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

Polygonal complexes

Ian Leary inquires whether a class of hyperbolic finitely presented groups are residually finite. We answer in the affirmative by giving a systematic version of a construction in his paper, which shows that the standard 2-complexes of these presentations have a VH-structure. This structure induces a splitting of these groups, which together with hyperbolicity, implies that these groups are residually finite

A self-controlled microcontrolled microvalve

Integrated microvalves are needed for a broad range of semiconductor-processing-related applications. These include precision mass microflow controllers (μFCs) for dry etch systems, miniature gas chromatography systems for real-time monitoring, point-of-use semiconductor process reactant generators, and compact control systems for mini-environments. This paper reports a pneumatically actuated, integrated silicon microvalve, which was developed as a forerunner to an 8b μFC intended for the precision control of semiconductor process gases in the range from 0.1 to 10 sccm. The structure was designed to be batch-fabricated and compatible with on-chip thermopneumatic actuation. Assembled single-bit μFC devices achieve the targeted flow rate of 5 sccm (determined by an in-line flow channel) at 20 psid (1034 torr). The valve alone may achieve significantly higher flow rates. The leak rate is 0.08 sccm under 26.1 psig actuation pressure, and the valve can seal against pressures greater than 29 psid (1500 torr). © 1998 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87556/2/937_1.pd

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

Electronic states and optical properties of PbSe nanorods and nanowires

A theory of the electronic structure and excitonic absorption spectra of PbS and PbSe nanowires and nanorods in the framework of a four-band effective mass model is presented. Calculations conducted for PbSe show that dielectric contrast dramatically strengthens the exciton binding in narrow nanowires and nanorods. However, the self-interaction energies of the electron and hole nearly cancel the Coulomb binding, and as a result the optical absorption spectra are practically unaffected by the strong dielectric contrast between PbSe and the surrounding medium. Measurements of the size-dependent absorption spectra of colloidal PbSe nanorods are also presented. Using room-temperature energy-band parameters extracted from the optical spectra of spherical PbSe nanocrystals, the theory provides good quantitative agreement with the measured spectra.Comment: 35 pages, 12 figure

The future of North American trade policy: lessons from NAFTA

This repository item contains a single issue of the Pardee Center Task Force Reports, a publication series that began publishing in 2009 by the Boston University Frederick S. Pardee Center for the Study of the Longer-Range Future.This Task Force Report written by an international group of trade policy experts calls for significant reforms to address adverse economic, environmental, labor and societal impacts created by the 1994 North American Free Trade Agreement (NAFTA). The report is intended to contribute to the discussion and decisions stemming from ongoing reviews of proposed reforms to NAFTA as well as to help shape future trade agreements. It offers detailed proposals on topics including services, manufacturing, agriculture, investment, intellectual property, labor, environment, and migration. Fifteen years after NAFTA was enacted, there is widespread agreement that the trade treaty among the United States, Canada and Mexico has fallen short of its stated goals. While proponents credit the agreement with stimulating the flow of goods, services, and investment among the North American countries, critics in all three countries argue that this has not brought improvements in the standards of living of most people. Rather than triggering a convergence across the three nations, NAFTA has accentuated the economic and regulatory asymmetries that had existed among the three countries. [TRUNCATED

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