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.

Motivations for eWOM exchanges in an online community : self-development, problem solving support, relaxation

Electronic word-of-mouth (eWOM) has gained significant attention from academics and practitioners since it has become an important source of consumers’ product information, which can influence consumer purchase intentions (Cheung & Lee, 2012). eWOM exchanges exist in two types of online communities: online communities of practice and online communities of interest. A few prior studies in online communities of interest have examined members’ motivations for product knowledge exchange (Hung & Li, 2007; Ma & Agarwal, 2007). However, there is a lack of understanding of member motivations for exchanging social bonds and enjoyment in addition to exchanging knowledge pertaining to products in the community. It is important to have an initial comprehension of motivation as an antecedent of these three eWOM exchanges so as to be able to determine the driving factors that lead members to generate eWOM communication. Thus, the research problem "What are the driving factors for members to exchange eWOM in an online community?" was justified for investigation. The purpose of this study was to examine different member motivations for exchanging three types of eWOM. Resource exchange theory and theory on consumer motivation and behavior were applied to develop a conceptual framework for this study. This study focused on an online beauty community since there is an increasing trend of consumers turning to online beauty resources so as to exchange useful beauty product information (SheSpot, 2011). As this study examined consumer motivation in an online beauty community, a web-based survey was the most effective and efficient way to gain responses from beauty community members and these members were appropriate samples from which to draw a conclusion about the whole population. Multiple regression analysis was used to test the relationships between member motivations and eWOM exchanges. It was found that members have different motivations for exchanging knowledge, social bonds, and enjoyment related to products: self-development, problem solving support, and relaxation, respectively. This study makes three theoretical contributions. First, this study identifies the influence of self-development motivation on knowledge exchange in an online community of interest, just as this motivation has previously been found in online communities of practice. This study highlights that members of the two different types of online communities share similar goals of knowledge exchange, despite the two communities evincing different attributes (e.g., member characteristics and tasks’ objectives). Further, this study will assist researchers to understand other motivations identified by prior research in online communities of practice since such motivations may be applicable to online communities of interest. Second, this study offers a new perspective on member motivation for social bonding. This study indicates that in addition to social support from friends and family, consumers are motivated to build social bonds with members in an online community of interest since they are an important source of problem solving support in regard to products. Finally, this study extends the body of knowledge pertaining to member motivation for enjoyment exchange. This study provides a basis for researchers to understand that members in an online community of interest value experiential aspects of enjoyable consumption activities, and thus based on group norms, members have a mutual desire for relaxation from enjoyment exchange. The major practical contribution is that this study provides an important guideline for marketing managers to develop different marketing strategies based on member motivations for exchanging three types of eWOM in an online community of interest, such as an online beauty community. This will potentially help marketing managers increase online traffic and revenue, and thus bring success to the community. Although, this study contributes to the literature by highlighting three distinctive member motivations for eWOM exchanges in an online community of interest, there are some possible research limitations. First, this study was conducted in an online beauty community in Australia. Hence, further research should replicate this study in other industries and nations so as to give the findings greater generalisability. Next, online beauty community members are female skewed. Thus, future research should examine whether similar patterns of motivations would emerge in other online communities that tend to be populated by males (e.g., communities focused on football). Further, a web-based survey has its limitations in terms of self-selection and self-reporting (Bhatnagar & Ghose, 2004). Therefore, further studies should test the framework by employing different research methods in order to overcome these weaknesses.

Revisiting the concept of the ‘problem young driver’ within the context of the ‘young driver problem’ : Who are they?

For decades there have been two young driver concepts: the ‘young driver problem’ where the driver cohort represents a key problem for road safety; and the ‘problem young driver’ where a sub-sample of drivers represents the greatest road safety problem. Given difficulties associated with identifying and then modifying the behaviour of the latter group, broad countermeasures such as graduated driver licensing (GDL) have generally been relied upon to address the young driver problem. GDL evaluations reveal general road safety benefits for young drivers, yet they continue to be overrepresented in fatality and injury statistics. Therefore it is timely for researchers to revisit the ‘problem young driver’ concept to assess its potential countermeasure implications. This is particularly relevant within the context of broader countermeasures that have been designed to address the ‘young driver problem’. Personal characteristics, behaviours and attitudes of 378 Queensland novice drivers aged 17-25 years were explored during their pre-, Learner and Provisional 1 (intermediate) licence as part of a larger longitudinal project. Self-reported risky driving was measured by the Behaviour of Young Novice Drivers Scale (BYNDS), and five subscale scores were used to cluster the drivers into three groups (high risk n=49, medium risk n=163, low risk n=166). High risk ‘problem young drivers’ were characterised by greater self-reported pre-Licence driving, unsupervised Learner driving, and speeding, driving errors, risky driving exposure, crash involvement, and offence detection during the Provisional period. Medium risk drivers were also characterised by more risky road use than the low risk group. Interestingly problem young drivers appear to have some insight into their high-risk driving, since they report significantly greater intentions to bend road rules in future driving. The results suggest that tailored intervention efforts may need to target problem young drivers within the context of broad countermeasures such as GDL which address the young driver problem in general. Experiences such as crash-involvement could be used to identify these drivers as a pre-intervention screening measure.

Can testosterone replacement decrease the memory problem of old age?

The world is rapidly ageing. It is against this backdrop that there are increasing incidences of dementia reported worldwide, with Alzheimer's disease (AD) being the most common form of dementia in the elderly. It is estimated that AD affects almost 4 million people in the US, and costs the US economy more than 65 million dollars annually. There is currently no cure for AD but various therapeutic agents have been employed in attempting to slow down the progression of the illness, one of which is oestrogen. Over the last decades, scientists have focused mainly on the roles of oestrogen in the prevention and treatment of AD. Newer evidences suggested that testosterone might also be involved in the pathogenesis of AD. Although the exact mechanisms on how androgen might affect AD are still largely unknown, it is known that testosterone can act directly via androgen receptor-dependent mechanisms or indirectly by converting to oestrogen to exert this effect. Clinical trials need to be conducted to ascertain the putative role of androgen replacement in Alzheimer's disease.

Enhancing critical analysis and problem-solving skills in undergraduate psychology : An evaluation of a collaborative learning and problem-based learning approach

Critical analysis and problem-solving skills are two graduate attributes that are important in ensuring that graduates are well equipped in working across research and practice settings within the discipline of psychology. Despite the importance of these skills, few psychology undergraduate programmes have undertaken any systematic development, implementation, and evaluation of curriculum activities to foster these graduate skills. The current study reports on the development and implementation of a tutorial programme designed to enhance the critical analysis and problem-solving skills of undergraduate psychology students. Underpinned by collaborative learning and problem-based learning, the tutorial programme was administered to 273 third year undergraduate students in psychology. Latent Growth Curve Modelling revealed that students demonstrated a significant linear increase in self-reported critical analysis and problem-solving skills across the tutorial programme. The findings suggest that the development of inquiry-based curriculum offers important opportunities for psychology undergraduates to develop critical analysis and problem-solving skills.

The architecture of children’s use of language and tools when problem solving collaboratively with robotics

This paper demonstrates, following Vygotsky, that language and tool use has a critical role in the collaborative problem-solving behaviour of school-age children. It reports original ethnographic classroom research examining the convergence of speech and practical activity in children’s collaborative problem solving with robotics programming tasks. The researchers analysed children’s interactions during a series of problem solving experiments in which Lego Mindstorms toolsets were used by teachers to create robotics design challenges among 24 students in a Year 4 Australian classroom (students aged 8.5–9.5 years). The design challenges were incrementally difficult, beginning with basic programming of straight line movement, and progressing to more complex challenges involving programming of the robots to raise Lego figures from conduit pipes using robots as pulleys with string and recycled materials. Data collection involved micro-genetic analysis of students’ speech interactions with tools, peers, and other experts, teacher interviews, and student focus group data. Coding the repeated patterns in the transcripts, the authors outline the structure of the children’s social speech in joint problem solving, demonstrating the patterns of speech and interaction that play an important role in the socialisation of the school-age child’s practical intellect.

A hybrid genetic algorithm for the minimum interconnection cut problem

In the real world there are many problems in network of networks (NoNs) that can be abstracted to a so-called minimum interconnection cut problem, which is fundamentally different from those classical minimum cut problems in graph theory. Thus, it is desirable to propose an efficient and effective algorithm for the minimum interconnection cut problem. In this paper we formulate the problem in graph theory, transform it into a multi-objective and multi-constraint combinatorial optimization problem, and propose a hybrid genetic algorithm (HGA) for the problem. The HGA is a penalty-based genetic algorithm (GA) that incorporates an effective heuristic procedure to locally optimize the individuals in the population of the GA. The HGA has been implemented and evaluated by experiments. Experimental results have shown that the HGA is effective and efficient.

Australia - taxation of trusts – the problem of aligning concepts of income

The Australian government is currently considering options for the rewrite and reform of the current provisions which apply to the taxation of trust income. This article provides a discussion of the current regime and the proposed reforms. It is suggested that a major revamp of taxation of trust income in Australia is problematic and a simpler approach may be to leave the law as is, with modification where necessary to address key issues as and when they arise.

An ontology-based method for sparsity problem in tag recommendation

Tags or personal metadata for annotating web resources have been widely adopted in Web 2.0 sites. However, as tags are freely chosen by users, the vocabularies are diverse, ambiguous and sometimes only meaningful to individuals. Tag recommenders may assist users during tagging process. Its objective is to suggest relevant tags to use as well as to help consolidating vocabulary in the systems. In this paper we discuss our approach for providing personalized tag recommendation by making use of existing domain ontology generated from folksonomy. Specifically we evaluated the approach in sparse situation. The evaluation shows that the proposed ontology-based method has improved the accuracy of tag recommendation in this situation.

A combined method for mitigating sparsity problem in tag recommendation

Tag recommendation is a specific recommendation task for recommending metadata (tag) for a web resource (item) during user annotation process. In this context, sparsity problem refers to situation where tags need to be produced for items with few annotations or for user who tags few items. Most of the state of the art approaches in tag recommendation are rarely evaluated or perform poorly under this situation. This paper presents a combined method for mitigating sparsity problem in tag recommendation by mainly expanding and ranking candidate tags based on similar items’ tags and existing tag ontology. We evaluated the approach on two public social bookmarking datasets. The experiment results show better accuracy for recommendation in sparsity situation over several state of the art methods.

The effect of surface tension and kinetic undercooling on a radially-symmetric melting problem

The addition of surface tension to the classical Stefan problem for melting a sphere causes the solution to blow up at a finite time before complete melting takes place. This singular behaviour is characterised by the speed of the solid-melt interface and the flux of heat at the interface both becoming unbounded in the blow-up limit. In this paper, we use numerical simulation for a particular energy-conserving one-phase version of the problem to show that kinetic undercooling regularises this blow-up, so that the model with both surface tension and kinetic undercooling has solutions that are regular right up to complete melting. By examining the regime in which the dimensionless kinetic undercooling parameter is small, our results demonstrate how physically realistic solutions to this Stefan problem are consistent with observations of abrupt melting of nanoscaled particles.

Distinguishing between mean-field, moment dynamics and stochastic descriptions of birth-death-movement processes

Mathematical descriptions of birth–death–movement processes are often calibrated to measurements from cell biology experiments to quantify tissue growth rates. Here we describe and analyze a discrete model of a birth–death-movement process applied to a typical two–dimensional cell biology experiment. We present three different descriptions of the system: (i) a standard mean–field description which neglects correlation effects and clustering; (ii) a moment dynamics description which approximately incorporates correlation and clustering effects, and; (iii) averaged data from repeated discrete simulations which directly incorporates correlation and clustering effects. Comparing these three descriptions indicates that the mean–field and moment dynamics approaches are valid only for certain parameter regimes, and that both these descriptions fail to make accurate predictions of the system for sufficiently fast birth and death rates where the effects of spatial correlations and clustering are sufficiently strong. Without any method to distinguish between the parameter regimes where these three descriptions are valid, it is possible that either the mean–field or moment dynamics model could be calibrated to experimental data under inappropriate conditions, leading to errors in parameter estimation. In this work we demonstrate that a simple measurement of agent clustering and correlation, based on coordination number data, provides an indirect measure of agent correlation and clustering effects, and can therefore be used to make a distinction between the validity of the different descriptions of the birth–death–movement process.

Incorporating spatial correlations into multispecies mean-field models

In biology, we frequently observe different species existing within the same environment. For example, there are many cell types in a tumour, or different animal species may occupy a given habitat. In modelling interactions between such species, we often make use of the mean field approximation, whereby spatial correlations between the locations of individuals are neglected. Whilst this approximation holds in certain situations, this is not always the case, and care must be taken to ensure the mean field approximation is only used in appropriate settings. In circumstances where the mean field approximation is unsuitable we need to include information on the spatial distributions of individuals, which is not a simple task. In this paper we provide a method that overcomes many of the failures of the mean field approximation for an on-lattice volume-excluding birth-death-movement process with multiple species. We explicitly take into account spatial information on the distribution of individuals by including partial differential equation descriptions of lattice site occupancy correlations. We demonstrate how to derive these equations for the multi-species case, and show results specific to a two-species problem. We compare averaged discrete results to both the mean field approximation and our improved method which incorporates spatial correlations. We note that the mean field approximation fails dramatically in some cases, predicting very different behaviour from that seen upon averaging multiple realisations of the discrete system. In contrast, our improved method provides excellent agreement with the averaged discrete behaviour in all cases, thus providing a more reliable modelling framework. Furthermore, our method is tractable as the resulting partial differential equations can be solved efficiently using standard numerical techniques.

A simplified approach for calculating the moments of action for linear reaction-diffusion equations

The mean action time is the mean of a probability density function that can be interpreted as a critical time, which is a finite estimate of the time taken for the transient solution of a reaction-diffusion equation to effectively reach steady state. For high-variance distributions, the mean action time under-approximates the critical time since it neglects to account for the spread about the mean. We can improve our estimate of the critical time by calculating the higher moments of the probability density function, called the moments of action, which provide additional information regarding the spread about the mean. Existing methods for calculating the nth moment of action require the solution of n nonhomogeneous boundary value problems which can be difficult and tedious to solve exactly. Here we present a simplified approach using Laplace transforms which allows us to calculate the nth moment of action without solving this family of boundary value problems and also without solving for the transient solution of the underlying reaction-diffusion problem. We demonstrate the generality of our method by calculating exact expressions for the moments of action for three problems from the biophysics literature. While the first problem we consider can be solved using existing methods, the second problem, which is readily solved using our approach, is intractable using previous techniques. The third problem illustrates how the Laplace transform approach can be used to study coupled linear reaction-diffusion equations.

Engineering based problem solving in the middle school : design and construction with simple machines

Incorporating engineering concepts into middle school curriculum is seen as an effective way to improve students’ problem-solving skills. A selection of findings is reported from a science, technology, engineering and mathematics (STEM)-based unit in which students in the second year (grade 8) of a three-year longitudinal study explored engineering concepts and principles pertaining to the functioning of simple machines. The culminating activity, the focus of this paper, required the students to design, construct, test, and evaluate a trebuchet catapult. We consider findings from one of the schools, a co-educational school, where we traced the design process developments of four student groups from two classes. The students’ descriptions and explanations of the simple machines used in their catapult design are examined, together with how they rated various aspects of their engineering designs. Included in the findings are students’ understanding of how their simple machines were simulated by the resources supplied and how the machines interacted in forming a complex machine. An ability to link physical materials with abstract concepts and an awareness of design constraints on their constructions were apparent, although a desire to create a ‘‘perfect’’ catapult despite limitations in the physical materials rather than a prototype for testing concepts was evident. Feedback from teacher interviews added further insights into the students’ developments as well as the teachers’ professional learning. An evolving framework for introducing engineering education in the pre-secondary years is proposed.