Mathematical modelling of soft callus formation in early murine bone repair

Fracture healing is a complicated coupling of many processes. Yet despite the apparent complexity, fracture repair is usually effective. There is, however, no comprehensive mathematical model addressing the multiple interactions of cells, cytokines and oxygen that includes extra-cellular matrix production and that results in the formation of the early stage soft callus. This thesis develops a one dimensional continuum transport model in the context of early fracture healing. Although fracture healing is a complex interplay of many local factors, critical components are identified and used to construct an hypothesis about regulation of the evolution of early callus formation. Multiple cell lines, cellular differentiation, oxygen levels and cytokine concentrations are examined as factors affecting this model of early bone repair. The model presumes diffusive and chemotactic cell migration mechanisms. It is proposed that the initial signalling regime and oxygen availability arising as consequences of bone fracture, are sufficient to determine the quantity and quality of early soft callus formation. Readily available software and purpose written algorithms have been used to obtain numerical solutions representative of various initial conditions. These numerical distributions of cellular populations reflect available histology obtained from murine osteotomies. The behaviour of the numerical system in response to differing initial conditions can be described by alternative in vivo healing pathways. An experimental basis, as illustrated in murine fracture histology, has been utilised to validate the mathematical model outcomes. The model developed in this thesis has potential for future extension, to incorporate processes leading to woven bone deposition, while maintaining the characteristics that regulate early callus formation.

A Human identification technique using images of the iris and wavelet transform

A new approach for recognizing the iris of the human eye is presented. Zero-crossings of the wavelet transform at various resolution levels are calculated over concentric circles on the iris, and the resulting one-dimensional (1-D) signals are compared with model features using different dissimilarity functions.

Integration of sentiment analysis into customer relational model : the importance of feature ontology and synonym

Online business or Electronic Commerce (EC) is getting popular among customers today, as a result large number of product reviews have been posted online by the customers. This information is very valuable not only for prospective customers to make decision on buying product but also for companies to gather information of customers’ satisfaction about their products. Opinion mining is used to capture customer reviews and separated this review into subjective expressions (sentiment word) and objective expressions (no sentiment word). This paper proposes a novel, multi-dimensional model for opinion mining, which integrates customers’ characteristics and their opinion about any products. The model captures subjective expression from product reviews and transfers to fact table before representing in multi-dimensions named as customers, products, time and location. Data warehouse techniques such as OLAP and Data Cubes were used to analyze opinionated sentences. A comprehensive way to calculate customers’ orientation on products’ features and attributes are presented in this paper.

Soil moisture monitoring at the field scale using neutron probe

Measurement of the moisture variation in soils is required for geotechnical design and research because soil properties and behavior can vary as moisture content changes. The neutron probe, which was developed more than 40 years ago, is commonly used to monitor soil moisture variation in the field. This study reports a full-scale field monitoring of soil moisture using a neutron moisture probe for a period of more than 2 years in the Melbourne (Australia) region. On the basis of soil types available in the Melbourne region, 23 sites were chosen for moisture monitoring down to a depth of 1500 mm. The field calibration method was used to develop correlations relating the volumetric moisture content and neutron counts. Observed results showed that the deepest “wetting front” during the wet season was limited to the top 800 to 1000 mm of soil whilst the top soil layer down to about 550mmresponded almost immediately to the rainfall events. At greater depths (550 to 800mmand below 800 mm), the moisture variations were relatively low and displayed predominantly periodic fluctuations. This periodic nature was captured with Fourier analysis to develop a cyclic moisture model on the basis of an analytical solution of a one-dimensional moisture flow equation for homogeneous soils. It is argued that the model developed can be used to predict the soil moisture variations as applicable to buried structures such as pipes.

Energy and matter-efficient size-selective growth of thin quantum wires in a plasma

It is shown that plasmas can minimize the adverse Gibbs-Thompson effect in thin quantum wire growth. The model of Si nanowirenucleation includes the unprecedented combination of the plasma sheath, ion- and radical-induced species creation and heating effects on the surface and within an Au catalyst nanoparticle. Compared to neutral gas thermal processes, much thinner, size-selective wires can nucleate at the same temperature and pressure while much lower energy and matter budget is needed to grow same-size wires. This explains the experimental observations and may lead to energy- and matter-efficient synthesis of a broader range of one-dimensional quantum structures.

Temperature-dependent growth mechanisms of low-dimensional ZnO nanostructures

One-dimensional ZnO nanostructures were successfully synthesized on single-crystal silicon substrates via a simple thermal evaporation and vapour-phase transport method under different process temperatures from 500 to 1000 °C. The detailed and in-depth analysis of the experimental results shows that the growth of ZnO nanostructures at process temperatures of 500, 800, and 1000 °C is governed by different growth mechanisms. At a low process temperature of 500 °C, the ZnO nanostructures feature flat and smooth tips, and their growth is primarily governed by the vapour-solid mechanism. At an intermediate process temperature of 800 °C, the ZnO nanostructures feature cone-shape tips, and their growth is primarily governed by the self-catalyzed and saturated vapour–liquid–solid mechanism. At a high process temperature of 1000 °C, the alloy tip appears on the front side of the ZnO nanostructures, and their growth is primarily governed by the common catalyst-assisted vapour–liquid–solid mechanism. It is also shown that the morphological, structural, optical, and compositional properties of the synthesized ZnO nanostructures are closely related to the process temperature. These results are highly relevant to the development of light-emitting diodes, chemical sensors, energy conversion devices, and other advanced applications.

Thermodynamical and plasma-driven kinetic growth of high-aspect-ratio nanostructures : effect of hydrogen termination

The results of studies on the growth of high-aspect nanostructures in low-temperature non-equilibrium plasmas of reactive gas mixtures with or without hydrogen are presented. The results suggest that the hydrogen in the reactive plasma strongly affects the length of the nanostructures. This phenomenon is explained in terms of selective hydrogen passivation of the lateral and top surfaces of the surface-supported nanostructures. The theoretical model describes the effect of the atomic hydrogen passivation on the nanostructure shape and predicts the critical hydrogen coverage of the lateral surfaces necessary to achieve the nanostructure growth with the pre-determined shape. Our results demonstrate that the use of a strongly non-equilibrium plasma is very effective in significantly improving the shape control of quasi-one-dimensional single-crystalline nanostructures.

Interacting motile agents : taking a mean-field approach beyond monomers and nearest-neighbor steps

We consider a discrete agent-based model on a one-dimensional lattice, where each agent occupies L sites and attempts movements over a distance of d lattice sites. Agents obey a strict simple exclusion rule. A discrete-time master equation is derived using a mean-field approximation and careful probability arguments. In the continuum limit, nonlinear diffusion equations that describe the average agent occupancy are obtained. Averaged discrete simulation data are generated and shown to compare very well with the solution to the derived nonlinear diffusion equations. This framework allows us to approach a lattice-free result using all the advantages of lattice methods. Since different cell types have different shapes and speeds of movement, this work offers insight into population-level behavior of collective cellular motion.

Collective motion of dimers

We consider a discrete agent-based model on a one-dimensional lattice and a two-dimensional square lattice, where each agent is a dimer occupying two sites. Agents move by vacating one occupied site in favor of a nearest-neighbor site and obey either a strict simple exclusion rule or a weaker constraint that permits partial overlaps between dimers. Using indicator variables and careful probability arguments, a discrete-time master equation for these processes is derived systematically within a mean-field approximation. In the continuum limit, nonlinear diffusion equations that describe the average agent occupancy of the dimer population are obtained. In addition, we show that multiple species of interacting subpopulations give rise to advection-diffusion equations. Averaged discrete simulation data compares very well with the solution to the continuum partial differential equation models. Since many cell types are elongated rather than circular, this work offers insight into population-level behavior of collective cellular motion.

Integration of Opinion Mining into customer analysis model

This research proposes a multi-dimensional model for Opinion Mining, which integrates customers' characteristics and their opinions about products (or services). Customer opinions are valuable for companies to deliver right products or services to their customers. This research presents a comprehensive framework to evaluate opinions' orientation based on products' hierarchy attributes. It also provides an alternative way to obtain opinion summaries for different groups of customers and different categories of produces.

The three-dimensional hydrogen-bonded structures in the ammonium and sodium salt hydrates of 4-aminophenylarsonic acid

The structures of two hydrated salts of 4-aminophenylarsonic acid (p-arsanilic acid), namely ammonium 4-aminophenylarsonate monohydrate, NH4(+)·C6H7AsNO3(-)·H2O, (I), and the one-dimensional coordination polymer catena-poly[[(4-aminophenylarsonato-κO)diaquasodium]-μ-aqua], [Na(C6H7AsNO3)(H2O)3]n, (II), have been determined. In the structure of the ammonium salt, (I), the ammonium cations, arsonate anions and water molecules interact through inter-species N-H...O and arsonate and water O-H...O hydrogen bonds, giving the common two-dimensional layers lying parallel to (010). These layers are extended into three dimensions through bridging hydrogen-bonding interactions involving the para-amine group acting both as a donor and an acceptor. In the structure of the sodium salt, (II), the Na(+) cation is coordinated by five O-atom donors, one from a single monodentate arsonate ligand, two from monodentate water molecules and two from bridging water molecules, giving a very distorted square-pyramidal coordination environment. The water bridges generate one-dimensional chains extending along c and extensive interchain O-H...O and N-H...O hydrogen-bonding interactions link these chains, giving an overall three-dimensional structure. The two structures reported here are the first reported examples of salts of p-arsanilic acid.

The production mechanisms of OH radicals in a pulsed direct current plasma jet

The production mechanism of OH radicals in a pulsed DC plasma jet is studied by a two-dimensional (2-D) plasma jet model and a one-dimensional (1-D) discharge model. For the plasma jet in the open air, electron-impact dissociation of H2O, electron neutralization of H2O+, as well as dissociation of H2O by O(1D) are found to be the main reactions to generate the OH species. The contribution of the dissociation of H2O by electron is more than the others. The additions of N2, O2, air, and H2O into the working gas increase the OH density outside the tube slightly, which is attributed to more electrons produced by Penning ionization. On the other hand, the additions of O2 and H2O into the working gas increase the OH density inside the tube substantially, which is attributed to the increased O (1D) and H2O concentration, respectively. The gas flow will transport high density OH out of the tube during pulse off period. It is also shown that the plasma chemistry and reactivity can be effectively controlled by the pulse numbers. These results are supported by the laser induced fluorescence measurements and are relevant to several applications of atmospheric-pressure plasmas in health care, medicine, and materials processing.

Cell Dynamics of Model Proteins

We design rapidly folding sequences by assigning the strongest couplings to the contacts present in a target native state in a two dimensional model of heteropolymers. The pathways to folding and their dependence on the temperature are illustrated via a mapping of the dynamics into motion within the space of the maximally compact cells.

Time-temperature histories of spherical food products during bulk forced-air precooling

A general mathematical model for forced air precooling of spherical food products in bulk is developed. The food products are arranged inline to form a rectangular parallelepiped. Chilled air is blown along the height of the package. The governing equations for the transient two-dimensional conduction with internal heat generation in the product, simultaneous heat and mass transfer at the product-air interface and one-dimensional transient energy and species conservation equations for the moist air are solved numerically using finite difference methods. Results are presented in the form of time-temperature histories. Experiments are conducted with model foods in a laboratory scale air precooling tunnel. The agreement between the theoretical and experimental results is found to be good. In general, a single product analysis fails to predict the precooling characteristics of bulk loads of food products. In the range of values investigated, the respiration heat is found to have a negligible effect.

Boundary element analysis of reinforced concrete structural elements

A simple and practical technique for the discrete representation of reinforcement in two-dimensional boundary element analysis of reinforced concrete structural elements is presented. The bond developed over the surface of contact between the reinforcing steel and concrete is represented using fictitious one-dimensional spring elements. Potentials of the model developed are demonstrated using a number of numerical examples. The results are seen to be in good agreement with the results obtained using standard finite element software.