A meshless method based on Point Interpolation Method (PIM) for the space fractional diffusion equation

This paper aims to develop a meshless approach based on the Point Interpolation Method (PIM) for numerical simulation of a space fractional diffusion equation. Two fully-discrete schemes for the one-dimensional space fractional diffusion equation are obtained by using the PIM and the strong-forms of the space diffusion equation. Numerical examples with different nodal distributions are studied to validate and investigate the accuracy and efficiency of the newly developed meshless approach.

Émile Durkheim and Thomas Luckmann: Religion, spirituality and mental health

This chapter examines connections between religion, spirituality and mental health. Religion and spirituality influence the way people conceive themselves, others and the world around them, as well as how they behave – and are strongly associated with numerous mental health outcomes. Religion and spirituality therefore demand the attention of those who seek a comprehensive understanding of the factors that affect mental health. Mental health professionals are increasingly being asked to consider their clients’ religious and/or spiritual beliefs when devising their treatment plans, making the study of religion and spirituality an essential area of learning for those working in the mental health field. Initial discussion in this chapter will focus on the different approaches taken by sociologists in studying mental health. Emile Durkheim, one of the founders of sociology, proposed that religion was fundamental to societal wellbeing and was the first to demonstrate a link between religion and mental health at a population level in the late 19th century. Durkheim’s classic theory of religion, together with the work of Thomas Luckmann and other contemporary social theorists who have sought to explain widespread religious change in Western countries since World War II will be examined. Two key changes during this period are the shift away from mainstream Christian religions and the widespread embracing of ‘spirituality’ as an alternative form of religious expression. In combination, the theories of Durkheim, Luckmann and other sociologists provide a platform from which to consider reasons for variations in rates of mental health problems observed in contemporary Western societies according to people’s religious/spiritual orientation. This analysis demonstrates the relevance of both classic and contemporary sociological theories to issues confronting societies in the present day.

Adolescent self-reported physical activity and autonomy: A case for constrained and structured environments?

The provision of autonomy supportive environments that promote physical activity engagement have become popular in contemporary youth settings. However, questions remain about whether adolescent perceptions of their autonomy have implications for physical activity. The purpose of this investigation was to examine the association between adolescents’ self-reported physical activity and their perceived autonomy. Participants (n = 384 adolescents) aged between 12 and 15 years were recruited from six secondary schools in metropolitan Brisbane, Australia. Self-reported measures of physical activity and autonomy were obtained. Logistic regression with inverse probability weights were used to examine the association between autonomy and the odds of meeting youth physical activity guidelines. Autonomy (OR 0.61, 95% CI 0.49-0.76) and gender (OR 0.62, 95% CI 0.46-0.83) were negatively associated with meeting physical activity guidelines. However, the model explained only a small amount of the variation in whether youth in this sample met physical activity guidelines (R2 = 0.023). For every 1 unit decrease in autonomy (on an index from 1 to 5), participants were 1.64 times more likely to meet physical activity guidelines. The findings, which are at odds with several previous studies, suggest that interventions designed to facilitate youth physical activity should limit opportunities for youth to make independent decisions about their engagement. However, the small amount of variation explained by the predictors in the model is a caveat, and should be considered prior to applying such suggestions in practical settings. Future research should continue to examine a larger age range, longitudinal observational or intervention studies to examine assertions of causality, as well as objective measurement of physical activity.

Mathematical modelling of gas production and compositional shift of a CSG (coal seam gas) field: Local model development

In this work we discuss the development of a mathematical model to predict the shift in gas composition observed over time from a producing CSG (coal seam gas) well, and investigate the effect that physical properties of the coal seam have on gas production. A detailed (local) one-dimensional, two-scale mathematical model of a coal seam has been developed. The model describes the competitive adsorption and desorption of three gas species (CH4, CO2 and N2) within a microscopic, porous coal matrix structure. The (diffusive) flux of these gases between the coal matrices (microscale) and a cleat network (macroscale) is accounted for in the model. The cleat network is modelled as a one-dimensional, volume averaged, porous domain that extends radially from a central well. Diffusive and advective transport of the gases occurs within the cleat network, which also contains liquid water that can be advectively transported. The water and gas phases are assumed to be immiscible. The driving force for the advection in the gas and liquid phases is taken to be a pressure gradient with capillarity also accounted for. In addition, the relative permeabilities of the water and gas phases are considered as functions of the degree of water saturation.

Populations of models, experimental designs and coverage of parameter space by Latin Hypercube and Orthogonal Sampling

In this paper we have used simulations to make a conjecture about the coverage of a t-dimensional subspace of a d-dimensional parameter space of size n when performing k trials of Latin Hypercube sampling. This takes the form P(k,n,d,t) = 1 - e^(-k/n^(t-1)). We suggest that this coverage formula is independent of d and this allows us to make connections between building Populations of Models and Experimental Designs. We also show that Orthogonal sampling is superior to Latin Hypercube sampling in terms of allowing a more uniform coverage of the t-dimensional subspace at the sub-block size level. These ideas have particular relevance when attempting to perform uncertainty quantification and sensitivity analyses.

Applying POVM to model non-orthogonality in quantum cognition

Much of the work currently occurring in the field of Quantum Interaction (QI) relies upon Projective Measurement. This is perhaps not optimal, cognitive states are not nearly as well behaved as standard quantum mechanical systems; they exhibit violations of repeatability, and the operators that we use to describe measurements do not appear to be naturally orthogonal in cognitive systems. Here we attempt to map the formalism of Positive Operator Valued Measure (POVM) theory into the domain of semantic memory, showing how it might be used to construct Bell-type inequalities.

Implementation of parallel tridiagonal solvers for a heterogeneous computing environment

Tridiagonal diagonally dominant linear systems arise in many scientific and engineering applications. The standard Thomas algorithm for solving such systems is inherently serial forming a bottleneck in computation. Algorithms such as cyclic reduction and SPIKE reduce a single large tridiagonal system into multiple small independent systems which can be solved in parallel. We have developed portable cyclic reduction and SPIKE algorithm OpenCL implementations with the intent to target a range of co-processors in a heterogeneous computing environment including Field Programmable Gate Arrays (FPGAs), Graphics Processing Units (GPUs) and other multi-core processors. In this paper, we evaluate these designs in the context of solver performance, resource efficiency and numerical accuracy.

Flow field and traverse times for fan forced injection of fumigant via circular or annular inlet into stored grain

Fan forced injection of phosphine gas fumigant into stored grain is a common method to treat infestation by insects. For low injection velocities the transport of fumigant can be modelled as Darcy flow in a porous medium where the gas pressure satisfies Laplace's equation. Using this approach, a closed form series solution is derived for the pressure, velocity and streamlines in a cylindrically stored grain bed with either a circular or annular inlet, from which traverse times are numerically computed. A leading order closed form expression for the traverse time is also obtained and found to be reasonable for inlet configurations close to the central axis of the grain storage. Results are interpreted for the case of a representative 6m high farm wheat store, where the time to advect the phosphine to almost the entire grain bed is found to be approximately one hour.

Mathematical modelling and numerical simulation of phosphine flow during grain fumigation in leaky cylindrical silos

The phosphine distribution in a cylindrical silo containing grain is predicted. A three-dimensional mathematical model, which accounts for multicomponent gas phase transport and the sorption of phosphine into the grain kernel is developed. In addition, a simple model is presented to describe the death of insects within the grain as a function of their exposure to phosphine gas. The proposed model is solved using the commercially available computational fluid dynamics (CFD) software, FLUENT, together with our own C code to customize the solver in order to incorporate the models for sorption and insect extinction. Two types of fumigation delivery are studied, namely, fan- forced from the base of the silo and tablet from the top of the silo. An analysis of the predicted phosphine distribution shows that during fan forced fumigation, the position of the leaky area is very important to the development of the gas flow field and the phosphine distribution in the silo. If the leak is in the lower section of the silo, insects that exist near the top of the silo may not be eradicated. However, the position of a leak does not affect phosphine distribution during tablet fumigation. For such fumigation in a typical silo configuration, phosphine concentrations remain low near the base of the silo. Furthermore, we find that half-life pressure test readings are not an indicator of phosphine distribution during tablet fumigation.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.