Novel analytical and numerical methods for solving fractional dynamical systems

During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes that are governed by anomalous diffusion. Hence, there is a growing need to find the solution behaviour of these fractional differential equations. However, the analytic solutions of most fractional differential equations generally cannot be obtained. As a consequence, approximate and numerical techniques are playing an important role in identifying the solution behaviour of such fractional equations and exploring their applications. The main objective of this thesis is to develop new effective numerical methods and supporting analysis, based on the finite difference and finite element methods, for solving time, space and time-space fractional dynamical systems involving fractional derivatives in one and two spatial dimensions. A series of five published papers and one manuscript in preparation will be presented on the solution of the space fractional diffusion equation, space fractional advectiondispersion equation, time and space fractional diffusion equation, time and space fractional Fokker-Planck equation with a linear or non-linear source term, and fractional cable equation involving two time fractional derivatives, respectively. One important contribution of this thesis is the demonstration of how to choose different approximation techniques for different fractional derivatives. Special attention has been paid to the Riesz space fractional derivative, due to its important application in the field of groundwater flow, system biology and finance. We present three numerical methods to approximate the Riesz space fractional derivative, namely the L1/ L2-approximation method, the standard/shifted Gr¨unwald method, and the matrix transform method (MTM). The first two methods are based on the finite difference method, while the MTM allows discretisation in space using either the finite difference or finite element methods. Furthermore, we prove the equivalence of the Riesz fractional derivative and the fractional Laplacian operator under homogeneous Dirichlet boundary conditions – a result that had not previously been established. This result justifies the aforementioned use of the MTM to approximate the Riesz fractional derivative. After spatial discretisation, the time-space fractional partial differential equation is transformed into a system of fractional-in-time differential equations. We then investigate numerical methods to handle time fractional derivatives, be they Caputo type or Riemann-Liouville type. This leads to new methods utilising either finite difference strategies or the Laplace transform method for advancing the solution in time. The stability and convergence of our proposed numerical methods are also investigated. Numerical experiments are carried out in support of our theoretical analysis. We also emphasise that the numerical methods we develop are applicable for many other types of fractional partial differential equations.

Spatial mapping and map exploitation : a bio-inspired engineering perspective

Probabilistic robot mapping techniques can produce high resolution, accurate maps of large indoor and outdoor environments. However, much less progress has been made towards robots using these maps to perform useful functions such as efficient navigation. This paper describes a pragmatic approach to mapping system development that considers not only the map but also the navigation functionality that the map must provide. We pursue this approach within a bio-inspired mapping context, and use esults from robot experiments in indoor and outdoor environments to demonstrate its validity. The research attempts to stimulate new research directions in the field of robot mapping with a proposal for a new approach that has the potential to lead to more complete mapping and navigation systems.

Wheat Production Systems And Global Climate Change

About this book: Over 100 authors present 25 contributions on the impacts of global change on terrestrial ecosystems including:key processes of the earth system such as the CO2 fertilization effect, shifts in disturbances and biome distribution, the saturation of the terrestrial carbon sink, and changes in functional biodiversity,ecosystem services such the production of wheat, pest control, and carbon storage in croplands, and sensitive regions in the world threaten by rapid changes in climate and land use such as high latitudes ecosystems, tropical forest in Southeast Asia, and ecosystems dominated by Monsoon climate.The book also explores new research developments on spatial thresholds and nonlinearities, the key role of urban development in global biogeochemical processes, and the integration of natural and social sciences to address complex problems of the human-environment system.

Spatial variability of soil carbon in forested and cultivated sites: Implications for change detection

The potential to sequester atmospheric carbon in agricultural and forest soils to offset greenhouse gas emissions has generated interest in measuring changes in soil carbon resulting from changes in land management. However, inherent spatial variability of soil carbon limits the precision of measurement of changes in soil carbon and hence, the ability to detect changes. We analyzed variability of soil carbon by intensively sampling sites under different land management as a step toward developing efficient soil sampling designs. Sites were tilled crop-land and a mixed deciduous forest in Tennessee, and old-growth and second-growth coniferous forest in western Washington, USA. Six soil cores within each of three microplots were taken as an initial sample and an additional six cores were taken to simulate resampling. Soil C variability was greater in Washington than in Tennessee, and greater in less disturbed than in more disturbed sites. Using this protocol, our data suggest that differences on the order of 2.0 Mg C ha(-1) could be detected by collection and analysis of cores from at least five (tilled) or two (forest) microplots in Tennessee. More spatial variability in the forested sites in Washington increased the minimum detectable difference, but these systems, consisting of low C content sandy soil with irregularly distributed pockets of organic C in buried logs, are likely to rank among the most spatially heterogeneous of systems. Our results clearly indicate that consistent intramicroplot differences at all sites will enable detection of much more modest changes if the same microplots are resampled.

Spatial variability of soil organic carbon in grasslands: implications for detecting change at different scales

Extensive data used to quantify broad soil C changes (without information about causation), coupled with intensive data used for attribution of changes to specific management practices, could form the basis of an efficient national grassland soil C monitoring network. Based on variability of extensive (USDA/NRCS pedon database) and intensive field-level soil C data, we evaluated the efficacy of future sample collection to detect changes in soil C in grasslands. Potential soil C changes at a range of spatial scales related to changes in grassland management can be verified (alpha=0.1) after 5 years with collection of 34, 224, 501 samples at the county, state, or national scales, respectively. Farm-level analysis indicates that equivalent numbers of cores and distinct groups of cores (microplots) results in lowest soil C coefficients of variation for a variety of ecosystems. Our results suggest that grassland soil C changes can be precisely quantified using current technology at scales ranging from farms to the entire nation. (C) 2001 Elsevier Science Ltd. All rights reserved.

Petri net modeling of spatial and temporal constraints in track allocation problem at railway stations

The track allocation problem (TAP) at a multi-track, multi-platform mainline railway station is defined by the station track layout and service timetable, which implies combinations of spatial and temporal conflicts. Feasible solutions are available from either traditional planning or advanced intelligent searching methods and their evaluations with respect to operational requirements are essential for the operators. To facilitate thorough analysis, a timed Coloured Petri Nets (CPN) model is presented here to encapsulate the inter-relationships of the spatial and temporal constraints in the TAP.

Developing spatial infrastructures for the Q.U.T. Samford Ecological Research Facility.

Staff and students of the Surveying and Spatial Sciences discipline at QUT have worked collaboratively with the Institute of Sustainable Resources in the creation and development of spatial information layers and infrastructure to support multi-disciplinary research efforts at the Samford Ecological Research Facility (SERF). The SERF property is unique in that it provides staff and students with a semi-rural controlled research base for multiple users. This paper aims to describe the development of a number of spatial information layers and network of survey monuments that assist and support research infrastructure at SERF. A brief historical background about the facility is presented along with descriptions of the surveying and mapping activities undertaken. These broad ranging activities include introducing monument infrastructure and a geodetic control network; surveying activities for aerial photography ground-control targets including precise levelling with barcode instruments; development of an ortho-rectified image spatial information layer; Real-Time-Kinematic Global Positioning Systems (RTK-GPS) surveying for constructing 100metre confluence points/monuments to support science-based disciplines to undertake environmental research transects and long-term ecological sampling; and real-world learning initiative to assist with water engineering projects and student experiential learning. The spatial information layers and physical infrastructure have been adopted by two specific yet diverse user groups with an interest in the long-term research focus of SERF.

A new undergraduate model for broadly based spatial science curriculum at Queensland University of Technology : diversity in surveying curriculum

This paper provides an overview of the current QUT Spatial Science undergraduate program based in Brisbane, Queensland, Australia. It discusses the development and implementation of a broad-based educational model for the faculty of built environment and engineering courses and specifically to the course structure of the new Bachelor of Urban Development (Spatial Science) study major. A brief historical background of surveying courses is discussed prior to the detailing of the three distinct and complementary learning themes of the new course structure with a graphical course matrix. Curriculum mapping of the spatial science major has been undertaken as the course approaches formal review in late 2010. Work-integrated learning opportunities have been embedded into the curriculum and a brief outline is presented. Some issues relevant to the tertiary surveying/ spatial sector are highlighted in the context of changing higher education environments in Australia.

Sustainable urban infrastructure management : integration of urban computer modelling

Purpose - This paper seeks to examine the complex relationships between urban planning, infrastructure management, sustainable urban development, and to illustrate why there is an urgent need for local governments to develop a robust planning support system which integrates with advance urban computer modelling tools to facilitate better infrastructure management and improve knowledge sharing between the community, urban planners, engineers and decision makers. Design/methodology/approach - The methods used in this paper includes literature review and practical project case observations. Originality/value - This paper provides an insight of how the Brisbane's planning support system established by Brisbane City Council has significantly improved the effectiveness of urban planning, infrastructure management and community engagement through better knowledge management processes. Practical implications - This paper presents a practical framework for setting up a functional planning support system within local government. The integration of the Brisbane Urban Growth model, Virtual Brisbane and the Brisbane Economic Activity Monitoring (BEAM) database have proven initially successful to provide a dynamic platform to assist elected officials, planners and engineers to understand the limitations of the local environment, its urban systems and the planning implications on a city. With the Brisbane's planning support system, planners and decision makers are able to provide better planning outcomes, policy and infrastructure that adequately address the local needs and achieve sustainable spatial forms.

Recognising audio-visual speech in vehicles using the AVICAR database

Interacting with technology within a vehicle environment using a voice interface can greatly reduce the effects of driver distraction. Most current approaches to this problem only utilise the audio signal, making them susceptible to acoustic noise. An obvious approach to circumvent this is to use the visual modality in addition. However, capturing, storing and distributing audio-visual data in a vehicle environment is very costly and difficult. One current dataset available for such research is the AVICAR [1] database. Unfortunately this database is largely unusable due to timing mismatch between the two streams and in addition, no protocol is available. We have overcome this problem by re-synchronising the streams on the phone-number portion of the dataset and established a protocol for further research. This paper presents the first audio-visual results on this dataset for speaker-independent speech recognition. We hope this will serve as a catalyst for future research in this area.

Spatial and temporal variations of mechanical properties and mineral content of the external callus during bone healing

After bone fracture, various cellular activities lead to the formation of different tissue types, which form the basis for the process of secondary bone healing. Although these tissues have been quantified by histology, their material properties are not well understood. Thus, the aim of this study is to correlate the spatial and temporal variations in the mineral content and the nanoindentation modulus of the callus formed via intramembranous ossification over the course of bone healing. Midshaft tibial samples from a sheep osteotomy model at time points of 2, 3, 6 and 9 weeks were employed. PMMA embedded blocks were used for quantitative back scattered electron imaging and nanoindentation of the newly formed periosteal callus near the cortex. The resulting indentation modulus maps show the heterogeneity in the modulus in the selected regions of the callus. The indentation modulus of the embedded callus is about 6 GPa at the early stage. At later stages of mineralization, the average indentation modulus reaches 14 GPa. There is a slight decrease in average indentation modulus in regions distant to the cortex, probably due to remodelling of the peripheral callus. The spatial and temporal distribution of mineral content in the callus tissue also illustrates the ongoing remodelling process observed from histological analysis. Most interestingly the average indentation modulus, even at 9 weeks, remains as low as 13 GPa, which is roughly 60% of that for cortical sheep bone. The decreased indentation modulus in the callus compared to cortex is due to the lower average mineral content and may be perhaps also due to the properties of the organic matrix which might be different from normal bone.

A crash avoidance framework for heavy equipment control systems using 3D imaging sensors

This paper presents a preliminary crash avoidance framework for heavy equipment control systems. Safe equipment operation is a major concern on construction sites since fatal on-site injuries are an industry-wide problem. The proposed framework has potential for effecting active safety for equipment operation. The framework contains algorithms for spatial modeling, object tracking, and path planning. Beyond generating spatial models in fractions of seconds, these algorithms can successfully track objects in an environment and produce a collision-free 3D motion trajectory for equipment.

A methodology for object identification and tracking in construction based on spatial modeling and image matching techniques

Understanding the motion characteristics of on-site objects is desirable for the analysis of construction work zones, especially in problems related to safety and productivity studies. This article presents a methodology for rapid object identification and tracking. The proposed methodology contains algorithms for spatial modeling and image matching. A high-frame-rate range sensor was utilized for spatial data acquisition. The experimental results indicated that an occupancy grid spatial modeling algorithm could quickly build a suitable work zone model from the acquired data. The results also showed that an image matching algorithm is able to find the most similar object from a model database and from spatial models obtained from previous scans. It is then possible to use the matched information to successfully identify and track objects.

Online urban information systems

Countless factors affect the inner workings of a city, so in an attempt to gain an understanding of place and making sound decisions, planners need to utilize decision support systems (DSS) or planning support systems (PSS). PSS were originally developed as DSS in academia for experimental purposes, but like many other technologies, they became one of the most innovative technologies in parallel to rapid developments in software engineering as well as developments and advances in networks and hardware. Particularly, in the last decade, the awareness of PSS have been dramatically heightened with the increasing demand for a better, more reliable and furthermore a transparent decision-making process (Klosterman, Siebert, Hoque, Kim, & Parveen, 2003). Urban planning as an act has quite different perspective from the PSS point of view. The unique nature of planning requires that spatial dimension must be considered within the context of PSS. Additionally, the rapid changes in socio-economic structure cannot be easily monitored or controlled without an effective PSS.