A general Approach to Methods with a Sparse Jacobian for Solving Nonlinear Systems of Equations

2000 Mathematics Subject Classification: 65H10.

Fungal spore fragmentation as a function of airflow rates and fungal generation methods

The aim of this study was to characterise and quantify the fungal fragment propagules derived and released from several fungal species (Penicillium, Aspergillus niger and Cladosporium cladosporioides) using different generation methods and different air velocities over the colonies. Real time fungal spore fragmentation was investigated using an Ultraviolet Aerodynamic Particle Sizer (UVASP) and a Scanning Mobility Particle Sizer (SMPS). The study showed that there were significant differences (p < 0.01) in the fragmentation percentage between different air velocities for the three generation methods, namely the direct, the fan and the fungal spore source strength tester (FSSST) methods. The percentage of fragmentation also proved to be dependant on fungal species. The study found that there was no fragmentation for any of the fungal species at an air velocity ≤ 0.4 m/s for any method of generation. Fluorescent signals, as well as mathematical determination also showed that the fungal fragments were derived from spores. Correlation analysis showed that the number of released fragments measured by the UVAPS under controlled conditions can be predicted on the basis of the number of spores, for Penicillium and Aspergillus niger, but not for Cladosporium cladosporioides. The fluorescence percentage of fragment samples was found to be significantly different to that of non-fragment samples (p < 0.0001) and the fragment sample fluorescence was always less than that of the non-fragment samples. Size distribution and concentration of fungal fragment particles were investigated qualitatively and quantitatively, by both UVAPS and SMPS, and it was found that the UVAPS was more sensitive than the SMPS for measuring small sample concentrations, and the results obtained from the UVAPS and SMAS were not identical for the same samples.

Wavelet based approaches and high resolution methods for complex process models

Many industrial processes and systems can be modelled mathematically by a set of Partial Differential Equations (PDEs). Finding a solution to such a PDF model is essential for system design, simulation, and process control purpose. However, major difficulties appear when solving PDEs with singularity. Traditional numerical methods, such as finite difference, finite element, and polynomial based orthogonal collocation, not only have limitations to fully capture the process dynamics but also demand enormous computation power due to the large number of elements or mesh points for accommodation of sharp variations. To tackle this challenging problem, wavelet based approaches and high resolution methods have been recently developed with successful applications to a fixedbed adsorption column model. Our investigation has shown that recent advances in wavelet based approaches and high resolution methods have the potential to be adopted for solving more complicated dynamic system models. This chapter will highlight the successful applications of these new methods in solving complex models of simulated-moving-bed (SMB) chromatographic processes. A SMB process is a distributed parameter system and can be mathematically described by a set of partial/ordinary differential equations and algebraic equations. These equations are highly coupled; experience wave propagations with steep front, and require significant numerical effort to solve. To demonstrate the numerical computing power of the wavelet based approaches and high resolution methods, a single column chromatographic process modelled by a Transport-Dispersive-Equilibrium linear model is investigated first. Numerical solutions from the upwind-1 finite difference, wavelet-collocation, and high resolution methods are evaluated by quantitative comparisons with the analytical solution for a range of Peclet numbers. After that, the advantages of the wavelet based approaches and high resolution methods are further demonstrated through applications to a dynamic SMB model for an enantiomers separation process. This research has revealed that for a PDE system with a low Peclet number, all existing numerical methods work well, but the upwind finite difference method consumes the most time for the same degree of accuracy of the numerical solution. The high resolution method provides an accurate numerical solution for a PDE system with a medium Peclet number. The wavelet collocation method is capable of catching up steep changes in the solution, and thus can be used for solving PDE models with high singularity. For the complex SMB system models under consideration, both the wavelet based approaches and high resolution methods are good candidates in terms of computation demand and prediction accuracy on the steep front. The high resolution methods have shown better stability in achieving steady state in the specific case studied in this Chapter.

Hardness of silicon nitride thin films characterised by nanoindentation and nanoscratch deconvolution methods

Plasma enhanced chemical vapour deposition silicon nitride thin films are widely used in microelectromechanical system devices as structural materials because the mechanical properties of those films can be tailored by adjusting deposition conditions. However, accurate measurement of the mechanical properties, such as hardness, of films with thicknesses at nanometric scale is challenging. In the present study, the hardness of the silicon nitride films deposited on silicon substrate under different deposit conditions was characterised using nanoindentation and nanoscratch deconvolution methods. The hardness values obtained from the two methods were compared. The effect of substrate on the measured results was discussed.

Observational research and verbal protocol methods

This paper describes observational research and verbal protocols methods, how these methods are applied and integrated within different contexts, and how they complement each other. The first case study focuses on nurses’ interaction during bandaging of patients’ lower legs. To maintain research rigor a triangulation approach was applied that links observations of current procedures, ‘talk-aloud’ protocol during interaction and retrospective protocol. Maps of interactions demonstrated that some nurses bandage more intuitively than others. Nurses who bandage intuitively assemble long sequences of bandaging actions while nurses who bandage less intuitively ‘focus-shift’ in between bandaging actions. Thus different levels of expertise have been identified. The second case study consists of two laboratory experiments. It focuses on analysing and comparing software and product design teams and how they approached a design problem. It is based on the observational and verbal data analysis. The coding scheme applied evolved during the analysis of the activity of each team and is identical for all teams. The structure of knowledge captured from the analysis of the design team maps of interaction is identified. The significance of this work is within its methodological approach. The maps of interaction are instrumental for understanding the activities and interactions of the people observed. By examining the maps of interaction, it is possible to draw conclusions about interactions, structure of knowledge captured and level of expertise. This research approach is transferable to other design domains. Designers will be able to transfer the interaction maps outcomes to systems and services they design.

A spectroscopic comparison of YBCO superconductors synthesised by solid-state and co-precipitation methods

Raman spectroscopy, X-ray diffraction (XRD), and scanning electron microscopy (SEM) have been used to compare samples of YBa2Cu3O7 (YBCO) synthesised by the solid-state method and a novel co-precipitation technique. XRD results indicate that YBCO prepared by these two methods are phase pure, however the Raman and SEM results show marked differences between these samples.

Assessing eco-environmental performance of agricultural production in OECD countries : combination of soil surface, soil system and farm gate methods of nutrient auditing

Nitrogen balance is increasingly used as an indicator of the environmental performance of agricultural sector in national, international, and global contexts. There are three main methods of accounting the national nitrogen balance: farm gate, soil surface, and soil system. OECD (2008) recently reported the nitrogen and phosphorus balances for member countries for the 1985 - 2004 period using the soil surface method. The farm gate and soil system methods were also used in some international projects. Some studies have provided the comparison among these methods and the conclusion is mixed. The motivation of this present paper was to combine these three methods to provide a more detailed auditing of the nitrogen balance and flows for national agricultural production. In addition, the present paper also provided a new strategy of using reliable international and national data sources to calculate nitrogen balance using the farm gate method. The empirical study focused on the nitrogen balance of OECD countries for the period from 1985 to 2003. The N surplus sent to the total environment of OECD surged dramatically in early 1980s, gradually decreased during 1990s but exhibited an increasing trends in early 2000s. The overall N efficiency however fluctuated without a clear increasing trend. The eco-environmental ranking shows that Australia and Ireland were the worst while Korea and Greece were the best.

A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non-classical diffusion or dispersion; that is, not adequately described by the classical theory of Brownian motion and Fick's law. We consider a space fractional advection-dispersion equation based on a fractional Fick's law. The equation involves the Riemann-Liouville fractional derivative which arises from assuming that particles may make large jumps. Finite difference methods for solving this equation have been proposed by Meerschaert and Tadjeran. In the variable coefficient case, the product rule is first applied, and then the Riemann-Liouville fractional derivatives are discretised using standard and shifted Grunwald formulas, depending on the fractional order. In this work, we consider a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Grunwald formulas are used to discretise the fractional derivatives at control volume faces. We compare the two methods for several case studies from the literature, highlighting the convenience of the finite volume approach.

A study of the phosphate mineral kapundaite NaCa(Fe3+)4(PO4)4(OH)3⋅5(H2O) using SEM/EDX and vibrational spectroscopic methods

Vibrational spectroscopy enables subtle details of the molecular structure of kapundaite to be determined. Single crystals of a pure phase from a Brazilian pegmatite were used. Kapundaite is the Fe3+ member of the wardite group. The infrared and Raman spectroscopy were applied to compare the structure of kapundaite with wardite. The Raman spectrum of kapundaite in the 800–1400 cm−1 spectral range shows two intense bands at 1089 and 1114 cm−1 assigned to the ν1PO43- symmetric stretching vibrations. The observation of two bands provides evidence for the non-equivalence of the phosphate units in the kapundaite structure. The infrared spectrum of kapundaite in the 500–1300 cm−1 shows much greater complexity than the Raman spectrum. Strong infrared bands are found at 966, 1003 and 1036 cm−1 and are attributed to the ν1PO43- symmetric stretching mode and ν3PO43- antisymmetric stretching mode. Raman bands in the ν4 out of plane bending modes of the PO43- unit support the concept of non-equivalent phosphate units in the kapundaite structure. In the 2600–3800 cm−1 spectral range, Raman bands for kapundaite are found at 2905, 3151, 3311, 3449 and 3530 cm−1. These bands are broad and are assigned to OH stretching vibrations. Broad infrared bands are also found at 2904, 3105, 3307, 3453 and 3523 cm−1 and are attributed to water. Raman spectroscopy complimented with infrared spectroscopy has enabled aspects of the structure of kapundaite to be ascertained and compared with that of other phosphate minerals.