Mode spectra of natural disturbances in a circular jet and the effect of acoustic forcing

A modal spectrum technique was used to study coherent instability modes (both axisymmetric and azimuthal) triggered by naturally occurring disturbances in a circular jet. This technique was applied to a high Reynolds number (400,000) jet for both untripped (transitional) and tripped (turbulent) nozzle exit boundary layers, with both cases having a core turbulence level of 0.15%. The region up to the end of the potential core was dominated by the axisymmetric mode, with the azimuthal modes dominating further downstream. The growth of the azimuthal modes was observed closer to the nozzle exit for the jet with a transitional boundary layer. Whether for locally parallel flow or slowly diverging flow, even at low levels of acoustic forcing, the inviscid linear theory is seen to be inadequate for predicting the amplitude of the forced mode. In contrast, the energy integral approach reasonably predicts the evolution of the forced mode.     

Highly stereoselective addition reactions of metallated trans-1,3-dithiane-1,3-dioxide to aldehydes

The sodium anion of trans-1,3-dithiane-1,3-dioxide reacts with unhindered aromatic and heteroaromatic aldehydes to give adducts with 95:5 to 97:3 diastereoselectivity.     

NMR studies of the superconducting state of copper oxide superconductors

The authors review and up-date their work on Knight shifts, spin-lattice relaxation, and indirect nuclear spin-spin coupling for YBa₂Cu₃O₇ in the superconducting state. The data are analyzed in particular to show what it may indicate about the orbital and spin pairing of the superconducting state.     

Flow to strong coupling in the two-dimensional Hubbard model

We extend the analysis of the renormalization group flow in the two-dimensional Hubbard model close to half-filling using the recently developed temperature flow formalism. We investigate the interplay of d-density wave and Fermi surface deformation tendencies with those towards d-wave pairing and antiferromagnetism. For a ratio of next nearest to nearest neighbor hoppings, t'/t = - 0.25, and band fillings where the Fermi surface is inside the Umklapp surface, only the d-pairing susceptibility diverges at low temperatures. When the Fermi surface intersects the Umklapp surface close to the saddle points, d-wave pairing, d-density wave, antiferromagnetic and, to a weaker extent, d-wave Fermi surface deformation susceptibilities grow together when the interactions flow to strong coupling. We interpret these findings as indications for a non-trivial strongly coupled phase with short-ranged superconducting and antiferromagnetic correlations, in close analogy with the spin liquid ground state in the well-understood two-leg Hubbard ladder. Received 23 January 2002     

Study on the Collapse of Pin-Reinforced Foam Sandwich Panel Cores

New fabrication technologies now allow for hybrid sandwich structures, known as X-core, to be manufactured. The X-core panels consist of a pin reinforced polymer foam core with carbon fiber face sheets. Carbon fiber or metallic (Titanium/Steel) pins are inserted into the foam core in the out-of-plane direction and extend from face sheet to face sheet. The through thickness three-point simply supported bending behavior of these panels is used to evaluate the collapse characteristics of the panels. Explicit experimental observations are used to calibrate analytical energy balance models describing the panel collapse as a function of geometry and properties. The mechanical response of X-core sandwich panels is compared to current sandwich materials for material selection.     

Strain localization in ductile single crystals

This paper is concerned with an analysis of strain localization in ductile crystals deforming by single slip. The plastic flow is modelled as rate-insensitive, and localization, viewed as a bifurcation from a homogeneous deformation mode to one which is concentrated in a narrow ‘shear band’, is found to be possible only when the plastic hardening modulus for the slip system has fallen to a certain critical value h_cr, sensitive to the precise form of the constitutive law governing incremental shear. We develop the general form of this constitutive law, incorporating within it the possibility of deviations from the Schmid rule of a critical resolved shear stress, and we show that h_cr may in fact be positive when there are deviations from the Schmid rule. It is suggested that micromechanical processes such as ‘cross-slip’ in crystals provide specific cases for which stresses other than the Schmid stress may influence plastic response and, further, there is an experimental association of localization with the onset of large amounts of cross-slip. Thus, we give the specific form of h_cr for a constitutive model that corresponds to non-Schmid effects in cross-slip, and we develop a dislocation model of the process from which we estimate the magnitude of the parameters involved. The work supports the notion that localization can occur with positive strain-hardening, h_cr > 0, and the often invoked notions of the attainment of an ideally-plastic or strain-softening state for localization may be unnecessary.     

Asymptotic analysis of growing plane strain tensile cracks in elastic-ideally plastic solids

An exact asymptotic analysis is presented of the stress and deformation fields near the tip of a quasistatically advancing plane strain tensile crack in an elastic-ideally plastic solid. In contrast to previous approximate analyses, no assumptions which reduce the yield condition, a priori, to the form of constant in-plane principal shear stress near the crack tip are made, and the analysis is valid for general Poisson ratio ν. Specific results are given for ν = 0.3 and 0.5, the latter duplicating solutions in previous work by L.I. Slepyan, Y.-C. Gao and the present authors. The crack tip field is shown to divide into five angular sectors of four different types ; in the order in which these sweep across a point in the vicinity of the advancing crack, they are : two plastic sectors which can be described asymptotically (i.e., as r → 0, where r is distance from the crack tip) in slip-line terminology as ‘constant stress’ and ‘centered fan’ sectors, respectively ; a plastic sector of non-constant stress which cannot be described asymptotically in terms of slip lines; an elastic unloading sector; and a trailing plastic sector of the same type as that directly preceding the elastic sector. Further, these four different sector types constitute the full set of asymptotically possible solutions at the crack tip. As is known from prior work, the plastic strain accumulated by a material point passing through such a moving ‘centered fan’ sector is O(ln r) as r → 0 ; it is proved in the present work that the plastic strain accumulated by a material point passing through the ‘constant stress’ sector ahead of a growing crack must be less singular than In r as r → 0. As suggested also in earlier studies, the rate of increase of opening gap δ at a point currently at a distance r behind, but very near, the crack tip is given for crack advance under contained yielding by

$\text{δ}\text{?}\text{=}\text{α}\text{J}\text{?}\text{σ}{}_0\text{+β(}\text{σ}{}_0\text{E}\text{)}\text{a}\text{?}\text{ln(}\text{R}\text{r}\text{)}$

where a is crack length, σ0 is tensile yield strength, E is Young's modulus, J is the value of the J-integral taken in surrounding elastic material, and the parameters α and R are undetermined by the asymptotic analysis. The exact solution for ν = 0.3 gives β = 5.462, which agrees very closely with estimates obtained from finite element solutions. An approximate analysis based on use of slip line representations in all plastic sectors is outlined in the Appendix.     

Synthesis and characterisation of luminescent rhenium tricarbonyl complexes with axially coordinated 1,2,3-triazole ligands

A series of 1-alkyl-4-aryl-1,2,3-triazoles (1-methyl-4-phenyl-1,2,3-triazole (1a); 1-propyl-4-phenyl-1,2,3-triazole (1b); 1-benzyl-4-phenyl-1,2,3-triazole (1c); 1-propyl-4-p-tolyl-1,2,3-triazole (1d)) have been prepared through a one-pot procedure involving in situ generation of the alkyl azide from a halide precursor followed by copper catalysed alkyne/azide cycloaddition (CuAAC) with the appropriate aryl alkyne. Cationic Re(I) complexes [Re(bpy)(CO)(3)(1a-d)]PF(6) (2a-d) were then prepared by stirring [Re(bpy)(CO)(3)Cl] with AgPF(6) in dichloromethane in the presence of ligands 1a-d. X-ray crystal structures were obtained for 2a and 2b. In the solid state, 2a adopts a highly distorted geometry, which is not seen for 2b, in which the plane of the triazole ligand tilts by 13° with respect to the Re-N bond as a result of a π-stacking interaction between the Ph substituent and one of the rings of the bpy ligand. This π-stacking interaction also results in severe twisting of the bpy ligand. Infrared spectra of 2a-d exhibit ν(CO) bands at ～2035 and ～1926 cm(-1) suggesting that these ligands are marginally better donors than pyridine (ν(CO) = 2037, 1932 cm(-1)). The complexes are luminescent in aerated dichloromethane at room temperature with emission maxima at 542 to 552 nm comparable to that of the pyridine analogue (549 nm) and blue shifted relative to the parent chloride complex. Long luminescent lifetimes are observed for the triazole complexes (475 to 513 ns) in aerated dichloromethane solutions at room temperature.