On the problem of algebraic completeness for the invariants of the Riemann Tensor: I

We present a new determining set, CZ, of Riemann invariants which possesses the minimum degree property. From an analysis on the possible independence of CZ, we are led to the division of all space-times into two distinct, invariantly characterized, classes: a general class M_G+, and a special, singular class M_S For each class, we provide an independent set of invariants (I_G+) ⊂ CZ and I_S ⊂ CZ, respectively) which, with the results of a sequel paper, will be shown to be algebraically complete.

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

We study the set CZ of invariants [Zakhary and Carminati, J. Math. Phys. 42, 1474 (2001)] for the class of space-times whose Ricci tensors possess a null eigenvector. We show that all cases are maximally backsolvable, in terms of sets of invariants from CZ, but that some cases are not completely backsolvable and these all possess an alignment between an eigenvector of the Ricci tensor with a repeated principal null vector of the Weyl tensor. We provide algebraically complete sets for each canonically different space-time and hence conclude with these results and those of a previous article [Carminati, Zakhary, and McLenaghan, J. Math. Phys. 43, 492 (2002)] that the CZ set is determining or maximal.

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}

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.

Preliminary investigations into tris(2,2'-bipyridyl) ruthenium (III) as a chemiluminescent reagent for the detection of 3,6-diacetylmorphine (heroin) on surfaces

The use of tris(2,2'-bipyridyl) ruthenium (III) as a chemiluminescent spray reagent spot-test for heroin is discussed. Two forms of the reagent are investigated an aqueous and an anhydrous where both were found to give vastly different results. The aqueous reagent giving slow, low intensity chemiluminescence whilst the anhydrous reagent gave a fast, bright response in the presence of 3,6-diacetylmorphine. The anhydrous reagent is less sensitive the slow, intensity response is characteristic of only two opiates tested 3,6-diacetylmorphine and 3-monoacetylmorphine.

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.

Lawsone : a novel reagent for the detection of latent fingermarks on paper surfaces

Lawsone (2-hydroxy-1,4-naphthoquinone) reacts with latent fingermark deposits on paper surfaces to yield purple-brown impressions of ridge details which are also photoluminescent; this compound represents the first in a completely new class of fingermark detection reagents.

Parametric modelling and the tessellation of architectural surfaces

Parametric modelling is gaining in popularity as both a fabrication and design tool, but its application in the architectural design industry has not been widely explored. This form of modelling has the ability to generate complex forms with intuitively reactive components, allowing designers to express and
fabricate structures previously too laborious and geometrically complex to realise. The key aim of the paper is to address the increasing need for seamless and bi-directional connectivity between the design, modelling and
fabrication ambit.

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.

Building surfaces and their effect on the urban thermal environment

Use of high reflectance surfaces reduces the amount of solar radiation absorbed through building envelopes and urban structures and thus keeping their surfaces cooler. The cooling energy savings by using high reflectance surfaces have been well documented. Higher surface temperatures add to increasing the ambient temperature as convection intensity is higher. Such temperature increase has significant impacts on the air conditioning energy utilization in hot climates. This study makes use of numerical simulations to analyze the effect of commonly used building materials on the air temperature. A part of the existing CBD (Central Business District) area of Singapore was selected for the study. A series of Computational Fluid Dynamics (CFD) simulations have been carried out using the software CFX-5.6. It was found that at low wind speeds, the effect of materials on the air temperature was significant and the temperature at the middle of a narrow canyon increased up to 2.5[degrees]C with the facade material having lower reflectance.

Measurement of the mass transfer coefficient at workpiece surfaces in heat treatment furnaces

The mass (e.g. carbon) transfer coefficient at a workpiece surface is an important kinetic factor to control the heat treatment process of the workpiece and to evaluate heat treatment equipment. The coefficient can be calculated from the carbon concentration at the surface of a sample carburized in a carburizing furnace for a given time. Two common measurement methods which use a thin plate and employ a component as samples respectively are evaluated and compared for sensitivity and uncertainty. The comparison shows that the use of a component produces higher measurement precision and also has the advantage in measuring the carbon transfer coefficients at different treated positions. This method is then extended and discussed methodologically. Also two equations are proposed to calculate the carbon transfer coefficient and its uncertainty, respectively. This method is also applied to measure the carbon transfer coefficient in a fluidized bed heat treatment furnace.

Tribology of lubricated nitrocarburised and titanium carbonitride surfaces

In the current work, two different coatings, nitrocarburised (CN) and titanium carbonitride (TiCN) on M2 grade high speed tool steel, were prepared by commercial diffusion and physical vapour deposition (PVD) techniques, respectively. Properties of the coating were characterised using a variety of techniques such as Glow-Discharge Optical Emission Spectrometry (GD-OES) and Scanning Electron Microscopy (SEM). Three non-commercial, oil-based lubricants with simplified formulations were used for this study. A tribological test was developed in which two nominally geometrically-identical crossed cylinders slide over each other under selected test conditions. This test was used to evaluate the effectiveness of a pre-applied lubricant film and a surface coating for various conditions of sliding wear. Engineered surface coatings can significantly improve wear resistance of the tool surface but their sliding wear performances strongly depend on the type of coating and lubricant combination used. These coating-lubricant interactions can also have a very strong effect on the useful life of the lubricant in a tribological system. Better performance of lubricants during the sliding wear testing was achieved hen used with the nitrocarburised (CN) coating. To understand the nature of the interactions and their possible effects on the coating-lubricant system, several surface analysis techniques were used. The molecular level investigation of Fourier Transform Infrared Spectroscopy (FTIR) revealed that oxidative degradation occurred in all used oil-based lubricants during the sliding wear test but the degradation behaviour of oil-based lubricants varied with the coating-lubricant system and the wear conditions. The main differences in the carbonyl oxidation region of the FTIR spectra (1900-1600 cm-1) between different coating-lubricant systems may relate to the effective lifetime of the lubricant during the sliding wear test. Secondary Ion Mass Spectrometry (SIMS) depth profiling shows that the CN coating has the highest lubricant absorbability among the tested tool surfaces. Diffusion of chlorine (C1), hydrogen (H) and oxygen (O) into the surface of subsurface of the tool suggested that strong interactions occurred between lubricant and tool surface during the sliding wear test. The possible effects of the interactions on the performance of whole tribological system are also discussed. The study of Time-of-Flight Secondary Ion Mass Spectrometry (TOF-SIMS) indicated that the envelope of hydrocarbons (CmHn) of oil lubricant in the positive TOF-SIMS spectra shifted to lower mass fragment after the sliding wear testing due to the breakage of long-chain hydrocarbons to short-chain ones during the degradation of lubricant. The shift of the mass fragment range of the hydrocarbon (CmHn) envelope caries with the type of both tool surface and lubricant, again confirming that variation in the performance of the tool-lubricant system relates to the changes in surface chemistry due to tribochemical interactions at the tool-lubricant interface under sliding wear conditions. The sliding wear conditions resulted in changes not only in topography of the tool surface due to mechanical interactions, as outlined in Chapter 5, but also in surface chemistry due to tribochemical interactions, as discussed in Chapters 6 and 7.

Bioactivating the surfaces of titanium by sol-gel process

In the present study, titanium (Ti) samples were surface-modified by titania (TiO₂), silica (SiO₂) and hydroxyapatite (HA) coatings using a sol-gel process. The bioactivity of the film-coated Ti samples was investigated by cell attachment and morphology study using human osteoblast-like SaOS-2 cells. Results of the cell attachment indicated that the densities of cell attachment on the surfaces of Ti samples were significantly increased by film coatings; the density of cell attachment on HA film-coated surface was higher than those on TiO₂ and SiO₂ film-coated surfaces. Cell morphology study showed that the cells attached, spread and grew well on the three kinds of film-coated surfaces. It can be concluded that the three kinds of film coatings can bioactivate the surfaces of Ti samples effectively. Overall, Ti sample with HA film-coated surface exhibited the best bioactivity.

Syzygies of the polynomial invariants of the Riemann tensor

This thesis introduces a novel way of writing polynomial invariants as network graphs, and applies this diagrammatic notation scheme, in conjunction with graph theory, to derive algorithms for constructing relationships (syzygies) between different invariants. These algorithms give rise to a constructive solution of a longstanding classical problem in invariant theory.