Pulse dynamics in a three-component system : stability and bifurcations

In this article, we analyze the stability and the associated bifurcations of several types of pulse solutions in a singularly perturbed three-component reaction-diffusion equation that has its origin as a model for gas discharge dynamics. Due to the richness and complexity of the dynamics generated by this model, it has in recent years become a paradigm model for the study of pulse interactions. A mathematical analysis of pulse interactions is based on detailed information on the existence and stability of isolated pulse solutions. The existence of these isolated pulse solutions is established in previous work. Here, the pulse solutions are studied by an Evans function associated to the linearized stability problem. Evans functions for stability problems in singularly perturbed reaction-diffusion models can be decomposed into a fast and a slow component, and their zeroes can be determined explicitly by the NLEP method. In the context of the present model, we have extended the NLEP method so that it can be applied to multi-pulse and multi-front solutions of singularly perturbed reaction-diffusion equations with more than one slow component. The brunt of this article is devoted to the analysis of the stability characteristics and the bifurcations of the pulse solutions. Our methods enable us to obtain explicit, analytical information on the various types of bifurcations, such as saddle-node bifurcations, Hopf bifurcations in which breathing pulse solutions are created, and bifurcations into travelling pulse solutions, which can be both subcritical and supercritical.

Child car restraints : mandating type and seating row according to age with positive effect in regional city in Queensland, Australia

Road trauma is a leading cause of child injury worldwide. In highly motorised countries, injury as a passenger represents a major proportion of all child road deaths and hospitalisations. Australia is no exception, particularly since there are high levels of private motor vehicle travel to school in most Australian states. Recently the legislation governing the type of car restraints required for children aged under 7 years has changed in Australia, aligning requirements better with accepted best practice. However, it is unclear what effect these changes have had on children’s seating positions or the types of restraints used. A mixed methods evaluation of the impact of the new legislation on compliance was conducted at three times: baseline (Time 1); after announcement that changes were going to be implemented but before enforcement began (Time 2); and after enforcement commenced (Time 3). Measures of compliance were obtained using two methods: road-side observations of vehicles with child passengers; and parental self-report (intercept interviews conducted at Time 2 and Time 3 only). Results from the observations suggested an overall positive effect. Proportions of children occupying front seats decreased overall and use of dedicated child seats increased to almost 40% of the observed children by Time 3. However, almost a quarter of the children observed still occupied front seats. These results differed from those of the interview study where almost no children were reported as usually travelling in the front seat, and reported use of dedicated restraints with children was almost 90%, over twice that of the observations.

Computational experiments involving population size for FPGA-based implementation of a GA for the TSP

The feasibility of using an in-hardware implementation of a genetic algorithm (GA) to solve the computationally expensive travelling salesman problem (TSP) is explored, especially in regard to hardware resource requirements for problem and population sizes. We investigate via numerical experiments whether a small population size might prove sufficient to obtain reasonable quality solutions for the TSP, thereby permitting relatively resource efficient hardware implementation on field programmable gate arrays (FPGAs). Software experiments on two TSP benchmarks involving 48 and 532 cities were used to explore the extent to which population size can be reduced without compromising solution quality, and results show that a GA allowed to run for a large number of generations with a smaller population size can yield solutions of comparable quality to those obtained using a larger population. This finding is then used to investigate feasible problem sizes on a targeted Virtex-7 vx485T-2 FPGA platform via exploration of hardware resource requirements for memory and data flow operations.

A comparison of calculated and experimental HRTEM images of twinned boron carbide

High resolution TEM images of boron carbide (B13C2) have been recorded and compared with images calculated using the multislice method as implemented by M. A. O'Keefe in the SHRLI programs. Images calculated for the [010] zone, using machine parameters for the JEOL 2000FX AEM operating at 200 keV, indicate that for the structure model of Will et al., the optimum defocus image can be interpreted such that white spots correspond to B12 icosahedra for thin specimens and to low density channels through the structure adjacent to the direct inter-icosahedral bonds for specimens of intermediate thickness (-40 > t > -100 nm). With this information, and from the symmetry observed in the TEM images, it is likely that the (101) twin plane passes through the center of icosahedron located at the origin. This model was tested using the method of periodic continuation. Resulting images compare favorably with experimental images, thus supporting the structural model. The introduction of a (101) twin plane through the origin creates distortions to the icosahedral linkages as well as to the intra-icosahedral bonding. This increases the inequivalence of adjacent icosahedral sites along the twin plane, and thereby increases the likelihood of bipolaron hopping.

Position, privacy and personnel : concerns for the (digital) future

Firms are moving away from decentralized regional offices. Last year the author spoke with a valuer working on the Sunshine Coast for a Brisbane firm. In years past this valuer would have left home in the morning to go to the office, as well as travelling during the day to client sites. Now they get up, have breakfast, change out of their pyjamas (if they have meetings!) and walk into their employer set-up home office to ‘punch-in’. Apart from travel for essential meetings at head office, or for the purpose of on-site inspections, they can attend work, engage with colleagues and clients and never leave home. While this practice may be a cost saving to the firm and a commuter-friendly way of working, it raises a range of issues to be managed.

Effects of changes to child car restraint legislation in Australia on seating position and restraint use

Road trauma is a leading cause of child injury worldwide and in highly motorised countries, injury as a passenger represents a major proportion of all child road deaths and hospitalisations. Australia is no exception, particularly since motorised transport to school is at high levels in most Australian states. Recently the legislation governing the type of car restraints required for children aged under 7 years has changed in most Australian states aligning requirements better with accepted best practice. However, it is unclear what effect these changes have had on children’s seating positions or the types of restraints used. A mixed methods evaluation of the impact of the new legislation on compliance was conducted at three times: baseline (Time 1); after announcement that changes were going to be implemented but before enforcement began (Time 2); and after enforcement commenced (Time 3). Measures of compliance were obtained using two methods: road-side observations of vehicles with child passengers; and parental self-report (intercept interviews conducted at Time 2 and Time 3 only). Results from the observations suggested an overall positive effect. Proportions of children occupying front seats decreased overall and use of dedicated child seas increased to almost 40% of the observed children by Time 3. However, almost a quarter of the children observed were still occupying the front seat. These results were very different from those of the interview study where almost no children were reported as usually travelling in the front seat, and the reported use of dedicated restraints with children was almost 90%, more than twice that in the observations.

Breast cancer detection from thermal images using bispectral invariant features

Highly sensitive infrared (IR) cameras provide high-resolution diagnostic images of the temperature and vascular changes of breasts. These images can be processed to emphasize hot spots that exhibit early and subtle changes owing to pathology. The resulting images show clusters that appear random in shape and spatial distribution but carry class dependent information in shape and texture. Automated pattern recognition techniques are challenged because of changes in location, size and orientation of these clusters. Higher order spectral invariant features provide robustness to such transformations and are suited for texture and shape dependent information extraction from noisy images. In this work, the effectiveness of bispectral invariant features in diagnostic classification of breast thermal images into malignant, benign and normal classes is evaluated and a phase-only variant of these features is proposed. High resolution IR images of breasts, captured with measuring accuracy of ±0.4% (full scale) and temperature resolution of 0.1 °C black body, depicting malignant, benign and normal pathologies are used in this study. Breast images are registered using their lower boundaries, automatically extracted using landmark points whose locations are learned during training. Boundaries are extracted using Canny edge detection and elimination of inner edges. Breast images are then segmented using fuzzy c-means clustering and the hottest regions are selected for feature extraction. Bispectral invariant features are extracted from Radon projections of these images. An Adaboost classifier is used to select and fuse the best features during training and then classify unseen test images into malignant, benign and normal classes. A data set comprising 9 malignant, 12 benign and 11 normal cases is used for evaluation of performance. Malignant cases are detected with 95% accuracy. A variant of the features using the normalized bispectrum, which discards all magnitude information, is shown to perform better for classification between benign and normal cases, with 83% accuracy compared to 66% for the original.

A comprehensive investigation of the risky driving behaviour of young novice drivers

Young novice drivers - that is, drivers aged 16-25 years who are relatively inexperienced in driving on the road and have a novice (Learner, Provisional) driver's licence - have been overrepresented in car crash, injury and fatality statistics around the world for decades. There are numerous persistent characteristics evident in young novice driver crashes, fatalities and offences, including variables relating to the young driver themselves, broader social influences which include their passengers, the car they drive, and when and how they drive, and their risky driving behaviour in particular. Moreover, there are a range of psychosocial factors influencing the behaviour of young novice drivers, including the social influences of parents and peers, and person-related factors such as age-related factors, attitudes, and sensation seeking. Historically, a range of approaches have been developed to manage the risky driving behaviour of young novice drivers. Traditional measures predominantly relying upon education have had limited success in regulating the risky driving behaviour of the young novice driver. In contrast, interventions such as graduated driver licensing (GDL) which acknowledges young novice drivers' limitations - principally pertaining to their chronological and developmental age, and their driving inexperience - have shown to be effective in ameliorating this pervasive public health problem. In practice, GDL is a risk management tool that is designed to reduce driving at risky times (e.g., at night) or in risky driving conditions (e.g., with passengers), while still enabling novice drivers to obtain experience. In this regard, the GDL program in Queensland, Australia, was considerably enhanced in July 2007, and major additions to the program include mandated Learner practice of 100 hours recorded in a logbook, and passenger limits during night driving in the Provisional phase. Road safety researchers have also continued to consider the influential role played by the young driver's psychosocial characteristics, including psychological traits and states. In addition, whilst the majority of road safety user research is epidemiological in nature, contemporary road safety research is increasingly applying psychological and criminological theories. Importantly, such theories not only can guide young novice driver research, they can also inform the development and evaluation of countermeasures targeting their risky driving behaviour. The research is thus designed to explore the self-reported behaviours - and the personal, psychosocial, and structural influences upon the behaviours - of young novice drivers This thesis incorporates three stages of predominantly quantitative research to undertake a comprehensive investigation of the risky driving behaviour of young novices. Risky driving behaviour increases the likelihood of the young novice driver being involved in a crash which may harm themselves or other road users, and deliberate risky driving such as driving in excess of the posted speed limits is the focus of the program of research. The extant literature examining the nature of the risky behaviour of the young novice driver - and the contributing factors for this behaviour - while comprehensive, has not led to the development of a reliable instrument designed specifically to measure the risky behaviour of the young novice driver. Therefore the development and application of such a tool (the Behaviour of Young Novice Drivers Scale, or BYNDS) was foremost in the program of research. In addition to describing the driving behaviours of the young novice, a central theme of this program of research was identifying, describing, and quantifying personal, behavioural, and environmental influences upon young novice driver risky behaviour. Accordingly the 11 papers developed from the three stages of research which comprise this thesis are framed within Bandura's reciprocal determinism model which explicitly considers the reciprocal relationship between the environment, the person, and their behaviour. Stage One comprised the foundation research and operationalised quantitative and qualitative methodologies to finalise the instrument used in Stages Two and Three. The first part of Stage One involved an online survey which was completed by 761 young novice drivers who attended tertiary education institutions across Queensland. A reliable instrument for measuring the risky driving behaviour of young novices was developed (the BYNDS) and is currently being operationalised in young novice driver research in progress at the Centre for Injury Research and Prevention in Philadelphia, USA. In addition, regression analyses revealed that psychological distress influenced risky driving behaviour, and the differential influence of depression, anxiety, sensitivity to punishments and rewards, and sensation seeking propensity were explored. Path model analyses revealed that punishment sensitivity was mediated by anxiety and depression; and the influence of depression, anxiety, reward sensitivity and sensation seeking propensity were moderated by the gender of the driver. Specifically, for males, sensation seeking propensity, depression, and reward sensitivity were predictive of self-reported risky driving, whilst for females anxiety was also influential. In the second part of Stage One, 21 young novice drivers participated in individual and small group interviews. The normative influences of parents, peers, and the Police were explicated. Content analysis supported four themes of influence through punishments, rewards, and the behaviours and attitudes of parents and friends. The Police were also influential upon the risky driving behaviour of young novices. The findings of both parts of Stage One informed the research of Stage Two. Stage Two was a comprehensive investigation of the pre-Licence and Learner experiences, attitudes, and behaviours, of young novice drivers. In this stage, 1170 young novice drivers from across Queensland completed an online or paper survey exploring their experiences, behaviours and attitudes as a pre- and Learner driver. The majority of novices did not drive before they were licensed (pre-Licence driving) or as an unsupervised Learner, submitted accurate logbooks, intended to follow the road rules as a Provisional driver, and reported practicing predominantly at the end of the Learner period. The experience of Learners in the enhanced-GDL program were also examined and compared to those of Learner drivers who progressed through the former-GDL program (data collected previously by Bates, Watson, & King, 2009a). Importantly, current-GDL Learners reported significantly more driving practice and a longer Learner period, less difficulty obtaining practice, and less offence detection and crash involvement than Learners in the former-GDL program. The findings of Stage Two informed the research of Stage Three. Stage Three was a comprehensive exploration of the driving experiences, attitudes and behaviours of young novice drivers during their first six months of Provisional 1 licensure. In this stage, 390 of the 1170 young novice drivers from Stage Two completed another survey, and data collected during Stages Two and Three allowed a longitudinal investigation of self-reported risky driving behaviours, such as GDL-specific and general road rule compliance; risky behaviour such as pre-Licence driving, crash involvement and offence detection; and vehicle ownership, paying attention to Police presence, and punishment avoidance. Whilst the majority of Learner and Provisional drivers reported compliance with GDL-specific and general road rules, 33% of Learners and 50% of Provisional drivers reported speeding by 10-20 km/hr at least occasionally. Twelve percent of Learner drivers reported pre-Licence driving, and these drivers were significantly more risky as Learner and Provisional drivers. Ten percent of males and females reported being involved in a crash, and 10% of females and 18% of males had been detected for an offence, within the first six months of independent driving. Additionally, 75% of young novice drivers reported owning their own car within six months of gaining their Provisional driver's licence. Vehicle owners reported significantly shorter Learner periods and more risky driving exposure as a Provisional driver. Paying attention to Police presence on the roads appeared normative for young novice drivers: 91% of Learners and 72% of Provisional drivers reported paying attention. Provisional drivers also reported they actively avoided the Police: 25% of males and 13% of females; 23% of rural drivers and 15% of urban drivers. Stage Three also allowed the refinement of the risky behaviour measurement tool (BYNDS) created in Stage One; the original reliable 44-item instrument was refined to a similarly reliable 36-item instrument. A longitudinal exploration of the influence of anxiety, depression, sensation seeking propensity and reward sensitivity upon the risky behaviour of the Provisional driver was also undertaken using data collected in Stages Two and Three. Consistent with the research of Stage One, structural equation modeling revealed anxiety, reward sensitivity and sensation seeking propensity predicted self-reported risky driving behaviour. Again, gender was a moderator, with only reward sensitivity predicting risky driving for males. A measurement model of Akers' social learning theory (SLT) was developed containing six subscales operationalising the four constructs of differential association, imitation, personal attitudes, and differential reinforcement, and the influence of parents and peers was captured within the items in a number of these constructs. Analyses exploring the nature and extent of the psychosocial influences of personal characteristics (step 1), Akers' SLT (step 2), and elements of the prototype/willingness model (PWM) (step 3) upon self-reported speeding by the Provisional driver in a hierarchical multiple regression model found the following significant predictors: gender (male), car ownership (own car), reward sensitivity (greater sensitivity), depression (greater depression), personal attitudes (more risky attitudes), and speeding (more speeding) as a Learner. The research findings have considerable implications for road safety researchers, policy-makers, mental health professionals and medical practitioners alike. A broad range of issues need to be considered when developing, implementing and evaluating interventions for both the intentional and unintentional risky driving behaviours of interest. While a variety of interventions have been historically utilised, including education, enforcement, rehabilitation and incentives, caution is warranted. A multi-faceted approach to improving novice road safety is more likely to be effective, and new and existing countermeasures should capitalise on the potential of parents, peers and Police to be a positive influence upon the risky behaviour of young novice drivers. However, the efficacy of some interventions remains undetermined at this time. Notwithstanding this caveat, countermeasures such as augmenting and strengthening Queensland's GDL program and targeting parents and adolescents particularly warrant further attention. The findings of the research program suggest that Queensland's current-GDL can be strengthened by increasing compliance of young novice drivers with existing conditions and restrictions. The rates of speeding reported by the young Learner driver are particularly alarming for a number of reasons. The Learner is inexperienced in driving, and travelling in excess of speed limits places them at greater risk as they are also inexperienced in detecting and responding appropriately to driving hazards. In addition, the Learner period should provide the foundation for a safe lifetime driving career, enabling the development and reinforcement of non-risky driving habits. Learners who sped reported speeding by greater margins, and at greater frequencies, when they were able to drive independently. Other strategies could also be considered to enhance Queensland's GDL program, addressing both the pre-Licence adolescent and their parents. Options that warrant further investigation to determine their likely effectiveness include screening and treatment of novice drivers by mental health professionals and/or medical practitioners; and general social skills training. Considering the self-reported pre-licence driving of the young novice driver, targeted education of parents may need to occur before their child obtains a Learner licence. It is noteworthy that those participants who reported risky driving during the Learner phase also were more likely to report risky driving behaviour during the Provisional phase; therefore it appears vital that the development of safe driving habits is encouraged from the beginning of the novice period. General education of parents and young novice drivers should inform them of the considerably-increased likelihood of risky driving behaviour, crashes and offences associated with having unlimited access to a vehicle in the early stages of intermediate licensure. Importantly, parents frequently purchase the car that is used by the Provisional driver, who typically lives at home with their parents, and therefore parents are ideally positioned to monitor the journeys of their young novice driver during this early stage of independent driving. Parents are pivotal in the development of their driving child: they are models who are imitated and are sources of attitudes, expectancies, rewards and punishments; and they provide the most driving instruction for the Learner. High rates of self-reported speeding by Learners suggests that GDL programs specifically consider the nature of supervision during the Learner period, encouraging supervisors to be vigilant to compliance with general and GDL-specific road rules, and especially driving in excess of speed limit. Attitudes towards driving are formed before the adolescent reaches the age when they can be legally licensed. Young novice drivers with risky personal attitudes towards driving reported more risky driving behaviour, suggesting that countermeasures should target such attitudes and that such interventions might be implemented before the adolescent is licensed. The risky behaviours and attitudes of friends were also found to be influential, and given that young novice drivers tend to carry their friends as their passengers, a group intervention such as provided in a school class context may prove more effective. Social skills interventions that encourage the novice to resist the negative influences of their friends and their peer passengers, and to not imitate the risky driving behaviour of their friends, may also be effective. The punishments and rewards anticipated from and administered by friends were also found to influence the self-reported risky behaviour of the young novice driver; therefore young persons could be encouraged to sanction the risky, and to reward the non-risky, driving of their novice friends. Adolescent health programs and related initiatives need to more specifically consider the risks associated with driving. Young novice drivers are also adolescents, a developmental period associated with depression and anxiety. Depression, anxiety, and sensation seeking propensity were found to be predictive of risky driving; therefore interventions targeting psychological distress, whilst discouraging the expression of sensation seeking propensity whilst driving, warrant development and trialing. In addition, given that reward sensitivity was also predictive, a scheme which rewards novice drivers for safe driving behaviour - rather than rewarding the novice through emotional and instrumental rewards for risky driving behaviour - requires further investigation. The Police were also influential in the risky driving behaviour of young novices. Young novice drivers who had been detected for an offence, and then avoided punishment, reacted differentially, with some drivers appearing to become less risky after the encounter, whilst for others their risky behaviour appeared to be reinforced and therefore was more likely to be performed again. Such drivers saw t

Gravity-driven fingering simulations for a thin liquid film flowing down the outside of a vertical cylinder

A numerical study is presented to examine the fingering instability of a gravity-driven thin liquid film flowing down the outer wall of a vertical cylinder. The lubrication approximation is employed to derive an evolution equation for the height of the film, which is dependent on a single parameter, the dimensionless cylinder radius. This equation is identified as a special case of that which describes thin film flow down an inclined plane. Fully three-dimensional simulations of the film depict a fingering pattern at the advancing contact line. We find the number of fingers observed in our simulations to be in excellent agreement with experimental observations and a linear stability analysis reported recently by Smolka & SeGall (Phys Fluids 23, 092103 (2011)). As the radius of the cylinder decreases, the modes of perturbation have an increased growth rate, thus increasing cylinder curvature partially acts to encourage the contact line instability. In direct competition with this behaviour, a decrease in cylinder radius means that fewer fingers are able to form around the circumference of the cylinder. Indeed, for a sufficiently small radius, a transition is observed, at which point the contact line is stable to transverse perturbations of all wavenumbers. In this regime, free surface instabilities lead to the development of wave patterns in the axial direction, and the flow features become perfectly analogous to the two-dimensional flow of a thin film down an inverted plane as studied by Lin & Kondic (Phys Fluids 22, 052105 (2010)). Finally, we simulate the flow of a single drop down the outside of the cylinder. Our results show that for drops with low volume, the cylinder curvature has the effect of increasing drop speed and hence promoting the phenomenon of pearling. On the other hand, drops with much larger volume evolve to form single long rivulets with a similar shape to a finger formed in the aforementioned simulations.

Influencing the experience of people in urban public places through mobile mediated interactions

This study presents research findings to informthe design and development of innovativemobile services aiming to enable collocated people to interact with each other in public urban places. The main goal of this research is to provide applications and deliver guidelines to positively influence the user experience of different public urban places during everyday urban life. This study describes the design and evaluation of mobile content and services enabling mobile mediated interactions in an anonymous way. The research described in this thesis is threefold. First, this study investigates how Information and Communication Technology (ICT) can be utilised in particular urban public places to influence the experience of urban dwellers during everyday life. The research into urban residents and public places guides the design of three different technologies that form case studies to investigate and discover possibilities to digitally augment the public urban space and make the invisible data of our interactions in the urban environment visible. • Capital Music enables urban dwellers to listen to their music on their mobile devices as usual but also visualises the artworks of songs currently being played and listened to by other users in ones’ vicinity. • PlaceTagz uses QR codes printed on stickers that link to a digital message board enabling collocated users to interact with each other over time resulting in a place-based digital memory. • Sapporo World Window, Brisbane Hot Spots, and YourScreen are interactive content applications allowing people to share data with their mobile phones on public urban screens. The applications employ mobile phones to mediate interactions in form of location and video sharing. Second, this study sets out to explore the quality and nature of the experiences created through the developed and deployed case study applications. The development of a user experience framework for evaluating mobile mediated interactions in urban public places is described and applied within each case. Third, drawing on research from urban sociology, psychology, urban design, and the findings from this study, this thesis discusses how such interactions can have an impact on the urban experience.

TrainRoulette : promoting situated in-train social interaction between passengers

Travelling by public transport is usually regarded as boring and uninteresting. Refraining from talking to the stranger next to you may be due to limitations that are self-imposed and further corroborated by social expectations and cultural norms that govern behaviour in public space. Our design research into passenger interactions on board of urban commuter trains has informed the development of the TrainRoulette prototype – a mobile app for situated, real-time chats between train passengers. We study the impact of our design intervention on shaping perceptions of the train journey experience. Moreover, we are interested in the implications of such ICT-mediated interactions within train journeys for stimulating social offline interactions and new forms of passenger engagement.

Cell migration and proliferation on homogeneous and non-homogeneous domains : modelling on the scale of individuals and populations

Cell migration is a behaviour critical to many key biological effects, including wound healing, cancerous cell invasion and morphogenesis, the development of an organism from an embryo. However, given that each of these situations is distinctly different and cells are extremely complicated biological objects, interest lies in more basic experiments which seek to remove conflating factors and present a less complex environment within which cell migration can be experimentally examined. These include in vitro studies like the scratch assay or circle migration assay, and ex vivo studies like the colonisation of the hindgut by neural crest cells. The reduced complexity of these experiments also makes them much more enticing as problems to mathematically model, like done here. The primary goal of the mathematical models used in this thesis is to shed light on which cellular behaviours work to generate the travelling waves of invasion observed in these experiments, and to explore how variations in these behaviours can potentially predict differences in this invasive pattern which are experimentally observed when cell types or chemical environment are changed. Relevant literature has already identified the difficulty of distinguishing between these behaviours when using traditional mathematical biology techniques operating on a macroscopic scale, and so here a sophisticated individual-cell-level model, an extension of the Cellular Potts Model (CPM), is been constructed and used to model a scratch assay experiment. This model includes a novel mechanism for dealing with cell proliferations that allowed for the differing properties of quiescent and proliferative cells to be implemented into their behaviour. This model is considered both for its predictive power and used to make comparisons with the travelling waves which result in more traditional macroscopic simulations. These comparisons demonstrate a surprising amount of agreement between the two modelling frameworks, and suggest further novel modifications to the CPM that would allow it to better model cell migration. Considerations of the model’s behaviour are used to argue that the dominant effect governing cell migration (random motility or signal-driven taxis) likely depends on the sort of invasion demonstrated by cells, as easily seen by microscopic photography. Additionally, a scratch assay simulated on a non-homogeneous domain consisting of a ’fast’ and ’slow’ region is also used to further differentiate between these different potential cell motility behaviours. A heterogeneous domain is a novel situation which has not been considered mathematically in this context, nor has it been constructed experimentally to the best of the candidate’s knowledge. Thus this problem serves as a thought experiment used to test the conclusions arising from the simulations on homogeneous domains, and to suggest what might be observed should this non-homogeneous assay situation be experimentally realised. Non-intuitive cell invasion patterns are predicted for diffusely-invading cells which respond to a cell-consumed signal or nutrient, contrasted with rather expected behaviour in the case of random-motility-driven invasion. The potential experimental observation of these behaviours is demonstrated by the individual-cell-level model used in this thesis, which does agree with the PDE model in predicting these unexpected invasion patterns. In the interest of examining such a case of a non-homogeneous domain experimentally, some brief suggestion is made as to how this could be achieved.

Fractional models for the migration of biological cells in complex spatial domains

Travelling wave phenomena are observed in many biological applications. Mathematical theory of standard reaction-diffusion problems shows that simple partial differential equations exhibit travelling wave solutions with constant wavespeed and such models are used to describe, for example, waves of chemical concentrations, electrical signals, cell migration, waves of epidemics and population dynamics. However, as in the study of cell motion in complex spatial geometries, experimental data are often not consistent with constant wavespeed. Non-local spatial models have successfully been used to model anomalous diffusion and spatial heterogeneity in different physical contexts. In this paper, we develop a fractional model based on the Fisher-Kolmogoroff equation and analyse it for its wavespeed properties, attempting to relate the numerical results obtained from our simulations to experimental data describing enteric neural crest-derived cells migrating along the intact gut of mouse embryos. The model proposed essentially combines fractional and standard diffusion in different regions of the spatial domain and qualitatively reproduces the behaviour of neural crest-derived cells observed in the caecum and the hindgut of mouse embryos during in vivo experiments.

Numerical solutions for thin film flow down the outside and inside of a vertical cylinder

We consider a model for thin film flow down the outside and inside of a vertical cylinder. Our focus is to study the effect that the curvature of the cylinder has on the gravity-driven instability of the advancing contact line and to simulate the resulting fingering patterns that form due to this instability. The governing partial differential equation is fourth order with a nonlinear degenerate diffusion term that represents the stabilising effect of surface tension. We present numerical solutions obtained by implementing an efficient alternating direction implicit scheme. When compared to the problem of flow down a vertical plane, we find that increasing substrate curvature tends to increase the fingering instability for flow down the outside of the cylinder, whereas flow down the inside of the cylinder substrate curvature has the opposite effect. Further, we demonstrate the existence of nontrivial travelling wave solutions which describe fingering patterns that propagate down the inside of a cylinder at constant speed without changing form. These solutions are perfectly analogous to those found previously for thin film flow down an inclined plane.

Investigation of ultra trace detection in functionalised-surface enhanced Raman spectroscopy (SERS)

We have developed an explanation for ultra trace detection found when using Au/Ag SERS nanoparticles linked to biochemical affinity tags, e.g. antibodies. The nanoparticle structure is not as usually assumed and the aggregated nanoparticles constitute hot spots that are indispensable for these very low levels of analyte detection, even more so when using a direct detection method.