A variable stepsize implementation for stochastic differential equations

Stochastic differential equations (SDEs) arise from physical systems where the parameters describing the system can only be estimated or are subject to noise. Much work has been done recently on developing higher order Runge-Kutta methods for solving SDEs numerically. Fixed stepsize implementations of numerical methods have limitations when, for example, the SDE being solved is stiff as this forces the stepsize to be very small. This paper presents a completely general variable stepsize implementation of an embedded Runge Kutta pair for solving SDEs numerically; in this implementation, there is no restriction on the value used for the stepsize, and it is demonstrated that the integration remains on the correct Brownian path.

Effects of average speed enforcement on speed compliance and crashes : a review of the literature

Average speed enforcement is a relatively new approach gaining popularity throughout Europe and Australia. This paper reviews the evidence regarding the impact of this approach on vehicle speeds, crashes rates and a number of additional road safety and public health outcomes. The economic and practical viability of the approach as a road safety countermeasure is also explored. A literature review, with an international scope, of both published and grey literature was conducted. There is a growing body of evidence to suggest a number of road safety benefits associated with average speed enforcement, including high rates of compliance with speed limits, reductions in average and 85th percentile speeds and reduced speed variability between vehicles. Moreover, the approach has been demonstrated to be particularly effective in reducing excessive speeding behaviour. Reductions in crash rates have also been reported in association with average speed enforcement, particularly in relation to fatal and serious injury crashes. In addition, the approach has been shown to improve traffic flow, reduce vehicle emissions and has also been associated with high levels of public acceptance. Average speed enforcement offers a greater network-wide approach to managing speeds that reduces the impact of time and distance halo effects associated with other automated speed enforcement approaches. Although comparatively expensive it represents a highly reliable approach to speed enforcement that produces considerable returns on investment through reduced social and economic costs associated with crashes.

A high frequency current source converter with adjustable magnitude to drive high power piezoelectric transducers

A general electrical model of a piezoelectric transducer for ultrasound applications consists of a capacitor in parallel with RLC legs. A high power voltage source converter can however generate significant voltage stress across the transducer that creates high leakage currents. One solution is to reduce the voltage stress across the piezoelectric transducer by using an LC filter, however a main drawback is changing the piezoelectric resonant frequency and its characteristics. Thereby it reduces the efficiency of energy conversion through the transducer. This paper proposes that a high frequency current source converter is a suitable topology to drive high power piezoelectric transducers efficiently.

Temporal dynamics of rod and cone photoreceptor interactions under mesopic illumination

Purpose: Photoreceptor interactions reduce the temporal bandwidth of the visual system under mesopic illumination. The dynamics of these interactions are not clear. This study investigated cone-cone and rod-cone interactions when the rod (R) and three cone (L, M, S) photoreceptor classes contribute to vision via shared post-receptoral pathways. Methods: A four-primary photostimulator independently controlled photoreceptor activity in human observers. To determine the temporal dynamics of receptoral (L, S, R) and post-receptoral (LMS, LMSR, +L-M) pathways (5 Td, 7° eccentricity) in Experiment 1, ON-pathway sensitivity was assayed with an incremental probe (25ms) presented relative to onset of an incremental sawtooth conditioning pulse (1000ms). To define the post-receptoral pathways mediating the rod stimulus, Experiment 2 matched the color appearance of increased rod activation (30% contrast, 25-1000ms; constant cone excitation) with cone stimuli (variable L+M, L/L+M, S/L+M; constant rod excitation). Results: Cone-cone interactions with luminance stimuli (LMS, LMSR, L-cone) reduced Weber contrast sensitivity by 13% and the time course of adaptation was 23.7±1ms (μ±SE). With chromatic stimuli (+L-M, S), cone pathway sensitivity was also reduced and recovery was slower (+L-M 8%, 2.9±0.1ms; S 38%, 1.5±0.3ms). Threshold patterns at ON-conditioning pulse onset were monophasic for luminance and biphasic for chromatic stimuli. Rod-rod interactions increased sensitivity(19%) with a recovery time of 0.7±0.2ms. Compared to cone-cone interactions, rod-cone interactions with luminance stimuli reduced sensitivity to a lesser degree (5%) with faster recovery (42.9±0.7ms). Rod-cone interactions were absent with chromatic stimuli. Experiment 2 showed that rod activation generated luminance (L+M) signals at all durations, and chromatic signals (L/L+M, S/L+M) for durations >75ms. Conclusions: Temporal dynamics of cone-cone interactions are consistent with contrast sensitivity loss in the MC pathway for luminance stimuli and chromatically opponent responses in the PC and KC pathway with chromatic stimuli. Rod-cone interactions limit contrast sensitivity loss during dynamic illumination changes and increase the speed of mesopic light adaptation. The change in relative weighting of the temporal rod signal within the major post-receptoral pathways modifies the sensitivity and dynamics of photoreceptor interactions.

Use of brain computer interface to drive : preliminary results

This paper reports on the implementation of a non-invasive electroencephalography-based brain-computer interface to control functions of a car in a driving simulator. The system is comprised of a Cleveland Medical Devices BioRadio 150 physiological signal recorder, a MATLAB-based BCI and an OKTAL SCANeR advanced driving experience simulator. The system utilizes steady-state visual-evoked potentials for the BCI paradigm, elicited by frequency-modulated high-power LEDs and recorded with the electrode placement of Oz-Fz with Fz as ground. A three-class online brain-computer interface was developed and interfaced with an advanced driving simulator to control functions of the car, including acceleration and steering. The findings are mainly exploratory but provide an indication of the feasibility and challenges of brain-controlled on-road cars for the future, in addition to a safe, simulated BCI driving environment to use as a foundation for research into overcoming these challenges.

Daylighting design and simulation : ease of use analysis of digital tools for architects

Good daylighting design in buildings not only provides a comfortable luminous environment, but also delivers energy savings and comfortable and healthy environments for building occupants. Yet, there is still no consensus on how to assess what constitutes good daylighting design. Currently amongst building performance guidelines, Daylighting factors (DF) or minimum illuminance values are the standard; however, previous research has shown the shortcomings of these metrics. New computer software for daylighting analysis contains new more advanced metrics for daylighting (Climate Base Daylight Metrics-CBDM). Yet, these tools (new metrics or simulation tools) are not currently understood by architects and are not used within architectural firms in Australia. A survey of architectural firms in Brisbane showed the most relevant tools used by industry. The purpose of this paper is to assess and compare these computer simulation tools and new tools available architects and designers for daylighting. The tools are assessed in terms of their ease of use (e.g. previous knowledge required, complexity of geometry input, etc.), efficiency (e.g. speed, render capabilities, etc.) and outcomes (e.g. presentation of results, etc. The study shows tools that are most accessible for architects, are those that import a wide variety of files, or can be integrated into the current 3d modelling software or package. These software’s need to be able to calculate for point in times simulations, and annual analysis. There is a current need in these software solutions for an open source program able to read raw data (in the form of spreadsheets) and show that graphically within a 3D medium. Currently, development into plug-in based software’s are trying to solve this need through third party analysis, however some of these packages are heavily reliant and their host program. These programs however which allow dynamic daylighting simulation, which will make it easier to calculate accurate daylighting no matter which modelling platform the designer uses, while producing more tangible analysis today, without the need to process raw data.

Effects of a defender on run-up velocity and ball speed when crossing a football

This study evaluated effects of defensive pressure on running velocity in footballers during the approach to kick a stationary football. Approach velocity and ball speed/accuracy data were recorded from eight football youth academy participants (15.25, SD=0.46 yrs). Participants were required to run to a football to cross it to a receiver to score against a goal-keeper. Defensive pressure was manipulated across three counterbalanced conditions: defender-absent (DA); defender-far (DF) and defender-near (DN). Pass accuracy (percentages of a total of 32 trials with 95% confidence limits in parenthesis) did not significantly reduce under changing defensive pressure: DA, 78% (55–100%); DF, 78% (61–96%); DN, 59% (40–79%). Ball speed (m·s−1) significantly reduced as defensive pressure was included and increased: DA, 23.10 (22.38–23.83); DF, 20.40 (19.69–21.11); DN, 19.22 (18.51–19.93). When defensive pressure was introduced, average running velocity of attackers did not change significantly: DA versus DF (m·s−1), 5.40 (5.30–5.51) versus 5.41 (5.34–5.48). Scaling defender starting positions closer to the start position of the attacker (DN) significantly increased average running velocity relative to the DA and DF conditions, 5.60 (5.50–5.71). In the final approach footfalls, all conditions significantly differed: DA, 5.69 (5.35–6.03); DF, 6 .22 (5.93–6.50); DN, 6.52 (6.23–6.80). Data suggested that approach velocity is constrained by both presence and initial distance of the defender during task performance. Implications are that the expression of kicking behaviour is specific to a performance context and some movement regulation features will not emerge unless a defender is present as a task constraint in practice.

Accuracy and functional variability in elite and developing fast bowlers

Objectives The relationship between performance variability and accuracy in cricket fast bowlers of different skill levels under three different task conditions was investigated. Bowlers of different skill levels were examined to observe if they could adapt movement patterns to maintain performance accuracy on a bowling skills test. Design 8 national, 12 emerging and 12 junior pace bowlers completed an adapted version of the Cricket Australia bowling skills test, in which they performed 30 trials involving short (n = 10), good (n = 10), and full (n = 10) length deliveries. Methods Bowling accuracy was recorded by digitising ball position relative to the centre of a target. Performance measures were mean radial error (accuracy), variable error (consistency), centroid error (bias), bowling score and ball speed. Radial error changes across the duration of the skills test were used to record accuracy adjustment in subsequent deliveries. Results Elite fast bowlers performed better in speed, accuracy, and test scores than developing athletes. Bowlers who were less variable were also more accurate across all delivery lengths. National and emerging bowlers were able to adapt subsequent performance trials within the same bowling session for short length deliveries. Conclusions Accuracy and adaptive variability were key components of elite performance in fast bowling which improved with skill level. In this study, only national elite bowlers showed requisite levels of adaptive variability to bowl a range of lengths to different pitch locations.

Drivers' intention to comply with the speed limit in school zones, in Malaysia

There has been an increasing number of fatal road crashes in Malaysia in the last two decades. Among those who die on Malaysian roads are children aged 0 to 18 years (i.e., 15.5% in 2009) (Mohamed, Wong, Hashim, & Othman, 2011) . The involvement of children in road trauma, and particularly children when they are in and around school zones, generates concern among the general public. The present study utilised an extended Theory of Planned Behaviour (TPB) framework, incorporating the additional predictors of mindfulness and habit, to understand drivers’ intention to comply with the school zone speed limit (SZSL). The study aimed to examine the extent to which TPB constructs, and additional predictors of mindfulness and habit, predicted drivers’ behavioural intention to comply with the SZSL. Malaysian drivers (N = 210) participated in this study via an online survey. Hierarchical regression was conducted, and the results showed that attitude, subjective norm, perceived behavioural control, and habit were significant predictors of intention to comply with the SZSL. Specifically, drivers who expressed more positive attitudes towards compliance, greater belief that significant others would want them to comply, and more confidence in their control of their speed were more likely to report an intention to comply. These drivers appear to have developed a positive habit of compliance, which may simply be a result of the engineering measures in place around school zones in Malaysia. Mindfulness was not a significant predictor in the final model. These findings provide some support for the explanatory value of the extended TPB framework in understanding the factors influencing drivers’ intention to comply with the SZSL. The present study also provides information of potential value in the development of interventions, such as public education and mass media campaigns, aimed at improving drivers’ compliance with the SZSL.

Conserved and variable features of gag structure and arrangement in immature retrovirus particles

The assembly of retroviruses is driven by oligomerization of the Gag polyprotein. We have used cryo-electron tomography together with subtomogram averaging to describe the three-dimensional structure of in vitro-assembled Gag particles from human immunodeficiency virus, Mason-Pfizer monkey virus, and Rous sarcoma virus. These represent three different retroviral genera: the lentiviruses, betaretroviruses and alpharetroviruses. Comparison of the three structures reveals the features of the supramolecular organization of Gag that are conserved between genera and therefore reflect general principles of Gag-Gag interactions and the features that are specific to certain genera. All three Gag proteins assemble to form approximately spherical hexameric lattices with irregular defects. In all three genera, the N-terminal domain of CA is arranged in hexameric rings around large holes. Where the rings meet, 2-fold densities, assigned to the C-terminal domain of CA, extend between adjacent rings, and link together at the 6-fold symmetry axis with a density, which extends toward the center of the particle into the nucleic acid layer. Although this general arrangement is conserved, differences can be seen throughout the CA and spacer peptide regions. These differences can be related to sequence differences among the genera. We conclude that the arrangement of the structural domains of CA is well conserved across genera, whereas the relationship between CA, the spacer peptide region, and the nucleic acid is more specific to each genus.

A variable step-size FxLMS algorithm for feedforward active noise control systems based on a new online secondary path modelling technique

Several approaches have been introduced in literature for active noise control (ANC) systems. Since FxLMS algorithm appears to be the best choice as a controller filter, researchers tend to improve performance of ANC systems by enhancing and modifying this algorithm. This paper proposes a new version of FxLMS algorithm. In many ANC applications an online secondary path modelling method using a white noise as a training signal is required to ensure convergence of the system. This paper also proposes a new approach for online secondary path modelling in feedfoward ANC systems. The proposed algorithm stops injection of the white noise at the optimum point and reactivate the injection during the operation, if needed, to maintain performance of the system. Benefiting new version of FxLMS algorithm and not continually injection of white noise makes the system more desirable and improves the noise attenuation performance. Comparative simulation results indicate effectiveness of the proposed approach.

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

A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non-classical diffusion or dispersion; that is, not adequately described by the classical theory of Brownian motion and Fick's law. We consider a space fractional advection-dispersion equation based on a fractional Fick's law. The equation involves the Riemann-Liouville fractional derivative which arises from assuming that particles may make large jumps. Finite difference methods for solving this equation have been proposed by Meerschaert and Tadjeran. In the variable coefficient case, the product rule is first applied, and then the Riemann-Liouville fractional derivatives are discretised using standard and shifted Grunwald formulas, depending on the fractional order. In this work, we consider a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Grunwald formulas are used to discretise the fractional derivatives at control volume faces. We compare the two methods for several case studies from the literature, highlighting the convenience of the finite volume approach.

Numerical methods of the variable-order Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative

Rayleigh–Stokes problems have in recent years received much attention due to their importance in physics. In this article, we focus on the variable-order Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivative. Implicit and explicit numerical methods are developed to solve the problem. The convergence, stability of the numerical methods and solvability of the implicit numerical method are discussed via Fourier analysis. Moreover, a numerical example is given and the results support the effectiveness of the theoretical analysis.

Numerical approximation for a variable-order nonlinear reaction–subdiffusion equation

Fractional reaction–subdiffusion equations are widely used in recent years to simulate physical phenomena. In this paper, we consider a variable-order nonlinear reaction–subdiffusion equation. A numerical approximation method is proposed to solve the equation. Its convergence and stability are analyzed by Fourier analysis. By means of the technique for improving temporal accuracy, we also propose an improved numerical approximation. Finally, the effectiveness of the theoretical results is demonstrated by numerical examples.