Propagation of low power low divergence Gaussian fields in unbiased self-defocusing photorefractive media and their interactions

Many optical networks are limited in speed and processing capability due to the necessity for the optical signal to be converted to an electrical signal and back again. In addition, electronically manipulated interconnects in an otherwise optical network lead to overly complicated systems. Optical spatial solitons are optical beams that propagate without spatial divergence. They are capable of phase dependent interactions, and have therefore been extensively researched as suitable all optical interconnects for over 20 years. However, they require additional external components, initially high voltage power sources were required, several years later, high power background illumination had replaced the high voltage. However, these additional components have always remained as the greatest hurdle in realising the applications of the interactions of spatial optical solitons as all optical interconnects. Recently however, self-focusing was observed in an otherwise self-defocusing photorefractive crystal. This observation raises the possibility of the formation of soliton-like fields in unbiased self-defocusing media, without the need for an applied electrical field or background illumination. This thesis will present an examination of the possibility of the formation of soliton-like low divergence fields in unbiased self-defocusing photorefractive media. The optimal incident beam and photorefractive media parameters for the formation of these fields will be presented, together with an analytical and numerical study of the effect of these parameters. In addition, preliminary examination of the interactions of two of these fields will be presented. In order to complete an analytical examination of the field propagating through the photorefractive medium, the spatial profile of the beam after propagation through the medium was determined. For a low power solution, it was found that an incident Gaussian field maintains its Gaussian profile as it propagates. This allowed the beam at all times to be described by an individual complex beam parameter, while also allowing simple analytical solutions to the appropriate wave equation. An analytical model was developed to describe the effect of the photorefractive medium on the Gaussian beam. Using this model, expressions for the required intensity dependent change in both the real and imaginary components of the refractive index were found. Numerical investigation showed that under certain conditions, a low powered Gaussian field could propagate in self-defocusing photorefractive media with divergence of approximately 0.1 % per metre. An investigation into the parameters of a Ce:BaTiO3 crystal showed that the intensity dependent absorption is wavelength dependent, and can in fact transition to intensity dependent transparency. Thus, with careful wavelength selection, the required intensity dependent change in both the real and imaginary components of the refractive index for the formation of a low divergence Gaussian field are physically realisable. A theoretical model incorporating the dependence of the change in real and imaginary components of the refractive index on propagation distance was developed. Analytical and numerical results from this model are congruent with the results from the previous model, showing low divergence fields with divergence less than 0.003 % over the propagation length of the photorefractive medium. In addition, this approach also confirmed the previously mentioned self-focusing effect of the self-defocusing media, and provided an analogy to a negative index GRIN lens with an intensity dependent focal length. Experimental results supported the findings of the numerical analysis. Two low divergence fields were found to possess the ability to interact in a Ce:BaTiO3 crystal in a soliton-like fashion. The strength of these interactions was found to be dependent on the degree of divergence of the individual beams. This research found that low-divergence fields are possible in unbiased self-defocusing photorefractive media, and that soliton-like interactions between two of these fields are possible. However, in order for these types of fields to be used in future all optical interconnects, the manipulation of these interactions, together with the ability for these fields to guide a second beam at a different wavelength, must be investigated.

An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell

We develop a new analytical solution for a reactive transport model that describes the steady-state distribution of oxygen subject to diffusive transport and nonlinear uptake in a sphere. This model was originally reported by Lin (Journal of Theoretical Biology, 1976 v60, pp449–457) to represent the distribution of oxygen inside a cell and has since been studied extensively by both the numerical analysis and formal analysis communities. Here we extend these previous studies by deriving an analytical solution to a generalized reaction-diffusion equation that encompasses Lin’s model as a particular case. We evaluate the solution for the parameter combinations presented by Lin and show that the new solutions are identical to a grid-independent numerical approximation.

Part-time job design : symptom and solution for a changing work environment

Part-time work presents a conundrum. Across industrialised countries, there has been significant growth in part-time work as a solution to resolving the diverse interests of employers, workers and families in managing time and resources. However, there are intrinsic disadvantages associated with part-time work; notably with pay and career prospects, which impact the same stakeholders it is intended to benefit. These disadvantages are particularly evident in professional services organisations, due to strong cultural norms of long work hours, single-focused commitment to work and 24x7 availability. There are indications, both in research and practice, that the design of part-time work arrangements could be improved to address some of the disadvantages associated with part-time work, and to challenge norms and dated assumptions that influence the structure of professional work. This study explored the changes made when professional service workers move from a full-time to part-time arrangement. The study drew on a recently proposed framework for work design, which extended previous models to reflect substantial changes in the contemporary work environment. The framework proved to be a useful perspective from which to explore the design of part-time work, principally because it integrated previously disconnected areas of literature and practice through a broader focus on the context of work. Exploration of the differences between part-time and full-time roles, and comparisons between part-time roles in similar types of work, provided insights into the design of professional part-time work. Analysis revealed that having a better understanding of design characteristics may help explain disadvantages associated with professional part-time work, and that some full-time roles can be more easily adapted to part-time arrangements than others. Importantly, comparisons revealed that even roles that are considered difficult to undertake on a part-time basis can potentially be re-designed to be more effective. Through empirical testing of the framework, a contextualised work design model is presented that may guide further research and the practice of crafting part-time arrangements. The findings also suggest that poor work design may lead to the symptoms associated with professional part-time work, and that improved work design may be a potential solution to these structural constraints.

A practical approach for identifying expected solution performance and robustness in operations research applications

A practical approach for identifying solution robustness is proposed for situations where parameters are uncertain. The approach is based upon the interpretation of a probability density function (pdf) and the definition of three parameters that describe how significant changes in the performance of a solution are deemed to be. The pdf is constructed by interpreting the results of simulations. A minimum number of simulations are achieved by updating the mean, variance, skewness and kurtosis of the sample using computationally efficient recursive equations. When these criterions have converged then no further simulations are needed. A case study involving several no-intermediate storage flow shop scheduling problems demonstrates the effectiveness of the approach.

A tissue engineering solution for segmental defect regeneration in load-bearing long bones

The reconstruction of large defects (>10 mm) in humans usually relies on bone graft transplantation. Limiting factors include availability of graft material, comorbidity, and insufficient integration into the damaged bone. We compare the gold standard autograft with biodegradable composite scaffolds consisting of medical-grade polycaprolactone and tricalcium phosphate combined with autologous bone marrow-derived mesenchymal stem cells (MSCs) or recombinant human bone morphogenetic protein 7 (rhBMP-7). Critical-sized defects in sheep - a model closely resembling human bone formation and structure - were treated with autograft, rhBMP-7, or MSCs. Bridging was observed within 3 months for both the autograft and the rhBMP-7 treatment. After 12 months, biomechanical analysis and microcomputed tomography imaging showed significantly greater bone formation and superior strength for the biomaterial scaffolds loaded with rhBMP-7 compared to the autograft. Axial bone distribution was greater at the interfaces. With rhBMP-7, at 3 months, the radial bone distribution within the scaffolds was homogeneous. At 12 months, however, significantly more bone was found in the scaffold architecture, indicating bone remodeling. Scaffolds alone or with MSC inclusion did not induce levels of bone formation comparable to those of the autograft and rhBMP-7 groups. Applied clinically, this approach using rhBMP-7 could overcome autograft-associated limitations.

Solution methods for advection-diffusion-reaction equations on growing domains and subdomains, with application to modelling skin substitutes

Problems involving the solution of advection-diffusion-reaction equations on domains and subdomains whose growth affects and is affected by these equations, commonly arise in developmental biology. Here, a mathematical framework for these situations, together with methods for obtaining spatio-temporal solutions and steady states of models built from this framework, is presented. The framework and methods are applied to a recently published model of epidermal skin substitutes. Despite the use of Eulerian schemes, excellent agreement is obtained between the numerical spatio-temporal, numerical steady state, and analytical solutions of the model.