A spatial sampling optimization package using MSN theory

The density and distribution of spatial samples heavily affect the precision and reliability of estimated population attributes. An optimization method based on Mean of Surface with Nonhomogeneity (MSN) theory has been developed into a computer package with the purpose of improving accuracy in the global estimation of some spatial properties, given a spatial sample distributed over a heterogeneous surface; and in return, for a given variance of estimation, the program can export both the optimal number of sample units needed and their appropriate distribution within a specified research area. (C) 2010 Elsevier Ltd. All rights reserved.

Modelling uncertainty in agricultural image analysis

C.M. Onyango, J.A. Marchant and R. Zwiggelaar, 'Modelling uncertainty in agricultural image analysis', Computers and Electronics in Agriculture 17 (3), 295-305 (1997)

Modelling random fuzzy renewal reward processes

Shen, Q., Zhao, R., Tang, W. (2008). Modelling random fuzzy renewal reward processes. IEEE Transactions on Fuzzy Systems, 16 (5),1379-1385

Generalized semi-geostrophic theory on a sphere

Douglas, Robert; Cullen, M.J.P.; Roulston, I.; Sewell, M.J., (2005) 'Generalized semi-geostrophic theory on a sphere', Journal of Fluid Mechanics 531 pp.123-157 RAE2008

The Oscillatory Squeeze flow rheometer: Comprehensive theory and a new experimental facility

Binding, David; Bell, D.; Walters, K., (2006) 'The Oscillatory Squeeze flow rheometer: Comprehensive theory and a new experimental facility', Rheologica Acta 46 pp.111-121 RAE2008

Mathematical modelling and optimisation of the formulation and manufacture of aggregate food products

In this PhD study, mathematical modelling and optimisation of granola production has been carried out. Granola is an aggregated food product used in breakfast cereals and cereal bars. It is a baked crispy food product typically incorporating oats, other cereals and nuts bound together with a binder, such as honey, water and oil, to form a structured unit aggregate. In this work, the design and operation of two parallel processes to produce aggregate granola products were incorporated: i) a high shear mixing granulation stage (in a designated granulator) followed by drying/toasting in an oven. ii) a continuous fluidised bed followed by drying/toasting in an oven. In addition, the particle breakage of granola during pneumatic conveying produced by both a high shear granulator (HSG) and fluidised bed granulator (FBG) process were examined. Products were pneumatically conveyed in a purpose built conveying rig designed to mimic product conveying and packaging. Three different conveying rig configurations were employed; a straight pipe, a rig consisting two 45° bends and one with 90° bend. It was observed that the least amount of breakage occurred in the straight pipe while the most breakage occurred at 90° bend pipe. Moreover, lower levels of breakage were observed in two 45° bend pipe than the 90° bend vi pipe configuration. In general, increasing the impact angle increases the degree of breakage. Additionally for the granules produced in the HSG, those produced at 300 rpm have the lowest breakage rates while the granules produced at 150 rpm have the highest breakage rates. This effect clearly the importance of shear history (during granule production) on breakage rates during subsequent processing. In terms of the FBG there was no single operating parameter that was deemed to have a significant effect on breakage during subsequent conveying. A population balance model was developed to analyse the particle breakage occurring during pneumatic conveying. The population balance equations that govern this breakage process are solved using discretization. The Markov chain method was used for the solution of PBEs for this process. This study found that increasing the air velocity (by increasing the air pressure to the rig), results in increased breakage among granola aggregates. Furthermore, the analysis carried out in this work provides that a greater degree of breakage of granola aggregates occur in line with an increase in bend angle.

Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.

First principles modelling of nucleation and growth during atomic layer deposition onto III-V substrates

Atomic layer deposition (ALD) is now used in semiconductor fabrication lines to deposit nanometre-thin oxide films, and has thus enabled the introduction of high-permittivity dielectrics into the CMOS gate stack. With interest increasing in transistors based on high mobility substrates, such as GaAs, we are investigating the surface treatments that may improve the interface characteristics. We focus on incubation periods of ALD processes on III-V substrates. We have applied first principles Density Functional Theory (DFT) to investigate detailed chemistry of these early stages of growth, specifically substrate and ALD precursor interaction. We have modelled the ‘clean-up’ effect by which organometallic precursors: trimethylaluminium (TMA) or hafnium and titanium amides clean arsenic oxides off the GaAs surface before ALD growth of dielectric commences and similar effect on Si3N4 substrate. Our simulations show that ‘clean-up’ of an oxide film strongly depends on precursor ligand, its affinity to the oxide and the redox character of the oxide. The predominant pathway for a metalloid oxide such as arsenic oxide is reduction, producing volatile molecules or gettering oxygen from less reducible oxides. An alternative pathway is non-redox ligand exchange, which allows non-reducible oxides (e.g. SiO2) to be cleaned-up. First principles study shows also that alkylamides are more susceptible to decomposition rather than migration on the oxide surface. This improved understanding of the chemical principles underlying ‘clean-up’ allows us to rationalize and predict which precursors will perform the reaction. The comparison is made between selection of metal chlorides, methyls and alkylamides precursors.

Multi-scale modelling of atomic layer deposition

High-permittivity ("high-k") dielectric materials are used in the transistor gate stack in integrated circuits. As the thickness of silicon oxide dielectric reduces below 2 nm with continued downscaling, the leakage current because of tunnelling increases, leading to high power consumption and reduced device reliability. Hence, research concentrates on finding materials with high dielectric constant that can be easily integrated into a manufacturing process and show the desired properties as a thin film. Atomic layer deposition (ALD) is used practically to deposit high-k materials like HfO2, ZrO2, and Al2O3 as gate oxides. ALD is a technique for producing conformal layers of material with nanometer-scale thickness, used commercially in non-planar electronics and increasingly in other areas of science and technology. ALD is a type of chemical vapor deposition that depends on self-limiting surface chemistry. In ALD, gaseous precursors are allowed individually into the reactor chamber in alternating pulses. Between each pulse, inert gas is admitted to prevent gas phase reactions. This thesis provides a profound understanding of the ALD of oxides such as HfO2, showing how the chemistry affects the properties of the deposited film. Using multi-scale modelling of ALD, the kinetics of reactions at the growing surface is connected to experimental data. In this thesis, we use density functional theory (DFT) method to simulate more realistic models for the growth of HfO2 from Hf(N(CH3)2)4/H2O and HfCl4/H2O and for Al2O3 from Al(CH3)3/H2O.Three major breakthroughs are discovered. First, a new reaction pathway, ’multiple proton diffusion’, is proposed for the growth of HfO2 from Hf(N(CH3)2)4/H2O.1 As a second major breakthrough, a ’cooperative’ action between adsorbed precursors is shown to play an important role in ALD. By this we mean that previously-inert fragments can become reactive once sufficient molecules adsorb in their neighbourhood during either precursor pulse. As a third breakthrough, the ALD of HfO2 from Hf(N(CH3)2)4 and H2O is implemented for the first time into 3D on-lattice kinetic Monte-Carlo (KMC).2 In this integrated approach (DFT+KMC), retaining the accuracy of the atomistic model in the higher-scale model leads to remarkable breakthroughs in our understanding. The resulting atomistic model allows direct comparison with experimental techniques such as X-ray photoelectron spectroscopy and quartz crystal microbalance.

Modelling induction melting energy savings

Electromagnetic processing of liquid metals involves dynamic change of the fluid volume interfacing with a melting solid material, gas or vacuum, and possibly a different liquid. Electromagnetic field and the associated force field are strongly coupled to the free surface dynamics and the heat-mass transfer. We present practical modelling examples of the flow and heat transfer using an accurate pseudo-spectral code and the k-omega turbulence model suitable for complex and transitional flows with free surfaces. The 'cold crucible' melting is modelled dynamically including the melting front gradual propagation and the magnetically confined free surrounding interface. Intermittent contact with the water-cooled segmented wall and the radiation heat losses are parts of the complex problem.

An experimental and numerical CFD study of turbulence in a tundish container

This paper describes work performed at IRSID/USINOR in France and the University of Greenwich, UK, to investigate flow structures and turbulence in a water-model container, simulating aspects typical of metal tundish operation. Extensive mean and fluctuating velocity measurements were performed at IRSID using LDA to determine the flow field and these form the basis for a numerical model validation. This apparently simple problem poses several difficulties for the CFD modelling. The flow is driven by the strong impinging jet at the inlet. Accurate description of the jet is most important and requires a localized fine grid, but also a turbulence model that predicts the correct spreading rates of jet and impinging wall boundary layers. The velocities in the bulk of the tundish tend to be (indeed need to be) much smaller than those of the jet, leading to damping of turbulence, or even laminar flow. The authors have developed several low-Reynolds number (low-Re) k–var epsilon model variants to compute this flow and compare against measurements. Best agreement is obtained when turbulence damping is introduced to account not only for walls, but also for low-Re regions in the bulk – the k–var epsilon model otherwise allows turbulence to accumulate in the container due to the restricted outlet. Several damping functions are tested and the results reported here. The k–ω model, which is more suited to transitional flow, also seems to perform well in this problem.

Utilising computational fluid dynamics (CFD) for the modelling of granular material in large-scale engineering processes

In this paper, the framework is described for the modelling of granular material by employing Computational Fluid Dynamics (CFD). This is achieved through the use and implementation in the continuum theory of constitutive relations, which are derived in a granular dynamics framework and parametrise particle interactions that occur at the micro-scale level. The simulation of a process often met in bulk solids handling industrial plants involving granular matter, (i.e. filling of a flat-bottomed bin with a binary material mixture through pneumatic conveying-emptying of the bin in core flow mode-pneumatic conveying of the material coming out of a the bin) is presented. The results of the presented simulation demonstrate the capability of the numerical model to represent successfully key granular processes (i.e. segregation/degradation), the prediction of which is of great importance in the process engineering industry.

Low Reynolds number turbulence models for accurate thermal simulations of electronic components

The electronics industry and the problems associated with the cooling of microelectronic equipment are developing rapidly. Thermal engineers now find it necessary to consider the complex area of equipment cooling at some level. This continually growing industry also faces heightened pressure from consumers to provide electronic product miniaturization, which in itself increases the demand for accurate thermal management predictions to assure product reliability. Computational fluid dynamics (CFD) is considered a powerful and almost essential tool for the design, development and optimization of engineering applications. CFD is now widely used within the electronics packaging design community to thermally characterize the performance of both the electronic component and system environment. This paper discusses CFD results for a large variety of investigated turbulence models. Comparison against experimental data illustrates the predictive accuracy of currently used models and highlights the growing demand for greater mathematical modelling accuracy with regards to thermal characterization. Also a newly formulated low Reynolds number (i.e. transitional) turbulence model is proposed with emphasis on hybrid techniques.

Mathematical modelling of the behaviour of granular material in a computational fluid dynamics framework using micro-mechanical models

In this paper, a Computational Fluid Dynamics framework is presented for the modelling of key processes which involve granular material (i.e. segregation, degradation, caking). Appropriate physical models and sophisticated algorithms have been developed for the correct representation of the different material components in a granular mixture. The various processes, which arise from the micromechanical properties of the different mixture species can be obtained and parametrised in a DEM / experimental framework, thus enabling the continuum theory to correctly account for the micromechanical properties of a granular system. The present study establishes the link between the micromechanics and continuum theory and demonstrates the model capabilities in simulations of processes which are of great importance to the process engineering industry and involve granular materials in complex geometries.

Modelling of jet-impingement cooling for power electronics

The use of an innovative jet impingement cooling system in a power electronics application is investigated using numerical analysis. The jet impingement system, outlined by Skuriat et al, consists of a series of cells each containing an array of holes. Cooling fluid is forced through the device, forming an array of impingement jets. The jets are arranged in a manner, which induces a high degree of mixing in the interface boundary layer. This increase in turbulent mixing is intended to induce higher Nusselt numbers and effective heat transfer coefficients. Enhanced cooling efficiency enables the power electronics module to operate at a lower temperature, greatly enhancing long-term reliability. The results obtained through numerical modelling deviates markedly from the experimentally derived data. The disparity is most likely due to the turbulence model selected and further analysis is required, involving evaluation of more advanced turbulence models.