Serre Duality, Abel's Theorem, and Jacobi Inversion for Supercurves Over a Thick Superpoint

The principal aim of this paper is to extend Abel's theorem to the setting of complex supermanifolds of dimension 1|q over a finite-dimensional local supercommutative C-algebra. The theorem is proved by establishing a compatibility of Serre duality for the supercurve with Poincare duality on the reduced curve. We include an elementary algebraic proof of the requisite form of Serre duality, closely based on the account of the reduced case given by Serre in Algebraic Groups and Class Fields, combined with an invariance result for the topology on the dual of the space of repartitions. Our Abel map, taking Cartier divisors of degree zero to the dual of the space of sections of the Berezinian sheaf, modulo periods, is defined via Penkov's characterization of the Berezinian sheaf as the cohomology of the de Rham complex of the sheaf D of differential operators, as a right module over itself. We discuss the Jacobi inversion problem for the Abel map and give an example demonstrating that if n is an integer sufficiently large that the generic divisor of degree n is linearly equivalent to an effective divisor, this need not be the case for all divisors of degree n.Comment: 14 page

Effective field theory approach to Casimir interactions on soft matter surfaces

We utilize an effective field theory approach to calculate Casimir interactions between objects bound to thermally fluctuating fluid surfaces or interfaces. This approach circumvents the complicated constraints imposed by such objects on the functional integration measure by reverting to a point particle representation. To capture the finite size effects, we perturb the Hamiltonian by DH that encapsulates the particles' response to external fields. DH is systematically expanded in a series of terms, each of which scales homogeneously in the two power counting parameters: \lambda \equiv R/r, the ratio of the typical object size (R) to the typical distance between them (r), and delta=kB T/k, where k is the modulus characterizing the surface energy. The coefficients of the terms in DH correspond to generalized polarizabilities and thus the formalism applies to rigid as well as deformable objects. Singularities induced by the point particle description can be dealt with using standard renormalization techniques. We first illustrate and verify our approach by re-deriving known pair forces between circular objects bound to films or membranes. To demonstrate its efficiency and versatility, we then derive a number of new results: The triplet interactions present in these systems, a higher order correction to the film interaction, and general scaling laws for the leading order interaction valid for objects of arbitrary shape and internal flexibility.Comment: 4 pages, 1 figur

Does Low Frequency X-ray QPO Behavior in GRS 1915+105 Influence Subsequent X-ray and Infrared Evolution?

Using observations with the Rossi X-ray Timing Explorer, we examine the behavior of 2-10 Hz quasi-periodic oscillations (QPOs) during spectrally-hard dips in the x-ray light curve of GRS 1915+105 that are accompanied by infrared flares. Of the twelve light-curves examined, nine are beta-class and three are alpha-class following the scheme of Belloni et al. (2000). In most cases, the QPO frequency is most strongly correlated to the power law flux, which partially contradicts some earlier claims that the strongest correlation is between QPO frequency and blackbody flux. Seven beta-class curves are highly correlated to blackbody features. In several cases, the QPO evolution appears to decouple from the spectral evolution. We find that beta-class light-curves with strong correlations can be distinguished from those without by their ``trigger spike'' morphology. We also show that the origin and strength of the subsequent infrared flare may be causally linked to the variations in QPO frequency evolution and not solely tied to the onset of soft x-ray flaring behavior. We divide the twelve alpha- and beta-class light-curves into three groups based on the evolution of the QPO, the morphology of the trigger spike, and the infrared flare strength. An apparent crossover case leads us to conclude that these groups are not unique modes but represent part of a continuum of accretion behaviors. We believe the QPO behavior at the initiation of the hard dip can ultimately be used to determine the terminating x-ray behavior, and the following infrared flaring behavior.Comment: 29 pages, 9 figures, to be published in Ap

Fluid-Induced Propulsion of Rigid Particles in Wormlike Micellar Solutions

In the absence of inertia, a reciprocal swimmer achieves no net motion in a viscous Newtonian fluid. Here, we investigate the ability of a reciprocally actuated particle to translate through a complex fluid that possesses a network using tracking methods and birefringence imaging. A geometrically polar particle, a rod with a bead on one end, is reciprocally rotated using magnetic fields. The particle is immersed in a wormlike micellar (WLM) solution that is known to be susceptible to the formation of shear bands and other localized structures due to shear-induced remodeling of its microstructure. Results show that the nonlinearities present in this WLM solution break time-reversal symmetry under certain conditions, and enable propulsion of an artificial "swimmer." We find three regimes dependent on the Deborah number (De): net motion towards the bead-end of the particle at low De, net motion towards the rod-end of the particle at intermediate De, and no appreciable propulsion at high De. At low De, where the particle time-scale is longer then the fluid relaxation time, we believe that propulsion is caused by an imbalance in the fluid first normal stress differences between the two ends of the particle (bead and rod). At De~1, however, we observe the emergence of a region of network anisotropy near the rod using birefringence imaging. This anisotropy suggests alignment of the micellar network, which is "locked in" due to the shorter time-scale of the particle relative to the fluid

D-modules on 1|1 Supercurves

It is known that to every 1|1 dimensional supercurve X there is associated a dual supercurve \hat{X}, and a superdiagonal \Delta in their product. We establish that the categories of D-modules on X, \hat{X}, and \Delta are equivalent. This follows from a more general result about D-modules and purely odd submersions. The equivalences preserve tensor products, and take vector bundles to vector bundles. Line bundles with connection are studied, and examples are given where X is a superelliptic curve.Comment: 18 page

High Energy Field Theory in Truncated AdS Backgrounds

In this letter we show that, in five-dimensional anti-deSitter space (AdS) truncated by boundary branes, effective field theory techniques are reliable at high energy (much higher than the scale suggested by the Kaluza-Klein mass gap), provided one computes suitable observables. We argue that in the model of Randall and Sundrum for generating the weak scale from the AdS warp factor, the high energy behavior of gauge fields can be calculated in a {\em cutoff independent manner}, provided one restricts Green's functions to external points on the Planck brane. Using the AdS/CFT correspondence, we calculate the one-loop correction to the Planck brane gauge propagator due to charged bulk fields. These effects give rise to non-universal logarithmic energy dependence for a range of scales above the Kaluza-Klein gap.Comment: LaTeX, 7 pages; minor typos fixe

CMB Signals of Neutrino Mass Generation

We propose signals in the cosmic microwave background to probe the type and spectrum of neutrino masses. In theories that have spontaneous breaking of approximate lepton flavor symmetries at or below the weak scale, light pseudo-Goldstone bosons recouple to the cosmic neutrinos after nucleosynthesis and affect the acoustic oscillations of the electron-photon fluid during the eV era. Deviations from the Standard Model are predicted for both the total energy density in radiation during this epoch, \Delta N_nu, and for the multipole of the n'th CMB peak at large n, \Delta l_n. The latter signal is difficult to reproduce other than by scattering of the known neutrinos, and is therefore an ideal test of our class of theories. In many models, the large shift, \Delta l_n \approx 8 n_S, depends on the number of neutrino species that scatter via the pseudo-Goldstone boson interaction. This interaction is proportional to the neutrino masses, so that the signal reflects the neutrino spectrum. The prediction for \Delta N_nu is highly model dependent, but can be accurately computed within any given model. It is very sensitive to the number of pseudo-Goldstone bosons, and therefore to the underlying symmetries of the leptons, and is typically in the region of 0.03 < \Delta N_nu < 1. This signal is significantly larger for Majorana neutrinos than for Dirac neutrinos, and, like the scattering signal, varies as the spectrum of neutrinos is changed from hierarchical to inverse hierarchical to degenerate.Comment: 40 pages, 4 figure

Validation of an electrogoniometry system as a measure of knee kinematics during activities of daily living

Purpose: The increasing use of electrogoniometry (ELG) in clinical research requires the validation of different instrumentation. The purpose of this investigation was to examine the concurrent validity of an ELG system during activities of daily living. Methods: Ten asymptomatic participants gave informed consent to participate. A Biometrics SG150 electrogoniometer was directly compared to a 12 camera three dimensional motion analysis system during walking, stair ascent, stair descent, sit to stand, and stand to sit activities for the measurement of the right knee angle. Analysis of validity was undertaken by linear regression. Standard error of estimate (SEE), standardised SEE (SSEE), and Pearson’s correlation coefficient r were computed for paired trials between systems for each functional activity. Results: The 95% confidence interval of SEE was reasonable between systems across walking (LCI = 2.43 °; UCI = 2.91 °), stair ascent (LCI = 2.09 °; UCI = 2.42 °), stair descent (LCI = 1.79 °; UCI = 2.10 °), sit to stand (LCI = 1.22 °; UCI = 1.41 °), and stand to sit (LCI = 1.17 °; UCI = 1.34 °). Pearson’s correlation coefficient r across walking (LCI = 0.983; UCI = 0.990), stair ascent (LCI = 0.995; UCI = 0.997), stair descent (LCI = 0.995; UCI = 0.997), sit to stand (LCI = 0.998; UCI = 0.999), and stand to sit (LCI = 0.996; UCI = 0.997) was indicative of a strong linear relationship between systems. Conclusion: ELG is a valid method of measuring the knee angle during activities representative of daily living. The range is within that suggested to be acceptable for the clinical evaluation of patients with musculoskeletal conditions

Non-Relativistic Gravitation: From Newton to Einstein and Back

We present an improvement to the Classical Effective Theory approach to the non-relativistic or Post-Newtonian approximation of General Relativity. The "potential metric field" is decomposed through a temporal Kaluza-Klein ansatz into three NRG-fields: a scalar identified with the Newtonian potential, a 3-vector corresponding to the gravito-magnetic vector potential and a 3-tensor. The derivation of the Einstein-Infeld-Hoffmann Lagrangian simplifies such that each term corresponds to a single Feynman diagram providing a clear physical interpretation. Spin interactions are dominated by the exchange of the gravito-magnetic field. Leading correction diagrams corresponding to the 3PN correction to the spin-spin interaction and the 2.5PN correction to the spin-orbit interaction are presented.Comment: 10 pages, 3 figures. v2: published version. v3: Added a computation of Einstein-Infeld-Hoffmann in higher dimensions within our improved ClEFT which partially confirms and partially corrects a previous computation. See notes added at end of introductio