Viscous vortex core generation

Summary The unsteady flow of a viscous incompressible fluid between two porous co-axial circular cylinders is analysed when the outer cylinder is impulsively set into rotation. When there is radial inflow, vorticity is transferred from an unsteady boundary layer initially over the outer cylinder to a steady boundary layer over the inner cylinder.With 1 Figure     

Quantized vortex ring dynamics and the vortex core radius in He II

Using a newly developed time-of-flight technique, we have determined the temperature dependence of the vortex core radius in the range 0.35 K T 0.60 K by means of precise measurements of vortex ring dynamics. One of us (W.I.G.) has extended this work to a measurement of the pressure dependence of the vortex core radius. Our results are in agreement with the earlier work of Rayfield and Reif atT=0.28 K and zero pressure ¹ and with a model of the vortex core proposed by Glaberson, Strayer, and Donnelly. ^2,3 The precision of our measurements enabled us to observe differences in the dynamics of oppositely charged vortex rings in the same electric field configurations. We were able to quantitively account for these differences in a simple way by incorporating the frictional drag associated with the ion bound on the vortex core into the equations of motion. Our results suggest that the negative ion shape is not greatly distorted by its presence on the vortex core, nor is the negative ion strongly shielded by the vortex velocity field. Some of our results have been previously reported. ^4–6 Research supported in part by the National Science Foundation.During part of the period of this research, M. Steingart held an N.D.E.A. Title IV Fellowship.Alfred P. Sloan Foundation Fellow.     

Restrained shrinkage tests of fibre-reinforced concrete ring specimens: effect of core thermal expansion

Restrained shrinkage tests of fresh concrete using conventional ring specimens with a steel core are sometimes not effective because of their relatively low cracking sensitivity. Modified ring specimens with a Perspex core having a high coefficient of thermal expansion were developed with the object of obtaining a test method which can provide cracking sensitivity results within a short time. An analysis of stress distribution is presented, taking into account the geometry and elasticity characteristics of the ring and core in specimens subjected to restrained shrinkage and heating. For tests of fresh plain and fibre-reinforced concretes, a Perspex core with additional stress concentrators (wedges) was used.

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Resume Les essais de retrait empêché du béton frais réases sur des éprouvettes annulaires conventionnelles avec un noyau d'acier sont parfois peu probants du fait d'une scresibilité à la fissuration relativement faible. On a fabrigre des éprouvettes modifiées dont le noyau en Perspex presente un coefficient élevé de dilatation thermique, afin d'obtenir une méthode d'essai capable de fournir des résultats sur la sensibilité à la fissuration. On présente une analyse de la répartition des contraintes qui prend en compte la géométrie et les caractéristiques élastiques de l'anneau et du noyau dans les éprouvettes soumises au retrait empêché et à l'élévation de température. Pour les essais de béton frais ordinaire et renforcé de fibres, on a utilisé un noyau en Perspex avec des concentrateurs de contraintes supplémentaires.

     

On the quantum core of an optical vortex

An optical vortex is a line around which the phase increases by an integer multiple of 2π. It follows that the phase on the line itself is undefined and hence the field must have zero amplitude there. Berry and Dennis have suggested that this line of darkness is smoothed by a ‘quantum core’ with a radius proportional to ?^1/2 and have illustrated this idea by considering the competition between stimulated and spontaneous emission by an excited atom placed in the vicinity of the vortex. We show here that a similar phenomenon may be seen in absorption when the quantum state of motion of the absorbing atom is taken into consideration. There is, however, an underlying quantum singularity in which the absorption events for an atom centred on the vortex core can take place only if accompanied by a transfer of angular momentum to the atomic motion. The nature of this singularity relies on the evolution of an entangled state between the electronic and motional degrees of freedom of the trapped atom. We comment briefly on the effects of field quantisation on this quantum core of the optical vortex.     

Impurity doping effect on photostriction in PLZT ceramics

Photostriction is the superposition of a photovoltaic and piezoelectric effects. In this study, photostrictive effects in the perovskite (Pb, La) (Zr, Ti)O₃ were investigated as a function of B-site impurity doping. Donor doping was found to reduce both the grain size and room-temperature dielectric constant, influencing photovoltaic response. WO₃ and Ta₂O₅ doping increase the photovoltaic response, but do not significantly affect the piezoelectric effect in this material. Maximum photostriction is obtained for samples with 0.4 at% WO₃ doped or 1 at% Ta₂O₅ doped PLZT     

The effect of wollastonite incorporation on the linear firing shrinkage and flexural strength of dental aluminous core ceramics: A preliminary study

The aim of this study is to evaluate the effect of wollastonite (CaSiO3) material on the linear firing shrinkage and flexural strength of dental aluminous core porcelain. Twenty five specimens were prepared in a manner that each five of them contained 0%, 2%, 3%, 4%, and 5% wollastonite by weight. The linear firing shrinkage values were determined according to the formula given in the standard ANSI/ADA (American National Standards Institute/American Dental Association) 69 and the flexural strength of the specimens was evaluated using 3-point bending test. The results of this study showed that addition of wollastonite reduced the linear firing shrinkage and increased the flexural strength of dental aluminous core porcelain. The highest reduction (approx. 20%) in the linear firing shrinkage was obtained by the addition of 5% wollastonite. Kruskal–Wallis test found a statistically significant difference among the mean linear firing shrinkage values of the porcelain groups at the 95% confidence level (p < 0.05). Mann Whitney U statistical test was performed to demonstrate which porcelain groups show statistically significant difference. In spite of achieving 30% increase in the flexural strength by the addition of 2% wollastonite, no statistically significant difference was found among the mean flexural strength values of the porcelain groups (p > 0.05).     

Mechanical effects in a vortex device with a rotating core

The process of the appearance of forced rotation of an axial core mounted in a modified vortex tube in the direction opposite to the rotation of the air vortex and the precession of its axis have been studied. It has been established that dynamical bending of a metal axial core arises in the process of rotation which causes mechanical wear of its end part and fracture in the fastening area of the bearing without residual curvature of the core axis. The excitation of rotation and observed force effects are not related to the mechanical action of rotating air flow on the axial core.     

Reactive effects of core fermion excitations on the inertial mass of a vortex

The time-dependent Schrödinger equation for a fermion two-dimensional super-fluid containing a moving vortex is solved using the adiabatic approximation. The expectation value of the linear momentum of the vortex is found dominated by core fermion excitations. The resulting inertial vortex mass, obtained in the adiabatic limit, is larger than the standard core mass by a factor of (k_F,)₂ where , is the coherence length at T = 0. Anamalous velocity dependence of the mass, associated with the breakdown of the adiabatic approximation, is predicted.     

Antiferromagnetic order and dielectric gap within the vortex core of antiferromagnetic superconductor

The structure of a superconducting vortex has been studied theoretically for a dirty antiferromagnetic superconductor (AFSC), modelling an AFSC as a doped semi-metal with s-wave superconducting pairing and antiferromagnetic (dielectric) interaction between electrons (holes). It is also supposed that the quasiparticles dispersion law possesses the property of nesting. The distribution of the superconducting and magnetic order parameters near the vortex core is calculated. It is shown that the antiferromagnetic order, been suppressed at large distances, is restored around the superconducting vortex and the vortex core is in fact insulating and antiferromagnetic, in stark contrast to the normal metal cores of traditional superconductors. Moreover, our model calculations predict that as the temperature decreases the flux region of the superconductivity and antiferromagnetism coexistence increases.     

New studies in vortex dynamics: Incompressible and compressible vortex reconnection,core dynamics,and coupling between large and small scales

Coherent structure dynamics in turbulent flows are explored by direct numerical simulations of the Navier-Stokes equations for idealized vortex configurations. For this purpose, two dynamically significant coherent structure interactions are examined: (i) incompressible and compressible vortex reconnection and (ii) core dynamics (with and without superimposed small-scale turbulence). Reconnection is studied for two antiparallel vortex tubes at a Reynolds number (Re) of 10³. Incompressible reconnection consists of three distinct phases: inviscid advection, bridging and threading. The key mechanism, bridging, involves the ‘cutting’ of vortex lines by viscous cross diffusion and their subsequent reconnection in front of the advancing vortex dipole. We conjecture that reconnection occurs in successive bursts and is a physical mechanism of cascade to smaller scales. Compressible reconnection is seen to be significantly affected by the choice of pressure and density initial conditions. We propose a polytropic initial condition which is consistent with experimental results and low-Mach number asymptotic theories. We also explain how compressibility initiates an early reconnection due to shocklet formation, but slows down the circulation transfer at late times. Thus, the reconnection timescale increases with increasing Mach number. Motivated by the important role of helical vortex lines in the reconnected vortices (bridges), we focus our attention on the dynamics of an axisymmetric vortex column with axial variation of core size. The resulting core dynamics is first explained via coupling between swirl and meridional flows. We then show that core dynamics can be better understood by applying a powerful analytical tool —helical wave decomposition — which extracts vorticity wave packets, thereby providing a simple explanation of the dynamics. The increase in core size variation with increasing Re in such a vortex demonstrates the limitation of the prevalent vortex filament models which assume constant core size. By studying the columnar vortex with superimposed small-scale, homogeneous, isotropic turbulence, we address the mutual interactions between large and small scales in turbulent flows. At its boundary the columnar vortex organizes the small scales, which, if Re is sufficiently high, induce bending waves on the vortex which further organize the small scales. Such backscatter from small scales cannot be modelled by an eddy viscosity. Based on the observation of such close coupling between large and small scales, we question the local isotropy assumption and conjecture a fractal vortex model for high Re turbulent flows.     

Aqueous carbon fibre composites: effect of matrix shrinkage on toughness

Carbon fibre pultrusions were made using as matrices frozen aqueous solutions of very soluble solids and infinitely miscible liquids. The solutes decreased the volume change on freezing, and it was possible by varying the amount of solute to cover a range of volume changes from about 8 1/2% increase to about 9% decrease. In this way internal stresses in the composites could be controlled over a wide range. The volume change on freezing, and hence the magnitude and sign of the internal stresses, did not appear to affect the shear strength of the composites directly, although there were changes in shear strength (both increases and decreases) which were attributable to other factors. The toughness of the composites on the other hand was strongly influenced by shrinkage stresses, and had a peak when there was a very slight positive pressure at the fibre-matrix interface.     

Asymptotic expansions of the Biot-Savart law for a slender vortex with core variation

The Method of Matched Asymptotic Expansion of Singular Integrals (MAESI) is used to expand the Biot-Savart law in terms of different parameters. This method is first used to find, in terms of the small distance r to a line vortex, the first orders of the known expansion of the potential flow induced by this line vortex. This method is also used to easily compare two equations of motion of a slender vortex filament: the one obtained in an ad-hoc way by a cut-off line-integral technique and the other derived from the Navier-Stokes equations by Callegari and Ting. Finally, this method is used to give the inner expansion of the flow induced by a slender vortex in terms of its slenderness . This is the first inner expansion up to order one in terms of of the Biot-Savart law for a slender vortex. An application of this inner expansion is then given to find the induced velocity of a family of non-circular vortex rings with axisymmetric axial-core variation. In order to understand the time-evolution of these initial conditions to the Navier-Stokes equations, a short time scale is introduced. A quasi-hyperbolic system that describes the leading-order dynamics of the axisymmetric axial core variation on a curved slender vortex filament is finally extracted from the Navier-Stokes equations.     

Numerical modeling of precessing vortex core in the presence of local heat sources

Based on the results of numerical simulation of a nonstationary, nonaxisymmetric turbulent swirling gas flow in a tube with local sources of heat release, it is shown that a precessing vortex core (PVC) appears at supercritical values of the swirl parameter as a result of the development of instability of a left-handed bending mode. The dependence of the PVC frequency on the mass flow rate of the gas and the heat-source power has been studied. As the heat-source power increases, the frequency of precession grows while the amplitude of vortex core oscillations drops.     

Ageing effect on tensile and shrinkage behaviour of new green hybrid fibre-reinforced cementitious composites

Ageing effects on both uniaxial tensile and shrinkage behaviour of new green cementitious composites reinforced with bagasse fibre and steel fibre with ultra-high volume of fly ash are investigated in this paper. The tensile behaviour of the composites is investigated at the age of 28 days, 3 months, 6 months and 10 months after curing in weather conditions. Restrained shrinkage behaviour of the composites after curing for 3 months is tested on ring specimens. SEM tests are also conducted to study the influence of the ageing on the microstructure of the new composites. The test results show that the tensile strength of the composites at all ages increases with the decrease of the content of the fly ash and the bagasse fibre, and that the increasing application of fly ash and bagasse fibre decreases the steel ring strain and restrains the development of crack. It is also found that the tensile strength and the shrinkage of the composites such as crack width ascend greatly with time.     

高吸水树脂对混凝土收缩开裂的改善作用及其机理

高吸水树脂(SAP)是能够吸收高倍率水溶液并在干燥环境中释放水分的高分子功能材料.文中通过混凝土早期开裂、限制收缩及非限制收缩的试验,研究了SAP对混凝土收缩开裂性能的改善作用,并与预浸轻集料的作用进行了对比较.试验结果表明,SAP可以使混凝土的开裂及收缩减小30%～50%,比采用预浸轻集料的内养护措施效果更佳,在易于发生收缩开裂和(或)不易养护的结构中有重要的推广应用价值.SAP改善混凝土的早期开裂及收缩性能的机理在于,SAP颗粒对水的吸收-解吸、部分吸收水与高分子链的氢键键合及SAP粒子表面成膜等作用延缓了水分的散失、改变了混凝土内部湿度状态及分布.     

Impurity effect on the anisotropy of the upper critical field in type II superconductors

The effect of the reduction in mean free path on the anisotropy of the upper critical fieldH _c2 has been studied in Nb by adding Ta and Mo as impurities. It is found that impurities suppress the degree of anisotropy, in qualitative accord with the theory of Hohenberg and Werthamer, which shows that in cubic materials with a nonspherical Fermi surface anisotropy arises from nonlocal corrections to the GLAG theory. The results were analyzed by fitting the observed anisotropy curves to an expansion in Kubic harmonics. It is found that the second harmonic coefficientA ₂, which depends on first nonlocal corrections, decreases initially with addition of Ta or Mo according to theory, but tends to level off to an approximately constant value in the dirty limit, where it should vanish. The value of the third harmonic coefficientA ₃, which depends on higher-order nonlocal terms, vanishes rapidly with the addition of impurity, the rate of decrease being more rapid for Mo. It is also found that the presence of an impurity does not affect the temperature dependence ofA ₂ for both Nb-Ta and Nb-Mo systems andA ₃ for the Nb-Ta system and has an approximately similar effect as for pure Nb.