Exotic differentiable structures and general relativity

We review recent developments in differential topology with special concern for their possible significance to physical theories, especially general relativity. In particular we are concerned here with the discovery of the existence of non-standard (fake or exotic) differentiable structures on topologically simple manifolds such asS ⁷, ⁴ andS ³ X ¹. Because of the technical difficulties involved in the smooth case, we begin with an easily understood toy example looking at the role which the choice of complex structures plays in the formulation of two-dimensional vacuum electrostatics. We then briefly review the mathematical formalisms involved with differentiable structures on topological manifolds, diffeomorphisms and their significance for physics. We summarize the important work of Milnor, Freedman, Donaldson, and others in developing exotic differentiable structures on well known topological manifolds. Finally, we discuss some of the geometric implications of these results and propose some conjectures on possible physical implications of these new manifolds which have never before been considered as physical models.     

Photoelectron spectroscopy of phosphorus hydride anions

Negative-ion photoelectron spectroscopy is applied to the PH-, PH2-, P2H-, P2H2-, and P2H3-molecular anions. Franck-Condon simulations of the photoelectron spectra are used to analyze the spectra and to identify various P2H(n)- species. The simulations employ density-functional theory calculations of molecular geometries and vibrational frequencies and normal modes, and coupled-cluster theory calculations of electron affinities. The following electron affinities are obtained: EA0(PH) = 1.027 +/- 0.006 eV, EA0(PH2) = 1.263 +/- 0.006 eV, and EA0(P2H) = 1.514 +/- 0.010 eV. A band is identified as a mixture of trans-HPPH- and cis-HPPH-. Although the trans and cis bands cannot be definitively assigned from experimental information, using theory as a guide we obtain EA0(trans-HPPH)= 1.00 +/- 0.01 eV and EA0(cis-HPPH) = 1.03 +/- 0.01 eV. A weak feature tentatively assigned to P2H3- has a vertical detachment energy of 1.74 eV. The derived gas-phase acidity of phosphine is delta(acid)G298(PH3) < or = 1509.7 +/- 2.1 kJ mo1(-1).     

Isolation,Structure Determination and Synthesis of New Acetylenic Steroids from the Sponge Calyx nicaaensis

Two acetylenic steroids, cholest-5-en-23-yn-3β-ol ( 5 ) and 26,27-dinorcholest-5-en-23-yn-3β-ol ( 3 ), and another unsaturated steroidalcohol, stigmasta-5,23-dien-3β-ol ( 7 ), were isolated from the sponge Calyx nicaaensis. The structures of these two acetylenic steroids were established by synthesis. Several attempts to synthesize the marine steroids alcohol calysterol ( 1 ), with a cyclopropene-containing side chain, starting from cholest-5-en-23-yn-3β-ol are also recorded. Addition of ethyl-diazo-acetate to the triple bond was performed, but the reduction to the methyl derivative yielded decomposition products.     

Data parallel large-scale molecular dynamics for liquids

An efficient data parallel computational scheme is presented for large-scale molecular dynamics (MD ) simulations of liquids with short-range interactions. The method is based on decomposition of the simulation cell into equally sized subcells, with the shortest side length equal to the cutoff radius. Inter- and intracell interactions are calculated in a coarse-grained manner. A geometric sorting procedure, based on particle distances to subcell boundaries, is used to minimize the overall computations and the nonproductive communications. Using only nearest-neighbor communications, an efficient scheme is developed for periodic updates of the contents of subcells due to the migration of particles. Special “null-particles” are introduced, which act as buffers during the periodic updates and allow for a globally uniform algorithm during the calculations. Communication cost is about 7% of the total CPU time. The method is found to be linearly scalable with the number of particles, performing better as the ratio of virtual to physical processors increases. The MD code is written in Fortran 90 and implemented on a CM-200. The overall speed is approximately 5.9 μs. per MD step and per particle for 1 million particles and 5.5 μs for 5 million particles. The method should be easily transferred to other massively parallel computers of SIMD and MIMD type. © 1993 John Wiley & Sons, Inc.     

Investigation by infrared absorption of the by-products of the cyanoethylation of cotton cellulose

The soluble cyanoethyl ether of cellulose, prepared by reaction in the presence of NaOH catalyst to high degrees of substitution (DS = 2.95), can be precipitated by various organic media and contains more nitrogen than can be accounted for by simple addition of acrylonitrile at each cellulose hydroxyl group. Infrared absorption spectra of such samples and of the reacted residues show various types of vibrational absorption bands, characteristic of amino groups. At advanced stages of the reaction the characteristic broad unresolved band of cellulose extending from 1200–950 cm.^?1 largely disappears, leaving only a few weaker bands which likely overlap those due to C–N stretching. Comparison is made of the spectra of the partially cyanoethylated cellulose and the polyacrylonitrile which forms in the stock acrylonitrile, to characterize the products. It is inferred that the highly cyanoethylated cellulose, partly dissolved in the acrylonitrile, further degrades and changes under a complex mechanism to various forms of amines. The yellow to orange color of the samples is assumed to be due to these by-products. The thermogravimetric analysis reveals that these products are more heat-resistant than the cyanoethylated cellulose.     

Synthesis of 4,12-dihydro-4-oxoquino-[1,8a,8-a,b]quinoxaline-5-carboxylic acid derivatives

The synthesis and antibacterial activity of 1-substituted amino-2-fluoro-4,12-dihydro-4-oxoquino[1,8a,8-a,b]quinoxaline-5-carboxylic acid derivatives are described. The synthetic route includes a carbon homologation and two intramolecular nucleophilic displacement cyclization reactions leading to the novel 4,12-dihydro-4-oxoquino[1,8a,8-a,b]quinoxaline-5-carboxylic acid heterocycle.