Numerical simulations of laminar flow over a 3D backward-facing step

A numerical investigation of laminar flow over a three-dimensional backward-facing step is presented with comparisons with detailed experimental data, available in the literature, serving to validate the numerical results. The continuity constraint method, implemented via a finite element weak statement, was employed to solve the unsteady three-dimensional Navier–Stokes equations for incompressible laminar isothermal flow. Two-dimensional numerical simulations of this step geometry underestimate the experimentally determined extent of the primary separation region for Reynolds numbers Re greater than 400. It has been postulated that this disagreement between physical and computational experiments is due to the onset of three-dimensional flow near Re ≈ 400. This paper presents a full three-dimensional simulation of the step geometry for 100⩽ Re⩽ 800 and correctly predicts the primary reattachment lengths, thus confirming the influence of three-dimensionality. Previous numerical studies have discussed possible instability modes which could induce a sudden onset of three-dimensional flow at certain critical Reynolds numbers. The current study explores the influence of the sidewall on the development of three-dimensional flow for Re greater than 400. Of particular interest is the characterization of three-dimensional vortices in the primary separation region immediately downstream of the step. The complex interaction of a wall jet, located at the step plane near the sidewall, with the mainstream flow reveals a mechanism for the increasing penetration (with increasing Reynolds number) of three-dimensional flow structures into a region of essentially two-dimensional flow near the midplane of the channel. The character and extent of the sidewall-induced flow are investigated for 100⩽Re⩽ 800. © 1997 John Wiley & Sons, Ltd.     

Symmetric Jack polynomials from non-symmetric theory

We show how a number of fundamental properties of the symmetric and anti-symmetric Jack polynomials can be derived from knowledge of the corresponding properties of the nonsymmetric Jack polynomials. These properties include orthogonality relations, normalization formulas, a specialization formula and the evaluation of a proportionality constant relating the anti-symmetric Jack polynomials to a product of differences multiplied by the symmetric Jack polynomials with a shifted parameter.This work was supported by the Australian Research Council.     

Multivariable Al–Salam & Carlitz Polynomials Associated with the Type A q–Dunkl Kernel

The Al–Salam & Carlitz polynomials are q–generalizations of the classical Hermite polynomials. Multivariable generalizations of these polynomials are introduced via a generating function involving a multivariable hypergeometric function which is the q–analogue of the type–A Dunkl integral kernel. An eigenoperator is established for these polynomials and this is used to prove orthogonality with respect to a certain Jackson integral inner product. This inner product is normalized by deriving a q–analogue of the Mehta integral, and the corresponding normalization of the multivariable Al–Salam & Carlitz polynomials is derived from a Pieri–type formula. Various other special properties of the polynomials are also presented, including their relationship to the shifted Macdonald polynomials and the big–q Jacobi polynomials.     

Longitudinal field muon spin relaxation (LF-μSR) measurements and evidence for a new muonium defect site in type Ia diamond

A new configuration for muonium, with hyperfine interaction parameters of less than axial symmetry, in nitrogen rich diamond is identified in Longitudinal Field Muon Spin Relaxation (LF-μSR) measurements. The TF-μSR measurements on the same sample show that almost the entire strength of the new configuration is accounted for by a “missing fraction”, typically seen in nitrogen rich type Ia diamond. The “missing fraction” is therefore the result of a T2 relaxation. This is consistent with muon trapping at or in some nitrogen related defect(s) followed by electron capture at random times. This revised version was published online in August 2006 with corrections to the Cover Date.     

Spatially Resolved Derivatization of Solid‐Phase‐Synthesis Beads with Fluorescent Dendrimers: Creation of Localized Microdomains

Second and third generation Newkome‐type trifurcated dendrimers, containing either a coumarin or dansyl fluorescent probe at the dendrimer core, have been synthesized and attached to ArgoGel ^® solid‐phase‐synthesis beads. Subsequent reaction with rhodamine dye shows that the dye can penetrate throughout the beads to acylate the remaining sites. Thus, it is possible to achieve a spatially resolved microdomain for library formation at the core of the dendrimer, primarily on the bead's periphery, and a second microdomain suitable for derivatization by other reagents such as encoding tags and fluorescent sensors.     

Synthesis and Structure of the Cyclic Borenium Cation 1,1,3,3-tetramethyl-1,3λ<Superscript>4</Superscript>,2-diazaborolidin-1-ium chloride

The solid state structure of an N-heterocyclic borane 1,1,3,3-tetramethyl-1,3λ⁴,2-diazaborolidin-1-ium chloride is reported. This molecule features numerous Cl?H hydrogen bonds.

Graphical Abstract

The crystal structure of 1,1,3,3-tetramethyl-1,3λ⁴,2-diazaborolidin-1-ium chloride shows multiple C–H?Cl interactions in the solid state.

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Amino Alcohols as Potential Antibiotic and Antifungal Leads

Five focused compound libraries (forty-nine compounds), based on prior studies in our laboratory were synthesized and screened for antibiotic and anti-fungal activity against S. aureus, E. coli, K. pneumoniae, P. aeruginosa, A. baumannii, C. albicans and C. neoformans. Low levels of activity, at the initial screening concentration of 32 μg/mL, were noted with analogues of (Z)-2-(3,4-dichlorophenyl)-3-phenylacrylonitriles which made up the first two focused libraries produced. The most promising analogues possessing additional substituents on the terminal aromatic ring of the synthesised acrylonitriles. Modifications of the terminal aromatic moiety were explored through epoxide installation flowed by flow chemistry mediated ring opening aminolysis with discreet sets of amines to the corresponding amino alcohols. Three new focused libraries were developed from substituted anilines, cyclic amines, and phenyl linked heterocyclic amines. The aniline-based compounds were inactive against the bacterial and fungal lines screened. The introduction of a cyclic, such as piperidine, piperazine, or morpholine, showed >50% inhibition when evaluated at 32 μg/mL compound concentration against methicillin-resistant Staphylococcus aureus. Examination of the terminal aromatic substituent via oxirane aminolysis allowed for the synthesis of three new focused libraries of afforded amino alcohols. Aromatic substituted piperidine or piperazine switched library activity from antibacterial to anti-fungal activity with ((Z)-2-(3,4-dichlorophenyl)-3-(4-(2-hydroxy-3-(4-methylpiperazin-1-yl)propoxy)phenyl)acrylonitrile), ((Z)-2-(3,4-dichlorophenyl)-3-(4-(2-hydroxy-3-(4-(4-hydroxyphenyl)piperazin-1-yl)propoxy)-phenyl)acrylonitrile) and ((Z)-3-(4-(3-(4-cyclohexylpiperazin-1-yl)-2-hydroxypropoxy)-phenyl)-2-(3,4-dichlorophenyl)-acrylonitrile) showing >95% inhibition of Cryptococcus neoformans var. grubii H99 growth at 32 μg/mL. While (Z)-3-(4-(3-(cyclohexylamino)-2-hydroxypropoxy)phenyl)-2-(3,4-dichlorophenyl)-acrylonitrile, (S,Z)-2-(3,4-dichlorophenyl)-3-(4-(2-hydroxy-3-(piperidin-1-yl)propoxy)phenyl)acrylonitrile, (R,Z)-2-(3,4-dichlorophenyl)-3-(4-(2-hydroxy-3-(piperidin-1-yl)propoxy)phenyl)acrylonitrile, (Z)-2-(3,4-dichlorophenyl)-3-(4-(2-hydroxy-3-(D-11-piperidin-1-yl)propoxy)phenyl)-acrylonitrile, and (Z)-3-(4-(3-(4-cyclohexylpiperazin-1-yl)-2-hydroxypropoxy)-phenyl)-2-(3,4-dichlorophenyl)-acrylonitrile 32 μg/mL against Staphylococcus aureus.     

Torsion points on modular curves

Let N≥23 be a prime number. In this paper, we prove a conjecture of Coleman, Kaskel, and Ribet about the ℚ-valued points of the modular curve X ₀(N) which map to torsion points on J ₀(N) via the cuspidal embedding. We give some generalizations to other modular curves, and to noncuspidal embeddings of X ₀(N) into J ₀(N). Oblatum 1-VI-1999 & 19-X-1999?Published online: 29 March 2000