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.

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.

Rural activity spaces and transport disadvantage : qualitative analysis of quantitative models integrating time and space

Current knowledge about the relationship between transport disadvantage and activity space size is limited to urban areas, and as a result, very little is known to date about this link in a rural context. In addition, although research has identified transport disadvantaged groups based on their size of activity spaces, these studies have, however, not empirically explained such differences and the result is often a poor identification of the problems facing disadvantaged groups. Research has shown that transport disadvantage varies over time. The static nature of analysis using the activity space concept in previous research studies has lacked the ability to identify transport disadvantage in time. Activity space is a dynamic concept; and therefore possesses a great potential in capturing temporal variations in behaviour and access opportunities. This research derives measures of the size and fullness of activity spaces for 157 individuals for weekdays, weekends, and for a week using weekly activity-travel diary data from three case study areas located in rural Northern Ireland. Four focus groups were also conducted in order to triangulate the quantitative findings and to explain the differences between different socio-spatial groups. The findings of this research show that despite having a smaller sized activity space, individuals were not disadvantaged because they were able to access their required activities locally. Car-ownership was found to be an important life line in rural areas. Temporal disaggregation of the data reveals that this is true only on weekends due to a lack of public transport services. In addition, despite activity spaces being at a similar size, the fullness of activity spaces of low-income individuals was found to be significantly lower compared to their high-income counterparts. Focus group data shows that financial constraint, poor connections both between public transport services and between transport routes and opportunities forced individuals to participate in activities located along the main transport corridors.

Combined time- and space-resolved Raman spectrometer for the non-invasive depth profiling of chemical hazards

A time-resolved inverse spatially offset Raman spectrometer was constructed for depth profiling of Raman-active substances under both the lab and the field environments. The system operating principles and performance are discussed along with its advantages relative to traditional continuous wave spatially offset Raman spectrometer. The developed spectrometer uses a combination of space- and time-resolved detection in order to obtain high-quality Raman spectra from substances hidden behind coloured opaque surface layers, such as plastic and garments, with a single measurement. The time-gated spatially offset Raman spectrometer was successfully used to detect concealed explosives and drug precursors under incandescent and fluorescent background light as well as under daylight. The average screening time was 50 s per measurement. The excitation energy requirements were relatively low (20 mW) which makes the probe safe for screening hazardous substances. The unit has been designed with nanosecond laser excitation and gated detection, making it of lower cost and complexity than previous picosecond-based systems, to provide a functional platform for in-line or in-field sensing of chemical substances.

Time and space-resolved measurement of a gas-puff laser-plasma x-ray source

The dynamic interaction processes between a nano-second laser pulse and a gas-puff target, such as those of plasma formation, laser heating, and x-ray emission, have been investigated quantitatively. Time and space-resolved x-ray and optical measurement techniques were used in order to investigate time-resolved laser absorption and subsequent x-ray generation. Efficient absorption of the incident laser energy into the gas-puff target of 17%, 12%, 38%, and 91% for neon, argon, krypton, and xenon, respectively, was shown experimentally. It was found that the laser absorption starts and, simultaneously, soft x-ray emission occurs. The soft x-ray lasts much longer than the laser pulse due to the recombination. Temporal evolution of the soft x-ray emission region was analyzed by comparing the experimental results to the results of the model calculation, in which the laser light propagation through a gas-puff plasma was taken into account. (C) 2003 American Institute of Physics.

Development of a time and space resolved sampling probe diagnostic for engine exhaust hydrocarbons

In order to understand how unburned hydrocarbons emerge from SI engines and, in particular, how non-fuel hydrocarbons are formed and oxidized, a new gas sampling technique has been developed. A sampling unit, based on a combination of techniques used in the Fast Flame Ionization Detector (FFID) and wall-mounted sampling valves, was designed and built to capture a sample of exhaust gas during a specific period of the exhaust process and from a specific location within the exhaust port. The sampling unit consists of a transfer tube with one end in the exhaust port and the other connected to a three-way valve that leads, on one side, to a FFID and, on the other, to a vacuum chamber with a high-speed solenoid valve. Exhaust gas, drawn by the pressure drop into the vacuum chamber, impinges on the face of the solenoid valve and flows radially outward. Once per cycle during a specified crank angle interval, the solenoid valve opens and traps exhaust gas in a storage unit, from which gas chromatography (GC) measurements are made. The port end of the transfer tube can be moved to different locations longitudinally or radially, thus allowing spatial resolution and capturing any concentration differences between port walls and the center of the flow stream. Further, the solenoid valve's opening and closing times can be adjusted to allow sampling over a window as small as 0.6 ms during any portion of the cycle, allowing resolution of a crank angle interval as small as 15°CA. Cycle averaged total HC concentration measured by the FFID and that measured by the sampling unit are in good agreement, while the sampling unit goes one step further than the FFID by providing species concentrations. Comparison with previous measurements using wall-mounted sampling valves suggests that this sampling unit is fully capable of providing species concentration information as a function of air/fuel ratio, load, and engine speed at specific crank angles. © Copyright 1996 Society of Automotive Engineers, Inc.

A generic time and space accurate numerical approach to closely coupled fluid-structure interaction problems

Fluid structure interaction, as applied to flexible structures, has wide application in diverse areas such as flutter in aircraft, flow in elastic pipes and blood vessels and extrusion of metals through dies. However a comprehensive computational model of these multi-physics phenomena is a considerable challenge. Until recently work in this area focused on one phenomenon and represented the behaviour of the other more simply even to the extent in metal forming, for example, that the deformation of the die is totally ignored. More recently, strategies for solving the full coupling between the fluid and soild mechanics behaviour have developed. Conventionally, the computational modelling of fluid structure interaction is problematical since computational fluid dynamics (CFD) is solved using finite volume (FV) methods and computational structural mechanics (CSM) is based entirely on finite element (FE) methods. In the past the concurrent, but rather disparate, development paths for the finite element and finite volume methods have resulted in numerical software tools for CFD and CSM that are different in almost every respect. Hence, progress is frustrated in modelling the emerging multi-physics problem of fluid structure interaction in a consistent manner. Unless the fluid-structure coupling is either one way, very weak or both, transferring and filtering data from one mesh and solution procedure to another may lead to significant problems in computational convergence. Using a novel three phase technique the full interaction between the fluid and the dynamic structural response are represented. The procedure is demonstrated on some challenging applications in complex three dimensional geometries involving aircraft flutter, metal forming and blood flow in arteries.

Standard Language in Bosna and Hercegovina - in Language Policy Documents

From the beginning of the standardisation of language in Bosnia and Herzegovina, i.e. from the acceptance of Karadzic's phonetic spelling in the mid-19th century, to the present day when there are three different language standards in force - Bosniac (Muslim), Croatian and Serbian, language in Bosnia and Herzegovina has been a subject of political conflict. Documents on language policy from this period show the degree to which domestic and foreign political factors influenced the standard language issue, beginning with the very appellation for the specific norm regulation. The material analysed (proclamations by political, cultural and other organisations as well as corresponding constitutional and statutory provisions on language use) shows the differing treatment of the standard language in Bosnia and Herzegovina in different historical periods. During the period of Turkish rule (until 1878) there was no real political interest in the issue. Under Austro-Hungarian rule (1878-1918) there was an attempt to use the language as a means of forming a united Bosnian nation, but this was later abandoned. During the first Yugoslavia (1918-1941) a uniform solution was imposed on Bosnia and Herzegovina, as throughout the Serbo-Croatian language area, while under the Independent State of Croatia (1941-1945), the official language of Bosnia and Herzegovina was Croatian. The period from 1945 to 1991 had two phases: the first a standard language unity of Serbs, Croats, Muslims and Montenegrins (until 1965), and the second a gradual but stormy separation of national languages, which has been largely completed since 1991. The introductory study includes a detailed analysis of all the expressions used, with special reference to the present state, and accompanies the collection of documents which represent the main outcome of the research.

Private Publishing in Moscow and St. Petersburg: Historical Background, Present Situation and Trends"

This research was a complex study of the economic and socio-cultural aspects of the development of Russian private publishing in the second half of the19th and early 20th centuries, during the periods of 'war communism' and the New Economic Policy of 1917 to 1930, and during the reform of book publishing in 1986-1999. Conclusions about private book publishing in Moscow and St. Petersburg were extrapolated to Russia-wide problems of the development of this field. Svichenskaya sees her main achievement as having identified the economic and legal concepts behind the development of private book publishing over the period in question in the context of state and corporate regulation of publishing. Here the state was the main influence on its development and there was a paradox in the relations between the state authorities and private publishers, in that the latter constantly suffered from repression by the former but at the same time were dependent on state support. The research identified the administrative process of the liquidation of private publishing at the end of the 1920s and showed that its present flourishing is closely linked with the establishment of a preferential mode for the development of this sector. Private publishing now represents around 80% of domestic publishing, in terms both of the number of publishing houses and of the number of volumes published, and so plays the major role in satisfying the demand for books in Russia. Svichenskaya predicts that in the coming years private publishing will see a further concentration of growth and a tendency to monopolies and also the increasing specialisation of the publishing repertoire. She outlines a suggested concept of state management in publishing and ways to optimise this. In the transitional period of adaptation to the market regulation of publishing, these include a continuing degree of state protectionism, the creation of a favourable investment climate, privatisation of the printing companies with the aim of modernising these, and the development of coordinated corporate policies.

Time and space partition platform for safe and secure flight software.

There are a number of research and development activities that are exploring Time and Space Partition (TSP) to implement safe and secure flight software. This approach allows to execute different real-time applications with different levels of criticality in the same computer board. In order to do that, flight applications must be isolated from each other in the temporal and spatial domains. This paper presents the first results of a partitioning platform based on the Open Ravenscar Kernel (ORK+) and the XtratuM hypervisor. ORK+ is a small, reliable real-time kernel supporting the Ada Ravenscar Computational model that is central to the ASSERT development process. XtratuM supports multiple virtual machines, i.e. partitions, on a single computer and is being used in the Integrated Modular Avionics for Space study. ORK+ executes in an XtratuM partition enabling Ada applications to share the computer board with other applications.

Time and space partitioning the EagleEye reference mission

We discuss experiences gained by porting a Software Validation Facility (SVF) and a satellite Central Software (CSW) to a platform with support for Time and Space Partitioning (TSP). The SVF and CSW are part of the EagleEye Reference mission of the European Space Agency (ESA). As a reference mission, EagleEye is a perfect candidate to evaluate practical aspects of developing satellite CSW for and on TSP platforms. The specific TSP platform we used consists of a simulate D LEON3 CPU controlled by the XtratuM separation micro-kernel. On top of this, we run five separate partitions. Each partition ru n s its own real-time operating system or Ada run-time kernel, which in turn are running the application software of the CSW. We describe issues related to partitioning; inter-partition communication; scheduling; I/O; and fault-detection, isolation, and recovery (FDIR)

Knot/Knotting Practice in Craft and Space

Knot/knotting Practice in Craft and Space is a three part research-creation project that used a study of knotting techniques to locate craft in an expanded field of spatial practice. The first part consisted of practical, studio based exercises in which I worked with various natural and synthetic fibres to learn common knotting techniques. The second part was an art historical study that combined craft and architecture history with critical theory related to the social production of space. The third part was an exhibition of drawing and knotted objects titled Opening Closures. This document unifies the lines inquiry that define my project. The first chapter presents the art historical justification for knotting to be understood as a spatial practice. Nineteenth-century German architect and theorist Gottfried Semper’s idea that architectural form is derived from four basic material practices allies craft and architecture in my project and is the point of departure from which I make my argument. In the second chapter, to consider the methodological concerns of research-creation as a form of knowledge production and dissemination, I adopt the format of an instruction manual to conduct an analysis of knot types and to provide instructions for the production of several common knots. In the third chapter, I address the formal and conceptual underpinnings of each artwork presented in my exhibition. I conclude with a proposal for an expanded field of spatial practice by adapting art critic and theorist Rosalind Krauss’s well-known framework for assessing sculpture in 1960s.