Efficient preconditioning of the method of lines for solving nonlinear two-sided space-fractional diffusion equations

A standard method for the numerical solution of partial differential equations (PDEs) is the method of lines. In this approach the PDE is discretised in space using �finite di�fferences or similar techniques, and the resulting semidiscrete problem in time is integrated using an initial value problem solver. A significant challenge when applying the method of lines to fractional PDEs is that the non-local nature of the fractional derivatives results in a discretised system where each equation involves contributions from many (possibly every) spatial node(s). This has important consequences for the effi�ciency of the numerical solver. First, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. Second, since the Jacobian matrix of the system is dense (partially or fully), methods that avoid the need to form and factorise this matrix are preferred. In this paper, we consider a nonlinear two-sided space-fractional di�ffusion equation in one spatial dimension. A key contribution of this paper is to demonstrate how an eff�ective preconditioner is crucial for improving the effi�ciency of the method of lines for solving this equation. In particular, we show how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

Composite SaaS placement and resource optimization in Cloud computing using evolutionary algorithms

Software as a Service (SaaS) is gaining more and more attention from software users and providers recently. This has raised many new challenges to SaaS providers in providing better SaaSes that suit everyone needs at minimum costs. One of the emerging approaches in tackling this challenge is by delivering the SaaS as a composite SaaS. Delivering it in such an approach has a number of benefits, including flexible offering of the SaaS functions and decreased cost of subscription for users. However, this approach also introduces new problems for SaaS resource management in a Cloud data centre. We present the problem of composite SaaS resource management in Cloud data centre, specifically on its initial placement and resource optimization problems aiming at improving the SaaS performance based on its execution time as well as minimizing the resource usage. Our approach differs from existing literature because it addresses the problems resulting from composite SaaS characteristics, where we focus on the SaaS requirements, constraints and interdependencies. The problems are tackled using evolutionary algorithms. Experimental results demonstrate the efficiency and the scalability of the proposed algorithms.

Relative entropy rate based model selection for linear hybrid system filters of uncertain nonlinear systems

Hybrid system representations have been exploited in a number of challenging modelling situations, including situations where the original nonlinear dynamics are too complex (or too imprecisely known) to be directly filtered. Unfortunately, the question of how to best design suitable hybrid system models has not yet been fully addressed, particularly in the situations involving model uncertainty. This paper proposes a novel joint state-measurement relative entropy rate based approach for design of hybrid system filters in the presence of (parameterised) model uncertainty. We also present a design approach suitable for suboptimal hybrid system filters. The benefits of our proposed approaches are illustrated through design examples and simulation studies.

Linear and nonlinear propagation of localised plasmon in metallic nanostructures

A major challenge in modern photonics and nano-optics is the diffraction limit of light which does not allow field localisation into regions with dimensions smaller than half the wavelength. Localisation of light into nanoscale regions (beyond its diffraction limit) has applications ranging from the design of optical sensors and measurement techniques with resolutions as high as a few nanometres, to the effective delivery of optical energy into targeted nanoscale regions such as quantum dots, nano-electronic and nano-optical devices. This field has become a major research direction over the last decade. The use of strongly localised surface plasmons in metallic nanostructures is one of the most promising approaches to overcome this problem. Therefore, the aim of this thesis is to investigate the linear and non-linear propagation of surface plasmons in metallic nanostructures. This thesis will focus on two main areas of plasmonic research –– plasmon nanofocusing and plasmon nanoguiding. Plasmon nanofocusing – The main aim of plasmon nanofocusing research is to focus plasmon energy into nanoscale regions using metallic nanostructures and at the same time achieve strong local field enhancement. Various structures for nanofocusing purposes have been proposed and analysed such as sharp metal wedges, tapered metal films on dielectric substrates, tapered metal rods, and dielectric V-grooves in metals. However, a number of important practical issues related to nanofocusing in these structures still remain unclear. Therefore, one of the main aims of this thesis is to address two of the most important of issues which are the coupling efficiency and heating effects of surface plasmons in metallic nanostructures. The method of analysis developed throughout this thesis is a general treatment that can be applied to a diversity of nanofocusing structures, with results shown here for the specific case of sharp metal wedges. Based on the geometrical optics approximation, it is demonstrated that the coupling efficiency from plasmons generated with a metal grating into the nanofocused symmetric or quasi-symmetric modes may vary between ~50% to ~100% depending on the structural parameters. Optimal conditions for nanofocusing with the view to minimise coupling and dissipative losses are also determined and discussed. It is shown that the temperature near the tip of a metal wedge heated by nanosecond plasmonic pulses can increase by several hundred degrees Celsius. This temperature increase is expected to lead to nonlinear effects, self-influence of the focused plasmon, and ultimately self-destruction of the metal tip. This thesis also investigates a different type of nanofocusing structure which consists of a tapered high-index dielectric layer resting on a metal surface. It is shown that the nanofocusing mechanism that occurs in this structure is somewhat different from other structures that have been considered thus far. For example, the surface plasmon experiences significant backreflection and mode transformation at a cut-off thickness. In addition, the reflected plasmon shows negative refraction properties that have not been observed in other nanofocusing structures considered to date. Plasmon nanoguiding – Guiding surface plasmons using metallic nanostructures is important for the development of highly integrated optical components and circuits which are expected to have a superior performance compared to their electronicbased counterparts. A number of different plasmonic waveguides have been considered over the last decade including the recently considered gap and trench plasmon waveguides. The gap and trench plasmon waveguides have proven to be difficult to fabricate. Therefore, this thesis will propose and analyse four different modified gap and trench plasmon waveguides that are expected to be easier to fabricate, and at the same time acquire improved propagation characteristics of the guided mode. In particular, it is demonstrated that the guided modes are significantly screened by the extended metal at the bottom of the structure. This is important for the design of highly integrated optics as it provides the opportunity to place two waveguides close together without significant cross-talk. This thesis also investigates the use of plasmonic nanowires to construct a Fabry-Pérot resonator/interferometer. It is shown that the resonance effect can be achieved with the appropriate resonator length and gap width. Typical quality factors of the Fabry- Pérot cavity are determined and explained in terms of radiative and dissipative losses. The possibility of using a nanowire resonator for the design of plasmonic filters with close to ~100% transmission is also demonstrated. It is expected that the results obtained in this thesis will play a vital role in the development of high resolution near field microscopy and spectroscopy, new measurement techniques and devices for single molecule detection, highly integrated optical devices, and nanobiotechnology devices for diagnostics of living cells.

A general method to determine sampling windows for nonlinear mixed effects models with an application to population pharmacokinetic studies

Optimal design methods have been proposed to determine the best sampling times when sparse blood sampling is required in clinical pharmacokinetic studies. However, the optimal blood sampling time points may not be feasible in clinical practice. Sampling windows, a time interval for blood sample collection, have been proposed to provide flexibility in blood sampling times while preserving efficient parameter estimation. Because of the complexity of the population pharmacokinetic models, which are generally nonlinear mixed effects models, there is no analytical solution available to determine sampling windows. We propose a method for determination of sampling windows based on MCMC sampling techniques. The proposed method attains a stationary distribution rapidly and provides time-sensitive windows around the optimal design points. The proposed method is applicable to determine sampling windows for any nonlinear mixed effects model although our work focuses on an application to population pharmacokinetic models.

Multi-objective design optimization of morphing UAV aerofoil/wing using hybridised MOGA

The paper investigates two advanced Computational Intelligence Systems (CIS) for a morphing Unmanned Aerial Vehicle (UAV) aerofoil/wing shape design optimisation. The first CIS uses Genetic Algorithm (GA) and the second CIS uses Hybridized GA (HGA) with the concept of Nash-Equilibrium to speed up the optimisation process. During the optimisation, Nash-Game will act as a pre-conditioner. Both CISs; GA and HGA, are based on Pareto optimality and they are coupled to Euler based Computational Fluid Dynamic (CFD) analyser and one type of Computer Aided Design (CAD) system during the optimisation.

Nonlinear H_infinity control of UAVs for collision avoidance in gusty environments

This paper proposes a nonlinear H_infinity controller for stabilization of velocities, attitudes and angular rates of a fixed-wing unmanned aerial vehicle (UAV) in a windy environment. The suggested controller aims to achieve a steady-state flight condition in the presence of wind gusts such that the host UAV can be maneuvered to avoid collision with other UAVs during cruise flight with safety guarantees. This paper begins with building a proper model capturing flight aerodynamics of UAVs. Then a nonlinear controller is developed with gust attenuation and rapid response properties. Simulations are conducted for the Shadow UAV to verify performance of the proposed con- troller. Comparative studies with the proportional-integral-derivative (PID) controllers demonstrate that the proposed controller exhibits great performance improvement in a gusty environment, making it suitable for integration into the design of flight control systems for cruise flight of UAVs.

Smart grid-demand side response model for optimization air conditioning

The growing demand of air-conditioning is one of the largest contributors to Australia’s overall electricity consumption. This has started to create peak load supply problems for some electricity utilities particularly in Queensland. This research aimed to develop consumer demand side response model to assist electricity consumers to mitigate peak demand on the electrical network. The model developed demand side response model to allow consumers to manage and control air conditioning for every period, it is called intelligent control. This research investigates optimal response of end-user toward electricity price for several cases in the near future, such as: no spike, spike and probability spike price cases. The results indicate the potential of the scheme to achieve energy savings, reducing electricity bills (costs) to the consumer and targeting best economic performance for electrical generation distribution and transmission.

Minimization of railhead edge stresses through shape optimization

The railhead is severely stressed under the localized wheel contact patch close to the gaps in insulated rail joints. A modified railhead profile in the vicinity of the gapped joint, through a shape optimization model based on a coupled genetic algorithm and finite element method, effectively alters the contact zone and reduces the railhead edge stress concentration significantly. Two optimization methods, a grid search method and a genetic algorithm, were employed for this optimization problem. The optimal results from these two methods are discussed and, in particular, their suitability for the rail end stress minimization problem is studied. Through several numerical examples, the optimal profile is shown to be unaffected by either the magnitude or the contact position of the loaded wheel. The numerical results are validated through a large-scale experimental study.

Optimization of human papillomavirus type 16 (HPV-16) L1 expression in plants: Comparison of the suitability of different HPV-16 L1 gene variants and different cell-compartment localization

Virus-like particle-based vaccines for high-risk human papillomaviruses (HPVs) appear to have great promise; however, cell culture-derived vaccines will probably be very expensive. The optimization of expression of different codon-optimized versions of the HPV-16 L1 capsid protein gene in plants has been explored by means of transient expression from a novel suite of Agrobacterium tumefaciens binary expression vectors, which allow targeting of recombinant protein to the cytoplasm, endoplasmic reticulum (ER) or chloroplasts. A gene resynthesized to reflect human codon usage expresses better than the native gene, which expresses better than a plant-optimized gene. Moreover, chloroplast localization allows significantly higher levels of accumulation of L1 protein than does cytoplasmic localization, whilst ER retention was least successful. High levels of L1 (>17% total soluble protein) could be produced via transient expression: the protein assembled into higher-order structures visible by electron microscopy, and a concentrated extract was highly immunogenic in mice after subcutaneous injection and elicited high-titre neutralizing antibodies. Transgenic tobacco plants expressing a human codon-optimized gene linked to a chloroplast-targeting signal expressed L1 at levels up to 11% of the total soluble protein. These are the highest levels of HPV L1 expression reported for plants: these results, and the excellent immunogenicity of the product, significantly improve the prospects of making a conventional HPV vaccine by this means. © 2007 SGM.

Optimization of chimeric HIV-1 virus-like particle production in a baculovirus-insect cell expression system

A baculovirus-insect cell expression system potentially provides the means to produce prophylactic HIV-1 virus-like particle (VLP) vaccines inexpensively and in large quantities. However, the system must be optimized to maximize yields and increase process efficiency. In this study, we optimized the production of two novel, chimeric HIV-1 VLP vaccine candidates (GagRT and GagTN) in insect cells. This was done by monitoring the effects of four specific factors on VLP expression: these were insect cell line, cell density, multiplicity of infection (MOI), and infection time. The use of western blots, Gag p24 ELISA, and four-factorial ANOVA allowed the determination of the most favorable conditions for chimeric VLP production, as well as which factors affected VLP expression most significantly. Both VLP vaccine candidates favored similar optimal conditions, demonstrating higher yields of VLPs when produced in the Trichoplusia ni Pro insect cell line, at a cell density of 1 × 106 cells/mL, and an infection time of 96 h post infection. It was found that cell density and infection time were major influencing factors, but that MOI did not affect VLP expression significantly. This work provides a potentially valuable guideline for HIV-1 protein vaccine optimization, as well as for general optimization of a baculovirus-based expression system to produce complex recombinant proteins. © 2009 American Institute of Chemical Engineers.