Graph Invariants of Vassiliev Type and Application to 4D Quantum Gravity

We consider a special class of Kauffman's graph invariants of rigid vertex isotopy (graph invariants of Vassiliev type). They are given by a functor from a category of colored and oriented graphs embedded into a 3-space to a category of representations of the quasi-triangular ribbon Hopf algebra $U_q(sl(2,\bf C))$. Coefficients in expansions of them with respect to $x$ ($q=e^x$) are known as the Vassiliev invariants of finite type. In the present paper, we construct two types of tangle operators of vertices. One of them corresponds to a Casimir operator insertion at a transverse double point of Wilson loops. This paper proposes a non-perturbative generalization of Kauffman's recent result based on a perturbative analysis of the Chern-Simons quantum field theory. As a result, a quantum group analog of Penrose's spin network is established taking into account of the orientation. We also deal with the 4-dimensional canonical quantum gravity of Ashtekar. It is verified that the graph invariants of Vassiliev type are compatible with constraints of the quantum gravity in the loop space representation of Rovelli and Smolin.Comment: 34 pages, AMS-LaTeX, no figures,The proof of thm.5.1 has been improve

Interpreting Helioseismic Structure Inversion Results of Solar Active Regions

Helioseismic techniques such as ring-diagram analysis have often been used to determine the subsurface structural differences between solar active and quiet regions. Results obtained by inverting the frequency differences between the regions are usually interpreted as the sound-speed differences between them. These in turn are used as a measure of temperature and magnetic-field strength differences between the two regions. In this paper we first show that the "sound-speed" difference obtained from inversions is actually a combination of sound-speed difference and a magnetic component. Hence, the inversion result is not directly related to the thermal structure. Next, using solar models that include magnetic fields, we develop a formulation to use the inversion results to infer the differences in the magnetic and thermal structures between active and quiet regions. We then apply our technique to existing structure inversion results for different pairs of active and quiet regions. We find that the effect of magnetic fields is strongest in a shallow region above 0.985R_sun and that the strengths of magnetic-field effects at the surface and in the deeper (r < 0.98R_sun) layers are inversely related, i.e., the stronger the surface magnetic field the smaller the magnetic effects in the deeper layers, and vice versa. We also find that the magnetic effects in the deeper layers are the strongest in the quiet regions, consistent with the fact that these are basically regions with weakest magnetic fields at the surface. Because the quiet regions were selected to precede or follow their companion active regions, the results could have implications about the evolution of magnetic fields under active regions.Comment: Accepted for publication in Solar Physic

Asymmetric Adjustment in the Ethanol and Grains Markets

This paper examines the long- and short-run asymmetric adjustments for nine pairs of spot and futures prices, itemized as three own pairs for three different bio-fuel ethanol types, three own pairs for three related agricultural products, namely corn, soybeans and sugar, and three cross pairs that included hybrids of the spot price of each of the agricultural products and an ethanol futures price. Most of the spreads’ asymmetric adjustments generally happen during narrowing. The three ethanol pairs that contain the eCBOT futures with each of Chicago spot, New York Harbor spot and Western European (Rotterdam) spot show different long-run adjustments, arbitrage profitable opportunities and price risk hedging capabilities. The asymmetric spread adjustments for the three grains are also different, with corn spread showing the strongest long-run widening adjustment, and sugar showing the weakest narrowing adjustment. Among others, the empirical analysis indicates the importance of potentially hedging the spot prices of agricultural commodities with ethanol futures contracts, which sends an important message that the ethanol futures market is capable of hedging price risk in agricultural commodity markets. The short-run asymmetric adjustments for individual prices in the nine pairs (with exception of the corn own pair underscore the importance of futures prices in the price discovery and hedging potential, particularly for ethanol futures

A unified Witten-Reshetikhin-Turaev invariant for integral homology spheres

We construct an invariant J_M of integral homology spheres M with values in a completion \hat{Z[q]} of the polynomial ring Z[q] such that the evaluation at each root of unity \zeta gives the the SU(2) Witten-Reshetikhin-Turaev invariant \tau_\zeta(M) of M at \zeta. Thus J_M unifies all the SU(2) Witten-Reshetikhin-Turaev invariants of M. As a consequence, \tau_\zeta(M) is an algebraic integer. Moreover, it follows that \tau_\zeta(M) as a function on \zeta behaves like an ``analytic function'' defined on the set of roots of unity. That is, the \tau_\zeta(M) for all roots of unity are determined by a "Taylor expansion" at any root of unity, and also by the values at infinitely many roots of unity of prime power orders. In particular, \tau_\zeta(M) for all roots of unity are determined by the Ohtsuki series, which can be regarded as the Taylor expansion at q=1.Comment: 66 pages, 8 figure

Photo--assisted current and shot noise in the fractional quantum Hall effect

The effect of an AC perturbation on the shot noise of a fractional quantum Hall fluid is studied both in the weak and the strong backscattering regimes. It is known that the zero-frequency current is linear in the bias voltage, while the noise derivative exhibits steps as a function of bias. In contrast, at Laughlin fractions, the backscattering current and the backscattering noise both exhibit evenly spaced singularities, which are reminiscent of the tunneling density of states singularities for quasiparticles. The spacing is determined by the quasiparticle charge $\nu e$ and the ratio of the DC bias with respect to the drive frequency. Photo--assisted transport can thus be considered as a probe for effective charges at such filling factors, and could be used in the study of more complicated fractions of the Hall effect. A non-perturbative method for studying photo--assisted transport at $\nu=1/2$ is developed, using a refermionization procedure.Comment: 14 pages, 6 figure

Controversies and priorities in amyotrophic lateral sclerosis

Two decades after the discovery that 20% of familial amyotrophic lateral sclerosis (ALS) cases were linked to mutations in the superoxide dismutase-1 (SOD1) gene, a substantial proportion of the remainder of cases of familial ALS have now been traced to an expansion of the intronic hexanucleotide repeat sequence in C9orf72. This breakthrough provides an opportunity to re-evaluate longstanding concepts regarding the cause and natural history of ALS, coming soon after the pathological unification of ALS with frontotemporal dementia through a shared pathological signature of cytoplasmic inclusions of the ubiquitinated protein TDP-43. However, with profound clinical, prognostic, neuropathological, and now genetic heterogeneity, the concept of ALS as one disease appears increasingly untenable. This background calls for the development of a more sophisticated taxonomy, and an appreciation of ALS as the breakdown of a wider network rather than a discrete vulnerable population of specialised motor neurons. Identification of C9orf72 repeat expansions in patients without a family history of ALS challenges the traditional division between familial and sporadic disease. By contrast, the 90% of apparently sporadic cases and incomplete penetrance of several genes linked to familial cases suggest that at least some forms of ALS arise from the interplay of multiple genes, poorly understood developmental, environmental, and age-related factors, as well as stochastic events

k=0Magnetic Structure and Absence of Ferroelectricity in SmFeO3

SmFeO3 has attracted considerable attention very recently due to the reported multiferroic properties above room-temperature. We have performed powder and single crystal neutron diffraction as well as complementary polarization dependent soft X-ray absorption spectroscopy measurements on floating-zone grown SmFeO3 single crystals in order to determine its magnetic structure. We found a k=0 G-type collinear antiferromagnetic structure that is not compatible with inverse Dzyaloshinskii-Moriya interaction driven ferroelectricity. While the structural data reveals a clear sign for magneto-elastic coupling at the N\'eel-temperature of ~675 K, the dielectric measurements remain silent as far as ferroelectricity is concerned

Stress corrosion cracking in Al-Zn-Mg-Cu aluminum alloys in saline environments

Copyright 2013 ASM International. This paper was published in Metallurgical and Materials Transactions A, 44A(3), 1230 - 1253, and is made available as an electronic reprint with the permission of ASM International. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplications of any material in this paper for a fee or for commercial purposes, or modification of the content of this paper are prohibited.Stress corrosion cracking of Al-Zn-Mg-Cu (AA7xxx) aluminum alloys exposed to saline environments at temperatures ranging from 293 K to 353 K (20 °C to 80 °C) has been reviewed with particular attention to the influences of alloy composition and temper, and bulk and local environmental conditions. Stress corrosion crack (SCC) growth rates at room temperature for peak- and over-aged tempers in saline environments are minimized for Al-Zn-Mg-Cu alloys containing less than ~8 wt pct Zn when Zn/Mg ratios are ranging from 2 to 3, excess magnesium levels are less than 1 wt pct, and copper content is either less than ~0.2 wt pct or ranging from 1.3 to 2 wt pct. A minimum chloride ion concentration of ~0.01 M is required for crack growth rates to exceed those in distilled water, which insures that the local solution pH in crack-tip regions can be maintained at less than 4. Crack growth rates in saline solution without other additions gradually increase with bulk chloride ion concentrations up to around 0.6 M NaCl, whereas in solutions with sufficiently low dichromate (or chromate), inhibitor additions are insensitive to the bulk chloride concentration and are typically at least double those observed without the additions. DCB specimens, fatigue pre-cracked in air before immersion in a saline environment, show an initial period with no detectible crack growth, followed by crack growth at the distilled water rate, and then transition to a higher crack growth rate typical of region 2 crack growth in the saline environment. Time spent in each stage depends on the type of pre-crack (“pop-in” vs fatigue), applied stress intensity factor, alloy chemistry, bulk environment, and, if applied, the external polarization. Apparent activation energies (E a) for SCC growth in Al-Zn-Mg-Cu alloys exposed to 0.6 M NaCl over the temperatures ranging from 293 K to 353 K (20 °C to 80 °C) for under-, peak-, and over-aged low-copper-containing alloys (~0.8 wt pct), they are typically ranging from 20 to 40 kJ/mol for under- and peak-aged alloys, and based on limited data, around 85 kJ/mol for over-aged tempers. This means that crack propagation in saline environments is most likely to occur by a hydrogen-related process for low-copper-containing Al-Zn-Mg-Cu alloys in under-, peak- and over-aged tempers, and for high-copper alloys in under- and peak-aged tempers. For over-aged high-copper-containing alloys, cracking is most probably under anodic dissolution control. Future stress corrosion studies should focus on understanding the factors that control crack initiation, and insuring that the next generation of higher performance Al-Zn-Mg-Cu alloys has similar longer crack initiation times and crack propagation rates to those of the incumbent alloys in an over-aged condition where crack rates are less than 1 mm/month at a high stress intensity factor

Physics of Solar Prominences: I - Spectral Diagnostics and Non-LTE Modelling

This review paper outlines background information and covers recent advances made via the analysis of spectra and images of prominence plasma and the increased sophistication of non-LTE (ie when there is a departure from Local Thermodynamic Equilibrium) radiative transfer models. We first describe the spectral inversion techniques that have been used to infer the plasma parameters important for the general properties of the prominence plasma in both its cool core and the hotter prominence-corona transition region. We also review studies devoted to the observation of bulk motions of the prominence plasma and to the determination of prominence mass. However, a simple inversion of spectroscopic data usually fails when the lines become optically thick at certain wavelengths. Therefore, complex non-LTE models become necessary. We thus present the basics of non-LTE radiative transfer theory and the associated multi-level radiative transfer problems. The main results of one- and two-dimensional models of the prominences and their fine-structures are presented. We then discuss the energy balance in various prominence models. Finally, we outline the outstanding observational and theoretical questions, and the directions for future progress in our understanding of solar prominences.Comment: 96 pages, 37 figures, Space Science Reviews. Some figures may have a better resolution in the published version. New version reflects minor changes brought after proof editin

New Insights into White-Light Flare Emission from Radiative-Hydrodynamic Modeling of a Chromospheric Condensation

(abridged) The heating mechanism at high densities during M dwarf flares is poorly understood. Spectra of M dwarf flares in the optical and near-ultraviolet wavelength regimes have revealed three continuum components during the impulsive phase: 1) an energetically dominant blackbody component with a color temperature of T $\sim$ 10,000 K in the blue-optical, 2) a smaller amount of Balmer continuum emission in the near-ultraviolet at lambda $<$ 3646 Angstroms and 3) an apparent pseudo-continuum of blended high-order Balmer lines. These properties are not reproduced by models that employ a typical "solar-type" flare heating level in nonthermal electrons, and therefore our understanding of these spectra is limited to a phenomenological interpretation. We present a new 1D radiative-hydrodynamic model of an M dwarf flare from precipitating nonthermal electrons with a large energy flux of $10^{13}$ erg cm$^{-2}$ s$^{-1}$. The simulation produces bright continuum emission from a dense, hot chromospheric condensation. For the first time, the observed color temperature and Balmer jump ratio are produced self-consistently in a radiative-hydrodynamic flare model. We find that a T $\sim$ 10,000 K blackbody-like continuum component and a small Balmer jump ratio result from optically thick Balmer and Paschen recombination radiation, and thus the properties of the flux spectrum are caused by blue light escaping over a larger physical depth range compared to red and near-ultraviolet light. To model the near-ultraviolet pseudo-continuum previously attributed to overlapping Balmer lines, we include the extra Balmer continuum opacity from Landau-Zener transitions that result from merged, high order energy levels of hydrogen in a dense, partially ionized atmosphere. This reveals a new diagnostic of ambient charge density in the densest regions of the atmosphere that are heated during dMe and solar flares.Comment: 50 pages, 2 tables, 13 figures. Accepted for publication in the Solar Physics Topical Issue, "Solar and Stellar Flares". Version 2 (June 22, 2015): updated to include comments by Guest Editor. The final publication is available at Springer via http://dx.doi.org/10.1007/s11207-015-0708-