Shear-free perfect fluids with a γ-law equation of state

 We investigate all shear-free perfect fluid solutions of the Einstein field equations where the pressure and energy density satisfy a (Formula presented.)-law equation of state with (Formula presented.). We prove that such a fluid is either non rotating or non expanding. As a consequence, it follows by combining our result with those of Collins and Wainwright that any such shear-free perfect fluid which models either an expand universe or a collapsing star must in fact be a Friedmann–Robertson–Walker spacetime.

Algebraically special coplanar shear-free perfect fluids in general relativity

We investigate all algebraically special, not conformally flat, shear-free, isentropic (p(w), w + p ≠ 0), perfect fluid solutions of Einstein's field equations. We show, using the GHP formalism, that if the repeated principle null direction of the Weyl tensor is coplanar with the fluid's 4-velocity and vorticity vector (assumed nonzero), then the fluid's expansion must vanish.

Shear- free perfect fluids with solenoidal magnetic curvature and a γ-law equation of state

We show that shear-free perfect fluids obeying an equation of state p = (γ − 1)μ are non-rotating or non-expanding under the assumption that the spatial divergence of the magnetic part of the Weyl tensor is zero.

Shear-free perfect fluids with a solenoidal magnetic curvature

We investigate shear-free perfect fluid solutions of the Einstein field equations where the fluid pressure satisfies a barotropic equation of state and the spatial divergence of the magnetic part of the Weyl tensor is zero. We prove, with the exception of certain quite restricted special cases within the class of solutions in which there exists a Killing vector aligned with the vorticity and for which the magnitude of the vorticity ω is not a function of the matter density μ alone, that such a fluid is either non-rotating or non-expanding. In the restricted cases the equation of state must satisfy an over-determined differential system.

Shear-free perfect fluids with a solenoidal electric curvature

We prove that the vorticity or the expansion vanishes for any shear-free perfect fluid solution of the Einstein field equations where the pressure satisfies a barotropic equation of state and the spatial divergence of the electric part of the Weyl tensor is zero.

Symbolic computation and perfect fluids in general relativity

Focuses on two areas within the field of general relativity. Firstly, the history and implications of the long-standing conjecture that general relativistic, shear-free perfect fluids which obey a barotropic equation of state p = p(w) such that w + p = 0, are either non-expanding or non-rotating. Secondly the application of the computer algebra system Maple to the area of tetrad formalisms in general relativity.

The GHP II package with applications

We present an advanced version of the Maple package GHP called GHPII. In it we provide a number of additional sophisticated tools to assist with problems formulated in the Geroch-Held-Penrose (ghp) formalism. The first part of this article discusses these new tools while in the second part we shall apply the ghp formalism, using the GHPII routines, to vacuum Petrov type D spacetimes and shear-free perfect fluids. We prove that for all shear-free perfect fluids with a barotropic equation of state, where two of the principal null directions are coplanar with the fluid four-velocity and vorticity then either the expansion or vorticity of the fluid must be zero.

On an alignment condition of the weyl tensor

We generalize an alignment condition of the Weyl tensor given by Barnes and Rowlingson. The alignment condition is then applied to Petrov type D perfect fluid spacetimes. In particular, purely magnetic, Petrov type D, shear-free perfect fluids are shown to be locally rotationally symmetric.

Recrystallization textures in course grained low carbon and interstitial free steels

The microstructures and textures of coarse grained cold rolled, partially recrystallized and fully recrystallized low carbon and interstitial free steel were examined by optical microscopy, scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD). The recrystallization textures of the two grades are markedly different, with the low carbon steel having a predominantly Goss {11O}<OOl> texture and the interstitial free steel having a <1ll>/1ND texture with a strong {III }<112> component. One possible explanation for the texture difference is that less severe localization of flow during deformation of interstitial free steels causes less Goss nuclei to be generated. While some support for this view is provided by the results presented in this paper, the results suggest that another mechanism may be at least partially responsible. Examination of micro
shear bands on the surface of pre-polished samples showed that a higher proportion of micro shear bands remained active at high rolling reductions in the low carbon steel, compared with the interstitial free grade. Regions of Goss orientation within bands that have ceased to operate rotate to
near-{ III }<112> orientations with further deformation. Consequently, the recrystallization texture of coarse grained interstitial free steels can be rationalized by a reduction in the availability of Goss nuclei and an increase in the availability of {Ill }<112> nuclei due to a "Goss to {Ill }<112>" rotation within micro shear bands that have ceased to operate.

Fragmentation of orientation within grains of a cold-rolled interstitial-free steel

The formation of a favourable recrystallization texture in interstitial-free (IF) steels depends on the availability and activation of particular nucleation sites in the deformed microstructure. This paper presents a description of the deformed microstructure of a commercially cold-rolled IF steel, with particular emphasis on the microstructural inhomogeneities and short-range orientational variation that provide suitable nucleation sites during recrystallization. RD-fibre regions deform relatively homogeneously and exhibit little short-range orientational variation. ND-fibre regions are heavily banded and exhibit considerable short-range orientational variation associated with the bands. While the overall orientational spread of ND-fibre grains frequently is about the ND-axis, the short-range orientational variation often involves rotation about axes in the TD-ND plane that are nearer to the TD than the ND.

The influence of solute carbon in cold-rolled steels on shear band formation and recrystallization texture

Two experiments were conducted to clarify the roles of grain size, solute carbon and strain in determining the recrystallization textures of cold-rolled and annealed steels. In the first experiment, samples of coarse-grained low-carbon (LC) and interstitial-free (IF) steels were cold-rolled to a 75% reduction in thickness. One sample from each steel was polished and cold-rolled an additional 5%, while the remaining samples were annealed for various times at 650°C. In the second experiment, three samples from a commercial LC steel sheet were rolled 70% at 300°C. Two of the samples were given a further rolling reduction of 5% of the original thickness, with one of the samples being given this additional reduction at 300°C and the other at room temperature. Goss recrystallization textures are strengthened by coarse initial grain sizes, the presence of solute carbon and rolling at a temperature where dynamic strain ageing occurs, but are weakened by additional rolling beyond a reduction of 70%, especially when this extra rolling is conducted at a temperature where dynamic strain ageing does not occur. Characterization of key features of the deformed and recrystallized steels using optical microscopy, scanning electron microscopy (SEM) and electron back-scatter diffraction (EBSD) supports a rationale for these effects based on the repeated activation and deactivation of shear bands and the influence of solute carbon and dynamic strain ageing on the operating life of the bands and the accumulation of strain within them.

On corrosion behaviour of magnesium alloy AZ31 in simulated body fluids and influence of ionic liquid pretreatments

This paper reports on the corrosion of Mg alloy AZ31 in simulated body fluid (SBF) using static immersion tests and electrochemical impedance spectroscopy. A preliminary study on the effect of flowing SBF on the corrosion behaviour of AZ31 has also been carried out. Low toxicity ionic liquids (ILs) trimethyl(butyl)phosphonium diphenyl phosphate P1444DPP and trihexyl(tetradecyl)-phosphonium bis-2,4,4trimethylpentyl-phosphinate [P66614][ i(C8) 2PO2] have been used to provide corrosion protection for AZ31 in SBF. Time dependent immersion tests indicate that under static conditions, AZ31 suffers severe localised corrosion in SBF, with pits developing predominantly beside the Al-Mn intermetallic phase in the α matrix. At longer immersion times, the corrosion product eventually precipitates and covers the entire specimen surface. When exposed to SBF under flowing conditions with a shear stress of 0·88 Pa, more uniform corrosion was observed. The optical profilometry results and electrochemical impedance spectroscopy analysis suggest that both P
1444DPP and [P66614][i(C8)2PO2] pretreatments can increase the corrosion resistance of AZ31 in SBF, in particular by decreasing the number of deeper pits found on the alloy surface. Cytotoxic test shows that the presence of the ILs P
1444DPP and [P66614][i(C8)2PO2] in cell culture media slightly inhibits the growth of human coronary artery endothelial cells in comparison with the good cell viability around the treated specimen. A pretreatment with IL is used in order to improve the corrosion resistance of this alloy in SBF. © 2012 Institute of Materials, Minerals and Mining.

Asymmetric rolling of interstitial-free steel using differential roll diameters. Part I : mechanical properties and deformation textures

IF steel sheets were processed by conventional symmetric and asymmetric rolling (ASR) at ambient temperature. The asymmetry was introduced in a geometric way using differential roll diameters with a number of different ratios. The material strength was measured by tensile testing and the microstructure was analyzed by optical and transmission electron microscopy as well as electron backscatter diffraction (EBSD) analysis. Texture was also successfully measured by EBSD using large surface areas. Finite element (FE) simulations were carried out for multiple passes to obtain the strain distribution after rolling. From the FE results, the velocity gradient along selected flow lines was extracted and the evolution of the texture was simulated using polycrystal plasticity modeling. The best mechanical properties were obtained after ASR using a roll diameter ratio of 2. The textures appeared to be tilted up to 12 deg around the transverse direction, which were simulated with the FE-combined polycrystal plasticity modeling in good agreement with measurements. The simulation work revealed that the shear component introduced by ASR was about the same magnitude as the normal component of the rolling strain tensor.

Coupling of U-Tube and shear layer oscillations in an interconnected flow compartment

Results of experiments conducted in a 2m high flume at large Reynolds numbers are reported in this paper. The flume was partitioned into two compartments. Flow entered the bottom of the upstream test compartment as a wall jet, at jet Reynolds number ranging from 11,000 to 170,000. Periodic oscillations of the free surface in the two compartments resembling the oscillatory flow in a liquid-filled U-tube, and large coherent structures formed above the potential core of the wall jet were observed. Coupling of the U-tube oscillations and vortex shedding is attributed to fluid-dynamic and fluid-resonant feedback processes. For test compartment length, Lc=0.8m , fluid-resonant feedback was found to be dominant, and the shear layer was observed to oscillate at the natural frequency of the two-compartment, U-tube system. The observed U-tube oscillations are initiated by the oscillations of the shear layer at a frequency equal to the subharmonic component for the U-tube. The flow oscillations were generally weaker for Lc=1.2 and 2.0m with oscillation frequencies governed by fluid-dynamic feedback, verified from a comparison with the results from a previously reported study.