Numerical analysis of the time variable fractional order mobile-immobile advection-dispersion model

Many physical processes exhibit fractional order behavior that varies with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider the time variable fractional order mobile-immobile advection-dispersion model. Numerical methods and analyses of stability and convergence for the fractional partial differential equations are quite limited and difficult to derive. This motivates us to develop efficient numerical methods as well as stability and convergence of the implicit numerical methods for the fractional order mobile immobile advection-dispersion model. In the paper, we use the Coimbra variable time fractional derivative which is more efficient from the numerical standpoint and is preferable for modeling dynamical systems. An implicit Euler approximation for the equation is proposed and then the stability of the approximation are investigated. As for the convergence of the numerical scheme we only consider a special case, i.e. the time fractional derivative is independent of time variable t. The case where the time fractional derivative depends both the time variable t and the space variable x will be considered in the future work. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

Numerical techniques for the variable order time fractional diffusion equation

In this paper we consider the variable order time fractional diffusion equation. We adopt the Coimbra variable order (VO) time fractional operator, which defines a consistent method for VO differentiation of physical variables. The Coimbra variable order fractional operator also can be viewed as a Caputo-type definition. Although this definition is the most appropriate definition having fundamental characteristics that are desirable for physical modeling, numerical methods for fractional partial differential equations using this definition have not yet appeared in the literature. Here an approximate scheme is first proposed. The stability, convergence and solvability of this numerical scheme are discussed via the technique of Fourier analysis. Numerical examples are provided to show that the numerical method is computationally efficient. Crown Copyright © 2012 Published by Elsevier Inc. All rights reserved.

Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation

Anomalous subdiffusion equations have in recent years received much attention. In this paper, we consider a two-dimensional variable-order anomalous subdiffusion equation. Two numerical methods (the implicit and explicit methods) are developed to solve the equation. Their stability, convergence and solvability are investigated by the Fourier method. Moreover, the effectiveness of our theoretical analysis is demonstrated by some numerical examples. © 2011 American Mathematical Society.

Numerical methods and analysis for a class of fractional advection-dispersion models

In this paper, a class of fractional advection–dispersion models (FADMs) is considered. These models include five fractional advection–dispersion models, i.e., the time FADM, the mobile/immobile time FADM with a time Caputo fractional derivative 0 < γ < 1, the space FADM with two sides Riemann–Liouville derivatives, the time–space FADM and the time fractional advection–diffusion-wave model with damping with index 1 < γ < 2. These equations can be used to simulate the regional-scale anomalous dispersion with heavy tails. We propose computationally effective implicit numerical methods for these FADMs. The stability and convergence of the implicit numerical methods are analysed and compared systematically. Finally, some results are given to demonstrate the effectiveness of theoretical analysis.

Empirical IEEE 802.11p performance evaluation on test tracks

IEEE 802.11p is the new standard for inter-vehicular communications (IVC) using the 5.9 GHz frequency band; it is planned to be widely deployed to enable cooperative systems. 802.11p uses and performance have been studied theoretically and in simulations over the past years. Unfortunately, many of these results have not been confirmed by on-tracks experimentation. In this paper, we describe field trials of 802.11p technology with our test vehicles. Metrics such as maximum range, latency and frame loss are examined.

Worthless and undeserving? : problematising the subjectivities of single parenthood

A considerable body of knowledge has been constructed perpetuating the notion single parenthood is a significant problem for society, and while this is supported by specific research designs and sampling practices, it is also maintained by two key discourses. The first constitutes single parenthood as a deficit, while the second identifies it as a risk. In both cases, these discourses are operationalised by the philosophy of neo-liberalism, which envisions good citizenship as economic autonomy. Historically, it has been the convergence of the risk and deficit discourses that has constituted single parenthood as a social problem. More recently, however, risk discourses have come to dominate thinking about single parenthood. As a result, this thesis terms risk discourses as dominant discourses. As dominant discourses, risk sidelines or discounts other ways of thinking about single parenthood. While a few exceptions are notable, including some feminist, poststructural and family resilience scholars, most researchers appear unable to see past the positioning of these discourses and envision another way of being for parents who are single. This means that alternative subjectivities are obscured and have limited influence in this field of research. Because this thesis aimed to problematise dominant subjectivities of single parenthood, a poststructural Foucauldian framework has been utilized in order to document the discursive constructions of single parenthood through literature, insider discourses, and outsider discourses. For the purposes of this thesis, outsider discourses are constituted as those outside the subjectivities of single parenthood, such as media and research discourses. An examination of the Australian media has been undertaken over a one year period, the results of which form the basis for the analysis of media discourses of single parenthood. Parents who are single were also targeted for self selection into this project to provide insider discourses about single parenthood. This analysis explored how respondents negotiated the discourses of single parenthood and how they themselves used or rejected the subjectivities constructed for them via these discourses to constitute their own subjectivities. This thesis aimed to explore the role of discourses in the construction of individuals' subjectivities. Specifically, it draws attention to the way in which knowledge and power work through discourses to emphasize what is allowable, both publicly and privately, in relation to single parenthood. Most importantly, this thesis offers alternative subjectivities for single parenthood to facilitate new ways of thinking about parents who are single.

Molecular investigation of the mechanical properties of single actin filaments based on vibration analyses

The mechanical vibration properties of single actin filaments from 50 to 288 nm are investigated by the molecular dynamics simulation in this study. The natural frequencies obtained from the molecular simulations agree with those obtained from the analytical solution of the equivalent Euler–Bernoulli beam model. Through the convergence study of the mechanical properties with respect to the filament length, it was found that the Euler–Bernoulli beam model can only be reliably used when the single actin filament is of the order of hundreds of nanometre scale. This molecular investigation not only provides the evidence for the use of the continuum beam model in characterising the mechanical properties of single actin filaments, but also clarifies the criteria for the effective use of the Euler–Bernoulli beam model.

Responsibilisation and Rights: Explorations in Comparative Youth Criminology

Studies of international youth justice, punishment and control are in their infancy but the issues of globalisation, transnationalisation, policy transfer and localisation are gradually being addressed. There also appears a growing demand in policy and pressure group circles in the UK to learn more about other jurisdictions in order to emulate ‘best practice’ and avoid the worst excesses of punitive populism. However, existing comparative work in this area rarely ventures much beyond country specific descriptions of historical development, powers and procedures. Statistical comparisons – predominantly of custody rates – are becoming more sophisticated but remain beset with problems of partial and inaccurate data collection. The extent to which different countries do things differently, and how and why such difference is maintained, remains a relatively unexcavated territory. This article suggests a conceptually comparative framework in which degrees of international, national and local convergence and divergence can begin to be revealed and assessed.

Illusions of Difference: Comparative Youth Justice in the Devolved UK

Surprisingly, there has been little or no systematic research to date that has explored the significance of UK devolution for youth justice policy and practice. This article explores the extent of differential justice in the United Kingdom, particularly as it is expressed in the myriad action plans, criminal justice reviews, frameworks for action, delivery plans and offending strategies that have surfaced since 1998. In particular, the article considers how far policy convergence and divergence are reflected through the discourses of risk, welfare, restoration and children's rights in the four administrations of England, Scotland, Wales and Northern Ireland. For comparative criminology, the United Kingdom offers a unique opportunity to explore how international and national pressures towards convergence and/or divergence can be challenged, rebranded, versioned, adapted or resisted at sub-national and local levels.

Effects of enhanced somatosensory information on postural stability in older people and people with Parkinson’s disease

The somatosensory system plays an important role in balance control and age-related changes to this system have been implicated in falls. Parkinson’s disease (PD) is a chronic and progressive disease of the brain, characterized by postural instability and gait disturbance. Previous research has shown that deficiencies in somatosensory feedback may contribute to the poorer postural control demonstrated by PD individuals. However, few studies have comprehensively explored differences in somatosensory function and postural control between PD participants and healthy older individuals. The soles of the feet contain many cutaneous mechanoreceptors that provide important somatosensory information sources for postural control. Different types of insole devices have been developed to enhance this somatosensory information and improve postural stability, but these devices are often too complex and expensive to integrate into daily life. Textured insoles provide a more passive intervention that may be an inexpensive and accessible means to enhance the somatosensory input from the plantar surface of the feet. However, to date, there has been little work conducted to test the efficacy of enhanced somatosensory input induced by textured insoles in both healthy and PD populations during standing and walking. Therefore, the aims of this thesis were to determine: 1) whether textured insole surfaces can improve postural stability by enhancing somatosensory information in younger and older adults, 2) the differences between healthy older participants and PD participants for measures of physiological function and postural stability during standing and walking, 3) how changes in somatosensory information affect postural stability in both groups during standing and walking; and 4), whether textured insoles can improve postural stability in both groups during standing and walking. To address these aims, Study 1 recruited seven older individuals and ten healthy young controls to investigate the effects of two textured insole surfaces on postural stability while performing standing balance tests on a force plate. Participants were tested under three insole surface conditions: 1) barefoot; 2) standing on a hard textured insole surface; and 3), standing on a soft textured insole surface. Measurements derived from the centre of pressure displacement included the range of anterior-posterior and medial-lateral displacement, path length and the 90% confidence elliptical area (C90 area). Results of study 1 revealed a significant Group*Surface*Insole interaction for the four measures. Both textured insole surfaces reduced postural sway for the older group, especially in the eyes closed condition on the foam surface. However, participants reported that the soft textured insole surface was more comfortable and, hence, the soft textured insoles were adopted for Studies 2 and 3. For Study 2, 20 healthy older adults (controls) and 20 participants with Parkinson’s disease were recruited. Participants were evaluated using a series of physiological assessments that included touch sensitivity, vibratory perception, and pain and temperature threshold detection. Furthermore, nerve function and somatosensory evoked potentials tests were utilized to provide detailed information regarding peripheral nerve function for these participants. Standing balance and walking were assessed on different surfaces using a force plate and the 3D Vicon motion analysis system, respectively. Data derived from the force plate included the range of anterior-posterior and medial-lateral sway, while measures of stride length, stride period, cadence, double support time, stance phase, velocity and stride timing variability were reported for the walking assessment. The results of this study demonstrated that the PD group had decrements in somatosensory function compared to the healthy older control group. For electrodiagnosis, PD participants had poorer nerve function than controls, as evidenced by slower nerve conduction velocities and longer latencies in sural nerve and prolonged latency in the P37 somatosensory evoked potential. Furthermore, the PD group displayed more postural sway in both the anterior-posterior and medial-lateral directions relative to controls and these differences were increased when standing on a foam surface. With respect to the gait assessment, the PD group took shorter strides and had a reduced stride period compared with the control group. Furthermore, the PD group spent more time in the stance phase and had increased cadence and stride timing variability than the controls. Compared with walking on the firm surface, the two groups demonstrated different gait adaptations while walking on the uneven surface. Controls increased their stride length and stride period and decreased their cadence, which resulted in a consistent walking velocity on both surfaces. Conversely, while the PD patients also increased their stride period and decreased their cadence and stance period on the uneven surface, they did not increase their stride length and, hence walked slower on the uneven surface. In the PD group, there was a strong positive association between decreased somatosensory function and decreased clinical balance, as assessed by the Tinetti test. Poorer somatosensory function was also strongly positively correlated with the temporospatial gait parameters, especially shorter stride length. Study 3 evaluated the effects of manipulating the somatosensory information from the plantar surface of the feet using textured insoles in the same populations assessed in Study 2. For this study, participants performed the standing and walking balance tests under three footwear conditions: 1) barefoot; 2) with smooth insoles; and 3), with textured insoles. Standing balance and walking were evaluated using a force plate and a Vicon motion analysis system and the data were analysed in the same way outlined for Study 2. The findings showed that the smooth and textured insoles caused different effects on postural control during both the standing and walking trials. Both insoles decreased medial-lateral sway to the same level on the firm surface. The greatest benefits were observed in the PD group while wearing the textured insole. When standing under a more challenging condition on the foam surface with eyes closed, only the textured insole decreased medial-lateral sway in the PD group. With respect to the gait trials, both insoles increased walking velocity, stride length and stride time and decreased cadence, but these changes were more pronounced for the textured insoles. The effects of the textured insoles were evident under challenging conditions in the PD group and increased walking velocity and stride length, while decreasing cadence. Textured insoles were also effective in reducing the time spent in the double support and stance phases of the gait cycle and did not increase stride timing variability, as was the case for the smooth insoles for the PD group. The results of this study suggest that textured insoles, such as those evaluated in this research, may provide a low-cost means of improving postural stability in high-risk groups, such as people with PD, which may act as an important intervention to prevent falls.

Developing a simulator application to test the billing platform in telecom industry

Billing Mediation Platform (BMP) in telecommunication industry is used to process real-time streams of Call Detail Records (CDRs) which can be a massive number a day. The generated records by BMP can be deployed for billing purposes, fraud detection, spam filtering, traffic analysis, and churn forecast. Several of these applications are distinguished by real-time processing requiring low-latency analysis of CDRs. Testing of such a platform carries diverse aspects like stress testing of analytics for scalability and what-if scenarios which require generating of CDRs with realistic volumetric and appropriate properties. The approach of this project is to build user friendly and flexible application which assists the development department to test their billing solution occasionally. These generators projects have been around for a while the only difference are the potions they cover and the purpose they will be used for. This paper proposes to use a simulator application to test the BMPs with simulating CDRs. The Simulated CDRs are modifiable based on the user requirements and represent real world data.

Analytical and numerical solutions of the space and time fractional bloch-torrey equation

Fractional order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brown-ian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As MRI is applied with increasing temporal and spatial resolution, the spin dynamics are being examined more closely; such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments where processes are often anisotropic. Anomalous diffusion in the human brain using fractional order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (see R.L. Magin et al., J. Magnetic Resonance, 190 (2008) 255-270). However effective numerical methods and supporting error analyses for the fractional Bloch-Torrey equation are still limited. In this paper, the space and time fractional Bloch-Torrey equation (ST-FBTE) is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE, and the stability and convergence of the INM are investigated. We prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.