Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by a Caputo fractional derivative, and the second order space derivative by a symmetric fractional derivative. First, a method of separating variables expresses the analytical solution of the TSS-FDE in terms of the Mittag--Leffler function. Second, we propose two numerical methods to approximate the Caputo time fractional derivative: the finite difference method; and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

Stability and convergence of an effective numerical method for the time-space fractional Fokker-Planck equation with a nonlinear source term

Fractional Fokker-Planck equations (FFPEs) have gained much interest recently for describing transport dynamics in complex systems that are governed by anomalous diffusion and nonexponential relaxation patterns. However, effective numerical methods and analytic techniques for the FFPE are still in their embryonic state. In this paper, we consider a class of time-space fractional Fokker-Planck equations with a nonlinear source term (TSFFPE-NST), which involve the Caputo time fractional derivative (CTFD) of order α ∈ (0, 1) and the symmetric Riesz space fractional derivative (RSFD) of order μ ∈ (1, 2). Approximating the CTFD and RSFD using the L1-algorithm and shifted Grunwald method, respectively, a computationally effective numerical method is presented to solve the TSFFPE-NST. The stability and convergence of the proposed numerical method are investigated. Finally, numerical experiments are carried out to support the theoretical claims.

Computationally efficient numerical methods for time- and space-fractional Fokker–Planck equations

Fractional Fokker–Planck equations have been used to model several physical situations that present anomalous diffusion. In this paper, a class of time- and space-fractional Fokker–Planck equations (TSFFPE), which involve the Riemann–Liouville time-fractional derivative of order 1-α (α(0, 1)) and the Riesz space-fractional derivative (RSFD) of order μ(1, 2), are considered. The solution of TSFFPE is important for describing the competition between subdiffusion and Lévy flights. However, effective numerical methods for solving TSFFPE are still in their infancy. We present three computationally efficient numerical methods to deal with the RSFD, and approximate the Riemann–Liouville time-fractional derivative using the Grünwald method. The TSFFPE is then transformed into a system of ordinary differential equations (ODE), which is solved by the fractional implicit trapezoidal method (FITM). Finally, numerical results are given to demonstrate the effectiveness of these methods. These techniques can also be applied to solve other types of fractional partial differential equations.

Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative and the second order space derivative by the symmetric fractional derivative. Firstly, a method of separating variables is used to express the analytical solution of the tss-fde in terms of the Mittag–Leffler function. Secondly, we propose two numerical methods to approximate the Caputo time fractional derivative, namely, the finite difference method and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results are presented to demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

Dwell-time and run-time control for DC mass rapid transit railways

Dwell times at stations and inter-station run times are the two major operational parameters to maintain train schedule in railway service. Current practices on dwell-time and run-time control are that they are only optimal with respect to certain nominal traffic conditions, but not necessarily the current service demand. The advantages of dwell-time and run-time control on trains are therefore not fully considered. The application of a dynamic programming approach, with the aid of an event-based model, to devise an optimal set of dwell times and run times for trains under given operational constraints over a regional level is presented. Since train operation is interactive and of multi-attributes, dwell-time and run-time coordination among trains is a multi-dimensional problem. The computational demand on devising trains' instructions, a prime concern in real-time applications, is excessively high. To properly reduce the computational demand in the provision of appropriate dwell times and run times for trains, a DC railway line is divided into a number of regions and each region is controlled by a dwell- time and run-time controller. The performance and feasibility of the controller in formulating the dwell-time and run-time solutions for real-time applications are demonstrated through simulations.

Examination of relationships between urban form, household activities, and time allocation in the Atlanta Metropolitan Region

A substantial body of research is focused on understanding the relationships between socio-demographics, land-use characteristics, and mode specific attributes on travel mode choice and time-use patterns. Residential and commercial densities, inter-mixing of land uses, and route directness in conjunction with transportation performance characteristics interact to influence accessibility to destinations as well as time spent traveling and engaging in activities. This study uniquely examines the activity durations undertaken for out-of-home subsistence; maintenance, and discretionary activities. Also examined are total tour durations (summing all activity categories within a tour). Cross-sectional activities are obtained from household activity travel survey data from the Atlanta Metropolitan Region. Time durations allocated to weekdays and weekends are compared. The censoring and endogeneity between activity categories and within individuals are captured using multiple equations Tobit models. The analysis and modeling reveal that land-use characteristics such as net residential density and the number of commercial parcels within a kilometer of a residence are associated with differences in weekday and weekend time-use allocations. Household type and structure are significant predictors across the three activity categories, but not for overall travel times. Tour characteristics such as time-of-day and primary travel mode of the tours also affect traveler's out-of-home activity-tour time-use patterns.

Household type and structure, time-use pattern, and trip-chaining behavior

In order to examine time allocation patterns within household-level trip-chaining, simultaneous doubly-censored Tobit models are applied to model time-use behavior within the context of household activity participation. Using the entire sample and a sub-sample of worker households from Tucson's Household Travel Survey, two sets of models are developed to better understand the phenomena of trip-chaining behavior among five types of households: single non-worker households, single worker households, couple non-worker households, couple one-worker households, and couple two-worker households. Durations of out-of-home subsistence, maintenance, and discretionary activities within trip chains are examined. Factors found to be associated with trip-chaining behavior include intra-household interactions with the household types and their structure and household head attributes.

Fuzzy logic traffic control at a road junction with time-varying flow rates

Fuzzy logic has been applied to control traffic at road junctions. A simple controller with one fixed rule-set is inadequate to minimise delays when traffic flow rate is time-varying and likely to span a wide range. To achieve better control, fuzzy rules adapted to the current traffic conditions are used.

Do walking and leisure-time physical activity protect against arthritis in older women?

Objective: To examine the prospective dose–response relationships between both leisure-time physical activity (LTPA) and walking with self-reported arthritis in older women. Design, setting and participants: Data came from women aged 73–78 years who completed mailed surveys in 1999, 2002 and 2005 for the Australian Longitudinal Study on Women’s Health. Women reported their weekly minutes of walking and moderate to vigorous physical activities. They also reported on whether they had been diagnosed with, or treated for, arthritis since the previous survey. General estimating equation analyses were performed to examine the longitudinal relationship between LTPA and arthritis and, for women who reported walking as their only physical activity, the longitudinal relationship between walking and arthritis. Women who reported arthritis or a limited ability to walk in 1999 were excluded, resulting in data from 3613 women eligible for inclusion in these analyses. Main results: ORs for self-reported arthritis were lowest for women who reported “moderate” levels of LTPA (OR 0.78; 95% CI 0.67 to 0.92), equivalent to 75 to <150 minutes of moderate-intensity LTPA per week. Slightly higher odds ratios were found for women who reported “high” (OR 0.81; 95% CI 0.69 to 0.95) or “very high” (OR 0.84; 95% CI 0.72 to 0.98) LTPA levels, indicating no further benefit from increased activity. For women whose only activity was walking, an inverse dose–response relationship between walking and arthritis was seen. Conclusions: The results support an inverse association between both LTPA and walking with self-reported arthritis over 6 years in older women who are able to walk.

Food literacy : time for a new term or just another buzzword?

Eating is an essential everyday life activity that has fascinated, captivated and defined society since time began. We currently exist in a society where over-consumption of food is an established risk factor chronic disease, the rate of which is increasing alarmingly. 'Food literacy' is an emerging term used to describe what we, as individuals and as a community know and understand about food and how to use it to meet our need, and thus potentially support and empower citizens to make healthy food choices. What exactly the components of food literacy are and how they influence food choice are poorly defined and understood, but increasingly gaining interest among health professionals, policy makers, community workers, educators and members of the public. This paper will build the argument for why concepts of 'food literacy' need to extend beyond existing terms and measures used in the literature to describe the food skills and knowledge needed to make use of public health nutrition messages.

Correlates of sitting time in working age Australian women : who should be targeted with interventions to decrease sitting time?

Background: While there is emerging evidence that sedentary behavior is negatively associated with health risk, research on the correlates of sitting time in adults is scarce. Methods: Self-report data from 7,724 women born between 1973-1978 and 8,198 women born between 1946-1951 were collected as part of the Australian Longitudinal Study on Women’s Health. Linear regression models were computed to examine whether demographic, family and caring duties, time use, health and health behavior variables were associated with weekday sitting time. Results: Mean sitting time (SD) was 6.60 (3.32) hours/day for the 1973-1978 cohort and 5.70 (3.04) hours/day for the 1946-1951 cohort. Indicators of socio-economic advantage, such as full11 time work and skilled occupations in both cohorts and university education in the mid-age cohort, were associated with high sitting time. A cluster of ‘healthy behaviours’ was associated with lower sitting time in the mid-aged women (moderate/high physical activity levels, non-smoking, non-drinking). For both cohorts, sitting time was highest in women in full-time work, in skilled occupations and in those who spent the most time in passive leisure. Conclusions: The results suggest that, in young and mid-aged women, interventions for reducing sitting time should focus on both occupational and leisure-time sitting.

Power network in loop : a paradigm for real-time simulation and hardware testing

This paper discusses a new paradigm of real-time simulation of power systems in which equipment can be interfaced with a real-time digital simulator. In this scheme, one part of a power system can be simulated by using a real-time simulator; while the other part is implemeneted as a physical system. The only interface of the physical system with the computer-based simulator is through data-acquisition system. The physical system is driven by a voltage-source converter (VSC)that mimics the power system simulated in the real-time simulator. In this papar, the VSC operates in a voltage-control mode to track the point of common coupling voltage signal supplied by the digital simulator. This type of splitting a network in two parts and running a real-time simulation with a physical system in parallel is called a power network in loop here. this opens up the possibility of study of interconnection o f one or several distributed generators to a complex power network. The proposed implementation is verified through simulation studies using PSCAD/EMTDC and through hardware implementation on a TMS320G2812 DSP.

Markov modelling of the IEEE 802.11 DCF for real-time applications with periodic traffic

Popular wireless network standards, such as IEEE 802.11/15/16, are increasingly adopted in real-time control systems. However, they are not designed for real-time applications. Therefore, the performance of such wireless networks needs to be carefully evaluated before the systems are implemented and deployed. While efforts have been made to model general wireless networks with completely random traffic generation, there is a lack of theoretical investigations into the modelling of wireless networks with periodic real-time traffic. Considering the widely used IEEE 802.11 standard, with the focus on its distributed coordination function (DCF), for soft-real-time control applications, this paper develops an analytical Markov model to quantitatively evaluate the network quality-of-service (QoS) performance in periodic real-time traffic environments. Performance indices to be evaluated include throughput capacity, transmission delay and packet loss ratio, which are crucial for real-time QoS guarantee in real-time control applications. They are derived under the critical real-time traffic condition, which is formally defined in this paper to characterize the marginal satisfaction of real-time performance constraints.

Working time arrangements and recreation : making time for weekends when working long hours

Work time spread across the entire week, rather than the conventional five day working week, has meant that workers are now less able to utilise longer stretches of recreation time especially in gaining access to a full two-day break over a weekend. This paper explores the issues contributing to workers' acquisition of longer recreation time. It seeks to determine the effects of this acquisition on the quality of working and non-working time for the employee through a study of work-life balance in the construction industry. It finds that weekends are more important to achieving work-life balance than shorter days over a six-day week when working long hours. Further, 'personal time' is a key element in achieving satisfactory work-life balance for employees, and this type of 'time' is often forgone in trying to integrate the necessary and desired non-work activities in the shorter time available to workers.

Output feedback control of discrete-time systems in networked environments

This correspondence paper addresses the problem of output feedback stabilization of control systems in networked environments with quality-of-service (QoS) constraints. The problem is investigated in discrete-time state space using Lyapunov’s stability theory and the linear inequality matrix technique. A new discrete-time modeling approach is developed to describe a networked control system (NCS) with parameter uncertainties and nonideal network QoS. It integrates a network-induced delay, packet dropout, and other network behaviors into a unified framework. With this modeling, an improved stability condition, which is dependent on the lower and upper bounds of the equivalent network-induced delay, is established for the NCS with norm-bounded parameter uncertainties. It is further extended for the output feedback stabilization of the NCS with nonideal QoS. Numerical examples are given to demonstrate the main results of the theoretical development.