A new algorithm for the Petrov classification of the Weyl tensor

A new algorithm for the Petrov classification of the Weyl tensor is introduced. It is similar to the Letniowski-McLenaghan algorithm [1] when someof the ¥'s are zero, but offers a completely new approach when all of the ¥'s are nonzero. In all cases, new code in Maple has been implemented.

The determination of all syzygies for the dependent polynomial invariants of the Riemann tensor. I. Pure Ricci and pure Weyl invariants

In this paper, we shall consider all pure Ricci and pure Weyl scalar invariants of any degree, in a four-dimensional Lorentzian space. We present a general graph-theoretic based reduction algorithm which decomposes, using syzygies, any pure invariant in terms of the independent base invariants {r₁,r₂,r₃} or {w₁,w₂}

A new algorithm for the Segre classification of the trace-free Ricci tensor

A new algorithm, based on the introduction of new spinor quantities, for the Segre classification of the trace-free Ricci tensor is presented. It is capable of automatically distinguishing between the two Segre types [1,1(11)] and [(1,1)11] where all other known algorithms fail to do so.

Influence of grain size on the compressive deformation of wrought Mg-3A1-1Zn

The influence of the grain size on the flow stress of extruded Mg–3Al–1Zn tested in compression is examined. Samples with grain sizes varying between 3 and 23 μm were prepared by altering the extrusion conditions. Compression testing of the extruded bar was carried out at temperatures between ambient and 200 °C. Twinning dominated the deformation at lower temperatures but this gave way to slip dominated flow when the temperature was raised. For tests carried out at intermediate temperatures, a similar transition was observed when the grain size was reduced. The transition was accompanied by a change in flow curve shape and Hall–Petch slope. The peak stresses achieved when twinning dominated the deformation were up to 100 MPa greater than those seen when slip dominated the flow. Critical grain sizes marking the twinning–slip transition were identified and these are described in terms of the deformation conditions.

Grain size effect on the warm deformation behaviour of a Ti-IF steel

The effect of grain size on the warm deformation behaviour of a titanium stabilized interstitial free (IF) steel was investigated using hot torsion. The initial work hardening regime is followed by the development of a broad stress peak after which work softening occurs. The hypothetical saturation stress (Estrin–Mecking model) and the stress at final strain were relatively insensitive to grain size. However, the strain to the peak stress was strongly dependent on the grain size at low values of the Zener–Hollomon parameter. A simple phenomenological approach, using a combined Estrin–Mecking model and an Avrami type equation, was used to model the flow curves. The hypothetical saturation stress, the stress at final strain and the strain to peak stress were modelled using three different hyperbolic sine laws. A comparison with independent data from the literature shows that the apparent activation energy of deformation determined in this work (Q=372 kJ/mol) can be used to rationalize the steady-state stress in compression data found in the literature.

Mapping the hot deformation microstructure of Ni-30Fe alloy

The evolution of structure during the hot working of an austenitic Ni-30%Fe alloy is studied using EBSD analysis of samples tested in torsion. A microstructural map in temperature-strain space that plots grain size, cell size, fracture and dynamic recrystallization is presented.

The determination of all syzygies for the dependent polynomial invariants of the Riemann Tensor. II. mixed invariants of Eeven degree in the Ricci Spinor

We continue our analysis of the polynomial invariants of the Riemann tensor in a four-dimensional Lorentzian space. We concentrate on the mixed invariants of even degree in the Ricci spinor Φ_ABȦḂ and show how, using constructive graph-theoretic methods, arbitrary scalar contractions between copies of the Weyl spinor ψ_ABCD, its conjugate ψ_ȦḂĊḊ and an even number of Ricci spinors can be expressed in terms of paired contractions between these spinors. This leads to an algorithm for the explicit expression of dependent invariants as polynomials of members of the complete set. Finally, we rigorously prove that the complete set as given by Sneddon [J. Math. Phys. 39, 1659-1679 (1998)] for this case is both complete and minimal.

Influence of aging pre-treatment on the compressive deformation of WE54 alloy

The effect of aging pre-treatment on the compressive deformation of a commercial WE54 alloy is studied. Age hardening treatments were performed at 170 °C, 250 °C and 300 °C. Compression testing was then carried out for the peak aged samples at temperatures between ambient and 450 °C. Twinning dominated the deformation at lower temperatures for all initial microstructures. This behaviour was replaced by slip dominated flow when the temperature was raised. The temperature of the transition from twinning to slip dominated flow was only mildly sensitive to the pre-treatment. It is also evident that dynamic recrystallization is retarded in this alloy.

Soft-sediment deformation structures interpreted as seismite from the Middle Permian of the southern Sydney Basin, southeastern Australia

The Middle Permian Wandrawandian Siltstone of the southern Sydney Basin is well exposed along the coastline from Lagoon Head in the south to North Head in the north near Ulladulla in southern New South Wales. The unit is dominated by fossiliferous siltstone and mudstone, with abundant dropstones and minor pebbly sandstone interbeds, and contains an interval of well-preserved and extensive soft-sediment deformation structures. These deformation structures occur mainly in the middle part of the cliff sections and are bounded above and below by undeformed sedimentary units of similar lithology. A wide range of soft-sediment deformation structures have been observed, including cracks, sandstone and sandy mudstone dykes, a possible sand volcano, networks of relatively small and closely connected fissure-like structures, metre-scale complex-type slump folds, flexural stratification, concave-up depressional structures, small-scale normal faults (with displacements usually <1 m), shear planes, and breccias (pseudonodules). The slumps and associated deformations are here collectively interpreted as representing a seismite deposit attributable to penecontemporaneous deformation of soft, hydroplastic sediment layers following a liquefaction triggered by seismic shocks. The timing of the inferred earthquake events appears to correspond to the onset of a major basin-wide tectonism during the Middle Permian.

Determination of all syzygies for the dependent polynomial invariants of the Riemann Tensor. III. mixed invariants of arbitrary degree in the Ricci Spinor

In this paper, we rigorously prove that the complete set of Riemann tensor invariants given by Sneddon [J. Math. Phys. 40, 5905 (1999)] is both minimal and complete. Furthermore, we provide a two-stage algorithm for the explicit construction of polynomial syzygies relating any dependent Riemann tensor invariant to members of the complete set.

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.

On the problem of algebraic completeness for the invariants of the Riemann tensor. II

We study the set of invariants CZ [E. Zakhary and J. Carminati, J. Math. Phys. 42, 1474 (2001)] for the class of space-times whose Ricci tensors do not possess a null eigenvector. We show that all cases are completely backsolvable in terms of sets of invariants from CZ. We provide algebraically complete sets for each canonically different space-time.