Asymptotic Interactions of Critically Coupled Vortices

 At critical coupling, the interactions of Ginzburg-Landau vortices are determined by the metric on the moduli space of static solutions. Here, a formula for the asymptotic metric for two well separated vortices is obtained, which depends on a modified Bessel function. A straightforward extension gives the metric for N vortices. The asymptotic metric is also shown to follow from a physical model, where each vortex is treated as a point-like particle carrying a scalar charge and a magnetic dipole moment of the same magnitude. The geodesic motion of two well separated vortices is investigated, and the asymptotic dependence of the scattering angle on the impact parameter is determined. Formulae for the asymptotic Ricci and scalar curvatures of the N-vortex moduli space are also obtained. Received: 25 June 2002 / Accepted: 7 February 2003 Published online: 17 April 2003 Communicated by A. Kupiainen     

Enantioselective epoxidation of linolenic acid catalysed by cytochrome P450(BM3) from Bacillus megaterium

Cytochrome P450(BM3), from Bacillus megaterium, catalyses the epoxidation of linolenic acid yielding 15,16-epoxyoctadeca-9,12-dienoic acid with complete regio- and moderate enantio-selectivity (60% ee). The absolute configuration of the product is tentatively assigned as 15(R),16(S)-. The Michaelis-Menten parameters kcat and Km for the reaction were determined to be 3126 +/- 226 min(-1) and 24 +/- 6 microM respectively.     

A Criterion for Finite Topological Determinacy of Map-Germs

Let f, g: (Rⁿ, 0) (R^p, 0) be two C map-germs. Then f and gare C⁰-equivalent if there exist homeomorphism-germs h and lof (Rⁿ, 0) and (R^p, 0) respectively such that g = l f h^–1.Let k be a positive integer. A germ f is k-C⁰-determined ifevery germ g with j^k g(0) = j^k f(0) is C⁰-equivalent to f. Moreover,we say that f is finitely topologically determined if f is k-C⁰-determinedfor some finite k. We prove a theorem giving a sufficient conditionfor a germ to be finitely topologically determined. We explainthis condition below. Let N and P be two C manifolds. Consider the jet bundle J^k(N,P) with fiber J^k(n, p). Let z in J^k(n, p) and let f be suchthat z = j^kf(0). Define Whether (f) < k depends only on z, not on f. We can thereforedefine the set Let W^k(N, P) be the subbundle of J^k(N, P) with fiber W^k(n, p).Mather has constructed a finite Whitney (b)-regular stratificationS^k(n, p) of J^k(n, p) – W^k(n, p) such that all strata aresemialgebraic and K-invariant, having the property that if S^k(N,P) denotes the corresponding stratification of J^k(N, P) –W^k(N, P) and f C(N, P) is a C map such that j^kf is multitransverseto S^k(N, P), j^kf(N) W^k(N, P) = and N is compact (or f is proper),then f is topologically stable. For a map-germ f: (Rⁿ, 0) (R^p, 0), we define a certain ojasiewiczinequality. The inequality implies that there exists a representativef: U R^p such that j^kf(U – 0) W^k (Rⁿ, R^p = and suchthat j^kf is multitransverse to S^k (Rⁿ, R^p) at any finite setof points S U – 0. Moreover, the inequality controlsthe rate j^kf becomes non-transverse as we approach 0. We showthat if f satisfies this inequality, then f is finitely topologicallydetermined. 1991 Mathematics Subject Classification: 58C27.     

Geodesic Incompleteness in the ℂP 1 Model on a Compact Riemann Surface

It is proved that the moduli space of static solutions of the P ¹ model on spacetime ×, where is any compact Riemann surface, is geodesically incomplete with respect to the metric induced by the kinetic energy functional. The geodesic approximation predicts, therefore, that lumps can collapse and form singularities in finite time in these models.     

Application of Spectroscopic Techniques to the Structural Analysis of Petroleum

INTRODUCTION

Petroleum, in the form of liquid oil or the solid asphalt, has been known for thousands of years (Speight, 1991) but, preceding the Industrial Revolution of the 19th century, its true potential was not realized. However, the advent of the Industrial Revolution caused man to turn from wood and coal to petroleum as the main source of liquid fuels. Furthermore, with the onset of the 20th century and the emergence of a technologically oriented society which has focused on the development of the automobile and the airplane, further uses have been found for petroleum products. Vast industries have emerged which rely upon the conversion of petroleum to a variety of by-products, and further uses for petroleumderived materials are still being addressed.     

Minimalist probes for studying protein dynamics: thioamide quenching of selectively excitable fluorescent amino acids

Fluorescent probe pairs that can be selectively excited in the presence of Trp and Tyr are of great utility in studying conformational changes in proteins. However, the size of these probe pairs can restrict their incorporation to small portions of a protein sequence where their effects on secondary and tertiary structure can be tolerated. Our findings show that a thioamide bond-a single atom substitution of the peptide backbone-can quench fluorophores that are red-shifted from intrinsic protein fluorescence, such as acridone. Using steady-state and fluorescence lifetime measurements, we further demonstrate that this quenching occurs through a dynamic electron-transfer mechanism. In a proof-of-principle experiment, we apply this technique to monitor unfolding in a model peptide system, the villin headpiece HP35 fragment. Thioamide analogues of the natural amino acids can be placed in a variety of locations in a protein sequence, allowing one to make a large number of measurements to model protein folding.     

1H and 13C solution- and solid-state NMR investigation into wax products from the Fischer-Tropsch process

(1)H and (13)C solid- and solution-state NMR have been used to characterise waxes produced in the Fischer-Tropsch reaction, using Co-based catalysts either unpromoted or promoted with approximately 1 wt% of either cerium or rhenium. The aim was to measure average structural information at the submolecular level of the hydrocarbon waxes produced, along with identification of the minor products, such as oxygenates and olefins, which are typically observed in these waxes. A parameter of key interest is the average number of carbon atoms within the hydrocarbon chain (N(C)). A wax prepared using an unpromoted Co/Al(2)O(3) catalyst had N(C)～20, whilst waxes made using rhenium- or cerium-promoted Co/Al(2)O(3) catalysts were found to have N(C)～21. All three samples contained small amounts of oxygenates and alkenes. The subtle differences found in the waxes, in particular the minor species produced, demonstrate that the different promoters have different effects during the reaction, with the Re-promoted catalyst producing the fewest by-products. It is shown in (13)C solid-state NMR spectra that for that for longer chain (compared to the lengths of chain in previous studies) waxes that the lack of resolution and the complexities added by the differential cross-polarisation (CP) dynamics mean that it is difficult to accurately determine N(C) from this approach. However the N(C) determined by (13)C CP magic angle spinning NMR is broadly consistent with the more accurate solution approaches used and suggest that the wax characteristics do not change in solution. On this basis an alternative approach for determining N(C) is suggested based on (1)H solution state NMR that provides a higher degree of accuracy of the chain length as well as information on the minor constituents.