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.

Bottlenecks detection of track allocation schemes at rail stations by Petri nets

Robustness of the track allocation problem is rarely addressed in literatures and the obtained track allocation schemes (TAS) embody some bottlenecks. Therefore, an approach to detect bottlenecks is needed to support local optimization. First a TAS is transformed to an executable model by Petri nets. Then disturbances analysis is performed using the model and the indicators of the total trains' departure delays are collected to detect bottlenecks when each train suffers a disturbance. Finally, the results of the tests based on a rail hub linking six lines and a TAS about thirty minutes show that the minimum buffer time is 21 seconds and there are two bottlenecks where the buffer times are 57 and 44 seconds respectively, and it indicates that the bottlenecks do not certainly locate at the area where there is minimum buffer time. The proposed approach can further support selection of multi schemes and robustness optimization.

Infrared and infrared emission spectroscopic study of China typical kaolinite and halloysite

The structure and thermal stability between typical China kaolinite and halloysite were analysed by X-ray diffraction (XRD), infrared spectroscopy, infrared emission spectroscopy (IES) and Raman spectroscopy. Infrared emission spectroscopy over the temperature range of 300 to 700 °C has been used to characterise the thermal decomposition of both kaolinite and halloysite. Halloysite is characterised by two bands in the water bending region at 1629 and 1648 cm-1, attributed to structure water and coordinated water in the interlayer. Well defined hydroxyl stretching bands at around 3695, 3679, 3652 and 3625 cm-1 are observed for both kaolinite and halloysite. In the 550 °C infrared emission spectrum of halloysite is similar to that of kaolinite in 650-1350 cm-1 region. The infrared emission spectra of halloysite were found to be considerably different to that of kaolinite at lower temperatures. This difference is attributed to the fundamental difference in the structure of the two minerals.

Transition of chromium oxyhydroxide nanomaterials to chromium oxide : a hot stage Raman spectroscopic study

The transition of disc-like chromium hydroxide nanomaterials to chromium oxide nanomaterials has been studied by hot stage Raman spectroscopy. The structure and morphology of α-CrO(OH) synthesised using hydrothermal treatment was confirmed by X-ray diffraction and transmission electron microscopy. The Raman spectrum of α-CrO(OH) is characterised by two intense bands at 823 and 630 cm-1 attributed to ν1 CrIII-O symmetric stretching mode, bands at 1179 cm-1 attributed to CrIII-OH δ deformation modes. No bands are observed above 3000 cm-1. The absence of characteristic OH vibrational bands may be due to short hydrogen bonds in the α-CrO(OH) structure. Upon thermal treatment of α-CrO(OH), new Raman bands are observed at 599, 542, 513, 396, 344 and 304 cm-1, which are attributed to Cr2O3. This hot-stage Raman study shows that the transition of α-CrO(OH) to Cr2O3 occurs before 350 °C.

Transition of synthetic chromium oxide gel to crystalline chromium oxide : a hot stage Raman spectroscopic study

Chromium oxide gel material was synthesised and appeared to be X-ray amorphous. The changes in the structure of the synthetic chromium oxide gel were investigated using hot-stage Raman spectroscopy based upon the results of thermogravimetric analysis. The thermally decomposed product of the synthetic chromium oxide gel in nitrogen atmosphere was confirmed to be crystalline Cr2O3 as determined by the hot-stage Raman spectra. Two bands were observed at 849 and 735 cm-1 in the Raman spectrum at 25 °C, which were attributed to the symmetric stretching modes of O-CrIII-OH and O-CrIII-O. With temperature increase, the intensity of the band at 849 cm-1 decreased, while the band at 735 cm-1 increased. These changes in intensity are attributed to the loss of OH groups and formation of O-CrIII-O units in the structure. A strongly hydrogen bonded water H-O-H bending band was found at 1704 cm-1 in the Raman spectrum of the chromium oxide gel, however this band shifted to around 1590 cm-1 due to destruction of the hydrogen bonds upon thermal treatment. Six new Raman bands were observed at 578, 540, 513, 390, 342 and 303 cm-1 attributed to the thermal decomposed product Cr2O3. The use of the hot-stage Raman microscope enabled low-temperature phase changes brought about through dehydration and dehydroxylation to be studied.

Research and application of Building Information Modelling (BIM) in the Architecture, Engineering and Construction (AEC) industry : a review and direction for future research

With an increasing level of collaboration amongst researchers, software developers and industry practitioners in the past three decades, building information modelling (BIM) is now recognized as an emerging technological and procedural shift within the architect, engineering and construction (AEC) industry. BIM is not only considered as a way to make a profound impact on the professions of AEC, but is also regarded as an approach to assist the industry to develop new ways of thinking and practice. Despite the widespread development and recognition of BIM, a succinct and systematic review of the existing BIM research and achievement is scarce. It is also necessary to take stock on existing applications and have a fresh look at where BIM should be heading and how it can benefit from the advances being made. This paper first presents a review of BIM research and achievement in AEC industry. A number of suggestions are then made for future research in BIM. This paper maintains that the value of BIM during design and construction phases is well documented over the last decade, and new research needs to expand the level of development and analysis from design/build stage to postconstruction and facility asset management. New research in BIM could also move beyond the traditional building type to managing the broader range of facilities and built assets and providing preventative maintenance schedules for sustainable and intelligent buildings

Thermal analysis and infrared emission spectroscopic study of halloysite-potassium acetate intercalation compound

The thermal decomposition of halloysite-potassium acetate intercalation compound was investigated by thermogravimetric analysis and infrared emission spectroscopy. The X-ray diffraction patterns indicated that intercalation of potassium acetate into halloysite caused an increase of the basal spacing from 1.00 to 1.41 nm. The thermogravimetry results show that the mass losses of intercalation the compound occur in main three main steps, which correspond to (a) the loss of adsorbed water (b) the loss of coordination water and (c) the loss of potassium acetate and dehydroxylation. The temperature of dehydroxylation and dehydration of halloysite is decreased about 100 °C. The infrared emission spectra clearly show the decomposition and dehydroxylation of the halloysite intercalation compound when the temperature is raised. The dehydration of the intercalation compound is followed by the loss of intensity of the stretching vibration bands at region 3600-3200 cm-1. Dehydroxylation is followed by the decrease in intensity in the bands between 3695 and 3620 cm-1. Dehydration was completed by 300 °C and partial dehydroxylation by 350 °C. The inner hydroxyl group remained until around 500 °C.

Cultural determinants of stress in the construction industry

The need to better understand and deal with workplace stress has major implications for the construction industry, especially on a project level, because of its potential to directly impact on site productivity and safety, and ultimately, the achievement of project objectives. While there has been some understanding of the effect of workplace stress within the construction industry, the majority of these studies have explored individual determinants of workplace stress among construction professionals such as architects, engineers, quantity surveyors etc. To date, very little research has focused on workplace stress as encountered by construction site operatives. This is an important research deficiency as construction site operatives typically make up a significant percentage of on-site workforce and contribute most directly to project success. To address this imbalance in research, this paper proposes a theoretical framework to better understand site operatives’ experience of stress from a cultural perspective on three levels: individual, project and organizational which has been largely neglected in previous studies.

Automatic generation of assertions to detect potential security vulnerabilities in C programs that use union and pointer types

Type unions, pointer variables and function pointers are a long standing source of subtle security bugs in C program code. Their use can lead to hard-to-diagnose crashes or exploitable vulnerabilities that allow an attacker to attain privileged access over classified data. This paper describes an automatable framework for detecting such weaknesses in C programs statically, where possible, and for generating assertions that will detect them dynamically, in other cases. Exclusively based on analysis of the source code, it identifies required assertions using a type inference system supported by a custom made symbol table. In our preliminary findings, our type system was able to infer the correct type of unions in different scopes, without manual code annotations or rewriting. Whenever an evaluation is not possible or is difficult to resolve, appropriate runtime assertions are formed and inserted into the source code. The approach is demonstrated via a prototype C analysis tool.

A general-purpose simulator for train operations

Computer simulation has been widely accepted as an essential tool for the analysis of many engineering systems. It is nowadays perceived to be the most readily available and feasible means of evaluating operations in real railway systems. Based on practical experience and theoretical models developed in various applications, this paper describes the design of a general-purpose simulation system for train operations. Its prime objective is to provide a single comprehensive computer-aided engineering tool for most studies on railway operations so that various aspects of the railway systems with different operation characteristics can be investigated and analysed in depth. This system consists of three levels of simulation. The first is a single-train simulator calculating the running time of a train between specific points under different track geometry and traction conditions. The second is a dual-train simulator which is to find the minimum headway between two trains under different movement constraints, such as signalling systems. The third is a whole-system multi-train simulator which carries out process simulation of the real operation of a railway system according to a practical or planned train schedule or headway; and produces an overall evaluation of system performance.

A multi-train movement simulator with moving blocking signalling

Abstract Being as a relatively new approach of signalling, moving-block scheme significantly increases line capacity, especially on congested railways. This paper describes a simulation system for multi-train operation under moving-block signalling scheme. The simulator can be used to calculate minimum headways and safety characteristics under pre-set timetables or headways and different geographic and traction conditions. Advanced software techniques are adopted to support the flexibility within the simulator so that it is a general-purpose computer-aided design tool to evaluate the performance of moving block signalling.

Small and medium enterprises’ solution to improve on-site waste management in office building retrofit projects

Office building retrofit projects are increasingly more intensified as existing buildings are aging. At the same time, building owners and occupants are looking for environmentally sustainable products. These retrofit projects usually take place in center business district (CBDs) with on-site waste becoming one of the critical issues. Small and Medium Enterprises (SMEs) carry out most of the work in retrofit projects as subcontractors. Despite their large involvement, they often do not have adequate resources to deal with the specific technical challenges and project risks related to waste. Few research has been done on their performance of waste management operations. This paper identifies characteristics of on-site waste in office building retrofit projects. It examines the specific requirements for contractors to manage waste in the projects before exploring the existing performance of SMEs. By comparing requirements for SMEs and their potential areas for improvement, a framework is established for performance promotion of SMEs in on-site waste management of office building retrofit projects. The paper will raise the consciousness and commitment of SMEs as sub-contractors to waste management. It also explores ways of supporting SMEs for experience accumulation, performance promotion and project culture establishment towards effective and efficient on-site waste management in the growing sector of office building retrofit and upgrade.