A two-Dimensional finite volume method for variable density flow and solute transport through saturated-unsaturated media

Extensive groundwater withdrawal has resulted in a severe seawater intrusion problem in the Gooburrum aquifers at Bundaberg, Queensland, Australia. Better management strategies can be implemented by understanding the seawater intrusion processes in those aquifers. To study the seawater intrusion process in the region, a two-dimensional density-dependent, saturated and unsaturated flow and transport computational model is used. The model consists of a coupled system of two non-linear partial differential equations. The first equation describes the flow of a variable-density fluid, and the second equation describes the transport of dissolved salt. A two-dimensional control volume finite element model is developed for simulating the seawater intrusion into the heterogeneous aquifer system at Gooburrum. The simulation results provide a realistic mechanism by which to study the convoluted transport phenomena evolving in this complex heterogeneous coastal aquifer.

Models of collective cell spreading with variable cell aspect ratio : a motivation for degenerate diffusion models

Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. In the cell modeling literature there is no guidance available with regard to which approach is more appropriate for representing the spreading of cell populations. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. Here we provide a link between individual-based and continuum models using a multi-scale approach in which we analyze the collective motion of a population of interacting agents in a generalized lattice-based exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description of the system is a linear diffusion equation, whereas for elongated rod-shaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is connected to the porous media equation (pme). The exponent in the nonlinear diffusivity function is related to the aspect ratio of the agents. Our work provides a physical connection between modeling collective cell spreading and the use of either the linear diffusion equation or the pme to represent cell density profiles. Results suggest that when using continuum models to represent cell population spreading, we should take care to account for variations in the cell aspect ratio because different aspect ratios lead to different continuum models.

Variable structure control for power systems stabilization

The application of variable structure control (VSC) for power systems stabilization is studied in this paper. It is the application, aspects and constraints of VSC which are of particular interest. A variable structure control methodology has been proposed for power systems stabilization. The method is implemented using thyristor controlled series compensators. A three machine power system is stabilized using a switching line control for large disturbances which becomes a sliding control as the disturbance becomes smaller. The results demonstrate the effectiveness of the methodology proposed as an useful tool to suppress the oscillations in power systems.

Calibration and operational analysis of variable speed limits for high flow condition

Variable Speed Limits (VSL) is a control tool of Intelligent Transportation Systems (ITS) which can enhance traffic safety and which has the potential to contribute to traffic efficiency. This study presents the results of a calibration and operational analysis of a candidate VSL algorithm for high flow conditions on an urban motorway of Queensland, Australia. The analysis was done using a framework consisting of a microscopic simulation model combined with runtime API and a proposed efficiency index. The operational analysis includes impacts on speed-flow curve, travel time, speed deviation, fuel consumption and emission.

Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term

In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Finally, some numerical examples are given and the results demonstrate the effectiveness of theoretical analysis. Keywords: The variable-order Galilei invariant advection diffusion equation with a nonlinear source term; The variable-order Riemann–Liouville fractional partial derivative; Stability; Convergence; Numerical scheme improving temporal accuracy

Queue protection parameters’ fine-tuning for variable speed limits

Any incident on motorways potentially can be followed by secondary crashes. Rear-end crashes also could happen as a result of queue formation downstream of high speed platoons. To decrease the occurrence of secondary crashes and rear-end crashes, Variable Speed Limits (VSL) can be applied to protect queue formed downstream. This paper focuses on fine tuning the Queue Protection algorithm of VSL. Three performance indicators: activation time, deactivation time and number of false alarms are selected to optimise the Queue Protection algorithm. A calibrated microscopic traffic simulation model of Pacific Motorway in Brisbane is used for the optimisation. Performance of VSL during an incident and heavy congestion and the benefit of VSL will be presented in the paper.

Learning from episodes of degradation and recovery in variable Australian rangelands

Land-change science emphasizes the intimate linkages between the human and environmental components of land management systems. Recent theoretical developments in drylands identify a small set of key principles that can guide the understanding of these linkages. Using these principles, a detailed study of seven major degradation episodes over the past century in Australian grazed rangelands was reanalyzed to show a common set of events: (i) good climatic and economic conditions for a period, leading to local and regional social responses of increasing stocking rates, setting the preconditions for rapid environmental collapse, followed by (ii) a major drought coupled with a fall in the market making destocking financially unattractive, further exacerbating the pressure on the environment; then (iii) permanent or temporary declines in grazing productivity, depending on follow-up seasons coupled again with market and social conditions. The analysis supports recent theoretical developments but shows that the establishment of environmental knowledge that is strictly local may be insufficient on its own for sustainable management. Learning systems based in a wider community are needed that combine local knowledge, formal research, and institutional support. It also illustrates how natural variability in the state of both ecological and social systems can interact to precipitate nonequilibrial change in each other, so that planning cannot be based only on average conditions. Indeed, it is this variability in both environment and social subsystems that hinders the local learning required to prevent collapse.

Variable Speed Limits : conceptual design for Queensland practice

Variable Speed Limits (VSL) is an Intelligent Transportation Systems (ITS) control tool which can enhance traffic safety and which has the potential to contribute to traffic efficiency. Queensland's motorways experience a large volume of commuter traffic in peak periods, leading to heavy recurrent congestion and a high frequency of incidents. Consequently, Queensland's Department of Transport and Main Roads have considered deploying VSL to improve safety and efficiency. This paper identifies three types of VSL and three applicable conditions for activating VSL on for Queensland motorways: high flow, queuing and adverse weather. The design objectives and methodology for each condition are analysed, and micro-simulation results are presented to demonstrate the effectiveness of VSL.

Numerical analysis for a variable-order nonlinear cable equation

In this paper, a variable-order nonlinear cable equation is considered. A numerical method with first-order temporal accuracy and fourth-order spatial accuracy is proposed. The convergence and stability of the numerical method are analyzed by Fourier analysis. We also propose an improved numerical method with second-order temporal accuracy and fourth-order spatial accuracy. Finally, the results of a numerical example support the theoretical analysis.

Predictive compensation for variable network delays and packet losses in networked control systems

Networked control systems (NCSs) offer many advantages over conventional control; however, they also demonstrate challenging problems such as network-induced delay and packet losses. This paper proposes an approach of predictive compensation for simultaneous network-induced delays and packet losses. Different from the majority of existing NCS control methods, the proposed approach addresses co-design of both network and controller. It also alleviates the requirements of precise process models and full understanding of NCS network dynamics. For a series of possible sensor-to-actuator delays, the controller computes a series of corresponding redundant control values. Then, it sends out those control values in a single packet to the actuator. Once receiving the control packet, the actuator measures the actual sensor-to-actuator delay and computes the control signals from the control packet. When packet dropout occurs, the actuator utilizes past control packets to generate an appropriate control signal. The effectiveness of the approach is demonstrated through examples.

The economics of happiness : a lifetime perspective

The three studies in this thesis focus on happiness and age and seek to contribute to our understanding of happiness change over the lifetime. The first study contributes by offering an explanation for what was evolving to a ‘stylised fact’ in the economics literature, the U-shape of happiness in age. No U-shape is evident if one makes a visual inspection of the age happiness relationship in the German socio-economic panel data, and, it seems counter-intuitive that we just have to wait until we get old to be happy. Eliminating the very young, the very old, and the first timers from the analysis did not explain away regression results supporting the U-shape of happiness in age, but fixed effect analysis did. Analysis revealed found that reverse causality arising from time-invariant individual traits explained the U-shape of happiness in age in the German population, and the results were robust across six econometric methods. Robustness was added to the German fixed effect finding by replicating it with the Australian and the British socio-economic panel data sets. During analysis of the German data an unexpected finding emerged, an exceedingly large negative linear effect of age on happiness in fixed-effect regressions. There is a large self-reported happiness decline by those who remain in the German panel. A similar decline over time was not evident in the Australian or the British data. After testing away age, time and cohort effects, a time-in-panel effect was found. Germans who remain in the panel for longer progressively report lower levels of happiness. Because time-in-panel effects have not been included in happiness regression specifications, our estimates may be biased; perhaps some economics of the happiness studies, that used German panel data, need revisiting. The second study builds upon the fixed-effect finding of the first study and extends our view of lifetime happiness to a cohort little visited by economists, children. Initial analysis extends our view of lifetime happiness beyond adulthood and revealed a happiness decline in adolescent (15 to 23 year-old) Australians that is twice the size of the happiness decline we see in older Australians (75 to 86 yearolds), who we expect to be unhappy due to declining income, failing health and the onset of death. To resolve a difference of opinion in the literature as to whether childhood happiness decreases, increases, or remains flat in age; survey instruments and an Internet-based survey were developed and used to collect data from four hundred 9 to 14 year-old Australian children. Applying the data to a Model of Childhood Happiness revealed that the natural environment life-satisfaction domain factor did not have a significant effect on childhood happiness. However, the children’s school environment and interactions with friends life-satisfaction domain factors explained over half a steep decline in childhood happiness that is three times larger than what we see in older Australians. Adding personality to the model revealed what we expect to see with adults, extraverted children are happier, but unexpectedly, so are conscientious children. With the steep decline in the happiness of young Australians revealed and explanations offered, the third study builds on the time-invariant individual trait finding from the first study by applying the Australian panel data to an Aggregate Model of Average Happiness over the lifetime. The model’s independent variable is the stress that arises from the interaction between personality and the life event shocks that affect individuals and peers throughout their lives. Interestingly, a graphic depiction of the stress in age relationship reveals an inverse U-shape; an inverse U-shape that looks like the opposite of the U-shape of happiness in age we saw in the first study. The stress arising from life event shocks is found to explain much of the change in average happiness over a lifetime. With the policy recommendations of economists potentially invoking unexpected changes in our lives, the ensuing stress and resulting (un)happiness warrant consideration before economists make policy recommendations.

Computationally efficient methods for solving time-variable-order time-space fractional reaction-diffusion equation

Fractional differential equations are becoming more widely accepted as a powerful tool in modelling anomalous diffusion, which is exhibited by various materials and processes. Recently, researchers have suggested that rather than using constant order fractional operators, some processes are more accurately modelled using fractional orders that vary with time and/or space. In this paper we develop computationally efficient techniques for solving time-variable-order time-space fractional reaction-diffusion equations (tsfrde) using the finite difference scheme. We adopt the Coimbra variable order time fractional operator and variable order fractional Laplacian operator in space where both orders are functions of time. Because the fractional operator is nonlocal, it is challenging to efficiently deal with its long range dependence when using classical numerical techniques to solve such equations. The novelty of our method is that the numerical solution of the time-variable-order tsfrde is written in terms of a matrix function vector product at each time step. This product is approximated efficiently by the Lanczos method, which is a powerful iterative technique for approximating the action of a matrix function by projecting onto a Krylov subspace. Furthermore an adaptive preconditioner is constructed that dramatically reduces the size of the required Krylov subspaces and hence the overall computational cost. Numerical examples, including the variable-order fractional Fisher equation, are presented to demonstrate the accuracy and efficiency of the approach.

Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media

Percolation flow problems are discussed in many research fields, such as seepage hydraulics, groundwater hydraulics, groundwater dynamics and fluid dynamics in porous media. Many physical processes appear to exhibit fractional-order behavior that may vary with time, or space, or space and time. The theory of pseudodifferential operators and equations has been used to deal with this situation. In this paper we use a fractional Darcys law with variable order Riemann-Liouville fractional derivatives, this leads to a new variable-order fractional percolation equation. In this paper, a new two-dimensional variable-order fractional percolation equation is considered. A new implicit numerical method and an alternating direct method for the two-dimensional variable-order fractional model is proposed. Consistency, stability and convergence of the implicit finite difference method are established. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of the methods. This technique can be used to simulate a three-dimensional variable-order fractional percolation equation.