Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation

Anomalous subdiffusion equations have in recent years received much attention. In this paper, we consider a two-dimensional variable-order anomalous subdiffusion equation. Two numerical methods (the implicit and explicit methods) are developed to solve the equation. Their stability, convergence and solvability are investigated by the Fourier method. Moreover, the effectiveness of our theoretical analysis is demonstrated by some numerical examples. © 2011 American Mathematical Society.

Monocular amblyopia and higher order aberrations

This study compared the corneal and total higher order aberrations between the fellow eyes in monocular amblyopia. Nineteen amblyopic subjects (8 refractive and 11 strabismic) (mean age 30 ± 11 years) were recruited. A range of biometric and optical measurements were collected from the amblyopic and non-amblyopic eye including; axial length, corneal topography and total higher order aberrations. For a sub-group of eleven non-presbyopic subjects (6 refractive and 5 strabismic amblyopes, mean age 29 ± 10 years) total higher order aberrations were also measured during accommodation (2.5 D stimuli). Amblyopic eyes were significantly shorter and more hyperopic compared to non-amblyopic eyes and the interocular difference in axial length correlated with both the magnitude of anisometropia and amblyopia (both p < 0.01). Significant differences in higher order aberrations were observed between fellow eyes, which varied with the type of amblyopia. Refractive amblyopes displayed higher levels of 4th order corneal aberrations C(4, 0)(spherical aberration), C(4, 2)(secondary astigmatism 90°) and C(4, −2)(secondary astigmatism along 45°) in the amblyopic eye compared to the non-amblyopic eye. Strabismic amblyopes exhibited significantly higher levels of C(3, 3)(trefoil) in the amblyopic eye for both corneal and total higher order aberrations. During accommodation, the amblyopic eye displayed a significantly greater lag of accommodation compared to the non-amblyopic eye, while the changes in higher order aberrations were similar in magnitude between fellow eyes. Asymmetric visual experience during development appears to be associated with asymmetries in higher order aberrations, in some cases proportional to the magnitude of anisometropia and dependent upon the amblyogenic factor.

Corneal nerve structure and function as markers of diabetic neuropathy

Diabetic neuropathy is a significant clinical problem that currently has no effective therapy, and in advanced cases, leads to foot ulceration and lower limb amputation. The accurate detection, characterisation and quantification of this condition are important in order to define at-risk patients, anticipate deterioration, monitor progression and assess new therapies. This thesis evaluates novel corneal methods of assessing diabetic neuropathy. Over the past several years two new non-invasive corneal markers have emerged, and in cross-sectional studies have demonstrated their ability to stratify the severity of this disease. Corneal confocal microscopy (CCM) allows quantification of corneal nerve parameters and non-contact corneal aesthesiometry (NCCA), the presumed functional correlate of corneal structure, assesses the sensitivity of the cornea. Both these techniques are quick to perform, produce little or no discomfort for the patient, and with automatic analysis paradigms developed, are suitable for clinical settings. Each has advantages and disadvantages over established techniques for assessing diabetic neuropathy. New information is presented regarding measurement bias of CCM images, and a unique sampling paradigm and associated accuracy determination method of combinations is described. A novel high-speed corneal nerve mapping procedure has been developed and application of this procedure in individuals with neuropathy has revealed regions of sub-basal nerve plexus that dictate further evaluation, as they appear to show earlier signs of damage than the central region of the cornea that has to date been examined. The discriminative capacity of corneal sensitivity measured by NCCA is revealed to have reasonable potential as a marker of diabetic neuropathy. Application of these new corneal markers for longitudinal evaluation of diabetic neuropathy has the potential to reduce dependence on more invasive, costly, and time-consuming assessments, such as skin biopsy.

Assessment of “change in flexibility method” in structural health monitoring systems

The modern structural diagnosis process is rely on vibration characteristics to assess safer serviceability level of the structure. This paper examines the potential of change in flexibility method to use in damage detection process and two main practical constraints associated with it. The first constraint addressed in this paper is reduction in number of data acquisition points due to limited number of sensors. Results conclude that accuracy of the change in flexibility method is influenced by the number of data acquisition points/sensor locations in real structures. Secondly, the effect of higher modes on damage detection process has been studied. This addresses the difficulty of extracting higher order modal data with available sensors. Four damage indices have been presented to identify their potential of damage detection with respect to different locations and severity of damage. A simply supported beam with two degrees of freedom at each node is considered only for a single damage cases throughout the paper.

Too sleepy to drive : self-perception and regulation of driving when sleepy

Background: Sleepiness is a direct contributor to a substantial proportion of fatal and severe road cashes. A number of technological solutions designed to detect sleepiness have been developed, but self-awareness of increasing sleepiness remains a critical component in on-road strategies for mitigating this risk. In order to take appropriate action when sleepy, drivers’ perceptions of their level of sleepiness must be accurate. Aims: This study aimed to assess capacity to accurately identify sleepiness and self-regulate driving cessation during a validated driving simulator task. Participants: Participants comprised 26 young adult drivers (20-28 years). The drivers had open licenses but no other exclusion criteria where used. Methods: Participants woke at 5am, and took part in a laboratory-based hazard perception driving simulation, either at mid-morning or mid-afternoon. Established physiological measures (including EEG) and subjective measures (sleepiness ratings) previously found sensitive to changes in sleepiness levels were utilised. Participants were instructed to ‘drive’ until they believed that sleepiness had impaired their ability to drive safely. They were then offered a nap opportunity. Results: The mean duration of the drive before cessation was 39 minutes (±18 minutes). Almost all (23/26) of the participants then achieved sleep during the nap opportunity. These data suggest that the participants’ perceptions of sleepiness were specific. However, EEG data from a number of participants suggested very high levels of sleepiness prior to driving cessation, suggesting poor sensitivity. Conclusions: Participants reported high levels of sleepiness while driving after very moderate sleep restriction. They were able to identify increasing sleepiness during the test period, could decide to cease driving and in most cases were sufficiently sleepy to achieve sleep during the daytime session. However, the levels of sleepiness achieved prior to driving cessation suggest poor accuracy in self-perception and regulation. This presents practical issues for the implementation of fatigue and sleep-related strategies to improve driver safety.

A least squares based finite volume method for the Cahn-Hilliard and Cahn-Hilliard-reaction equations

A vertex-centred finite volume method (FVM) for the Cahn-Hilliard (CH) and recently proposed Cahn-Hilliard-reaction (CHR) equations is presented. Information at control volume faces is computed using a high-order least-squares approach based on Taylor series approximations. This least-squares problem explicitly includes the variational boundary condition (VBC) that ensures that the discrete equations satisfy all of the boundary conditions. We use this approach to solve the CH and CHR equations in one and two dimensions and show that our scheme satisfies the VBC to at least second order. For the CH equation we show evidence of conservative, gradient stable solutions, however for the CHR equation, strict gradient-stability is more challenging to achieve.

An investigation on the accuracy of regional ocean models through field trials

Recent efforts in mission planning for underwater vehicles have utilised predictive models to aid in navigation, optimal path planning and drive opportunistic sampling. Although these models provide information at a unprecedented resolutions and have proven to increase accuracy and effectiveness in multiple campaigns, most are deterministic in nature. Thus, predictions cannot be incorporated into probabilistic planning frameworks, nor do they provide any metric on the variance or confidence of the output variables. In this paper, we provide an initial investigation into determining the confidence of ocean model predictions based on the results of multiple field deployments of two autonomous underwater vehicles. For multiple missions conducted over a two-month period in 2011, we compare actual vehicle executions to simulations of the same missions through the Regional Ocean Modeling System in an ocean region off the coast of southern California. This comparison provides a qualitative analysis of the current velocity predictions for areas within the selected deployment region. Ultimately, we present a spatial heat-map of the correlation between the ocean model predictions and the actual mission executions. Knowing where the model provides unreliable predictions can be incorporated into planners to increase the utility and application of the deterministic estimations.