Arc Operads and Arc Algebras

Several topological and homological operads based on families of projectively weighted arcs in bounded surfaces are introduced and studied. The spaces underlying the basic operad are identified with open subsets of a compactification due to Penner of a space closely related to Riemann's moduli space. Algebras over these operads are shown to be Batalin-Vilkovisky algebras, where the entire BV structure is realized simplicially. Furthermore, our basic operad contains the cacti operad up to homotopy, and it similarly acts on the loop space of any topological space. New operad structures on the circle are classified and combined with the basic operad to produce geometrically natural extensions of the algebraic structure of BV algebras, which are also computed.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper15.abs.htm

On several varieties of cacti and their relations

Motivated by string topology and the arc operad, we introduce the notion of quasi-operads and consider four (quasi)-operads which are different varieties of the operad of cacti. These are cacti without local zeros (or spines) and cacti proper as well as both varieties with fixed constant size one of the constituting loops. Using the recognition principle of Fiedorowicz, we prove that spineless cacti are equivalent as operads to the little discs operad. It turns out that in terms of spineless cacti Cohen's Gerstenhaber structure and Fiedorowicz' braided operad structure are given by the same explicit chains. We also prove that spineless cacti and cacti are homotopy equivalent to their normalized versions as quasi-operads by showing that both types of cacti are semi-direct products of the quasi-operad of their normalized versions with a re-scaling operad based on R>0. Furthermore, we introduce the notion of bi-crossed products of quasi-operads and show that the cacti proper are a bi-crossed product of the operad of cacti without spines and the operad based on the monoid given by the circle group S^1. We also prove that this particular bi-crossed operad product is homotopy equivalent to the semi-direct product of the spineless cacti with the group S^1. This implies that cacti are equivalent to the framed little discs operad. These results lead to new CW models for the little discs and the framed little discs operad.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-13.abs.htm

Approximate Theoretical Calculation of Continuum Opacities

An approxhnate procedure is described for the theoretical calculation of the spectral absorption coefficient produced by bound-free and free-free transitions in plasmas containing polyelectronic atoms and ions. Our method of calculation is based on the assumption that only two ionized species make important contributions to the opacity and that these two ionic constituents are present in equal concentrations. The approximate formulas are shown to yield results that are in good accord with estimates based on detailed numerical computations for nitrogen

Similarity parameters for radiative energy transfer in isothermal and non-isothermal gas mixtures

The similarity groups for multicomponent, reacting gas mixtures with radiative energy transport are derived (Section I). The resulting relations are used to consider the feasibility if scaling for flow processes with radiative energy transport under highly simplified conditions (Sections 2 and 3). Next the scaling parameters are derived for radiant energy emission from isobaric and isothermal gases for arbitrary opacities and various spectral line and molecular band models (Section 4). Scaling parameters for radiant energy emission from isobaric but non-isothermal systems are discussed for arbitrary opacities and various spectral line and molecular band models under the restrictions imposed on the allowed temperature profiles for dispersion and Doppler lines by the Eddington-Barbier approximation (Section 5). Finally, we consider the radiative scaling properties for representative temperature profiles for both collision-broadened and Doppler-broadened line profiles on the basis if exact numerical calculations that we have performed for a rotational spectral line belonging to a molecular vibration-rotation band. (Section 6). It appears that simple scaling rules generally constitute a fair approximation for dispersion lines in non-isothermal systems but that corresponding relations apply to lines with Doppler contour only in the transparent gas regime

Filtered screens and augmented Teichm\"uller space

We study a new bordification of the decorated Teichm\"uller space for a multiply punctured surface F by a space of filtered screens on the surface that arises from a natural elaboration of earlier work of McShane-Penner. We identify necessary and sufficient conditions for paths in this space of filtered screens to yield short curves having vanishing length in the underlying surface F. As a result, an appropriate quotient of this space of filtered screens on F yields a decorated augmented Teichm\"uller space which is shown to admit a CW decomposition that naturally projects to the augmented Teichm\"uller space by forgetting decorations and whose strata are indexed by a new object termed partially oriented stratum graphs.Comment: Final version to appear in Geometriae Dedicat

AC impedance analysis of polypyrrole thin films

The AC impedance spectra of thin polypyrrole films were obtained at open circuit potentials from -0.4 to 0.4 V vs SCE. Two limiting cases are discussed for which simplified equivalent circuits are applicable. At very positive potentials, the predominantly nonfaradaic AC impedance of polypyrrole is very similar to that observed previously for finite porous metallic films. Modeling of the data with the appropriate equivalent circuit permits effective pore diameter and pore number densities of the oxidized film to be estimated. At potentials from -0.4 to -0.3 V, the polypyrrole film is essentially nonelectronically conductive and diffusion of polymer oxidized sites with their associated counterions can be assumed to be linear from the film/substrate electrode interface. The equivalent circuit for the polypyrrole film at these potentials is that previously described for metal oxide, lithium intercalation thin films. Using this model, counterion diffusion coefficients are determined for both semi-infinite and finite diffusion domains. In addition, the limiting low frequency resistance and capacitance of the polypyrrole thin fims was determined and compared to that obtained previously for thicker films of the polymer. The origin of the observed potential dependence of these low frequency circuit components is discussed

The emission of radiation from diatomic gases. III. Numerical emissivity calculations for carbon monoxide for low optical densities at 300°K and atmospheric pressure

Numerical emissivity calculations at 300°K and atmospheric pressure for nonoverlapping rotational lines have been carried out for CO using a dispersion formula for the line-shape representation. Use of the best available experimental data on integrated absorption and rotational line-width leads to calculated emissivities which are in excellent agreement with extrapolated empirical data published by Hottel and Ullrich. In particular, the theoretical dependence of emissivity on optical density, for small optical densities at 300°K, has been shown to follow experimental observations with satisfactory precision.For small optical densities the calculated emissivity is found to be proportional to the square root of the assumed rotational line-width, thus emphasizing the need for accurate line-width determinations at elevated temperatures. The limits of validity of the treatment utilizing nonoverlapping rotational lines are defined by examining overlapping between adjacent weak and strong rotational lines.The calculation of emissivities can be simplified by the use of approximate treatments. Thus absolute values of the emissivity can be predicted within 10 percent by utilizing a treatment for nonoverlapping, equally spaced, and equally intense lines, together with empirically determined values for the equivalent mean integrated absorption of the rotational lines of CO. A better analytic solution, which does not involve the assumptions of equal spacing and equal intensity of the rotational lines, has been obtained by utilizing asymptotic relations for large values of modified Bessel functions

Multiple-path technique for the determination of physico-chemical data behind shock fronts

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