Scaling laws for localised states in a nonlocal amplitude equation

It is well known that, although a uniform magnetic field inhibits the onset of small amplitude thermal convection in a layer of fluid heated from below, isolated convection cells may persist if the fluid motion within them is sufficiently vigorous to expel magnetic flux. Such fully nonlinear(‘‘convecton’’) solutions for magnetoconvection have been investigated by several authors. Here we explore a model amplitude equation describing this separation of a fluid layer into a vigorously convecting part and a magnetically-dominated part at rest. Our analysis elucidates the origin of the scaling laws observed numerically to form the boundaries in parameter space of the region of existence of these localised states, and importantly, for the lowest thermal forcing required to sustain them.

The dynamics of cellular automata on 2-manifolds is affected by topology

In this paper, we demonstrate that the distribution of Wolfram classes within a cellular automata rule space in the triangular tessellation is not consistent across different topological general. Using a statistical mechanics approach, cellular automata dynamical classes were approximated for cellular automata defined on genus-0, genus-1 and genus-2 2-manifolds. A distribution-free equality test for empirical distributions was applied to identify cases in which Wolfram classes were distributed differently across topologies. This result implies that global structure and local dynamics contribute to the long term evolution of cellular automata.

On the effect of topology on cellular automata rule spaces

This thesis presents an empirical study of the effects of topology on cellular automata rule spaces. The classical definition of a cellular automaton is restricted to that of a regular lattice, often with periodic boundary conditions. This definition is extended to allow for arbitrary topologies. The dynamics of cellular automata within the triangular tessellation were analysed when transformed to 2-manifolds of topological genus 0, genus 1 and genus 2. Cellular automata dynamics were analysed from a statistical mechanics perspective. The sample sizes required to obtain accurate entropy calculations were determined by an entropy error analysis which observed the error in the computed entropy against increasing sample sizes. Each cellular automata rule space was sampled repeatedly and the selected cellular automata were simulated over many thousands of trials for each topology. This resulted in an entropy distribution for each rule space. The computed entropy distributions are indicative of the cellular automata dynamical class distribution. Through the comparison of these dynamical class distributions using the E-statistic, it was identified that such topological changes cause these distributions to alter. This is a significant result which implies that both global structure and local dynamics play a important role in defining long term behaviour of cellular automata.

Characterization of the tail-specific protease (Tsp) from Legionella

Bacterial tail-specific proteases (Tsps) have been attributed a wide variety of functions including intracellular virulence, cell wall morphology, proteolytic signal cascades and stress response. This study tested the hypothesis that Tsp has a key function for the transmissive form of Legionella pneumophila. A tsp mutant was generated in Legionella pneumophila 130b and the characteristics of this strain and the isogenic wild-type were examined using a range of growth and proteomic analyses. Recombinant Tsp protein was also produced and analyzed. The L. pneumophila tsp mutant showed no defect in growth on rich media or during thermo-osmotic stress conditions. In addition, no defects in cellular morphology were observed when the cells were examined using transmission electron microscopy. Purified recombinant Tsp was found to be an active protease with a narrow substrate range. Proteome analysis using iTRAQ (5% coverage of the proteome) found that, of those proteins detected, only 5 had different levels in the tsp mutant compared to the wild type. ACP (Acyl Carrier Protein), which has a key role for Legionella differentiation to the infectious form, was reduced in the tsp mutant; however, tsp(-) was able to infect and replicate inside macrophages to the same extent as the wild type. Combined, these data demonstrate that Tsp is a protease but is not essential for Legionella growth or cell infection. Thus, Tsp may have functional redundancy in Legionella.

Coherent phonon decay and the boron isotope effect for MgB2

Ab-initio DFT calculations for the phonon dispersion (PD) and the Phonon Density Of States (PDOS) of the two isotopic forms (10B and 11B) of MgB2 demonstrate that use of a reduced symmetry super-lattice provides an improved approximation to the dynamical, phonon-distorted P6/mmm crystal structure. Construction of phonon frequency plots using calculated values for these isotopic forms gives linear trends with integer multiples of a base frequency that change in slope in a manner consistent with the isotope effect (IE). Spectral parameters inferred from this method are similar to that determined experimentally for the pure isotopic forms of MgB2. Comparison with AlB2 demonstrates that a coherent phonon decay down to acoustic modes is not possible for this metal. Coherent acoustic phonon decay may be an important contributor to superconductivity for MgB2.

Novel solutions for a model of wound healing angiogenesis

We prove the existence of novel, shock-fronted travelling wave solutions to a model of wound healing angiogenesis studied in Pettet et al (2000 IMA J. Math. App. Med. 17 395–413) assuming two conjectures hold. In the previous work, the authors showed that for certain parameter values, a heteroclinic orbit in the phase plane representing a smooth travelling wave solution exists. However, upon varying one of the parameters, the heteroclinic orbit was destroyed, or rather cut-off, by a wall of singularities in the phase plane. As a result, they concluded that under this parameter regime no travelling wave solutions existed. Using techniques from geometric singular perturbation theory and canard theory, we show that a travelling wave solution actually still exists for this parameter regime. We construct a heteroclinic orbit passing through the wall of singularities via a folded saddle canard point onto a repelling slow manifold. The orbit leaves this manifold via the fast dynamics and lands on the attracting slow manifold, finally connecting to its end state. This new travelling wave is no longer smooth but exhibits a sharp front or shock. Finally, we identify regions in parameter space where we expect that similar solutions exist. Moreover, we discuss the possibility of more exotic solutions.

Canards in advection-reaction-diffusion systems in one spatial dimension

This thesis contains a mathematical investigation of the existence of travelling wave solutions to singularly perturbed advection-reaction-diffusion models of biological processes. An enhanced mathematical understanding of these solutions and models is gained via the identification of canards (special solutions of fast/slow dynamical systems) and their role in the existence of the most biologically relevant, shock-like solutions. The analysis focuses on two existing models. A new proof of existence of a whole family of travelling waves is provided for a model describing malignant tumour invasion, while new solutions are identified for a model describing wound healing angiogenesis.

Recent advances in modeling the vulnerability of transportation networks

It is well known that, for major infrastructure networks such as electricity, gas, railway, road, and urban water networks, disruptions at one point have a knock on effect throughout the network. There is an impressive amount of individual research projects examining the vulnerability of critical infrastructure network. However, there is little understanding of the totality of the contribution made by these projects and their interrelationships. This makes their review a difficult process for both new and existing researchers in the field. To address this issue, a two-step literature review process is used, to provide an overview of the vulnerability of the transportation network in terms of four main themes - research objective, transportation mode, disruption scenario and vulnerability indicator –involving the analysis of related articles from 2001 to 2013. Two limitations of existing research are identified: (1) the limited amount of studies relating to multi-layer transportation network vulnerability analysis, and (2) the lack of evaluation methods to explore the relationship between structure vulnerability and dynamical functional vulnerability. In addition to indicating that more attention needs to be paid to these two aspects in future, the analysis provides a new avenue for the discovery of knowledge, as well as an improved understanding of transportation network vulnerability.

Injection velocity control of thermoplastic injection molding via a double controller scheme

Injection velocity has been recognized as a key variable in thermoplastic injection molding. Its closed-loop control is, however, difficult due to the complexity of the process dynamic characteristics. The basic requirements of the control system include tracking of a pre-determined injection velocity curve defined in a profile, load rejection and robustness. It is difficult for a conventional control scheme to meet all these requirements. Injection velocity dynamics are first analyzed in this paper. Then a novel double-controller scheme is adopted for the injection velocity control. This scheme allows an independent design of set-point tracking and load rejection and has good system robustness. The implementation of the double-controller scheme for injection velocity control is discussed. Special techniques such as profile transformation and shifting are also introduced to improve the velocity responses. The proposed velocity control has been experimentally demonstrated to be effective for a wide range of processing conditions.

Butterfly catastrophe for fronts in a three-component reaction–diffusion system

We study the dynamics of front solutions in a three-component reaction–diffusion system via a combination of geometric singular perturbation theory, Evans function analysis, and center manifold reduction. The reduced system exhibits a surprisingly complicated bifurcation structure including a butterfly catastrophe. Our results shed light on numerically observed accelerations and oscillations and pave the way for the analysis of front interactions in a parameter regime where the essential spectrum of a single front approaches the imaginary axis asymptotically.

Determination of effective moisture diffusivity of banana using thermogravimetric analysis

Drying has been extensively used as a food preservation procedure. The longer life attained by drying is however accompanied by huge energy consumption and deterioration of quality. Moisture diffusivity is an important factor that is considered essential to understand for design, analysis, and optimization of drying processes for food and other materials. Without an accurate value of moisture diffusivity, drying kinetics, energy consumption, quality attributes such as shrinkage, texture, and microstructure cannot be predicted properly. However, moisture diffusivities differ due to variation of composition and microstructure of foodstuff and drying variables. For a particular food, it changes with many factors including moisture content, water holding capacity, process variables and physiochemical attributes of food. Published information on moisture diffusivities of banana is inadequate and sometimes inconsistent due to lack of precise repeatable analysis techniques. In this work, the effective moisture diffusivity of banana was determined by Thermogravimetric Analysis (TGA), which ensures precise measurements and reproduction of experiments. A TGA Q500 V20.13 Build 39 was deployed to obtain the drying curve of the food material. It was found that effective moisture diffusivity ranged from 6.63 x10-10 to 1.03 x10-9 and 1.34 x10-10 to 6.60 x10-10 for isothermal at 70 0C and non-isothermal process respectively.These values are consistent with the value of moisture diffusivity found in the literature.

A semi-alternating direction method for a 2-D fractional FitzHugh–Nagumo monodomain model on an approximate irregular domain

A FitzHugh-Nagumo monodomain model has been used to describe the propagation of the electrical potential in heterogeneous cardiac tissue. In this paper, we consider a two-dimensional fractional FitzHugh-Nagumo monodomain model on an irregular domain. The model consists of a coupled Riesz space fractional nonlinear reaction-diffusion model and an ordinary differential equation, describing the ionic fluxes as a function of the membrane potential. Secondly, we use a decoupling technique and focus on solving the Riesz space fractional nonlinear reaction-diffusion model. A novel spatially second-order accurate semi-implicit alternating direction method (SIADM) for this model on an approximate irregular domain is proposed. Thirdly, stability and convergence of the SIADM are proved. Finally, some numerical examples are given to support our theoretical analysis and these numerical techniques are employed to simulate a two-dimensional fractional Fitzhugh-Nagumo model on both an approximate circular and an approximate irregular domain.

Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy

This article aims to fill in the gap of the second-order accurate schemes for the time-fractional subdiffusion equation with unconditional stability. Two fully discrete schemes are first proposed for the time-fractional subdiffusion equation with space discretized by finite element and time discretized by the fractional linear multistep methods. These two methods are unconditionally stable with maximum global convergence order of $O(\tau+h^{r+1})$ in the $L^2$ norm, where $\tau$ and $h$ are the step sizes in time and space, respectively, and $r$ is the degree of the piecewise polynomial space. The average convergence rates for the two methods in time are also investigated, which shows that the average convergence rates of the two methods are $O(\tau^{1.5}+h^{r+1})$. Furthermore, two improved algorithms are constrcted, they are also unconditionally stable and convergent of order $O(\tau^2+h^{r+1})$. Numerical examples are provided to verify the theoretical analysis. The comparisons between the present algorithms and the existing ones are included, which show that our numerical algorithms exhibit better performances than the known ones.