dispersion relationship.Comment: 5 pages, 4 figures, submitted for publicatio

Translational Invariance and the Anisotropy of the Cosmic Microwave Background

Primordial quantum fluctuations produced by inflation are conventionally assumed to be statistically homogeneous, a consequence of translational invariance. In this paper we quantify the potentially observable effects of a small violation of translational invariance during inflation, as characterized by the presence of a preferred point, line, or plane. We explore the imprint such a violation would leave on the cosmic microwave background anisotropy, and provide explicit formulas for the expected amplitudes $$ of the spherical-harmonic coefficients.Comment: Notation improve

The X-ray luminosity function of AGN at z~3

We combine Lyman-break colour selection with ultradeep (> 200 ks) Chandra X-ray imaging over a survey area of ~0.35 deg^2 to select high redshift AGN. Applying careful corrections for both the optical and X-ray selection functions, the data allow us to make the most accurate determination to date of the faint end of the X-ray luminosity function (XLF) at z~3. Our methodology recovers a number density of X-ray sources at this redshift which is at least as high as previous surveys, demonstrating that it is an effective way of selecting high z AGN. Comparing to results at z=1, we find no evidence that the faint slope of the XLF flattens at high z, but we do find significant (factor ~3.6) negative evolution of the space density of low luminosity AGN. Combining with bright end data from very wide surveys we also see marginal evidence for continued positive evolution of the characteristic break luminosity L*. Our data therefore support models of luminosity-dependent density evolution between z=1 and z=3. A sharp upturn in the the XLF is seen at the very lowest luminosities (Lx < 10^42.5 erg s^-1), most likely due to the contribution of pure X-ray starburst galaxies at very faint fluxes.Comment: 16 pages, 9 figures, accepted for publication in MNRA

MacDowell-Mansouri gravity and Cartan geometry

The geometric content of the MacDowell-Mansouri formulation of general relativity is best understood in terms of Cartan geometry. In particular, Cartan geometry gives clear geometric meaning to the MacDowell-Mansouri trick of combining the Levi-Civita connection and coframe field, or soldering form, into a single physical field. The Cartan perspective allows us to view physical spacetime as tangentially approximated by an arbitrary homogeneous "model spacetime", including not only the flat Minkowski model, as is implicitly used in standard general relativity, but also de Sitter, anti de Sitter, or other models. A "Cartan connection" gives a prescription for parallel transport from one "tangent model spacetime" to another, along any path, giving a natural interpretation of the MacDowell-Mansouri connection as "rolling" the model spacetime along physical spacetime. I explain Cartan geometry, and "Cartan gauge theory", in which the gauge field is replaced by a Cartan connection. In particular, I discuss MacDowell-Mansouri gravity, as well as its more recent reformulation in terms of BF theory, in the context of Cartan geometry.Comment: 34 pages, 5 figures. v2: many clarifications, typos correcte

Criteria for the experimental observation of multi-dimensional optical solitons in saturable media

Criteria for experimental observation of multi-dimensional optical solitons in media with saturable refractive nonlinearities are developed. The criteria are applied to actual material parameters (characterizing the cubic self-focusing and quintic self-defocusing nonlinearities, two-photon loss, and optical-damage threshold) for various glasses. This way, we identify operation windows for soliton formation in these glasses. It is found that two-photon absorption sets stringent limits on the windows. We conclude that, while a well-defined window of parameters exists for two-dimensional solitons (spatial or spatiotemporal), for their three-dimensional spatiotemporal counterparts such a window \emph{does not} exist, due to the nonlinear loss in glasses.Comment: 8 pages, to appear in Phys. Rev.

Designing adaptive structures for whole life energy savings

Designing structures with minimal environmental impact is emerging as a seriou concern in the construction sector. Conventional structural design practice involves designing first for strength, followed by secondary checks on deflections and other serviceability limits states. If these limits are exceeded, the con-ventional solution has been to add material to increase stiffness. When the design is governed by unpredicta-ble events such as fluctuating loads, strong wind storms or earthquakes, the structure is effectively overde-signed for most of its working life. This paper presents a methodology to design adaptive structures that minimize the whole life energy consumption. The methodology is illustrated on plane pin-jointed trusses, both determinate and indeterminate. Strategically placing actuators allow the internal flow of forces to be ho-mogenized and displacements to be controlled. The actuators only start working when the loads reach a cer-tain threshold. Below this threshold, the structure resists loads mainly passively thereby limiting significantly the operational energy used. It was found that both indeterminate and determinate topologies bring substantial energy savings up to 70% of the total energy