Numerical methods for fractional partial differential equations with Riesz space fractional derivatives

In this paper, we consider the numerical solution of a fractional partial differential equation with Riesz space fractional derivatives (FPDE-RSFD) on a finite domain. Two types of FPDE-RSFD are considered: the Riesz fractional diffusion equation (RFDE) and the Riesz fractional advection–dispersion equation (RFADE). The RFDE is obtained from the standard diffusion equation by replacing the second-order space derivative with the Riesz fractional derivative of order αset membership, variant(1,2]. The RFADE is obtained from the standard advection–dispersion equation by replacing the first-order and second-order space derivatives with the Riesz fractional derivatives of order βset membership, variant(0,1) and of order αset membership, variant(1,2], respectively. Firstly, analytic solutions of both the RFDE and RFADE are derived. Secondly, three numerical methods are provided to deal with the Riesz space fractional derivatives, namely, the L1/L2-approximation method, the standard/shifted Grünwald method, and the matrix transform method (MTM). Thirdly, the RFDE and RFADE are transformed into a system of ordinary differential equations, which is then solved by the method of lines. Finally, numerical results are given, which demonstrate the effectiveness and convergence of the three numerical methods.

The Media City: Media, Architecture and Urban Space

The article reviews the book "The Media City: Media, Architecture and Urban Space," by Scott McQuire.

Robot path planning in dynamic environments using a simulated annealing based approach

Mobile robots are widely used in many industrial fields. Research on path planning for mobile robots is one of the most important aspects in mobile robots research. Path planning for a mobile robot is to find a collision-free route, through the robot’s environment with obstacles, from a specified start location to a desired goal destination while satisfying certain optimization criteria. Most of the existing path planning methods, such as the visibility graph, the cell decomposition, and the potential field are designed with the focus on static environments, in which there are only stationary obstacles. However, in practical systems such as Marine Science Research, Robots in Mining Industry, and RoboCup games, robots usually face dynamic environments, in which both moving and stationary obstacles exist. Because of the complexity of the dynamic environments, research on path planning in the environments with dynamic obstacles is limited. Limited numbers of papers have been published in this area in comparison with hundreds of reports on path planning in stationary environments in the open literature. Recently, a genetic algorithm based approach has been introduced to plan the optimal path for a mobile robot in a dynamic environment with moving obstacles. However, with the increase of the number of the obstacles in the environment, and the changes of the moving speed and direction of the robot and obstacles, the size of the problem to be solved increases sharply. Consequently, the performance of the genetic algorithm based approach deteriorates significantly. This motivates the research of this work. This research develops and implements a simulated annealing algorithm based approach to find the optimal path for a mobile robot in a dynamic environment with moving obstacles. The simulated annealing algorithm is an optimization algorithm similar to the genetic algorithm in principle. However, our investigation and simulations have indicated that the simulated annealing algorithm based approach is simpler and easier to implement. Its performance is also shown to be superior to that of the genetic algorithm based approach in both online and offline processing times as well as in obtaining the optimal solution for path planning of the robot in the dynamic environment. The first step of many path planning methods is to search an initial feasible path for the robot. A commonly used method for searching the initial path is to randomly pick up some vertices of the obstacles in the search space. This is time consuming in both static and dynamic path planning, and has an important impact on the efficiency of the dynamic path planning. This research proposes a heuristic method to search the feasible initial path efficiently. Then, the heuristic method is incorporated into the proposed simulated annealing algorithm based approach for dynamic robot path planning. Simulation experiments have shown that with the incorporation of the heuristic method, the developed simulated annealing algorithm based approach requires much shorter processing time to get the optimal solutions in the dynamic path planning problem. Furthermore, the quality of the solution, as characterized by the length of the planned path, is also improved with the incorporated heuristic method in the simulated annealing based approach for both online and offline path planning.

Emergency department surge capacity : Recommendations of the Australasian surge strategy working group

Background For more than a decade emergency medicine organizations have produced guidelines, training and leadership for disaster management. However to date, there have been limited guidelines for emergency physicians needing to provide a rapid response to a surge in demand. The aim of this study is to identify strategies which may guide surge management in the Emergency Department. Method A working group of individuals experienced in disaster medicine from the Australasian College for Emergency Medicine Disaster Medicine Subcommittee (the Australasian Surge Strategy Working Group) was established to undertake this work. The Working Group used a modified Delphi technique to examine response actions in surge situations. The Working Group identified underlying assumptions from epidemiological and empirical understanding and then identified remedial strategies from literature and from personal experience and collated these within domains of space, staff, supplies, and system operation. Findings These recommendations detail 22 potential actions available to an emergency physician working in the context of surge. The Working Group also provides detailed guidance on surge recognition, triage, patient flow through the emergency department and clinical goals and practices. Discussion These strategies provide guidance to emergency physicians confronting the challenges of a surge in demand. The paper also identifies areas that merit future research including the measurement of surge capacity, constraints to strategy implementation, validation of surge strategies and measurement of strategy impacts on throughput, cost, and quality of care.

A phenomenological study of contemplative experiences : implications for interior design

This research reports on a project concerned with the relationship between the person and the environment in the context of achieving a contemplative or existential state – a state which can be experienced either consciously or subconsciously. The need for such a study originated with the desire to contribute to the design of multicultural spaces which could be used for a range of activities within the public and the personal arena, activities including contemplation, meditation and prayer. The concept of ‘sacred’ is explored in the literature review and in primary interviews with the participants of this study. Given that the word ‘sacred’ is highly value-laden and potentially alienating for some people, it was decided to use the more accessible term ‘contemplative’. The outcomes of the study inform the practice of interior design and architecture which tends currently to neglect the potential for all spaces to be existentially meaningful. Informed by phenomenological methodology, data were collected from a diverse group of people, using photo-elicitation and interviews. The technique of photo-elicitation proved to be highly effective in helping people reveal their everyday lived experience of contemplative spaces. Reflective analysis (Van Manen 2000) was used to explore the data collected. The initial stage of analysis produced three categories of data: varying conceptions of contemplation, aspects of the person involved in the contemplation, and aspects of environment involved in contemplation. From this, it was found that achieving a state of contemplation involves both the person and the environment in a dialectic process of unfolding. The unfolding has various physical, psycho-social, and existential dimensions or qualities which operate sequentially and simultaneously. Two concepts emerged as being central to unfolding: ‘Cleansing’ and ‘Nothingness’. Unfolding is found to comprise the Core; Distinction; Manifestation; Cleansing; Creation; and Sharing. This has a parallel with Mircea Eliade’s (1959) definition of sacred as something that manifests itself as different from the profane. The power of design, re-contextualization through utility and purpose, and the existential engagements between the person and environment are used as a basis for establishing the potential contribution of the study to interior design. In this way, the study makes a contribution to our understanding of how space and its elements inspire, support and sustain person environment interaction – particularly at the existential level – as well as to our understanding of the multi-dimensional and holistic nature of this interaction. In addition, it points to the need for a phenomenological re-conceptualisation of the design/client relationship. In summary, the contributions of this research are: the exploration of contemplative experience as sacred experience; an understanding of the design of space as creating engagement between person and environment; a rationale for the introduction of a phenomenological approach to the relationship between designer and clients; and raising awareness of the spiritual in a holistic approach to design.

Learning in the third space : a sociocultural perspective on learning with analogies

Research on analogies in science education has focussed on student interpretation of teacher and textbook analogies, psychological aspects of learning with analogies and structured approaches for teaching with analogies. Few studies have investigated how analogies might be pivotal in students’ growing participation in chemical discourse. To study analogies in this way requires a sociocultural perspective on learning that focuses on ways in which language, signs, symbols and practices mediate participation in chemical discourse. This study reports research findings from a teacher-research study of two analogy-writing activities in a chemistry class. The study began with a theoretical model, Third Space, which informed analyses and interpretation of data. Third Space was operationalized into two sub-constructs called Dialogical Interactions and Hybrid Discourses. The aims of this study were to investigate sociocultural aspects of learning chemistry with analogies in order to identify classroom activities where students generate Dialogical Interactions and Hybrid Discourses, and to refine the operationalization of Third Space. These aims were addressed through three research questions. The research questions were studied through an instrumental case study design. The study was conducted in my Year 11 chemistry class at City State High School for the duration of one Semester. Data were generated through a range of data collection methods and analysed through discourse analysis using the Dialogical Interactions and Hybrid Discourse sub-constructs as coding categories. Results indicated that student interactions differed between analogical activities and mathematical problem-solving activities. Specifically, students drew on discourses other than school chemical discourse to construct analogies and their growing participation in chemical discourse was tracked using the Third Space model as an interpretive lens. Results of this study led to modification of the theoretical model adopted at the beginning of the study to a new model called Merged Discourse. Merged Discourse represents the mutual relationship that formed during analogical activities between the Analog Discourse and the Target Discourse. This model can be used for interpreting and analysing classroom discourse centred on analogical activities from sociocultural perspectives. That is, it can be used to code classroom discourse to reveal students’ growing participation with chemical (or scientific) discourse consistent with sociocultural perspectives on learning.

Modeling the impact of potential vaccines on epidemics of sexually transmitted chlamydia trachomatis infection

Background. We investigated the likely impact of vaccines on the prevalence of and morbidity due to Chlamydia trachomatis (chlamydia) infections in heterosexual populations. Methods.An individual‐based mathematical model of chlamydia transmission was developed and linked to the infection course in chlamydia‐infected individuals. The model describes the impact of a vaccine through its effect on the chlamydial load required to infect susceptible individuals (the “critical load”), the load in infected individuals, and their subsequent infectiousness. The model was calibrated using behavioral, biological, and clinical data. Results.A fully protective chlamydia vaccine administered before sexual debut can theoretically eliminate chlamydia epidemics within 20 years. Partially effective vaccines can still greatly reduce the incidence of chlamydia infection. Vaccines should aim primarily to increase the critical load in susceptible individuals and secondarily to decrease the peak load and/or the duration of infection in vaccinated individuals who become infected. Vaccinating both sexes has a beneficial impact on chlamydia‐related morbidity, but targeting women is more effective than targeting men. Conclusions.Our findings can be used in laboratory settings to evaluate vaccine candidates in animal models, by regulatory bodies in the promotion of candidates for clinical trials, and by public health authorities in deciding on optimal intervention strategies.

Fundamental solution and discrete random walk model for time-space fractional diffusion equation

In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.

Spun from four horizons : re-writing the Sydney Harbour Bridge

The Sydney Harbour Bridge provides an imaginative space that is revisited by Australian writers in particular ways. In this space novelists, poets, and cultural historians negotiate questions of emotional and psychological transformation as well as reflect on social and environmental change in the city of Sydney. The writerly tensions that mark these accounts often alter, or query, representations of the Bridge as a symbol of material progress and demonstrate a complex creative engagement with the Bridge. This discussion of ‘the Bridge’ focuses on the work of four authors, Eleanor Dark, P.R. Stephensen, Peter Carey and Vicki Hastrich and includes a range of other fictional and non-fictional accounts of ‘Bridge-writing.’ The ideas proffered are framed by a theorising of space, especially referencing the work of Michel de Certeau, whose writing on the spatial ambiguity of a bridge is important to the examination of the diverse ways in which Australian writers have engaged with the imaginative potential and almost mythic resonance of the Sydney Harbour Bridge.