An Invariant Theory of Surfaces in the Four-Dimensional Euclidean or Minkowski Space

2010 Mathematics Subject Classification: 53A07, 53A35, 53A10.

Some surface profiles of a strip after plane-strain indentation by rigid bodies with serrated surfaces

This paper is concerned with the surface profiles of a strip after rigid bodies with serrated (saw-teeth) surfaces indent the strip and are subsequently removed. Plane-strain conditions are assumed. This has application in roughness transfer of final metal forming process. The effects of the semi-angle of the teeth, the depth of indentation and the friction on the contact surface on the profile are considered.

Understanding the physical processes of pollutant build-up and wash-off on roof surfaces

Pollutants originating with roof runoff can have a significant impact to urban stormwater quality. This signifies the importance of understanding pollutant processes on roof surfaces. Additionally, knowledge of pollutant processes on roof surfaces is important as roofs are used as the primary catchment surface for domestic rainwater harvesting. In recent years, rainwater harvesting has become one of the primary sustainable water management techniques to counteract the growing demand for potable water. Similar to all impervious services, pollutants associated with roof runoff undergo two primary processes: build-up and wash-off. The knowledge relating to these processes is limited. This paper presents outcomes of an in-depth research study into pollutant build-up and wash-off for roof surfaces. The knowledge will be important in order to develop appropriate strategies to safeguard rainwater users from possible health risks.

Validation of 3D models of the outer and inner surfaces of an ovine femur

The validation of Computed Tomography (CT) based 3D models takes an integral part in studies involving 3D models of bones. This is of particular importance when such models are used for Finite Element studies. The validation of 3D models typically involves the generation of a reference model representing the bones outer surface. Several different devices have been utilised for digitising a bone’s outer surface such as mechanical 3D digitising arms, mechanical 3D contact scanners, electro-magnetic tracking devices and 3D laser scanners. However, none of these devices is capable of digitising a bone’s internal surfaces, such as the medullary canal of a long bone. Therefore, this study investigated the use of a 3D contact scanner, in conjunction with a microCT scanner, for generating a reference standard for validating the internal and external surfaces of a CT based 3D model of an ovine femur. One fresh ovine limb was scanned using a clinical CT scanner (Phillips, Brilliance 64) with a pixel size of 0.4 mm2 and slice spacing of 0.5 mm. Then the limb was dissected to obtain the soft tissue free bone while care was taken to protect the bone’s surface. A desktop mechanical 3D contact scanner (Roland DG Corporation, MDX 20, Japan) was used to digitise the surface of the denuded bone. The scanner was used with the resolution of 0.3 × 0.3 × 0.025 mm. The digitised surfaces were reconstructed into a 3D model using reverse engineering techniques in Rapidform (Inus Technology, Korea). After digitisation, the distal and proximal parts of the bone were removed such that the shaft could be scanned with a microCT (µCT40, Scanco Medical, Switzerland) scanner. The shaft, with the bone marrow removed, was immersed in water and scanned with a voxel size of 0.03 mm3. The bone contours were extracted from the image data utilising the Canny edge filter in Matlab (The Mathswork).. The extracted bone contours were reconstructed into 3D models using Amira 5.1 (Visage Imaging, Germany). The 3D models of the bone’s outer surface reconstructed from CT and microCT data were compared against the 3D model generated using the contact scanner. The 3D model of the inner canal reconstructed from the microCT data was compared against the 3D models reconstructed from the clinical CT scanner data. The disparity between the surface geometries of two models was calculated in Rapidform and recorded as average distance with standard deviation. The comparison of the 3D model of the whole bone generated from the clinical CT data with the reference model generated a mean error of 0.19±0.16 mm while the shaft was more accurate(0.08±0.06 mm) than the proximal (0.26±0.18 mm) and distal (0.22±0.16 mm) parts. The comparison between the outer 3D model generated from the microCT data and the contact scanner model generated a mean error of 0.10±0.03 mm indicating that the microCT generated models are sufficiently accurate for validation of 3D models generated from other methods. The comparison of the inner models generated from microCT data with that of clinical CT data generated an error of 0.09±0.07 mm Utilising a mechanical contact scanner in conjunction with a microCT scanner enabled to validate the outer surface of a CT based 3D model of an ovine femur as well as the surface of the model’s medullary canal.

Enhanced human bone marrow stromal cell affinity for modified poly(L-lactide) surfaces by the upregulation of adhesion molecular genes

To enhance and regulate cell affinity for poly (l-lactic acid) (PLLA) based materials, two hydrophilic ligands, poly (ethylene glycol) (PEG) and poly (l-lysine) (PLL), were used to develop triblock copolymers: methoxy-terminated poly (ethylene glycol)-block-poly (l-lactide)-block-poly (l-lysine) (MPEG-b-PLLA-b-PLL) in order to regulate protein absorption and cell adhesion. Bone marrow stromal cells (BMSCs) were cultured on different composition of MPEG-b-PLLA-b-PLL copolymer films to determine the effect of modified polymer surfaces on BMSC attachment. To understand the molecular mechanism governing the initial cell adhesion on difference polymer surfaces, the mRNA expression of 84 human extracellular matrix (ECM) and adhesion molecules was analysed using quantitative reverse transcriptase polymerase chain reaction (qRT-PCR). It was found that down regulation of adhesion molecules was responsible for the impaired BMSC attachment on PLLA surface. MPEG-b-PLLA-b-PLL copolymer films improved significantly the cell adhesion and cytoskeleton expression by upregulation of relevant molecule genes significantly. Six adhesion genes (CDH1, ITGL, NCAM1, SGCE, COL16A1, and LAMA3) were most significantly influenced by the modified PLLA surfaces. In summary, polymer surfaces altered adhesion molecule gene expression of BMSCs, which consequently regulated cell initial attachment on modified PLLA surfaces.

External pressure in the hardening of phosphate in tribofilm on iron surfaces

Purpose: In the present work we consider our (in progress) spectroscopy study of zinc and iron phosphates under the influence external high pressure to determine zinc ion change coordination from tetrahedral to octahedral (or hexahedral) structure.----- Design/methodology/approach: The standard equipment is the optical high pressure cell with diamond (DAC). The DAC is assembled and then vibrational or electronic spectra are collected by mounting the cell in an infrared, Raman, EXAFS or UV-visible spectrometer.----- Findings: Mechanism by which zinc and iron methaphosphate material is transformed to glassy meta-phosphate is enhancing mechanical properties of tribofilm. The two decades of intensive study demonstrates that Zn (II) and Fe (III) ions participate to cross-link network under friction, hardening the phosphate.----- Research limitations/implications: Transition metal atoms with d orbital have flexible coordination numbers, for example zinc acts as a cross-linking agent increasing hardness, by changing coordination from tetrahedral to octahedral. Perhaps the external pressure effect on the [Zn–(O-P-)4 ] complex causes a transformation to an [Zn –(O-P-)6] grouping.----- Originality/value: This paper analyses high-pressure spectroscopy which has been applied for the investigation of 3D transition metal ions in solids. When studying pressure effects on coordination compounds structure, we can expect changes in ground electronic state (spin-crossovers), electronic spectra due to structural distortions (piezochromism), and changes in the ligand field causing shifts in the electronic transitions.

Calculation of habitable dwelling surfaces : an empirical analysis for the agglomerations of Munich and Sydney

In many countries the calculation of habitable dwelling surface is characterised by a chaotic variety of calculation variants hardly comprehensible for the end user - sometimes not even reproducible for the expert. Therefore dossiers were analysed on the basis of a random choice in order to determine the method according to which the habitable dwelling surface was measured and to find out wether customers can scrutinize the calculations. The paper compares Sydney and Munich, where in both cases property prices are situated at the high end of the market

Corona discharges on the surfaces of high voltage composite insulators

The degradation of high voltage electrical insulation is a prime factor that can significantly influence the reliability performance and the costs of maintaining high voltage electricity networks. Little information is known about the system of localized degradation from corona discharges on the relatively new silicone rubber sheathed composite insulators that are now being widely used in high voltage applications. This current work focuses on the fundamental principles of electrical corona discharge phenomena to provide further insights to where damaging surface discharges may localize and examines how these discharges may degrade the silicone rubber material. Although water drop corona has been identified by many authors as a major cause of deterioration of silicone rubber high voltage insulation until now no thorough studies have been made of this phenomenon. Results from systematic measurements taken using modern digital instrumentation to simultaneously record the discharge current pulses and visible images associated with corona discharges from between metal electrodes, metal electrodes and water drops, and between waters drops on the surface of silicone rubber insulation, using a range of 50 Hz voltages are inter compared. Visual images of wet electrodes show how water drops can play a part in encouraging flashover, and the first reproducible visual images of water drop corona at the triple junction of water air and silicone rubber insulation are presented. A study of the atomic emission spectra of the corona produced by the discharge from its onset up to and including spark-over, using a high resolution digital spectrometer with a fiber optic probe, provides further understanding of the roles of the active species of atoms and molecules produced by the discharge that may be responsible for not only for chemical changes of insulator surfaces, but may also contribute to the degradation of the metal fittings that support the high voltage insulators. Examples of real insulators and further work specific to the electrical power industry are discussed. A new design concept to prevent/reduce the damaging effects of water drop corona is also presented.

Modeling corneal surfaces with rational functions for high-speed videokeratoscopy data compression

High-speed videokeratoscopy is an emerging technique that enables study of the corneal surface and tear-film dynamics. Unlike its static predecessor, this new technique results in a very large amount of digital data for which storage needs become significant. We aimed to design a compression technique that would use mathematical functions to parsimoniously fit corneal surface data with a minimum number of coefficients. Since the Zernike polynomial functions that have been traditionally used for modeling corneal surfaces may not necessarily correctly represent given corneal surface data in terms of its optical performance, we introduced the concept of Zernike polynomial-based rational functions. Modeling optimality criteria were employed in terms of both the rms surface error as well as the point spread function cross-correlation. The parameters of approximations were estimated using a nonlinear least-squares procedure based on the Levenberg-Marquardt algorithm. A large number of retrospective videokeratoscopic measurements were used to evaluate the performance of the proposed rational-function-based modeling approach. The results indicate that the rational functions almost always outperform the traditional Zernike polynomial approximations with the same number of coefficients.