Axiomatic Holonomy Maps and Generalized Yang-Mills Moduli Space

This article is a follow-up of ``Holonomy and Path Structures in General Relativity and Yang-Mills Theory" by Barrett, J. W. (Int.J.Theor.Phys., vol.30, No.9, 1991). Its main goal is to provide an alternative proof of this part of the reconstruction theorem which concerns the existence of a connection. A construction of connection 1-form is presented. The formula expressing the local coefficients of connection in terms of the holonomy map is obtained as an immediate consequence of that construction. Thus the derived formula coincides with that used in "On Loop Space Formulation of Gauge Theories" by Chan, H.-M., Scharbach, P. and Tsou S.T. (Ann.Phys., vol.167, 454-472, 1986). The reconstruction and representation theorems form a generalization of the fact that the pointed configuration space of the classical Yang-Mills theory is equivalent to the set of all holonomy maps. The point of this generalization is that there is a one-to-one correspondence not only between the holonomy maps and the orbits in the space of connections, but also between all maps from the loop space on $M$ to group $G$ fulfilling some axioms and all possible equivalence classes of $P(M,G)$ bundles with connection, where the equivalence relation is defined by bundle isomorphism in a natural way.Comment: amslatex, 7 pages, no figure

Modeling of secondary organic aerosol yields from laboratory chamber data

Laboratory chamber data serve as the basis for constraining models of secondary organic aerosol (SOA) formation. Current models fall into three categories: empirical two-product (Odum), product-specific, and volatility basis set. The product-specific and volatility basis set models are applied here to represent laboratory data on the ozonolysis of α-pinene under dry, dark, and low-NOx conditions in the presence of ammonium sulfate seed aerosol. Using five major identified products, the model is fit to the chamber data. From the optimal fitting, SOA oxygen-to-carbon (O/C) and hydrogen-to-carbon (H/C) ratios are modeled. The discrepancy between measured H/C ratios and those based on the oxidation products used in the model fitting suggests the potential importance of particle-phase reactions. Data fitting is also carried out using the volatility basis set, wherein oxidation products are parsed into volatility bins. The product-specific model is most likely hindered by lack of explicit inclusion of particle-phase accretion compounds. While prospects for identification of the majority of SOA products for major volatile organic compounds (VOCs) classes remain promising, for the near future empirical product or volatility basis set models remain the approaches of choice

Observation of the single-electron regime in a highly tunable silicon quantum dot

We report on low-temperature electronic transport measurements of a silicon metal-oxide-semiconductor quantum dot, with independent gate control of electron densities in the leads and the quantum dot island. This architecture allows the dot energy levels to be probed without affecting the electron density in the leads, and vice versa. Appropriate gate biasing enables the dot occupancy to be reduced to the single-electron level, as evidenced by magnetospectroscopy measurements of the ground state of the first two charge transitions. Independent gate control of the electron reservoirs also enables discrimination between excited states of the dot and density of states modulations in the leads.Comment: 4 pages, 3 figures, accepted for Applied Physics Letter

Quantitative assessment of the cervical spinal cord damage in neuromyelitis optica using diffusion tensor imaging at 3T

postprintThe Joint Annual Meeting of ISMRM-ESMRMB 2010, Stockholm, Sweden, 1-7 May 2010

An Algebra of Pieces of Space -- Hermann Grassmann to Gian Carlo Rota

We sketch the outlines of Gian Carlo Rota's interaction with the ideas that Hermann Grassmann developed in his Ausdehnungslehre of 1844 and 1862, as adapted and explained by Giuseppe Peano in 1888. This leads us past what Rota variously called 'Grassmann-Cayley algebra', or 'Peano spaces', to the Whitney algebra of a matroid, and finally to a resolution of the question "What, really, was Grassmann's regressive product?". This final question is the subject of ongoing joint work with Andrea Brini, Francesco Regonati, and William Schmitt. The present paper was presented at the conference "The Digital Footprint of Gian-Carlo Rota: Marbles, Boxes and Philosophy" in Milano on 17 Feb 2009. It will appear in proceedings of that conference, to be published by Springer Verlag.Comment: 28 page

Yields of oxidized volatile organic compounds during the OH radical initiated oxidation of isoprene, methyl vinyl ketone, and methacrolein under high-NO_x conditions

We present first-generation and total production yields of glyoxal, methylglyoxal, glycolaldehyde, and hydroxyacetone from the oxidation of isoprene, methyl vinyl ketone (MVK), and methacrolein (MACR) with OH under high NO_x conditions. Several of these first-generation yields are not included in commonly used chemical mechanisms, such as the Leeds Master Chemical Mechanism (MCM) v. 3.2. The first-generation yield of glyoxal from isoprene was determined to be 2.1 (±0.6)%. Inclusion of first-generation production of glyoxal, glycolaldehyde and hydroxyacetone from isoprene greatly improves performance of an MCM based model during the initial part of the experiments. In order to further improve performance of the MCM based model, higher generation glyoxal production was reduced by lowering the first-generation yield of glyoxal from C5 hydroxycarbonyls. The results suggest that glyoxal production from reaction of OH with isoprene under high NO_x conditions can be approximated by inclusion of a first-generation production term together with secondary production only via glycolaldehyde. Analogously, methylglyoxal production can be approximated by a first-generation production term from isoprene, and secondary production via MVK, MACR and hydroxyacetone. The first-generation yields reported here correspond to less than 5% of the total oxidized yield from isoprene and thus only have a small effect on the fate of isoprene. However, due to the abundance of isoprene, the combination of first-generation yields and reduced higher generation production of glyoxal from C5 hydroxycarbonyls is important for models that include the production of the small organic molecules from isoprene

Analysis of photochemical and dark glyoxal uptake: Implications for SOA formation

The dependence of glyoxal uptake onto deliquesced ammonium sulfate seed aerosol was studied under photochemical (light + hydroxyl radical (OH)) and dark conditions. In this study, the chemical composition of aerosol formed from glyoxal is identical in the presence or absence of OH. In addition, there was no observed OH dependence on either glyoxal uptake or glyoxal-driven aerosol growth for this study. These findings demonstrate that, for the system used here, glyoxal uptake is not affected by the presence of OH. In combination with previous studies, this shows that the exact nature of the type of seed aerosol, in particular the presence of a coating, has a large influence on fast photochemical uptake of glyoxal. Due to the challenge of relating this seed aerosol dependence to ambient conditions, this work highlights the resulting difficulty in quantitatively including SOA formation from glyoxal in models

Wormholes in String Theory

A wormhole is constructed by cutting and joining two spacetimes satisfying the low energy string equations with a dilaton field. In spacetimes described by the "string metric" the dilaton energy-momentum tensor need not satisfy the weak or dominant energy conditions. In the cases considered here the dilaton field violates these energy conditions and is the source of the exotic matter required to maintain the wormhole. There is also a surface stress-energy, that must be produced by additional matter, where the spacetimes are joined. It is shown that wormholes can be constructed for which this additional matter satisfies the weak and dominant energy conditions, so that it could be a form of "normal" matter. Charged dilaton wormholes with a coupling between the dilaton and the electromagnetic field that is more general than in string theory are also briefly discussed.Comment: 9 pages, LaTex, submitted to Phys. Rev.