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.

A new analytic approach for power system fault diagnosis employing the temporal information of alarm messages

Traditional analytic models for power system fault diagnosis are usually formulated as an unconstrained 0–1 integer programming problem. The key issue of the models is to seek the fault hypothesis that minimizes the discrepancy between the actual and the expected states of the concerned protective relays and circuit breakers. The temporal information of alarm messages has not been well utilized in these methods, and as a result, the diagnosis results may be not unique and hence indefinite, especially when complicated and multiple faults occur. In order to solve this problem, this paper presents a novel analytic model employing the temporal information of alarm messages along with the concept of related path. The temporal relationship among the actions of protective relays and circuit breakers, and the different protection configurations in a modern power system can be reasonably represented by the developed model, and therefore, the diagnosed results will be more definite under different circumstances of faults. Finally, an actual power system fault was served to verify the proposed method.

A new method for quantifying the contribution of different critical agents on railway bridge deterioration

Railway Bridges deteriorate over time due to different critical factors including, flood, wind, earthquake, collision, and environment factors, such as corrosion, wear, termite attack, etc. In current practice, the contributions of the critical factors, towards the deterioration of railway bridges, which show their criticalities, are not appropriately taken into account. In this paper, a new method for quantifying the criticality of these factors will be introduced. The available knowledge as well as risk analyses conducted in different Australian standards and developed for bridge-design will be adopted. The analytic hierarchy process (AHP) is utilized for prioritising the factors. The method is used for synthetic rating of railway bridges developed by the authors of this paper. Enhancing the reliability of predicting the vulnerability of railway bridges to the critical factors, will be the significant achievement of this research.

Dynamic pattern of suicide in Australia, 1986-2005: A descriptive-analytic study

Objective This study explores the spatiotemporal variations of suicide across Australia from 1986 to 2005, discusses the reasons for dynamic changes, and considers future suicide research and prevention strategies. Design Suicide (1986–2005) and population data were obtained from the Australian Bureau of Statistics. A series of analyses were conducted to examine the suicide pattern by sex, method and age group over time and geography. Results Differences in suicide rates across sex, age groups and suicide methods were found across geographical areas. Male suicides were mainly completed by hanging, firearms, gases and self-poisoning. Female suicides were primarily completed by hanging and self-poisoning. Suicide rates were higher in rural areas than in urban areas (capital cities and regional centres). Suicide rates by firearms were higher in rural areas than in urban areas, while the pattern for self-poisoning showed the reverse trend. Suicide rates had relatively stable trend for the total population and those aged between 15 and 54, while suicide decreased among 55 years and over during the study period. There was a decrease in suicides by firearms during the study period especially after 1996 when a new firearm control law was implemented, while suicide by hanging continued to increase. Areas with a high proportion of indigenous population (eg, northwest of Queensland and top north of the Northern Territory) had shown a substantial increase in suicide incidence after 1995. Conclusions Suicide rates varied over time and space and across sexes, age groups and suicide methods. This study provides detailed patterns of suicide to inform suicide control and prevention strategies for specific subgroups and areas of high and increased risk.

A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.

Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions

In this paper, a space fractional di®usion equation (SFDE) with non- homogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Analytic solutions of the SFDE are derived. Finally, some numerical results are given to demonstrate that the MTT is a computationally e±cient and accurate method for solving SFDE.