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.

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.

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.

Embedding human expert cognition and real-time trajectory planning in autonomous UAS

This thesis presents a new approach to compute and optimize feasible three dimensional (3D) flight trajectories using aspects of Human Decision Making (HDM) strategies, for fixed wing Unmanned Aircraft (UA) operating in low altitude environments in the presence of real time planning deadlines. The underlying trajectory generation strategy involves the application of Manoeuvre Automaton (MA) theory to create sets of candidate flight manoeuvres which implicitly incorporate platform dynamic constraints. Feasible trajectories are formed through the concatenation of predefined flight manoeuvres in an optimized manner. During typical UAS operations, multiple objectives may exist, therefore the use of multi-objective optimization can potentially allow for convergence to a solution which better reflects overall mission requirements and HDM preferences. A GUI interface was developed to allow for knowledge capture from a human expert during simulated mission scenarios. The expert decision data captured is converted into value functions and corresponding criteria weightings using UTilite Additive (UTA) theory. The inclusion of preferences elicited from HDM decision data within an Automated Decision System (ADS) allows for the generation of trajectories which more closely represent the candidate HDM’s decision strategies. A novel Computationally Adaptive Trajectory Decision optimization System (CATDS) has been developed and implemented in simulation to dynamically manage, calculate and schedule system execution parameters to ensure that the trajectory solution search can generate a feasible solution, if one exists, within a given length of time. The inclusion of the CATDS potentially increases overall mission efficiency and may allow for the implementation of the system on different UAS platforms with varying onboard computational capabilities. These approaches have been demonstrated in simulation using a fixed wing UAS operating in low altitude environments with obstacles present.

A human-simulated immune evolutionary computation approach

Premature convergence to local optimal solutions is one of the main difficulties when using evolutionary algorithms in real-world optimization problems. To prevent premature convergence and degeneration phenomenon, this paper proposes a new optimization computation approach, human-simulated immune evolutionary algorithm (HSIEA). Considering that the premature convergence problem is due to the lack of diversity in the population, the HSIEA employs the clonal selection principle of artificial immune system theory to preserve the diversity of solutions for the search process. Mathematical descriptions and procedures of the HSIEA are given, and four new evolutionary operators are formulated which are clone, variation, recombination, and selection. Two benchmark optimization functions are investigated to demonstrate the effectiveness of the proposed HSIEA.