Porous Ca-Si-based nanospheres : a potential intra-canal disinfectant-carrier for infected canal treatment

The aim of this study is to develop a new intra-canal disinfectant-carrier for infected canal treatment. To achieve this purpose, a new porous Ca-Si (CS)-based nanosphere was synthesized and characterized. Results showed that the nanospheres can infiltrate into dentinal tubules and released the ampicillin over one week time in a sustained manner. The release of ampicillin from spheres has significantly antibacterial property. Extensive and well-organized in vitro mineralization and crystallization of apatite were induced on the surface of dentin slices covered by CS nanospheres. All these features indicate that the porous CS nanospheres may be developed into a new intra-canal disinfectant-carrier for infected canal treatment.

Semantic service discovery in the service ecosystem

Electronic services are a leitmotif in ‘hot’ topics like Software as a Service, Service Oriented Architecture (SOA), Service oriented Computing, Cloud Computing, application markets and smart devices. We propose to consider these in what has been termed the Service Ecosystem (SES). The SES encompasses all levels of electronic services and their interaction, with human consumption and initiation on its periphery in much the same way the ‘Web’ describes a plethora of technologies that eventuate to connect information and expose it to humans. Presently, the SES is heterogeneous, fragmented and confined to semi-closed systems. A key issue hampering the emergence of an integrated SES is Service Discovery (SD). A SES will be dynamic with areas of structured and unstructured information within which service providers and ‘lay’ human consumers interact; until now the two are disjointed, e.g., SOA-enabled organisations, industries and domains are choreographed by domain experts or ‘hard-wired’ to smart device application markets and web applications. In a SES, services are accessible, comparable and exchangeable to human consumers closing the gap to the providers. This requires a new SD with which humans can discover services transparently and effectively without special knowledge or training. We propose two modes of discovery, directed search following an agenda and explorative search, which speculatively expands knowledge of an area of interest by means of categories. Inspired by conceptual space theory from cognitive science, we propose to implement the modes of discovery using concepts to map a lay consumer’s service need to terminologically sophisticated descriptions of services. To this end, we reframe SD as an information retrieval task on the information attached to services, such as, descriptions, reviews, documentation and web sites - the Service Information Shadow. The Semantic Space model transforms the shadow's unstructured semantic information into a geometric, concept-like representation. We introduce an improved and extended Semantic Space including categorization calling it the Semantic Service Discovery model. We evaluate our model with a highly relevant, service related corpus simulating a Service Information Shadow including manually constructed complex service agendas, as well as manual groupings of services. We compare our model against state-of-the-art information retrieval systems and clustering algorithms. By means of an extensive series of empirical evaluations, we establish optimal parameter settings for the semantic space model. The evaluations demonstrate the model’s effectiveness for SD in terms of retrieval precision over state-of-the-art information retrieval models (directed search) and the meaningful, automatic categorization of service related information, which shows potential to form the basis of a useful, cognitively motivated map of the SES for exploratory search.

A hierarchical evolutionary algorithmic design (HEAD) system for generating and evolving building design models

This thesis develops a detailed conceptual design method and a system software architecture defined with a parametric and generative evolutionary design system to support an integrated interdisciplinary building design approach. The research recognises the need to shift design efforts toward the earliest phases of the design process to support crucial design decisions that have a substantial cost implication on the overall project budget. The overall motivation of the research is to improve the quality of designs produced at the author's employer, the General Directorate of Major Works (GDMW) of the Saudi Arabian Armed Forces. GDMW produces many buildings that have standard requirements, across a wide range of environmental and social circumstances. A rapid means of customising designs for local circumstances would have significant benefits. The research considers the use of evolutionary genetic algorithms in the design process and the ability to generate and assess a wider range of potential design solutions than a human could manage. This wider ranging assessment, during the early stages of the design process, means that the generated solutions will be more appropriate for the defined design problem. The research work proposes a design method and system that promotes a collaborative relationship between human creativity and the computer capability. The tectonic design approach is adopted as a process oriented design that values the process of design as much as the product. The aim is to connect the evolutionary systems to performance assessment applications, which are used as prioritised fitness functions. This will produce design solutions that respond to their environmental and function requirements. This integrated, interdisciplinary approach to design will produce solutions through a design process that considers and balances the requirements of all aspects of the design. Since this thesis covers a wide area of research material, 'methodological pluralism' approach was used, incorporating both prescriptive and descriptive research methods. Multiple models of research were combined and the overall research was undertaken following three main stages, conceptualisation, developmental and evaluation. The first two stages lay the foundations for the specification of the proposed system where key aspects of the system that have not previously been proven in the literature, were implemented to test the feasibility of the system. As a result of combining the existing knowledge in the area with the newlyverified key aspects of the proposed system, this research can form the base for a future software development project. The evaluation stage, which includes building the prototype system to test and evaluate the system performance based on the criteria defined in the earlier stage, is not within the scope this thesis. The research results in a conceptual design method and a proposed system software architecture. The proposed system is called the 'Hierarchical Evolutionary Algorithmic Design (HEAD) System'. The HEAD system has shown to be feasible through the initial illustrative paper-based simulation. The HEAD system consists of the two main components - 'Design Schema' and the 'Synthesis Algorithms'. The HEAD system reflects the major research contribution in the way it is conceptualised, while secondary contributions are achieved within the system components. The design schema provides constraints on the generation of designs, thus enabling the designer to create a wide range of potential designs that can then be analysed for desirable characteristics. The design schema supports the digital representation of the human creativity of designers into a dynamic design framework that can be encoded and then executed through the use of evolutionary genetic algorithms. The design schema incorporates 2D and 3D geometry and graph theory for space layout planning and building formation using the Lowest Common Design Denominator (LCDD) of a parameterised 2D module and a 3D structural module. This provides a bridge between the standard adjacency requirements and the evolutionary system. The use of graphs as an input to the evolutionary algorithm supports the introduction of constraints in a way that is not supported by standard evolutionary techniques. The process of design synthesis is guided as a higher level description of the building that supports geometrical constraints. The Synthesis Algorithms component analyses designs at four levels, 'Room', 'Layout', 'Building' and 'Optimisation'. At each level multiple fitness functions are embedded into the genetic algorithm to target the specific requirements of the relevant decomposed part of the design problem. Decomposing the design problem to allow for the design requirements of each level to be dealt with separately and then reassembling them in a bottom up approach reduces the generation of non-viable solutions through constraining the options available at the next higher level. The iterative approach, in exploring the range of design solutions through modification of the design schema as the understanding of the design problem improves, assists in identifying conflicts in the design requirements. Additionally, the hierarchical set-up allows the embedding of multiple fitness functions into the genetic algorithm, each relevant to a specific level. This supports an integrated multi-level, multi-disciplinary approach. The HEAD system promotes a collaborative relationship between human creativity and the computer capability. The design schema component, as the input to the procedural algorithms, enables the encoding of certain aspects of the designer's subjective creativity. By focusing on finding solutions for the relevant sub-problems at the appropriate levels of detail, the hierarchical nature of the system assist in the design decision-making process.

Middle school social sciences : exploring teachers’ conceptions of essential knowledge

This study examines teachers’ conceptions of essential knowledge in the humanities and social sciences, commonly referred to as "social education", in the middle years of schooling. Social education has long been a highly contested area of the curriculum in Australia. In Queensland, social education comprises the integrated learning area of Studies of Society and Environment (SOSE). However, the new Australian Curriculum marks a return to discipline-based study of history and geography. This phenomenographic study addresses a perceived lack of understanding in the current research literature in Australia of the nature of middle school teachers’ professional knowledge for teaching the social sciences. Teachers are conceptualised in this study as curriculum makers in the classroom and, as such, their conceptions of essential knowledge are significant. Shulman’s (1986, 1987) theory of teachers’ knowledge forms the theoretical foundation of the study, which is contextualised in Federal and State education policies and the literature on the middle phase of schooling. Transcripts of interviews conducted with a group of thirty-one Queensland middle school teachers of SOSE were subjected to phenomenographic analysis, revealing seven qualitatively different categories of description. Essential aspects of knowledge for social education emerging from the study were: (1) discipline-based knowledge; (2) curriculum knowledge; (3) knowledge derived from teaching experience; (4) knowledge of middle years learners; (5) knowledge of integration; (6) knowledge of current affairs; and (7) knowledge invested in teacher identity. The three dimensions of variation that linked and differentiated the categories were: (1) content; (2) inquiry learning; and (3) teacher autonomy. These findings are presented as an outcome space where the categories are grouped as knowledge of the learning area, knowledge of contexts and knowledge of self as teacher. The results of the study suggest that social education teachers’ identity and knowledge of self are critical aspects of their knowledge as curriculum makers. The results illustrate that the professional and personal domains intersect, extending Shulman’s (1986, 1987) original theorisation of teachers’ knowledge into the personal arena. Further, middle years teachers’ conceptions of essential knowledge reveal a practice-based theorisation of knowledge for social education that fits the goals of middle schooling. The research concludes that attention to teacher identity in teacher education and in-service professional development has considerable potential to grow teachers’ knowledge in the social sciences and enhance their capacity for school-based curriculum leadership.

Hospital outpatient responses to potential driving impairment due to prescribed medications

Driving and using prescription medicines that have the potential to impair driving is an emerging research area. To date it is characterised by a limited (although growing) number of studies and methodological complexities that make generalisations about impairment due to medications difficult. Consistent evidence has been found for the impairing effects of hypnotics, sedative antidepressants and antihistamines, and narcotic analgesics, although it has been estimated that as many as nine medication classes have the potential to impair driving (Alvarez & del Rio, 2000; Walsh, de Gier, Christopherson, & Verstraete, 2004). There is also evidence for increased negative effects related to concomitant use of other medications and alcohol (Movig et al., 2004; Pringle, Ahern, Heller, Gold, & Brown, 2005). Statistics on the high levels of Australian prescription medication use suggest that consumer awareness of driving impairment due to medicines should be examined. One web-based study has found a low level of awareness, knowledge and risk perceptions among Australian drivers about the impairing effects of various medications on driving (Mallick, Johnston, Goren, & Kennedy, 2007). The lack of awareness and knowledge brings into question the effectiveness of the existing countermeasures. In Australia these consist of the use of ancillary warning labels administered under mandatory regulation and professional guidelines, advice to patients, and the use of Consumer Medicines Information (CMI) with medications that are known to cause impairment. The responsibility for the use of the warnings and related counsel to patients primarily lies with the pharmacist when dispensing relevant medication. A review by the Therapeutic Goods Administration (TGA) noted that in practice, advice to patients may not occur and that CMI is not always available (TGA, 2002). Researchers have also found that patients' recall of verbal counsel is very low (Houts, Bachrach, Witmer, Tringali, Bucher, & Localio, 1998). With healthcare observed as increasingly being provided in outpatient conditions (Davis et al., 2006; Vingilis & MacDonald, 2000), establishing the effectiveness of the warning labels as a countermeasure is especially important. There have been recent international developments in medication categorisation systems and associated medication warning labels. In 2005, France implemented a four-tier medication categorisation and warning system to improve patients' and health professionals' awareness and knowledge of related road safety issues (AFSSAPS, 2005). This warning system uses a pictogram and indicates the level of potential impairment in relation to driving performance through the use of colour and advice on the recommended behaviour to adopt towards driving. The comparable Australian system does not indicate the severity level of potential effects, and does not provide specific guidelines on the attitude or actions that the individual should adopt towards driving. It is reliant upon the patient to be vigilant in self-monitoring effects, to understand the potential ways in which they may be affected and how serious these effects may be, and to adopt the appropriate protective actions. This thesis investigates the responses of a sample of Australian hospital outpatients who receive appropriate labelling and counselling advice about potential driving impairment due to prescribed medicines. It aims to provide baseline data on the understanding and use of relevant medications by a Queensland public hospital outpatient sample recruited through the hospital pharmacy. It includes an exploration and comparison of the effect of the Australian and French medication warning systems on medication user knowledge, attitudes, beliefs and behaviour, and explores whether there are areas in which the Australian system may be improved by including any beneficial elements of the French system. A total of 358 outpatients were surveyed, and a follow-up telephone survey was conducted with a subgroup of consenting participants who were taking at least one medication that required an ancillary warning label about driving impairment. A complementary study of 75 French hospital outpatients was also conducted to further investigate the performance of the warnings. Not surprisingly, medication use among the Australian outpatient sample was high. The ancillary warning labels required to appear on medications that can impair driving were prevalent. A subgroup of participants was identified as being potentially at-risk of driving impaired, based on their reported recent use of medications requiring an ancillary warning label and level of driving activity. The sample reported previous behaviour and held future intentions that were consistent with warning label advice and health protective action. Participants did not express a particular need for being advised by a health professional regarding fitness to drive in relation to their medication. However, it was also apparent from the analysis that the participants would be significantly more likely to follow advice from a doctor than a pharmacist. High levels of knowledge in terms of general principles about effects of alcohol, illicit drugs and combinations of substances, and related health and crash risks were revealed. This may reflect a sample specific effect. Emphasis is placed in the professional guidelines for hospital pharmacists that make it essential that advisory labels are applied to medicines where applicable and that warning advice is given to all patients on medication which may affect driving (SHPA, 2006, p. 221). The research program applied selected theoretical constructs from Schwarzer's (1992) Health Action Process Approach, which has extended constructs from existing health theories such as the Theory of Planned Behavior (Ajzen, 1991) to better account for the intention-behaviour gap often observed when predicting behaviour. This was undertaken to explore the utility of the constructs in understanding and predicting compliance intentions and behaviour with the mandatory medication warning about driving impairment. This investigation revealed that the theoretical constructs related to intention and planning to avoid driving if an effect from the medication was noticed were useful. Not all the theoretical model constructs that had been demonstrated to be significant predictors in previous research on different health behaviours were significant in the present analyses. Positive outcome expectancies from avoiding driving were found to be important influences on forming the intention to avoid driving if an effect due to medication was noticed. In turn, intention was found to be a significant predictor of planning. Other selected theoretical constructs failed to predict compliance with the Australian warning label advice. It is possible that the limited predictive power of a number of constructs including risk perceptions is due to the small sample size obtained at follow up on which the evaluation is based. Alternately, it is possible that the theoretical constructs failed to sufficiently account for issues of particular relevance to the driving situation. The responses of the Australian hospital outpatient sample towards the Australian and French medication warning labels, which differed according to visual characteristics and warning message, were examined. In addition, a complementary study with a sample of French hospital outpatients was undertaken in order to allow general comparisons concerning the performance of the warnings. While a large amount of research exists concerning warning effectiveness, there is little research that has specifically investigated medication warnings relating to driving impairment. General established principles concerning factors that have been demonstrated to enhance warning noticeability and behavioural compliance have been extrapolated and investigated in the present study. The extent to which there is a need for education and improved health messages on this issue was a core issue of investigation in this thesis. Among the Australian sample, the size of the warning label and text, and red colour were the most visually important characteristics. The pictogram used in the French labels was also rated highly, and was salient for a large proportion of the sample. According to the study of French hospital outpatients, the pictogram was perceived to be the most important visual characteristic. Overall, the findings suggest that the Australian approach of using a combination of visual characteristics was important for the majority of the sample but that the use of a pictogram could enhance effects. A high rate of warning recall was found overall and a further important finding was that higher warning label recall was associated with increased number of medication classes taken. These results suggest that increased vigilance and care are associated with the number of medications taken and the associated repetition of the warning message. Significantly higher levels of risk perception were found for the French Level 3 (highest severity) label compared with the comparable mandatory Australian ancillary Label 1 warning. Participants' intentions related to the warning labels indicated that they would be more cautious while taking potentially impairing medication displaying the French Level 3 label compared with the Australian Label 1. These are potentially important findings for the Australian context regarding the current driving impairment warnings about displayed on medication. The findings raise other important implications for the Australian labelling context. An underlying factor may be the differences in the wording of the warning messages that appear on the Australian and French labels. The French label explicitly states "do not drive" while the Australian label states "if affected, do not drive", and the difference in responses may reflect that less severity is perceived where the situation involves the consumer's self-assessment of their impairment. The differences in the assignment of responsibility by the Australian (the consumer assesses and decides) and French (the doctor assesses and decides) approaches for the decision to drive while taking medication raises the core question of who is most able to assess driving impairment due to medication: the consumer, or the health professional? There are pros and cons related to knowledge, expertise and practicalities with either option. However, if the safety of the consumer is the primary aim, then the trend towards stronger risk perceptions and more consistent and cautious behavioural intentions in relation to the French label suggests that this approach may be more beneficial for consumer safety. The observations from the follow-up survey, although based on a small sample size and descriptive in nature, revealed that just over half of the sample recalled seeing a warning label about driving impairment on at least one of their medications. The majority of these respondents reported compliance with the warning advice. However, the results indicated variation in responses concerning alcohol intake and modifying the dose of medication or driving habits so that they could continue to drive, which suggests that the warning advice may not be having the desired impact. The findings of this research have implications for current countermeasures in this area. These have included enhancing the role that prescribing doctors have in providing warnings and advice to patients about the impact that their medication can have on driving, increasing consumer perceptions of the authority of pharmacists on this issue, and the reinforcement of the warning message. More broadly, it is suggested that there would be benefit in a wider dissemination of research-based information on increased crash risk and systematic monitoring and publicity about the representation of medications in crashes resulting in injuries and fatalities. Suggestions for future research concern the continued investigation of the effects of medications and interactions with existing medical conditions and other substances on driving skills, effects of variations in warning label design, individual behaviours and characteristics (particularly among those groups who are dependent upon prescription medication) and validation of consumer self-assessment of impairment.

Potential retrofitting of existing campus buildings to green buildings

Green building is building that the focus is to maximize the energy efficiency and resources used. While, retrofitting is the process of renovate or refurnish the existing building. Therefore by retrofit existing buildings that comply with green building requirement, it improves the environmental attributes of the buildings. In Malaysia, existing buildings and its communities contribute over 40% of green house gases to the environment. This paper describes a study that explores the potential to retrofit existing campus buildings that response to sustainable green building standard. A validation survey was carried out and the data collected was analysed using SPSS in order to confirm the significance of retrofitting Universiti Teknologi Malaysia (UTM) buildings toward green building initiative. The results show that all the twenty eight identified green elements recorded average index of higher than 3.5 which means that there is significant needs to retrofit the existing buildings to green buildings. This study concludes that it is urgently need for the campus to response to green building requirements in order to achieve higher energy effeciency and this can be done through effective etrofitting of existing buildings.

Negative space and positive environment : mapping opportunities for urban resilience

Cities have long held a fascination for people – as they grow and develop, there is a desire to know and understand the intricate interplay of elements that makes cities ‘live’. In part, this is a need for even greater efficiency in urban centres, yet the underlying quest is for a sustainable urban form. In order to make sense of the complex entities that we recognise cities to be, they have been compared to buildings, organisms and more recently machines. However the search for better and more elegant urban centres is hardly new, healthier and more efficient settlements were the aim of Modernism’s rational sub-division of functions, which has been translated into horizontal distribution through zoning, or vertical organisation thought highrise developments. However both of these approaches have been found to be unsustainable, as too many resources are required to maintain this kind or urbanisation and social consequences of either horizontal or vertical isolation must also be considered. From being absolute consumers of resources, of energy and of technology, cities need to change, to become sustainable in order to be more resilient and more efficient in supporting culture, society as well as economy. Our urban centres need to be re-imagined, re-conceptualised and re-defined, to match our changing society. One approach is to re-examine the compartmentalised, mono-functional approach of urban Modernism and to begin to investigate cities like ecologies, where every element supports and incorporates another, fulfilling more than just one function. This manner of seeing the city suggests a framework to guide the re-mixing of urban settlements. Beginning to understand the relationships between supporting elements and the nature of the connecting ‘web’ offers an invitation to investigate the often ignored, remnant spaces of cities. This ‘negative space’ is the residual from which space and place are carved out in the Contemporary city, providing the link between elements of urban settlement. Like all successful ecosystems, cities need to evolve and change over time in order to effectively respond to different lifestyles, development in culture and society as well as to meet environmental challenges. This paper seeks to investigate the role that negative space could have in the reorganisation of the re-mixed city. The space ‘in-between’ is analysed as an opportunity for infill development or re-development which provides to the urban settlement the variety that is a pre-requisite for ecosystem resilience. An analysis of the urban form is suggested as an empirical tool to map the opportunities already present in the urban environment and negative space is evaluated as a key element in achieving a positive development able to distribute diverse environmental and social facilities in the city.

Wing shape as a potential discriminator of morphologically similar pest taxa within the Bactrocera dorsalis species complex (Diptera: Tephritidae)

Four morphologically cryptic species of the Bactrocera dorsalis fruit fly complex (B. dorsalis s.s., B. papayae, B. carambolae and B. philippinensis) are serious agricultural pests. As they are difficult to diagnose using traditional taxonomic techniques, we examined the potential for geometric morphometric analysis of wing size and shape to discriminate between them. Fifteen wing landmarks generated size and shape data for 245 specimens for subsequent comparisons among three geographically distinct samples of each species. Intraspecific wing size was significantly different within samples of B. carambolae and B. dorsalis s.s. but not within samples of B. papayae or B. philippinensis. Although B. papayae had the smallest wings (average centroid size=6.002 mm±0.061 SE) and B. dorsalis s.s. the largest (6.349 mm±0.066 SE), interspecific wing size comparisons were generally non-informative and incapable of discriminating species. Contrary to the wing size data, canonical variate analysis based on wing shape data discriminated all species with a relatively high degree of accuracy; individuals were correctly reassigned to their respective species on average 93.27% of the time. A single sample group of B. carambolae from locality 'TN Malaysia' was the only sample to be considerably different from its conspecific groups with regards to both wing size and wing shape. This sample was subsequently deemed to have been originally misidentified and likely represents an undescribed species. We demonstrate that geometric morphometric techniques analysing wing shape represent a promising approach for discriminating between morphologically cryptic taxa of the B. dorsalis species complex.

Investigating the potential value of individual parameters of histological grading systems in a sheep model of cartilage damage : the modified Mankin method

A total histological grade does not necessarily distinguish between different manifestations of cartilage damage or degeneration. An accurate and reliable histological assessment method is required to separate normal and pathological tissue within a joint during treatment of degenerative joint conditions and to sub-classify the latter in meaningful ways. The Modified Mankin method may be adaptable for this purpose. We investigated how much detail may be lost by assigning one composite score/grade to represent different degenerative components of the osteoarthritic condition. We used four ovine injury models (sham surgery, anterior cruciate ligament/medial collateral ligament instability, simulated anatomic anterior cruciate ligament reconstruction and meniscal removal) to induce different degrees and potentially 'types' (mechanisms) of osteoarthritis. Articular cartilage was systematically harvested, prepared for histological examination and graded in a blinded fashion using a Modified Mankin grading method. Results showed that the possible permutations of cartilage damage were significant and far more varied than the current intended use that histological grading systems allow. Of 1352 cartilage specimens graded, 234 different manifestations of potential histological damage were observed across 23 potential individual grades of the Modified Mankin grading method. The results presented here show that current composite histological grading may contain additional information that could potentially discern different stages or mechanisms of cartilage damage and degeneration in a sheep model. This approach may be applicable to other grading systems.

Alternating direction implicit numerical method for the space and time fractional Bloch-Torrey equation in 3-D

Recently, some authors have considered a new diffusion model–space and time fractional Bloch-Torrey equation (ST-FBTE). Magin et al. (2008) have derived analytical solutions with fractional order dynamics in space (i.e., _ = 1, β an arbitrary real number, 1 < β ≤ 2) and time (i.e., 0 < α < 1, and β = 2), respectively. Yu et al. (2011) have derived an analytical solution and an effective implicit numerical method for solving ST-FBTEs, and also discussed the stability and convergence of the implicit numerical method. However, due to the computational overheads necessary to perform the simulations for nuclear magnetic resonance (NMR) in three dimensions, they present a study based on a two-dimensional example to confirm their theoretical analysis. Alternating direction implicit (ADI) schemes have been proposed for the numerical simulations of classic differential equations. The ADI schemes will reduce a multidimensional problem to a series of independent one-dimensional problems and are thus computationally efficient. In this paper, we consider the numerical solution of a ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. A fractional alternating direction implicit scheme (FADIS) for the ST-FBTE in 3-D is proposed. Stability and convergence properties of the FADIS are discussed. Finally, some numerical results for ST-FBTE are given.

A new implicit numerical method for the space and time fractional Bloch-Torrey equation

In recent years, it has been found that many phenomena in engineering, physics, chemistry and other sciences can be described very successfully by models using mathematical tools from fractional calculus. Recently, noted a new space and time fractional Bloch-Torrey equation (ST-FBTE) has been proposed (see Magin et al. (2008)), and successfully applied to analyse diffusion images of human brain tissues to provide new insights for further investigations of tissue structures. In this paper, we consider the ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we propose a new effective implicit numerical method (INM) for the STFBTE whereby we discretize the Riesz fractional derivative using a fractional centered difference. Secondly, we prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent, and the order of convergence of the implicit numerical method is ( T2 - α + h2 x + h2 y + h2 z ). Finally, some numerical results are presented to support our theoretical analysis.

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

The field of fractional differential equations provides a means for modelling transport processes within complex media which are governed by anomalous transport. Indeed, the application to anomalous transport has been a significant driving force behind the rapid growth and expansion of the literature in the field of fractional calculus. In this paper, we present a finite volume method to solve the time-space two-sided fractional advection dispersion equation on a one-dimensional domain. Such an equation allows modelling different flow regime impacts from either side. The finite volume formulation provides a natural way to handle fractional advection-dispersion equations written in conservative form. The novel spatial discretisation employs fractionally-shifted Gr¨unwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes, while the L1-algorithm is used to discretise the Caputo time fractional derivative. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

An implicit RBF meshless method for a fractal mobile/immobile transport model

Fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBF) to discretize the space variable. By contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example is presented to describe the fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating of fractional differential equations, and it has good potential in development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

A second-order accurate numerical approximation for the Riesz space fractional advection-dispersion equation

In this paper, we consider a space Riesz fractional advection-dispersion equation. The equation is obtained from the standard advection-diffusion equation by replacing the ¯rst-order and second-order space derivatives by the Riesz fractional derivatives of order β 1 Є (0; 1) and β2 Є(1; 2], respectively. Riesz fractional advection and dispersion terms are approximated by using two fractional centered difference schemes, respectively. A new weighted Riesz fractional ¯nite difference approximation scheme is proposed. When the weighting factor Ѳ = 1/2, a second- order accurate numerical approximation scheme for the Riesz fractional advection-dispersion equation is obtained. Stability, consistency and convergence of the numerical approximation scheme are discussed. A numerical example is given to show that the numerical results are in good agreement with our theoretical analysis.