Asymptotic and numerical results for a model of solvent-dependent drug diffusion through polymeric spheres

A model for drug diffusion from a spherical polymeric drug delivery device is considered. The model contains two key features. The first is that solvent diffuses into the polymer, which then transitions from a glassy to a rubbery state. The interface between the two states of polymer is modelled as a moving boundary, whose speed is governed by a kinetic law; the same moving boundary problem arises in the one-phase limit of a Stefan problem with kinetic undercooling. The second feature is that drug diffuses only through the rubbery region, with a nonlinear diffusion coefficient that depends on the concentration of solvent. We analyse the model using both formal asymptotics and numerical computation, the latter by applying a front-fixing scheme with a finite volume method. Previous results are extended and comparisons are made with linear models that work well under certain parameter regimes. Finally, a model for a multi-layered drug delivery device is suggested, which allows for more flexible control of drug release.

Path planning, guidance and control for a UAV forced landing

A forced landing is an unscheduled event in flight requiring an emergency landing, and is most commonly attributed to engine failure, failure of avionics or adverse weather. Since the ability to conduct a successful forced landing is the primary indicator for safety in the aviation industry, automating this capability for unmanned aerial vehicles (UAVs) will help facilitate their integration into, and subsequent routine operations over civilian airspace. Currently, there is no commercial system available to perform this task; however, a team at the Australian Research Centre for Aerospace Automation (ARCAA) is working towards developing such an automated forced landing system. This system, codenamed Flight Guardian, will operate onboard the aircraft and use machine vision for site identification, artificial intelligence for data assessment and evaluation, and path planning, guidance and control techniques to actualize the landing. This thesis focuses on research specific to the third category, and presents the design, testing and evaluation of a Trajectory Generation and Guidance System (TGGS) that navigates the aircraft to land at a chosen site, following an engine failure. Firstly, two algorithms are developed that adapts manned aircraft forced landing techniques to suit the UAV planning problem. Algorithm 1 allows the UAV to select a route (from a library) based on a fixed glide range and the ambient wind conditions, while Algorithm 2 uses a series of adjustable waypoints to cater for changing winds. A comparison of both algorithms in over 200 simulated forced landings found that using Algorithm 2, twice as many landings were within the designated area, with an average lateral miss distance of 200 m at the aimpoint. These results present a baseline for further refinements to the planning algorithms. A significant contribution is seen in the design of the 3-D Dubins Curves planning algorithm, which extends the elementary concepts underlying 2-D Dubins paths to account for powerless flight in three dimensions. This has also resulted in the development of new methods in testing for path traversability, in losing excess altitude, and in the actual path formation to ensure aircraft stability. Simulations using this algorithm have demonstrated lateral and vertical miss distances of under 20 m at the approach point, in wind speeds of up to 9 m/s. This is greater than a tenfold improvement on Algorithm 2 and emulates the performance of manned, powered aircraft. The lateral guidance algorithm originally developed by Park, Deyst, and How (2007) is enhanced to include wind information in the guidance logic. A simple assumption is also made that reduces the complexity of the algorithm in following a circular path, yet without sacrificing performance. Finally, a specific method of supplying the correct turning direction is also used. Simulations have shown that this new algorithm, named the Enhanced Nonlinear Guidance (ENG) algorithm, performs much better in changing winds, with cross-track errors at the approach point within 2 m, compared to over 10 m using Park's algorithm. A fourth contribution is made in designing the Flight Path Following Guidance (FPFG) algorithm, which uses path angle calculations and the MacCready theory to determine the optimal speed to fly in winds. This algorithm also uses proportional integral- derivative (PID) gain schedules to finely tune the tracking accuracies, and has demonstrated in simulation vertical miss distances of under 2 m in changing winds. A fifth contribution is made in designing the Modified Proportional Navigation (MPN) algorithm, which uses principles from proportional navigation and the ENG algorithm, as well as methods specifically its own, to calculate the required pitch to fly. This algorithm is robust to wind changes, and is easily adaptable to any aircraft type. Tracking accuracies obtained with this algorithm are also comparable to those obtained using the FPFG algorithm. For all three preceding guidance algorithms, a novel method utilising the geometric and time relationship between aircraft and path is also employed to ensure that the aircraft is still able to track the desired path to completion in strong winds, while remaining stabilised. Finally, a derived contribution is made in modifying the 3-D Dubins Curves algorithm to suit helicopter flight dynamics. This modification allows a helicopter to autonomously track both stationary and moving targets in flight, and is highly advantageous for applications such as traffic surveillance, police pursuit, security or payload delivery. Each of these achievements serves to enhance the on-board autonomy and safety of a UAV, which in turn will help facilitate the integration of UAVs into civilian airspace for a wider appreciation of the good that they can provide. The automated UAV forced landing planning and guidance strategies presented in this thesis will allow the progression of this technology from the design and developmental stages, through to a prototype system that can demonstrate its effectiveness to the UAV research and operations community.

The impact of nonlinear exposure risk relationships on seasonal time series data: modelling danish neonatal birth anthropometric data

Background Birth weight and length have seasonal fluctuations. Previous analyses of birth weight by latitude effects identified seemingly contradictory results, showing both 6 and 12 monthly periodicities in weight. The aims of this paper are twofold: (a) to explore seasonal patterns in a large, Danish Medical Birth Register, and (b) to explore models based on seasonal exposures and a non-linear exposure-risk relationship. Methods Birth weight and birth lengths on over 1.5 million Danish singleton, live births were examined for seasonality. We modelled seasonal patterns based on linear, U- and J-shaped exposure-risk relationships. We then added an extra layer of complexity by modelling weighted population-based exposure patterns. Results The Danish data showed clear seasonal fluctuations for both birth weight and birth length. A bimodal model best fits the data, however the amplitude of the 6 and 12 month peaks changed over time. In the modelling exercises, U- and J-shaped exposure-risk relationships generate time series with both 6 and 12 month periodicities. Changing the weightings of the population exposure risks result in unexpected properties. A J-shaped exposure-risk relationship with a diminishing population exposure over time fitted the observed seasonal pattern in the Danish birth weight data. Conclusion In keeping with many other studies, Danish birth anthropometric data show complex and shifting seasonal patterns. We speculate that annual periodicities with non-linear exposure-risk models may underlie these findings. Understanding the nature of seasonal fluctuations can help generate candidate exposures.

Position, rotation, and scale invariant recognition of images using higher-order spectra

A new approach to recognition of images using invariant features based on higher-order spectra is presented. Higher-order spectra are translation invariant because translation produces linear phase shifts which cancel. Scale and amplification invariance are satisfied by the phase of the integral of a higher-order spectrum along a radial line in higher-order frequency space because the contour of integration maps onto itself and both the real and imaginary parts are affected equally by the transformation. Rotation invariance is introduced by deriving invariants from the Radon transform of the image and using the cyclic-shift invariance property of the discrete Fourier transform magnitude. Results on synthetic and actual images show isolated, compact clusters in feature space and high classification accuracies

Numerical analysis for a variable-order nonlinear cable equation

In this paper, a variable-order nonlinear cable equation is considered. A numerical method with first-order temporal accuracy and fourth-order spatial accuracy is proposed. The convergence and stability of the numerical method are analyzed by Fourier analysis. We also propose an improved numerical method with second-order temporal accuracy and fourth-order spatial accuracy. Finally, the results of a numerical example support the theoretical analysis.

Higher-order spectral analysis of nonlinear ocean surface gravity waves

Higher-order spectral analysis is used to detect the presence of secondary and tertiary forced waves associated with the nonlinearity of energetic swell observed in 8- and 13-m water depths. Higher-order spectral analysis techniques are first described and then applied to the field data, followed by a summary of the results.

Higher-Order spectra of nonlinear polynomial models for Chua's circuit

Polynomial models are shown to simulate accurately the quadratic and cubic nonlinear interactions (e.g. higher-order spectra) of time series of voltages measured in Chua's circuit. For circuit parameters resulting in a spiral attractor, bispectra and trispectra of the polynomial model are similar to those from the measured time series, suggesting that the individual interactions between triads and quartets of Fourier components that govern the process dynamics are modeled accurately. For parameters that produce the double-scroll attractor, both measured and modeled time series have small bispectra, but nonzero trispectra, consistent with higher-than-second order nonlinearities dominating the chaos.

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.

Instantaneous phase of the autocorrelation and robustness to signal-dependent noise

The phase of an analytic signal constructed from the autocorrelation function of a signal contains significant information about the shape of the signal. Using Bedrosian's (1963) theorem for the Hilbert transform it is proved that this phase is robust to multiplicative noise if the signal is baseband and the spectra of the signal and the noise do not overlap. Higher-order spectral features are interpreted in this context and shown to extract nonlinear phase information while retaining robustness. The significance of the result is that prior knowledge of the spectra is not required.

A nonlinear PI and backstepping based controller for tractor-steerable trailer influenced by slip

Autonomous guidance of agricultural vehiclesis vital as mechanized farming production becomes more prevalent. It is crucial that tractor-trailers are guided with accuracy in both lateral and longitudinal directions, whilst being affected by large disturbance forces, or slips, owing to uncertain and undulating terrain. Successful research has been concentrated on trajectory control which can provide longitudinal and lateral accuracy if the vehicle moves without sliding, and the trailer is passive. In this paper, the problem of robust trajectory tracking along straight and circular paths of a tractor-steerable trailer is addressed. By utilizing a robust combination of backstepping and nonlinear PI control, a robust, nonlinear controller is proposed. For vehicles subjected to sliding, the proposed controller makes the lateral deviations and the orientation errors of the tractor and trailer converge to a neighborhood near the origin. Simulation results are presented to illustrate that the suggested controller ensures precise trajectory tracking in the presence of slip.