Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

Generalized fractional partial differential equations have now found wide application for describing important physical phenomena, such as subdiffusive and superdiffusive processes. However, studies of generalized multi-term time and space fractional partial differential equations are still under development. In this paper, the multi-term time-space Caputo-Riesz fractional advection diffusion equations (MT-TSCR-FADE) with Dirichlet nonhomogeneous boundary conditions are considered. The multi-term time-fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0, 1], [1, 2] and [0, 2], respectively. These are called respectively the multi-term time-fractional diffusion terms, the multi-term time-fractional wave terms and the multi-term time-fractional mixed diffusion-wave terms. The space fractional derivatives are defined as Riesz fractional derivatives. Analytical solutions of three types of the MT-TSCR-FADE are derived with Dirichlet boundary conditions. By using Luchko's Theorem (Acta Math. Vietnam., 1999), we proposed some new techniques, such as a spectral representation of the fractional Laplacian operator and the equivalent relationship between fractional Laplacian operator and Riesz fractional derivative, that enabled the derivation of the analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations. © 2012.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

A novel quadratic Edge-based Smoothed Conforming Point Interpolation Method (ES-CPIM) for elasticity problems

his paper formulates an edge-based smoothed conforming point interpolation method (ES-CPIM) for solid mechanics using the triangular background cells. In the ES-CPIM, a technique for obtaining conforming PIM shape functions (CPIM) is used to create a continuous and piecewise quadratic displacement field over the whole problem domain. The smoothed strain field is then obtained through smoothing operation over each smoothing domain associated with edges of the triangular background cells. The generalized smoothed Galerkin weak form is then used to create the discretized system equations. Numerical studies have demonstrated that the ES-CPIM possesses the following good properties: (1) ES-CPIM creates conforming quadratic PIM shape functions, and can always pass the standard patch test; (2) ES-CPIM produces a quadratic displacement field without introducing any additional degrees of freedom; (3) The results of ES-CPIM are generally of very high accuracy.

Clinical performance of a new silicone hydrogel contact lens over 6 months of extended wear

Purpose: Silicone hydrogel contact lenses (CLs) are becoming increasingly popular for daily wear (DW), extended wear (EW) and continuous wear (CW), due to their higher oxygen transmissibility compared to hydrogel CLs. The aim of this study was to investigate the clinical and subjective performance of asmofilcon A (Menicon Co., Ltd), a new surface treated silicone hydrogel CL, during 6-night EW over 6 months (M). Methods: A prospective, randomised, single-masked, monadic study was conducted. N=60 experienced DW soft CL wearers were randomly assigned to wear either asmofilcon A (test: Dk=129, water content (WC)=40%, Nanogloss surface treatment) or senofilcon A (control: Dk=103, WC=38%, PVP internal wetting agent, Vistakon, Johnson & Johnson Vision Care) CLs bilaterally for 6 M on an EW basis. A PHMB-preserved solution (Menicon Co., Ltd) was dispensed for CL care. Evaluations were conducted at CL delivery and after 1 week (W), 4 W, 3 M and 6 M of EW. At each visit, a range of objective and subjective clinical performance measures were assessed. Results: N=50 subjects (83%) successfully completed the study, with the majority of discontinuations due to loss to follow-up (n=3) or moving away/travel (n=5). N=2 subjects experienced adverse events; n=1 unilateral red eye with asmofilcon A and n=1 asymptomatic infiltrate with senofilcon A. There were no significant differences in high or low contrast distance visual acuity (HCDVA or LCDVA) between asmofilcon A and senofilcon A; however, LCDVA decreased significantly over time with both CL types (p<0.05). The two CL types did not vary significantly with respect to any of the objective and subjective measures assessed (p>0.05); CL fitting characteristics and CL surface measurements were very similar and mean bulbar and limbal redness measures were always less than grade 1.0. Superior palpebral conjunctival injection showed a statistically, but not clinically, significant increase over time with both CL types (p<0.05). Corneal staining did not vary significantly between asmofilcon A and senofilcon A (p>0.05), with low median gradings of less than 0.5 observed for all areas assessed. There were no solution-related staining reactions observed with either CL type. The asmofilcon A and senofilcon A CLs were both rated highly with respect to overall comfort, with medians of 14 or 15 hours of comfortable lens wearing time per day reported at each of the study visits (p>0.05). Conclusions: Over 6 months of EW, the asmofilcon A and senofilcon A CLs performed in a similar manner with respect to visual acuity, ocular health and CL performance measures. Some changes over time were observed with both CL types, including reduced LCDVA and increased superior palpebral injection, which warrant further investigation in longer-term EW studies. Asmofilcon A appeared to be equivalent in performance to senofilcon A.

Tooth fracture risk analysis based on a new finite element dental structure models using micro-CT data

The finite element (FE) analysis is an effective method to study the strength and predict the fracture risk of endodontically-treated teeth. This paper presents a rapid method developed to generate a comprehensive tooth FE model using data retrieved from micro-computed tomography (μCT). With this method, the inhomogeneity of material properties of teeth was included into the model without dividing the tooth model into different regions. The material properties of the tooth were assumed to be related to the mineral density. The fracture risk at different tooth portions was assessed for root canal treatments. The micro-CT images of a tooth were processed by a Matlab software programme and the CT numbers were retrieved. The tooth contours were obtained with thresholding segmentation using Amira. The inner and outer surfaces of the tooth were imported into Solidworks and a three-dimensional (3D) tooth model was constructed. An assembly of the tooth model with the periodontal ligament (PDL) layer and surrounding bone was imported into ABAQUS. The material properties of the tooth were calculated from the retrieved CT numbers via ABAQUS user's subroutines. Three root canal geometries (original and two enlargements) were investigated. The proposed method in this study can generate detailed 3D finite element models of a tooth with different root canal enlargements and filling materials, and would be very useful for the assessment of the fracture risk at different tooth portions after root canal treatments.

What health problems overcrowd hospital emergency departments in Queensland and has this changed over time? A case study of two hospitals in Queensland 2001 - 2009

Aim: to describe what health problems patients attending emergency department with and whether this changed over time. Methods: Electronic data was retrieved from EDIS (Emergency Department Information System) and HBCIS (Hospital Based Clinical Information System) in two hospitals in Queensland in the period 2001-2009. The ICD-10 code of patient's diagnosis was then extrapolated and then group into ICD-10 chapters, such that the health problem can be presented. Results: Among the specific health problems, Chapter XIX 'Injury and poisoning' ranked number one consistently (ranging from 22.1% to 31.2% of the total presentations) in both the urban and remote hospitals in Queensland. The top ten specific presenting health problems in both the urban and remote hospital include Chapter XI 'Digestive system', Chapter XIV 'Genitourinary system', Chapter IX 'Circulatory system', and Chapter XIII 'Musculoskeletal system and connective tissue'. Chapter X 'Respiratory system' made the top ten presenting Chapters in both hospitals, but ranked much higher (number four consistently for the eight years, ranging from 6.8% to 8.3%) in the remote hospital. Chapter XV 'Pregnancy childbirth and puerperium' made to the top ten in the urban hospital only while Chapter XII 'Skin and subcutaneous tissue', Chapter I 'Infectious and parasitic diseases' made the top ten in the remote hospital only. Conclusion: The number one health problem presenting to both the urban and remote hospitals in Queensland is Chapter XIX 'Injury and poisoning', and it did not change in the period 211 - 2009.

Towards local cultures of sustainability : facilitating community created environment education centres through design

Ecological sustainability has been proposed to address the problem of human impacts increasingly degrading planetary resources and ecosystems, threatening biodiversity, eco-services and human survival. Ecological sustainability is an imperative, with Australia having one of the highest eco-footprints per person worldwide. While significant progress has been made via implementation of ecologically sustainable design in urban communities, relatively little has been undertaken in small, disparate regional communities in Australia. Regional communities are disadvantaged by rural economic decline associated with structural change and inequities of resource transfer. The ecologically sustainable solution is holistic, so all settlements need to be globally wise, richly biodiverse yet locally specific. As a regional solution to this global problem, this research offers the practical means by which a small regional community can contribute. It focuses on the design and implementation of a community centre and the fostering of transformative community learning through an integrated ‘learning community’ awareness of ecologically sustainable best practice. Lessons learned are documented by the participant researcher who as a designer, facilitator, local resident and social narrator has been deeply connected with the Tweed-Caldera region over a period since 1980. The collective action of the local community of Chillingham has been diligently recorded over a decade of design and development. Over this period, several positive elements emerged in terms of improvements to the natural and built environment, greater social cohesion and co-operative learning along with a shift towards a greener local economy. Behavioural changes in the community were noted as residents strived to embrace ecological ideals and reduce fossil fuel dependency. They found attractive local solutions to sourcing of food and using local employment opportunities to up skill their residents via transformative learning as a community in transition. Finally, the catalytic impact of external partnering has also been documented. How well the region as a whole has achieved its ecologically sustainable objectives is measured in terms of the delivered success of private and public partnering with the community, the creation of a community centre cum environment education centre, the restoration of local heritage buildings, the repair of riparian forests and improved water conditions in local river systems, better roads and road safety, local skills and knowledge transfer, support of local food and local/regional growers markets to attract tourists via the integrated trails network. In aggregate, each and every element contributes to a measure of eco-positive development for the built environment, its social organisation and its economy that has guided the local community to find its own pathway to sustainability. Within the Tweed-Caldera bioregion in northern New South Wales, there has been a lack of strategic planning, ecologically sustainable knowledge and facilities in isolated communities that could support the development of a local sustained green economy, provide a hub for socio-cultural activities and ecology based education. The first challenge in this research was to model a whole systems approach to eco-positive development in Chillingham, NSW, a small community where Nature and humanity know no specific boundary. The net result was the creation of a community environment education centre featuring best-affordable ecological practice and regionally distinctive, educational building form from a disused heritage building (cow bale). This development, implemented over a decade, resonated with the later regional wide programs that were linked in the Caldera region by the common purpose of extending the reach of local and state government assistance to regional NSW in economic transition coupled with sustainability. The lessons learned from these linked projects reveal that subsequent programs have been significantly easier to initiate, manage, develop and deliver results. In particular, pursuing collaborative networks with all levels of government and external private partners has been economically effective. Each community’s uniqueness has been celebrated and through drawing out these distinctions, has highlighted local vision, strategic planning, sense of belonging and connection of people with place. This step has significantly reduced the level of friction between communities that comes from natural competition for the finite pool of funds. Following the pilot Tweed-Caldera study, several other NSW regional communities are now undertaking a Community Economic Transition Program based on the processes, trials and positive experiences witnessed in the Tweed-Caldera region where it has been demonstrated that regional community transition programs can provide an opportunity to plan and implement effective long term strategies for sustainability, empowering communities to participate in eco-governance. This thesis includes the design and development of a framework for community created environment education centres to provide an equal access place for community to participate to meet their essential needs locally. An environment centre that facilitates community transition based on easily accessible environmental education, skills and infrastructure is necessary to develop local cultures of sustainability. This research draws upon the literatures of ecologically sustainable development, environmental education and community development in the context of regional community transition towards ‘strong sustainability’. The research approach adapted is best described as a four stage collaborative action research cycle where the participant researcher (me) has a significant involvement in the process to foster local cultures of sustainability by empowering its citizens to act locally and in doing so, become more self reliant and socially resilient. This research also draws upon the many fine working exemplars, such as the resilience of the Cuban people, the transition town initiative in Totnes, U.K. and the models of Australian Community Gardens, such as CERES (Melbourne) and Northey Street (Brisbane). The objectives of this study are to research and evaluate exemplars of ecologically sustainable environment education centres, to facilitate the design and development of an environment education centre created by a small regional community as an ecologically sustainable learning environment; to facilitate a framework for community transition based on environmental education, skills and infrastructure necessary to develop local cultures of sustainability. The research was undertaken as action research in the Tweed Caldera in Northern NSW. This involved the author as participant researcher, designer and volunteer in two interconnected initiatives: the Chillingham Community Centre development and the Caldera Economic Transition Program (CETP). Both initiatives involved a series of design-led participatory community workshops that were externally facilitated with the support of government agency partnerships, steering committees and local volunteers. Together the Caldera research programs involved communities participating in developing their own strategic planning process and outcomes. The Chillingham Community Centre was developed as a sustainable community centre/hub using a participatory design process. The Caldera Economic Transition Program (CETP) prioritised Caldera region projects: the Caldera farmer’s market; community gardens and community kitchens; community renewable energy systems and an integrated trails network. The significant findings were: the CETP projects were capable of moving towards an eco-positive design benchmark through transformative learning. Community transition to sustainability programs need to be underpinned by sustainability and environmental education based frameworks and practical on ground experience in local needs based projects through transformative learning. The actioned projects were successfully undertaken through community participation and teamwork. Ecological footprint surveys were undertaken to guide and assess the ongoing community transition process, however the paucity of responses needs to be revisited. The concept of ecologically sustainable development has been adopted internationally, however existing design and planning strategies do not assure future generations continued access to healthy natural life support systems. Sustainable design research has usually been urban focussed, with little attention paid to regional communities. This study seeks to redress this paucity through the design of ecologically sustainable (deep green) learning environments for small regional communities. Through a design-led process of environmental education, this study investigates how regional communities can be facilitated to model the principles of eco-positive development to support transition to local cultures of sustainability. This research shows how community transition processes and projects can incorporate sustainable community development as transformative learning through design. Regional community transition programs can provide an opportunity to plan long term strategies for sustainability, empowering people to participate in eco-governance. A framework is developed for a community created environment education centre to provide an equal access place for the local community to participate in implementing ways to meet their essential needs locally. A community environment education centre that facilitates community transition based on holistic environmental education, skills and infrastructure is necessary to develop local cultures of sustainability.

Design and fabrication of tubular scaffolds via direct writing in a melt electrospinning mode

Flexible tubular structures fabricated from solution electrospun fibers are finding increasing use in tissue engineering applications. However it is difficult to control the deposition of fibers due to the chaotic nature of the solution electrospinning jet. By using non-conductive polymer melts instead of polymer solutions the path and collection of the fiber becomes predictable. In this work we demonstrate the melt electrospinning of polycaprolactone in a direct writing mode onto a rotating cylinder. This allows the design and fabrication of tubes using 20 μm diameter fibers with controllable micropatterns and mechanical properties. A key design parameter is the fiber winding angle, where it allows control over scaffold pore morphology (e.g. size, shape, number and porosity). Furthermore, the establishment of a finite element model as a predictive design tool is validated against mechanical testing results of melt electrospun tubes to show that a lesser winding angle provides improved mechanical response to uniaxial tension and compression. In addition, we show that melt electrospun tubes support the growth of three different cell types in vitro and are therefore promising scaffolds for tissue engineering applications.

An invasive grass shows colonization advantages over native grasses under conditions of low resource availability

Increased or fluctuating resources may facilitate opportunities for invasive exotic plants to dominate. This hypothesis does not, however, explain how invasive species succeed in regions characterized by low resource conditions or how these species persist in the lulls between high resource periods. We compare the growth of three co-occurring C4 perennial bunchgrasses under low resource conditions: an exotic grass, Eragrostis curvula (African lovegrass) and two native grasses, Themeda triandra and Eragrostis sororia. We grew each species over 12 weeks under low nutrients and three low water regimes differentiated by timing: continuous, pulsed, and mixed treatments (switched from continuous to pulsed and back to continuous). Over time, we measured germination rates, time to germination (first and second generations), height, root biomass, vegetative biomass, and reproductive biomass. Contrary to our expectations that the pulsed watering regime would favor the invader, water-supply treatments had little significant effect on plant growth. We did find inherent advantages in a suite of early colonization traits that likely favor African lovegrass over the natives including faster germination speed, earlier flowering times, faster growth rates and from 2 weeks onward it was taller. African lovegrass also showed similar growth allocation strategies to the native grasses in terms of biomass levels belowground, but produced more vegetative biomass than kangaroo grass. Overall our results suggest that even under low resource conditions invasive plant species like African lovegrass can grow similarly to native grasses, and for some key colonization traits, like germination rate, perform better than natives.

The development of ground impact models for the analysis of the risks associated with Unmanned Aircraft Operations over inhabited areas

With the emergence of Unmanned Aircraft Systems (UAS) there is a growing need for safety standards and regulatory frameworks to manage the risks associated with their operations. The primary driver for airworthiness regulations (i.e., those governing the design, manufacture, maintenance and operation of UAS) are the risks presented to people in the regions overflown by the aircraft. Models characterising the nature of these risks are needed to inform the development of airworthiness regulations. The output from these models should include measures of the collective, individual and societal risk. A brief review of these measures is provided. Based on the review, it was determined that the model of the operation of an UAS over inhabited areas must be capable of describing the distribution of possible impact locations, given a failure at a particular point in the flight plan. Existing models either do not take the impact distribution into consideration, or propose complex and computationally expensive methods for its calculation. A computationally efficient approach for estimating the boundary (and in turn area) of the impact distribution for fixed wing unmanned aircraft is proposed. A series of geometric templates that approximate the impact distributions are derived using an empirical analysis of the results obtained from a 6-Degree of Freedom (6DoF) simulation. The impact distributions can be aggregated to provide impact footprint distributions for a range of generic phases of flight and missions. The maximum impact footprint areas obtained from the geometric template are shown to have a relative error of typically less than 1% compared to the areas calculated using the computationally more expensive 6DoF simulation. Computation times for the geometric models are on the order of one second or less, using a standard desktop computer. Future work includes characterising the distribution of impact locations within the footprint boundaries.

Finite element modelling of load bearing steel stud walls under real building fires

Fire safety has become an important part in structural design due to the ever increasing loss of properties and lives during fires. Conventionally the fire rating of load bearing wall systems made of Light gauge Steel Frames (LSF) is determined using fire tests based on the standard time-temperature curve given in ISO 834 (ISO, 1999). The standard time-temperature curve given in ISO 834 (ISO, 1999) originated from the application of wood burning furnaces in the early 1900s. However, modern commercial and residential buildings make use of thermoplastic materials, which mean considerably high fuel loads. Hence a detailed fire research study into the performance of LSF walls was undertaken using the developed real fire curves based on Eurocode parametric curves (ECS, 2002) and Barnett’s BFD curves (Barnett, 2002) using both full scale fire tests and numerical studies. It included LSF walls without any insulation, and the recently developed externally insulated composite panel system. This paper presents the details of the numerical studies and the results. It also includes brief details of the development of real building fire curves and experimental studies.

A least squares based finite volume method for the Cahn-Hilliard and Cahn-Hilliard-reaction equations

A vertex-centred finite volume method (FVM) for the Cahn-Hilliard (CH) and recently proposed Cahn-Hilliard-reaction (CHR) equations is presented. Information at control volume faces is computed using a high-order least-squares approach based on Taylor series approximations. This least-squares problem explicitly includes the variational boundary condition (VBC) that ensures that the discrete equations satisfy all of the boundary conditions. We use this approach to solve the CH and CHR equations in one and two dimensions and show that our scheme satisfies the VBC to at least second order. For the CH equation we show evidence of conservative, gradient stable solutions, however for the CHR equation, strict gradient-stability is more challenging to achieve.