T-Duality for Torus Bundles with H-Fluxes via Noncommutative Topology

It is known that the T-dual of a circle bundle with H-flux (given by a Neveu-Schwarz 3-form) is the T-dual circle bundle with dual H-flux. However, it is also known that torus bundles with H-flux do not necessarily have a T-dual which is a torus bundle. A big puzzle has been to explain these mysterious missing T-duals. Here we show that this problem is resolved using noncommutative topology. It turns out that every principal T²-bundle with H-flux does indeed have a T-dual, but in the missing cases (which we characterize), the T-dual is non-classical and is a bundle of noncommutative tori. The duality comes with an isomorphism of twisted K-theories, just as in the classical case. The isomorphism of twisted cohomology which one gets in the classical case is replaced by an isomorphism of twisted cyclic homology.VM was supported by the Australian Research Council.JR was partially supported by NSF Grant DMS-0103647, and thanks the Department of Pure Mathematics of the University of Adelaide for its hospitality in January 2004, which made this collaboration possible.     

Intermediate colloidal formation and the varying width of periodic precipitation bands in reaction-diffusion systems

The mechanism of rhythmic pattern formation in reaction-diffusion systems is investigated theoretically by introducing a new concept. The boundary that separates the two reacting species virtually migrates as the diffusion proceeds into the gelatinous medium. Based on this boundary migration scenario, all the well-established relations on Liesegang patterns could be proved, in a rather modified way. The idea of formation of intermediate colloidal haze prior to patterning along with the moving boundary model proved to be efficient in predicting the concentration dependence of the width of the spatiotemporal patterns. The experimental observations support the width law relation developed.     

Direct removal of SU-8 using focused laser writing

SU-8 photoresist is an important material used in the development of micro-devices [1]. Cross-linked SU-8 structures have been known for their thermal stability and their strong resistance to standard solvent, acid and base. Due to the inert properties of this polymer, it is difficult to further modify or remove SU-8 once it is completely cured. We report an effective process to pattern cured SU-8 photoresist on glass using focused laser beam. Laser fabrication has been an important tool in various fields of research [2]. We made use of this laser cutting method to create interesting and useful two-dimensional SU-8 structures. The shapes and sizes of the structures created can be controlled by varying the power of the laser, angle of incident of the focused laser beam, the relative speed with which the laser beam traverse through the SU-8 film and the magnification of objective lens used. Besides two-dimensional structures, we can also create three-dimensional structures. In this case, we made use of a combination of controlled depth cutting and undercutting where focused laser beam is transmitted through the transparent substrate. Some possible applications of the laser patterned SU-8 film are also demonstrated in this work. PACS 42.62-b; 42.82.Cr; 79.60.Fr; 79.20.Ds; 78.66.-w     

Suppression of beating noise of narrow-linewidth erbium-doped fiber ring lasers by use of a semiconductor optical amplifier

Beating noise in narrow-linewidth erbium-doped fiber ring lasers puts severe limitations on applications of the lasers. We demonstrate the suppression of beating noise in fiber ring lasers by using a semiconductor optical amplifier in the laser cavity, which acts as a high-pass filter. Two different ring structures are presented as examples to demonstrate this beating noise suppression.     

Analysis of elastic scattering of 0.8 GeV polarized protons from 116Sn and 124Sn

Differential cross section and analyzing power data for elastic scattering of 0.8 GeV polarized protons from ¹¹⁶Sn and ¹²⁴Sn are analyzed in terms of a spin-dependent Kerman-McManus-Thaler formalism. Neutron matter densities and rms radii are deduced with careful attention to sources of error, and found to be in good agreement with Hartree-Fock predictions.     

Preparation and characterization of tris(iso‐propyl)stibine complexes of palladium and platinum

Tris(iso‐propyl)stibine complexes of palladium and platinum of the type [MX₂(SbⁱPr₃)₂] [M, X = Pd, Cl (1a), Pd, Br (1b), Pd, I (1c), Pt, Cl (2)] have been prepared and characterized by elemental analysis, IR and ¹H NMR spectral data. The structure of 1a, established by X‐ray structural analysis, revealed that the palladium atom is in a square planar environment with mutually trans SbⁱPr₃ ligands. Copyright © 2001 John Wiley & Sons, Ltd.     

Modeling of the electrostatic corona discharge reactor

A model is presented for the electrostatic corona discharge reactor (ECDR) in a pin-plate configuration. The main objective is to describe the fundamental chemistry and physics governing the discharge behavior and to predict the ECDR performance under various operating conditions. The electric field strength is estimated assuming a space-charge-free field. A two-term spherical harmonic expansion is used to solve the Boltzmann equation for the electron energy distribution function (EEDF) and calculate the electron-molecule reaction rates using collision cross-section data. Species continuity equations are solved for the dry and wet air systems to predict ozone and NO_x at various feed flow rates (1630, 4890, 14, 670 cm/s) and an applied voltage of 10 kV. Among the various results reported, it is noted that the calculations indicate the Maxwell EEDF cannot be used because it overpredicts the electron-molecule rate coefficients by several orders of magnitude     

Four-component reactions for a new diastereoselective synthesis of chiral quaternary centers

The one-pot preparation of chiral homoallylic alcohol and amine derivatives was easily achieved by carbocupration of alkynyl sulfoxides followed by an in situ zinc homologation and reaction with aldehydes or imines. In this process, three new carbon-carbon bonds were created as well as quaternary and tertiary chiral centers with excellent diastereo- and enantioselectivities.     

ULTRAVIOLET-INDUCED REACTIONS OF THYMINE AND URACIL IN THE PRESENCE OF CYSTEINE

Abstract —Ultraviolet-radiation photolysis of thymine in the presence of cysteine gives rise to four isomeric dimers, dihydrothymine, and at least five cysteine addition products. Similar reactions occur for uracil but the products have not all been characterized in detail. The addition reactions arise from the triplet state of the pyrimidine. The initial step is production of a hydropyrimidine radical, which then reacts with cysteine to give the addition products. The triplet is quenched by cysteine with a rate constant of about 2 times 10⁸ M^-1 s^-1 for thymine and 2–9 times 10⁸ for uracil. The total yield of products gives a lower-limit estimate of the triplet yield and hence of the intersystem-crossing efficiency. These studies, combined with earlier determinations of dimer yields, show that 93% of the thymine triplets which interact with another thymine molecule are quenched without forming stable dimers. For uracil, the corresponding figure is 75%.     

Crystal structure of 3β-acetoxy-17α-hydroxy-16α-methylallopregnan-20-one hemihydrate

3β-Acetoxy-17α-hydroxy-16α-methylallopregnan-20-one, C₂₄H₃₈O₄·0.5H₂O, is an intermediate towards the synthesis of dexamethasone, an important corticosteroid. The compound crystallizes in the monoclinic space group C2 with unit cell parameters: a = 10.665(2) ?, b = 7.497(1) ?, c = 28.200(4) ?, β = 92.74(2)°, Z = 4. The crystal structure has been solved by direct methods and refined to R = 0.0419 for 1579 observed reflections. All rings of the steroid skeleton are trans connected. Rings A, B, and C are all in the chair conformation. Ring D is in envelop conformation. The acetoxy and acetyl substituents are twisted with respect to the average molecular plane of the steroid. The twist along the length of the steroid molecule is negligible [C19–C10···C13–C18 = 2.3°]. In the crystal structure, the water molecule lies on a twofold axis which links the molecules into infinite supramolecular chains through OW–H···O and O–H···OW hydrogen bonds.