The Refractive Index of Curved Spacetime II: QED, Penrose Limits and Black Holes

This work considers the way that quantum loop effects modify the propagation of light in curved space. The calculation of the refractive index for scalar QED is reviewed and then extended for the first time to QED with spinor particles in the loop. It is shown how, in both cases, the low frequency phase velocity can be greater than c, as found originally by Drummond and Hathrell, but causality is respected in the sense that retarded Green functions vanish outside the lightcone. A "phenomenology" of the refractive index is then presented for black holes, FRW universes and gravitational waves. In some cases, some of the polarization states propagate with a refractive index having a negative imaginary part indicating a potential breakdown of the optical theorem in curved space and possible instabilities.Comment: 62 pages, 14 figures, some signs corrected in formulae and graph

Topological representations of matroid maps

The Topological Representation Theorem for (oriented) matroids states that every (oriented) matroid can be realized as the intersection lattice of an arrangement of codimension one homotopy spheres on a homotopy sphere. In this paper, we use a construction of Engstr\"om to show that structure-preserving maps between matroids induce topological mappings between their representations; a result previously known only in the oriented case. Specifically, we show that weak maps induce continuous maps and that the process is a functor from the category of matroids with weak maps to the homotopy category of topological spaces. We also give a new and conceptual proof of a result regarding the Whitney numbers of the first kind of a matroid.Comment: Final version, 21 pages, 8 figures; Journal of Algebraic Combinatorics, 201

Epidemiology of Aortic Aneurysm Repair in the United States from 1993 to 2003

The epidemiology of abdominal aortic aneurysm (AAA) disease has been well described over the preceding 50 years. This disease primarily affects elderly males with smoking, hypertension, and a positive family history contributing to an increased risk of aneurysm formation. The aging population as well as increased screening in high-risk populations has led some to suggest that the incidence of AAAs is increasing. The National Inpatient Sample (1993 2003), a national representative database, was used in this study to determine trends in mortality following AAA repair in the United States. In addition, the impact of the introduction of less invasive endovascular AAA repair was assessed. Overall rates of treated unruptured and ruptured AAAs remained stable (unruptured 12 to 15 100,000; ruptured 1 to 3 100,000). In 2003, 42.7 of unruptured and 8.8 of ruptured AAAs were repaired through an endovascular approach. Inhospital mortality following unruptured AAA repair continues to decline for open repair (5.3 to 4.7 , P 0.007). Mortality after elective endovascular AAA repair also has statistically decreased (2.1 to 1.0 , P 0.024) and remains lower than open repair. Mortality rates for ruptured AAAs following repair remain high (open: 46.5 to 40.7 , P 0.01; endovascular: 40.0 to 35.3 , P 0.823). These data suggest that the numbers of patients undergoing elective AAA repair have remained relatively stable despite the introduction of less invasive technology. A shift in the treatment paradigm is occurring with a higher percentage of patients subjected to elective endovascular AAA repair compared to open repair. This shift, at least in the short term, appears justified as the mortality in patients undergoing elective endovascular AAA repair is significantly reduced compared to patients undergoing open AAA repair.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73855/1/annals.1383.030.pd

Combinatorial Markov chains on linear extensions

We consider generalizations of Schuetzenberger's promotion operator on the set L of linear extensions of a finite poset of size n. This gives rise to a strongly connected graph on L. By assigning weights to the edges of the graph in two different ways, we study two Markov chains, both of which are irreducible. The stationary state of one gives rise to the uniform distribution, whereas the weights of the stationary state of the other has a nice product formula. This generalizes results by Hendricks on the Tsetlin library, which corresponds to the case when the poset is the anti-chain and hence L=S_n is the full symmetric group. We also provide explicit eigenvalues of the transition matrix in general when the poset is a rooted forest. This is shown by proving that the associated monoid is R-trivial and then using Steinberg's extension of Brown's theory for Markov chains on left regular bands to R-trivial monoids.Comment: 35 pages, more examples of promotion, rephrased the main theorems in terms of discrete time Markov chain

Stochastic Model for Surface Erosion Via Ion-Sputtering: Dynamical Evolution from Ripple Morphology to Rough Morphology

Surfaces eroded by ion-sputtering are sometimes observed to develop morphologies which are either ripple (periodic), or rough (non-periodic). We introduce a discrete stochastic model that allows us to interpret these experimental observations within a unified framework. We find that a periodic ripple morphology characterizes the initial stages of the evolution, whereas the surface displays self-affine scaling in the later time regime. Further, we argue that the stochastic continuum equation describing the surface height is a noisy version of the Kuramoto-Sivashinsky equation.Comment: 4 pages, 7 postscript figs., Revtex, to appear in Phys. Rev. Let

Temporal deconvolution of vascular plant-derived fatty acids exported from terrestrial watersheds

Relatively little is known about the amount of time that lapses between the photosynthetic fixation of carbon by vascular land plants and its incorporation into the marine sedimentary record, yet the dynamics of terrestrial carbon sequestration have important implications for the carbon cycle. Vascular plant carbon may encounter multiple potential intermediate storage pools and transport trajectories, and the age of vascular plant carbon accumulating in marine sediments will reflect these different pre-depositional histories. Here, we examine down-core 14C profiles of higher plant leaf wax-derived fatty acids isolated from high fidelity sedimentary sequences spanning the so-called “bomb-spike”, and encompassing a ca. 60-degree latitudinal gradient from tropical (Cariaco Basin), temperate (Saanich Inlet), and polar (Mackenzie Delta) watersheds to constrain integrated vascular plant carbon storage/transport times (“residence times”). Using a modeling framework, we find that, in addition to a "young" (conditionally defined as < 50 y) carbon pool, an old pool of compounds comprises 49 to 78 % of the fractional contribution of organic carbon (OC) and exhibits variable ages reflective of the environmental setting. For the Mackenzie Delta sediments, we find a mean age of the old pool of 28 ky (±9.4, standard deviation), indicating extensive pre-aging in permafrost soils, whereas the old pools in Saanich Inlet and Cariaco Basin sediments are younger, 7.9 (±5.0) and 2.4 (±0.50) to 3.2 (±0.54) ky, respectively, indicating less protracted storage in terrestrial reservoirs. The "young" pool showed clear annual contributions for Saanich Inlet and Mackenzie Delta sediments (comprising 24% and 16% of this pool, respectively), likely reflecting episodic transport of OC from steep hillside slopes surrounding Saanich Inlet and annual spring flood deposition in the Mackenzie Delta, respectively. Contributions of 5-10 year old OC to the Cariaco Basin show a short delay of OC inflow, potentially related to transport time to the offshore basin. Modeling results also indicate that the Mackenzie Delta has an influx of young but decadal material (20-30 years of age), pointing to the presence of an intermediate reservoir. Overall, these results show that a significant fraction of vascular plant C undergoes pre-aging in terrestrial reservoirs prior to accumulation in deltaic and marine sediments. The age distribution, reflecting both storage and transport times, likely depends on landscape-specific factors such as local topography, hydrographic characteristics, and mean annual temperature of the catchment, all of which affect the degree of soil buildup and preservation. We show that catchment-specific carbon residence times across landscapes can vary by an order of magnitude, with important implications both for carbon cycle studies and for the interpretation of molecular terrestrial paleoclimate records preserved in sedimentary sequences

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial

We derive some new structural results for the transfer matrix of square-lattice Potts models with free and cylindrical boundary conditions. In particular, we obtain explicit closed-form expressions for the dominant (at large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as the solution of a special one-dimensional polymer model. We also obtain the large-q expansion of the bulk and surface (resp. corner) free energies for the zero-temperature antiferromagnet (= chromatic polynomial) through order q^{-47} (resp. q^{-46}). Finally, we compute chromatic roots for strips of widths 9 <= m <= 12 with free boundary conditions and locate roughly the limiting curves.Comment: 111 pages (LaTeX2e). Includes tex file, three sty files, and 19 Postscript figures. Also included are Mathematica files data_CYL.m and data_FREE.m. Many changes from version 1: new material on series expansions and their analysis, and several proofs of previously conjectured results. Final version to be published in J. Stat. Phy

On the Behavior of the Effective QCD Coupling alpha_tau(s) at Low Scales

The hadronic decays of the tau lepton can be used to determine the effective charge alpha_tau(m^2_tau') for a hypothetical tau-lepton with mass in the range 0 < m_tau' < m_tau. This definition provides a fundamental definition of the QCD coupling at low mass scales. We study the behavior of alpha_tau at low mass scales directly from first principles and without any renormalization-scheme dependence by looking at the experimental data from the OPAL Collaboration. The results are consistent with the freezing of the physical coupling at mass scales s = m^2_tau' of order 1 GeV^2 with a magnitude alpha_tau ~ 0.9 +/- 0.1.Comment: 15 pages, 4 figures, submitted to Physical Review D, added references, some text added, no results nor figures change