Numerical schemes and multivariate extrapolation of a two-dimensional anomalous sub-diffusion equation

Anomalous dynamics in complex systems have gained much interest in recent years. In this paper, a two-dimensional anomalous subdiffusion equation (2D-ASDE) is considered. Two numerical methods for solving the 2D-ASDE are presented. Their stability, convergence and solvability are discussed. A new multivariate extrapolation is introduced to improve the accuracy. Finally, numerical examples are given to demonstrate the effectiveness of the schemes and confirm the theoretical analysis.

Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation

In this paper, we consider the variable-order nonlinear fractional diffusion equation View the MathML source where xRα(x,t) is a generalized Riesz fractional derivative of variable order View the MathML source and the nonlinear reaction term f(u,x,t) satisfies the Lipschitz condition |f(u1,x,t)-f(u2,x,t)|less-than-or-equals, slantL|u1-u2|. A new explicit finite-difference approximation is introduced. The convergence and stability of this approximation are proved. Finally, some numerical examples are provided to show that this method is computationally efficient. The proposed method and techniques are applicable to other variable-order nonlinear fractional differential equations.

Primary students' group metacognitive processes in a computer supported collaborative learning environment

The current understanding of students’ group metacognition is limited. The research on metacognition has focused mainly on the individual student. The aim of this study was to address the void by developing a conceptual model to inform the use of scaffolds to facilitate group metacognition during mathematical problem solving in computer supported collaborative learning (CSCL) environments. An initial conceptual framework based on the literature from metacognition, cooperative learning, cooperative group metacognition, and computer supported collaborative learning was used to inform the study. In order to achieve the study aim, a design research methodology incorporating two cycles was used. The first cycle focused on the within-group metacognition for sixteen groups of primary school students working together around the computer; the second cycle included between-group metacognition for six groups of primary school students working together on the Knowledge Forum® CSCL environment. The study found that providing groups with group metacognitive scaffolds resulted in groups planning, monitoring, and evaluating the task and team aspects of their group work. The metacognitive scaffolds allowed students to focus on how their group was completing the problem-solving task and working together as a team. From these findings, a revised conceptual model to inform the use of scaffolds to facilitate group metacognition during mathematical problem solving in computer supported collaborative learning (CSCL) environments was generated.

Context change archetypes : understanding the impact of context change on business processes

The emergence of Enterprise Resource Planning systems and Business Process Management have led to improvements in the design, implementation, and overall management of business processes. However, the typical focus of these initiatives has been on internal business operations, assuming a defined and stable context in which the processes are designed to operate. Yet, a lack of context-awareness for external change leads to processes and supporting information systems that are unable to react appropriately and timely enough to change. To increase the alignment of processes with environmental change, we propose a conceptual framework that facilitates the identification of context change. Based on a secondary data analysis of published case studies about process adaptation, we exemplify the framework and identify four general archetypes of context-awareness. The framework, in combination with the learning from the case analysis, provides a first understanding of what, where, how, and when processes are subjected to change.

Theoretical investigation of thermal tweezers for parallel manipulation of atoms and nanoparticles on surfaces

A major focus of research in nanotechnology is the development of novel, high throughput techniques for fabrication of arbitrarily shaped surface nanostructures of sub 100 nm to atomic scale. A related pursuit is the development of simple and efficient means for parallel manipulation and redistribution of adsorbed atoms, molecules and nanoparticles on surfaces – adparticle manipulation. These techniques will be used for the manufacture of nanoscale surface supported functional devices in nanotechnologies such as quantum computing, molecular electronics and lab-on-achip, as well as for modifying surfaces to obtain novel optical, electronic, chemical, or mechanical properties. A favourable approach to formation of surface nanostructures is self-assembly. In self-assembly, nanostructures are grown by aggregation of individual adparticles that diffuse by thermally activated processes on the surface. The passive nature of this process means it is generally not suited to formation of arbitrarily shaped structures. The self-assembly of nanostructures at arbitrary positions has been demonstrated, though these have typically required a pre-patterning treatment of the surface using sophisticated techniques such as electron beam lithography. On the other hand, a parallel adparticle manipulation technique would be suited for directing the selfassembly process to occur at arbitrary positions, without the need for pre-patterning the surface. There is at present a lack of techniques for parallel manipulation and redistribution of adparticles to arbitrary positions on the surface. This is an issue that needs to be addressed since these techniques can play an important role in nanotechnology. In this thesis, we propose such a technique – thermal tweezers. In thermal tweezers, adparticles are redistributed by localised heating of the surface. This locally enhances surface diffusion of adparticles so that they rapidly diffuse away from the heated regions. Using this technique, the redistribution of adparticles to form a desired pattern is achieved by heating the surface at specific regions. In this project, we have focussed on the holographic implementation of this approach, where the surface is heated by holographic patterns of interfering pulsed laser beams. This implementation is suitable for the formation of arbitrarily shaped structures; the only condition is that the shape can be produced by holographic means. In the simplest case, the laser pulses are linearly polarised and intersect to form an interference pattern that is a modulation of intensity along a single direction. Strong optical absorption at the intensity maxima of the interference pattern results in approximately a sinusoidal variation of the surface temperature along one direction. The main aim of this research project is to investigate the feasibility of the holographic implementation of thermal tweezers as an adparticle manipulation technique. Firstly, we investigate theoretically the surface diffusion of adparticles in the presence of sinusoidal modulation of the surface temperature. Very strong redistribution of adparticles is predicted when there is strong interaction between the adparticle and the surface, and the amplitude of the temperature modulation is ~100 K. We have proposed a thin metallic film deposited on a glass substrate heated by interfering laser beams (optical wavelengths) as a means of generating very large amplitude of surface temperature modulation. Indeed, we predict theoretically by numerical solution of the thermal conduction equation that amplitude of the temperature modulation on the metallic film can be much greater than 100 K when heated by nanosecond pulses with an energy ~1 mJ. The formation of surface nanostructures of less than 100 nm in width is predicted at optical wavelengths in this implementation of thermal tweezers. Furthermore, we propose a simple extension to this technique where spatial phase shift of the temperature modulation effectively doubles or triples the resolution. At the same time, increased resolution is predicted by reducing the wavelength of the laser pulses. In addition, we present two distinctly different, computationally efficient numerical approaches for theoretical investigation of surface diffusion of interacting adparticles – the Monte Carlo Interaction Method (MCIM) and the random potential well method (RPWM). Using each of these approaches we have investigated thermal tweezers for redistribution of both strongly and weakly interacting adparticles. We have predicted that strong interactions between adparticles can increase the effectiveness of thermal tweezers, by demonstrating practically complete adparticle redistribution into the low temperature regions of the surface. This is promising from the point of view of thermal tweezers applied to directed self-assembly of nanostructures. Finally, we present a new and more efficient numerical approach to theoretical investigation of thermal tweezers of non-interacting adparticles. In this approach, the local diffusion coefficient is determined from solution of the Fokker-Planck equation. The diffusion equation is then solved numerically using the finite volume method (FVM) to directly obtain the probability density of adparticle position. We compare predictions of this approach to those of the Ermak algorithm solution of the Langevin equation, and relatively good agreement is shown at intermediate and high friction. In the low friction regime, we predict and investigate the phenomenon of ‘optimal’ friction and describe its occurrence due to very long jumps of adparticles as they diffuse from the hot regions of the surface. Future research directions, both theoretical and experimental are also discussed.

Unstructured strategic decision-making processes : CRE decision-making in the Italian consulting industry

This thesis aims at developing a better understanding of unstructured strategic decision making processes and the conditions for achieving successful decision outcomes. Specifically it focuses on the processes used to make CRE (Corporate Real Estate) decisions. The starting point for this thesis is that our knowledge of such processes is incomplete. A comprehensive study of the most recent CRE literature together with Behavioural Organization Theory has provided a research framework for the exploration of CRE recommended =best practice‘, and of how organizational variables impact on and shape these practices. To reveal the fundamental differences between CRE decision-making in practice and the prescriptive =best practice‘ advocated in the CRE literature, a study of seven Italian management consulting firms was undertaken addressing the aspects of content and process of decisions. This thesis makes its primary contribution by identifying the importance and difficulty of finding the right balance between problem complexity, process richness and cohesion to ensure a decision-making process that is sufficiently rich and yet quick enough to deliver a prompt outcome. While doing so, this research also provides more empirical evidence to some of the most established theories of decision-making while reinterpreting their mono-dimensional arguments in a multi-dimensional model of successful decision-making.