A mathematical model of chlamydial infection incorporating movement of chlamydial particles

We present a spatiotemporal mathematical model of chlamydial infection, host immune response and spatial movement of infectious particles. The re- sulting partial differential equations model both the dynamics of the infection and changes in infection profile observed spatially along the length of the host genital tract. This model advances previous chlamydia modelling by incorporating spatial change, which we also demonstrate to be essential when the timescale for movement of infectious particles is equal to, or shorter than, the developmental cycle timescale. Numerical solutions and model analysis are carried out, and we present a hypothesis regarding the potential for treatment and prevention of infection by increasing chlamydial particle motility.

Identification of dispersion-dependent hexagonal cavity modes of an individual ZnO nanonail

The hexagonal resonator characteristics of an individual ZnO-nanonail’s head were investigated via spatially resolved cathodoluminescence (CL) at room temperature. The positions of most of distinct CL peaks in visible range were well matched to those of whispering gallery modes (WGMs) of a hexagonal dielectric cavity when we took birefringence and dispersion of refractive indices into account. The broad and weak peaks for TE polarization in long wavelength range were consistent with refractive-index values below the threshold for total internal inflection. CL peaks that were not matched to WGMs were identified as either triangular quasi-WGM or Fabry–Pérot resonance modes.

Clinical strategies for the alleviation of contractures from a predictive mathematical model of dermal repair

Hypertrophic scars arise when there is an overproduction of collagen during wound healing. These are often associated with poor regulation of the rate of programmed cell death(apoptosis) of the cells synthesizing the collagen or by an exuberant inflammatory response that prolongs collagen production and increases wound contraction. Severe contractures that occur, for example, after a deep burn can cause loss of function especially if the wound is over a joint such as the elbow or knee. Recently, we have developed a morphoelastic mathematical model for dermal repair that incorporates the chemical, cellular and mechanical aspects of dermal wound healing. Using this model, we examine pathological scarring in dermal repair by first assuming a smaller than usual apoptotic rate for myofibroblasts, and then considering a prolonged inflammatory response, in an attempt to determine a possible optimal intervention strategy to promote normal repair, or terminate the fibrotic scarring response. Our model predicts that in both cases it is best to apply the intervention strategy early in the wound healing response. Further, the earlier an intervention is made, the less aggressive the intervention required. Finally, if intervention is conducted at a late time during healing, a significant intervention is required; however, there is a threshold concentration of the drug or therapy applied, above which minimal further improvement to wound repair is obtained.

Mathematical modelling of tumour-induced angiogenesis

The growth of solid tumours beyond a critical size is dependent upon angiogenesis, the formation of new blood vessels from an existing vasculature. Tumours may remain dormant at microscopic sizes for some years before switching to a mode in which growth of a supportive vasculature is initiated. The new blood vessels supply nutrients, oxygen, and access to routes by which tumour cells may travel to other sites within the host (metastasize). In recent decades an abundance of biological research has focused on tumour-induced angiogenesis in the hope that treatments targeted at the vasculature may result in a stabilisation or regression of the disease: a tantalizing prospect. The complex and fascinating process of angiogenesis has also attracted the interest of researchers in the field of mathematical biology, a discipline that is, for mathematics, relatively new. The challenge in mathematical biology is to produce a model that captures the essential elements and critical dependencies of a biological system. Such a model may ultimately be used as a predictive tool. In this thesis we examine a number of aspects of tumour-induced angiogenesis, focusing on growth of the neovasculature external to the tumour. Firstly we present a one-dimensional continuum model of tumour-induced angiogenesis in which elements of the immune system or other tumour-cytotoxins are delivered via the newly formed vessels. This model, based on observations from experiments by Judah Folkman et al., is able to show regression of the tumour for some parameter regimes. The modelling highlights a number of interesting aspects of the process that may be characterised further in the laboratory. The next model we present examines the initiation positions of blood vessel sprouts on an existing vessel, in a two-dimensional domain. This model hypothesises that a simple feedback inhibition mechanism may be used to describe the spacing of these sprouts with the inhibitor being produced by breakdown of the existing vessel's basement membrane. Finally, we have developed a stochastic model of blood vessel growth and anastomosis in three dimensions. The model has been implemented in C++, includes an openGL interface, and uses a novel algorithm for calculating proximity of the line segments representing a growing vessel. This choice of programming language and graphics interface allows for near-simultaneous calculation and visualisation of blood vessel networks using a contemporary personal computer. In addition the visualised results may be transformed interactively, and drop-down menus facilitate changes in the parameter values. Visualisation of results is of vital importance in the communication of mathematical information to a wide audience, and we aim to incorporate this philosophy in the thesis. As biological research further uncovers the intriguing processes involved in tumourinduced angiogenesis, we conclude with a comment from mathematical biologist Jim Murray, Mathematical biology is : : : the most exciting modern application of mathematics.

Mathematical modelling of the drying of sol gel microspheres

This thesis presents a mathematical model of the evaporation of colloidal sol droplets suspended within an atmosphere consisting of water vapour and air. The main purpose of this work is to investigate the causes of the morphologies arising within the powder collected from a spray dryer into which the precursor sol for Synroc™ is sprayed. The morphology is of significant importance for the application to storage of High Level Liquid Nuclear Waste. We begin by developing a model describing the evaporation of pure liquid droplets in order to establish a framework. This model is developed through the use of continuum mechanics and thermodynamic theory, and we focus on the specific case of pure water droplets. We establish a model considering a pure water vapour atmosphere, and then expand this model to account for the presence of an atmospheric gas such as air. We model colloidal particle-particle interactions and interactions between colloid and electrolyte using DLVO Theory and reaction kinetics, then incorporate these interactions into an expression for net interaction energy of a single particle with all other particles within the droplet. We account for the flow of material due to diffusion, advection, and interaction between species, and expand the pure liquid droplet models to account for the presence of these species. In addition, the process of colloidal agglomeration is modelled. To obtain solutions for our models, we develop a numerical algorithm based on the Control Volume method. To promote numerical stability, we formulate a new method of convergence acceleration. The results of a MATLAB™ code developed from this algorithm are compared with experimental data collected for the purposes of validation, and further analysis is done on the sensitivity of the solution to various controlling parameters.

New modes of governance and the commodification of criminological knowledge

This article explores the influence of new modes of governance on the production of criminological knowledge. In doing so, it examines the rise of discourses on risk and critiques the ways in which academic environments are changing under new managerialist philosophies. The article further explores the increasing 'commodification of criminological knowledge' and analyses its effect on contemporary criminological scholarship. Finally, this article examines the contours of critical criminological scholarship and advocates for a criminology of resistance.

Small-signal stability analysis of a DFIG-based wind power system under different modes of operation

This paper focuses on the super/subsynchronous operation of the doubly fed induction generator (DFIG) system. The impact of a damping controller on the different modes of operation for the DFIG-based wind generation system is investigated. The coordinated tuning of the damping controller to enhance the damping of the oscillatory modes using bacteria foraging technique is presented. The results from eigenvalue analysis are presented to elucidate the effectiveness of the tuned damping controller in the DFIG system. The robustness issue of the damping controller is also investigated.

Strolling through the (post)modern city: Modes of being a flaneur in picture books

The city and the urban condition, popular subjects of art, literature, and film, have been commonly represented as fragmented, isolating, violent, with silent crowds moving through the hustle and bustle of a noisy, polluted cityspace. Included in this diverse artistic field is children’s literature—an area of creative and critical inquiry that continues to play a central role in illuminating and shaping perceptions of the city, of city lifestyles, and of the people who traverse the urban landscape. Fiction’s textual representations of cities, its sites and sights, lifestyles and characters have drawn on traditions of realist, satirical, and fantastic writing to produce the protean urban story—utopian, dystopian, visionary, satirical—with the goal of offering an account or critique of the contemporary city and the urban condition. In writing about cities and urban life, children’s literature variously locates the child in relation to the social (urban) space. This dialogic relation between subject and social space has been at the heart of writings about/of the flâneur: a figure who experiences modes of being in the city as it transforms under the influences of modernism and postmodernism. Within this context of a changing urban ontology brought about by (post)modern styles and practices, this article examines five contemporary picture books: The Cows Are Going to Paris by David Kirby and Allen Woodman; Ooh-la-la (Max in love) by Maira Kalman; Mr Chicken Goes to Paris and Old Tom’s Holiday by Leigh Hobbs; and The Empty City by David Megarrity. I investigate the possibility of these texts reviving the act of flânerie, but in a way that enables different modes of being a flâneur, a neo-flâneur. I suggest that the neo-flâneur retains some of the characteristics of the original flâneur, but incorporates others that take account of the changes wrought by postmodernity and globalization, particularly tourism and consumption. The dual issue at the heart of the discussion is that tourism and consumption as agents of cultural globalization offer a different way of thinking about the phenomenon of flânerie. While the flâneur can be regarded as the precursor to the tourist, the discussion considers how different modes of flânerie, such as the tourist-flâneur, are an inevitable outcome of commodification of the activities that accompany strolling through the (post)modern urban space.