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.

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 which 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. Zhang et al. [Water Resources Research, 43(5)(2007)] considered such an equation with variable coefficients, which they dis- cretised using the finite difference method proposed by Meerschaert and Tadjeran [Journal of Computational and Applied Mathematics, 172(1):65-77 (2004)]. For this method the presence of variable coef- ficients necessitates applying the product rule before discretising the Riemann–Liouville fractional derivatives using standard and shifted Gru ̈nwald formulas, depending on the fractional order. As an alternative, we propose using a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Gru ̈nwald formulas are used to discretise the Riemann–Liouville fractional derivatives at control volume faces, eliminating the need for product rule expansions. We compare the two methods for several case studies, highlighting the convenience of the finite volume approach.

Eldercare demands, mental health, and work performance : the moderating role of satisfaction with eldercare tasks

Due to demographic changes, a growing number of employees provide in-home care to an elderly family member. Previous research suggested a negative relationship between employees' eldercare demands and their work performance. However, the empirical nature of this relationship and its boundary conditions and mediating mechanisms have been neglected. The goal of this multisource study was to examine a mediated-moderation model of eldercare demands, mental health, and work performance. Drawing on the theory of conservation of resources (Hobfoll, 1989), it was expected that employees' satisfaction with eldercare tasks would buffer the negative relationship between eldercare demands and work performance, and that mental health would mediate this moderating effect. Data were collected from 165 employees providing in-home eldercare, as well as from one colleague and one family member of each employee. Results of mediated-moderation analyses supported the hypothesized model. The findings suggest that interventions that aim to increase employees' satisfaction with eldercare tasks may help protect employees from the negative effects of high eldercare demands on mental health and, subsequently, on work performance.

Satisfaction with emergency department service among non-English-speaking background patients

Objective: The present study aims to investigate non-English-speaking background (NESB) patients’ satisfaction with hospital ED service and compare it with that of English-speaking background (ESB) patients. Methods: A cross-sectional survey was conducted at the ED of an adult tertiary referral hospital in Queensland, Australia. Patients assigned an Australasian Triage Scale score of 3, 4 or 5 were surveyed in the ED, before and after their ED service. Pearson χ2- test and multivariate logistic regression analyses were performed to examine the differences between the ESB and NESB groups in terms of patient-reported satisfaction. Results: In total, 828 patients participated in the present study. Although the overall satisfaction with the service was high – 95.1% (ESB) and 90.5% (NESB) – the NESB patients who did not use an interpreter were less satisfied with their ED service than the ESB patients (odds ratio 0.5, 95% confidence interval 0.3–0.8, P = 0.013). The promptness of service received the lowest satisfaction rates (ESB 85.4% [82.4–88.0], NESB 74.5% [68.5– 79.7], P < 0.001), whereas courtesy and friendliness received the highest satisfaction rates (ESB 98.8 [97.6–99.4], NESB 97.0 [93.9–98.5], P = 0.063). All participants reported the promptness of service (33.5%), quality and professional care (18.5%) and communication (17.6%) as the most important elements of ED service. Conclusion: The NESB patients were significantly less satisfied than the ESB patients with the ED service. Use of an interpreter improved the NESB patients’ level of satisfaction. Further research is required to examine what NESB patients’ expectations of ED service are.

Low-frequency dispersion properties of plasmas with variable-charge impurities

A theory of low-frequency dust-acoustic waves in low-temperature collisional plasmas containing variable-charge impurities is presented. Physical processes such as dust-charge relaxation, ionization-recombination of the electrons and ions, electron and ion elastic collisions with neutrals and dusts, as well as charging collisions with the dusts, are taken into account. Inclusion of these processes allows a balance of the plasma particles and thus a self-consistent determination of the stationary state of the unperturbed plasma. The generalized dispersion relation describing the propagation and damping of the dust acoustic waves is derived and analyzed. © 2000 American Institute of Physics.

A fast semi-implicit difference method for a nonlinear two-sided space-fractional diffusion equation with variable diffusivity coefficients

In this paper, we derive a new nonlinear two-sided space-fractional diffusion equation with variable coefficients from the fractional Fick’s law. A semi-implicit difference method (SIDM) for this equation is proposed. The stability and convergence of the SIDM are discussed. For the implementation, we develop a fast accurate iterative method for the SIDM by decomposing the dense coefficient matrix into a combination of Toeplitz-like matrices. This fast iterative method significantly reduces the storage requirement of O(n2)O(n2) and computational cost of O(n3)O(n3) down to n and O(nlogn)O(nlogn), where n is the number of grid points. The method retains the same accuracy as the underlying SIDM solved with Gaussian elimination. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.

Women's perceptions of communication in pregnancy and childbirth: Influences on participation and satisfaction with care

In this study, 3531 Queensland women, who had recently given birth, completed a questionnaire that included questions about their participation in decision making during pregnancy, their ratings of client centred care and perceived quality of care. These data tested a version of Street’s (2001) linguistic model of patient participation in care (LMOPPC), adapted to the maternity context. We investigated how age and education influenced women’s perceptions of their participation and quality of care. Hierarchical multiple regressions revealed that women’s perceived ability to make decisions, and the extent of client-centred communication with maternity care providers were the most influential predictors of participation and perceived quality of care. Participation in care predicted perceived quality of care, but the influence of client-centred communication by a care provider and a woman’s confidence in decision making were stronger predictors of perceived quality of care. Age and education level were not important predictors. These findings extend and support the use of LMOPPC in the maternity context.

Linking client and employee perceptions of the organization: A study of client satisfaction with health care services

Client satisfaction with health care services has usually been researched in terms of socio-demographic and predispositional characteristics associated with the client. The present study included organizational characteristics as predictors of client satisfaction with health care services. Participants in the research were clients and employees of an Australian public-sector health care organization who responded to separate client and employee questionnaires. Hierarchical regression analyses indicated that, after controlling for a number of client characteristics, organizational characteristics, as perceived by employees, accounted for a significant proportion of additional variance in client satisfaction with health care services. Results of the present study provided some support for the proposition that employee perceptions of the working environment should be considered in a more comprehensive understanding of client satisfaction with health care services. Limitations of the study highlight practical difficulties in the assessment of client outcomes and methodological complexities in linking individual and organizational processes.

The role of engagement on stakeholder's satisfaction with the destination marketing organisation's performance

In the tourism literature there has been a lack of research related to stakeholders' satisfaction with destination marketing organisations (DMO). This study addresses this research gap, in the context of the national tourism office of Oman, by investigating the relationship between stakeholder's perceptions of DMO performance and their overall satisfaction with the DMO. Conceptually the study found DMO engagement with stakeholders to partially mediate satisfaction, a finding of relevance to destination marketers in other parts of the world. From a practical perspective the research was supported by the Oman national tourism office, which has only been in operation for 10 years.

A new family of multivariate heavy-tailed distributions with variable marginal amounts of tailweight: Application to robust clustering

We propose a family of multivariate heavy-tailed distributions that allow variable marginal amounts of tailweight. The originality comes from introducing multidimensional instead of univariate scale variables for the mixture of scaled Gaussian family of distributions. In contrast to most existing approaches, the derived distributions can account for a variety of shapes and have a simple tractable form with a closed-form probability density function whatever the dimension. We examine a number of properties of these distributions and illustrate them in the particular case of Pearson type VII and t tails. For these latter cases, we provide maximum likelihood estimation of the parameters and illustrate their modelling flexibility on simulated and real data clustering examples.

Student satisfaction with models of field placement supervision

Field placements provide social work students with the opportunity to integrate their classroom learning with the knowledge and skills used in various human service programs. The supervision structure that has most commonly been used is the intensive one-to-one, clinical teaching model. However, this model is being challenged by significant changes in educational and industry sectors, which have led to an increased use of alternative fieldwork structures and supervision arrangements, including task supervision, group supervision, external supervision, and shared supervisory arrangements. This study focuses on identifying models of supervision and student satisfaction with their learning experiences and the supervision received on placement. The study analysed responses to a questionnaire administered to 263 undergraduate social work students enrolled in three different campuses in Australia after they had completed their first or final field placement. The study identified that just over half of the placements used the traditional one student to one social work supervisor model. A number of “emerging” models were also identified, where two or more social workers were involved in the professional supervision of the student. High levels of dissatisfaction were reported by those students who received external social work supervision. Results suggest that students are more satisfied across all aspects of the placement where there is a strong on-site social work presence.

Student satisfaction with models of field placement supervision

Field placements provide social work students with the opportunity to integrate their classroom learning with the knowledge and skills used in various human service programs. The supervision structure that has most commonly been used is the intensive one-to-one, clinical teaching model. However, this model is being challenged by significant changes in educational and industry sectors, which have led to an increased use of alternative fieldwork structures and supervision arrangements, including task supervision, group supervision, external supervision, and shared supervisory arrangements. This study focuses on identifying models of supervision and student satisfaction with their learning experiences and the supervision received on placement. The study analysed responses to a questionnaire administered to 263 undergraduate social work students enrolled in three different campuses in Australia after they had completed their first or final field placement. The study identified that just over half of the placements used the traditional one student to one social work supervisor model. A number of “emerging” models were also identified, where two or more social workers were involved in the professional supervision of the student. High levels of dissatisfaction were reported by those students who received external social work supervision. Results suggest that students are more satisfied across all aspects of the placement where there is a strong on-site social work presence.

The effectiveness of a short-term group music therapy intervention for parents who have a child with a disability

The relationship between the quality of parent-child interactions and positive child developmental trajectories is well established (Guralnick, 2006; Shonkoff & Meissels, 2000; Zubrick et al., 2008). However, a range of parental, family, and socio-economic factors can pose risks to parents’ capacity to participate in quality interactions with their children. In particular, families with a child with a disability have been found to have higher levels of parenting stress, and are more likely to experience economic disadvantage, as well as social isolation. The importance of early interventions to promote positive parenting and child development for these families is widely recognised (Shonkoff & Meissels, 2000). However, to date, there is a lack of evidence about the effectiveness of early parenting programs for families who have a young child with a disability. This thesis investigates the impact of a music therapy parenting program, Sing & Grow, on 201 parent-child dyads who attended programs specifically targeted to parents who had a young child with a disability. Sing & Grow is an Australian national early parenting intervention funded by the Australian Government Department of Families, Housing, Community Services and Indigenous Affairs and delivered by Playgroup Queensland. It is designed and delivered by Registered Music Therapists for families with children aged from birth to three years. It aims to improve parenting skills and confidence, improve family functioning (positive parent-child interactions), enhance child development, and provide social networking opportunities to socially isolated families. The intervention targets a range of families in circumstances that have the potential to impact negatively on family functioning. This thesis uses data from the National Evaluation Study of Sing & Grow from programs which were targeted at families who had a young child with a disability. Three studies were conducted to address the objectives of this thesis. Study 1 examines the effects of the Sing & Grow intervention on parent reported pre and post parent mental health, parenting confidence, parenting skills, and child development, and other parent reported outcomes including social support, use of intervention resources, satisfaction with the intervention and perceived benefits of and barriers to participation. Significant improvements from pre to post were found for parent mental health and parent reported child communication and social skills, along with evidence that parents were very satisfied with the program and that it brought social benefits to families. Study 2 explored the pre to post effects of the intervention on children’s developmental skills and parent-child interactions using observational ratings made by clinicians. Significant pre to post improvements were found for parenting sensitivity, parental engagement with child and acceptance of child as well as for child responsiveness to parent, interest, and participation in the intervention, and social skills. Study 3 examined the nature of child and family characteristics that predicted better outcomes for families while taking account of the level of participation in the program. An overall outcome index was calculated and served as the dependent variable in a logistic regression analysis. Families who attended six or more sessions and mothers who had not completed high school were more likely to have higher outcome scores at post intervention than those who attended fewer sessions and those with more educated mothers respectively. The findings of this research indicate that the intervention had a positive impact on participants’ mental health, parenting behaviours and child development and that level of attendance was associated with better outcomes. There was also evidence that the program reached its target of high risk families (i.e., families in which mothers had lower educational levels) and that for these families better outcomes were achieved. There were also indications that the program was accessible and highly regarded by families and that it promoted social connections for participants. A theoretical model of how the intervention is currently working for families is proposed to explain the connections between early parenting, child development and maternal wellbeing. However, more research is required to further elucidate the mechanisms by which the intervention creates change for families. This research presents promising evidence that a short term group music therapy program can elicit important therapeutic benefits for families who have a child with a disability.

Consumer satisfaction and redress with a government third-party complaints agency

As governments around the world adopt a marketing orientation, the importance of consumer satisfaction to the effectiveness of the organization is being recognized. While some investigation of satisfaction with a government agencies' service has occurred, there is little examination of satisfaction with a government agency that acts as a third-party on the behalf of consumers to gain marketplace redress. Given the number of third-party complaints is increasing as a result of internet access to complaint channels, this research is a timely investigation. This study reports the findings of a survey of 454 complainants to an Australian Government agency: the Office of Fair Trading (OFT). The findings show that satisfaction with the service was subjectively experienced, based around individual expectations of the redress and satisfaction levels were higher when the redress sought was financial compared with non-financial forms of redress such as apology.