Non-linear principal components analysis : an alternative method for finding patterns in environmental data

The main purpose of this article is to gain an insight into the relationships between variables describing the environmental conditions of the Far Northern section of the Great Barrier Reef, Australia. Several of the variables describing these conditions had different measurement levels and often they had non-linear relationships. Using non-linear principal component analysis, it was possible to acquire an insight into these relationships. Furthermore, three geographical areas with unique environmental characteristics could be identified.

A novel identification method for ultra trace detection of biomolecules using functionalised Surface Enhanced Raman Spectroscopy (SERS)

This thesis developed a new method for measuring extremely low amounts of organic and biological molecules, using Surface enhanced Raman Spectroscopy. This method has many potential applications, e.g. medical diagnosis, public health, food provenance, antidoping, forensics and homeland security. The method development used caffeine as the small molecule example, and erythropoietin (EPO) as the large molecule. This method is much more sensitive and specific than currently used methods; rapid, simple and cost effective. The method can be used to detect target molecules in beverages and biological fluids without the usual preparation steps.

A finite volume scheme with preconditioned Lanczos method for two-dimensional space-fractional reaction–diffusion equations

Fractional differential equations have been increasingly used as a powerful tool to model the non-locality and spatial heterogeneity inherent in many real-world problems. However, a constant challenge faced by researchers in this area is the high computational expense of obtaining numerical solutions of these fractional models, owing to the non-local nature of fractional derivatives. In this paper, we introduce a finite volume scheme with preconditioned Lanczos method as an attractive and high-efficiency approach for solving two-dimensional space-fractional reaction–diffusion equations. The computational heart of this approach is the efficient computation of a matrix-function-vector product f(A)bf(A)b, where A A is the matrix representation of the Laplacian obtained from the finite volume method and is non-symmetric. A key aspect of our proposed approach is that the popular Lanczos method for symmetric matrices is applied to this non-symmetric problem, after a suitable transformation. Furthermore, the convergence of the Lanczos method is greatly improved by incorporating a preconditioner. Our approach is show-cased by solving the fractional Fisher equation including a validation of the solution and an analysis of the behaviour of the model.

Modelling airport passenger group dynamics using an agent-based method

This thesis investigates the influence of passenger group dynamics on passengers' behaviour in an international airport. A simulation model is built to analyse passengers' behaviour during airport departure processes and during an emergency event. Results from the model showed that passengers' group dynamics have significant influences on the performance and utilisation of airport services. The agent-based model also provides a convenient way to investigate the effectiveness of space design and service allocations, which may contribute to the enhancement of passenger airport experiences.

Ultra sensitive label free surface enhanced Raman spectroscopy method for the detection of biomolecules

We present a proof of concept for a novel nanosensor for the detection of ultra-trace amounts of bio-active molecules in complex matrices. The nanosensor is comprised of gold nanoparticles with an ultra-thin silica shell and antibody surface attachment, which allows for the immobilization and direct detection of bio-active molecules by surface enhanced Raman spectroscopy (SERS) without requiring a Raman label. The ultra-thin passive layer (~1.3 nm thickness) prevents competing molecules from binding non-selectively to the gold surface without compromising the signal enhancement. The antibodies attached on the surface of the nanoparticles selectively bind to the target molecule with high affinity. The interaction between the nanosensor and the target analyte result in conformational rearrangements of the antibody binding sites, leading to significant changes in the surface enhanced Raman spectra of the nanoparticles when compared to the spectra of the un-reacted nanoparticles. Nanosensors of this design targeting the bio-active compounds erythropoietin and caffeine were able to detect ultra-trace amounts the analyte to the lower quantification limits of 3.5×10−13 M and 1×10−9 M, respectively.

Two dynamic discrete choice estimation problems and simulation method solutions

This paper considers two problems that frequently arise in dynamic discrete choice problems but have not received much attention with regard to simulation methods. The first problem is how to simulate unbiased simulators of probabilities conditional on past history. The second is simulating a discrete transition probability model when the underlying dependent variable is really continuous. Both methods work well relative to reasonable alternatives in the application discussed. However, in both cases, for this application, simpler methods also provide reasonably good results.

The renormalization group: A perturbation method for the graduate curriculum

In this paper the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. Lett., 73 (1994), pp.1311-1315; Phys. Rev. E, 54 (1996), pp.376-394] is presented in a pedagogical way to increase its visibility in applied mathematics and to argue favorably for its incorporation into the corresponding graduate curriculum.The method is illustrated by some linear and nonlinear singular perturbation problems. Key word. © 2012 Society for Industrial and Applied Mathematics.

A Combined Renormalization Group-Multiple Scale Method for Singularly Perturbed Problems

This paper introduces a straightforward method to asymptotically solve a variety of initial and boundary value problems for singularly perturbed ordinary differential equations whose solution structure can be anticipated. The approach is simpler than conventional methods, including those based on asymptotic matching or on eliminating secular terms. © 2010 by the Massachusetts Institute of Technology.

Determination of battery storage capacity in energy buffer for wind farm

Design of a battery energy storage system (BESS) in a buffer scheme is examined for the purpose of attenuating the effects of unsteady input power from wind farms. The design problem is formulated as maximization of an objective function that measures the economic benefit obtainable from the dispatched power from the wind farm against the cost of the BESS. Solution to the problem results in the determination of the capacity of the BESS to ensure constant dispatched power to the connected grid, while the voltage level across the dc-link of the buffer is kept within preset limits. A computational procedure to determine the BESS capacity and the evaluation of the dc voltage is shown. Illustrative examples using the proposed design method are included.