The quantum inspired modelling of changing attitudes and self-organising societies

We utilise the well-developed quantum decision models known to the QI community to create a higher order social decision making model. A simple Agent Based Model (ABM) of a society of agents with changing attitudes towards a social issue is presented, where the private attitudes of individuals in the system are represented using a geometric structure inspired by quantum theory. We track the changing attitudes of the members of that society, and their resulting propensities to act, or not, in a given social context. A number of new issues surrounding this "scaling up" of quantum decision theories are discussed, as well as new directions and opportunities.

A view from the edge of the forest : recent progress in understanding the relationships of the insect orders

Research over the last two decades has significantly increased our understanding of the evolutionary position of the insects among other arthropods, and the relationships among the insect Orders. Many of these insights have been established through increasingly sophisticated analyses of DNA sequence data from a limited number of genes. Recent results have established the relationships of the Holometabola, but relationships among the hemimetabolous orders have been more difficult to elucidate. A strong consensus on the relationships among the Palaeoptera (Ephemeroptera and Odonata) and their relationship to the Neoptera has not emerged with all three possible resolutions supported by different data sets. While polyneopteran relationships generally have resisted significant resolution, it is now clear that termites, Isoptera, are nested within the cockroaches, Blattodea. The newly discovered order Mantophasmatodea is difficult to place with the balance of studies favouring Grylloblattodea as sister-group. While some studies have found the paraneopteran orders (Hemiptera, Thysanoptera, Phthiraptera and Psocoptera) monophyletic, evidence suggests that parasitic lice (Phthiraptera) have evolved from groups within the book and bark lice (Psocoptera), and may represent parallel evolutions of parasitism within two major louse groups. Within Holometabola, it is now clear that Hymenoptera are the sister to the other orders, that, in turn are divided into two clades, the Neuropteroidea (Coleoptera, Neuroptera and relatives) and the Mecopterida (Trichoptera, Lepidoptera, Diptera and their relatives). The enigmatic order Strepsiptera, the twisted wing insects, have now been placed firmly near Coleoptera, rejecting their close relationship to Diptera that was proposed some 15years ago primarily based on ribosomal DNA data. Phylogenomic-scale analyses are just beginning to be focused on the relationships of the insect orders, and this is where we expect to see resolution of palaeopteran and polyneopteran relationships. Future research will benefit from greater coordination between intra and inter-ordinal analyses. This will maximise the opportunities for appropriate outgroup choice at the intraordinal level and provide the background knowledge for the interordinal analyses to span the maximum phylogenetic scope within groups.

Influence of medium range transport of particles from nucleation burst on particle number concentration within the urban airshed

An elevated particle number concentration (PNC) observed during nucleation events could play a significant contribution to the total particle load and therefore to the air pollution in the urban environments. Therefore, a field measurement study of PNC was commenced to investigate the temporal and spatial variations of PNC within the urban airshed of Brisbane, Australia. PNC was monitored at urban (QUT), roadside (WOO) and semi-urban (ROC) areas around the Brisbane region during 2009. During the morning traffic peak period, the highest relative fraction of PNC reached about 5% at QUT and WOO on weekdays. PNC peaks were observed around noon, which correlated with the highest solar radiation levels at all three stations, thus suggesting that high PNC levels were likely to be associated with new particle formation caused by photochemical reactions. Wind rose plots showed relatively higher PNC for the NE direction, which was associated with industrial pollution, accounting for 12%, 9% and 14% of overall PNC at QUT, WOO and ROC, respectively. Although there was no significant correlation between PNC at each station, the variation of PNC was well correlated among three stations during regional nucleation events. In addition, PNC at ROC was significantly influenced by upwind urban pollution during the nucleation burst events, with the average enrichment factor of 15.4. This study provides an insight into the influence of regional nucleation events on PNC in the Brisbane region and it the first study to quantify the effect of urban pollution on semi-urban PNC through the nucleation events. © 2012 Author(s).

Alternating direction implicit numerical method for the space and time fractional Bloch-Torrey equation in 3-D

Recently, some authors have considered a new diffusion model–space and time fractional Bloch-Torrey equation (ST-FBTE). Magin et al. (2008) have derived analytical solutions with fractional order dynamics in space (i.e., _ = 1, β an arbitrary real number, 1 < β ≤ 2) and time (i.e., 0 < α < 1, and β = 2), respectively. Yu et al. (2011) have derived an analytical solution and an effective implicit numerical method for solving ST-FBTEs, and also discussed the stability and convergence of the implicit numerical method. However, due to the computational overheads necessary to perform the simulations for nuclear magnetic resonance (NMR) in three dimensions, they present a study based on a two-dimensional example to confirm their theoretical analysis. Alternating direction implicit (ADI) schemes have been proposed for the numerical simulations of classic differential equations. The ADI schemes will reduce a multidimensional problem to a series of independent one-dimensional problems and are thus computationally efficient. In this paper, we consider the numerical solution of a ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. A fractional alternating direction implicit scheme (FADIS) for the ST-FBTE in 3-D is proposed. Stability and convergence properties of the FADIS are discussed. Finally, some numerical results for ST-FBTE are given.

Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media

Percolation flow problems are discussed in many research fields, such as seepage hydraulics, groundwater hydraulics, groundwater dynamics and fluid dynamics in porous media. Many physical processes appear to exhibit fractional-order behavior that may vary with time, or space, or space and time. The theory of pseudodifferential operators and equations has been used to deal with this situation. In this paper we use a fractional Darcys law with variable order Riemann-Liouville fractional derivatives, this leads to a new variable-order fractional percolation equation. In this paper, a new two-dimensional variable-order fractional percolation equation is considered. A new implicit numerical method and an alternating direct method for the two-dimensional variable-order fractional model is proposed. Consistency, stability and convergence of the implicit finite difference method are established. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of the methods. This technique can be used to simulate a three-dimensional variable-order fractional percolation equation.

A second-order accurate numerical approximation for the Riesz space fractional advection-dispersion equation

In this paper, we consider a space Riesz fractional advection-dispersion equation. The equation is obtained from the standard advection-diffusion equation by replacing the ¯rst-order and second-order space derivatives by the Riesz fractional derivatives of order β 1 Є (0; 1) and β2 Є(1; 2], respectively. Riesz fractional advection and dispersion terms are approximated by using two fractional centered difference schemes, respectively. A new weighted Riesz fractional ¯nite difference approximation scheme is proposed. When the weighting factor Ѳ = 1/2, a second- order accurate numerical approximation scheme for the Riesz fractional advection-dispersion equation is obtained. Stability, consistency and convergence of the numerical approximation scheme are discussed. A numerical example is given to show that the numerical results are in good agreement with our theoretical analysis.

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.

Prandtl number scaling of the unsteady natural convection boundary layer adjacent to a vertical flat plate for Pr > 1 subject to ramp surface heat flux

It is found in the literature that the existing scaling results for the boundary layer thickness, velocity and steady state time for the natural convection flow over an evenly heated plate provide a very poor prediction of the Prandtl number dependency of the flow. However, those scalings provide a good prediction of two other governing parameters’ dependency, the Rayleigh number and the aspect ratio. Therefore, an improved scaling analysis using a triple-layer integral approach and direct numerical simulations have been performed for the natural convection boundary layer along a semi-infinite flat plate with uniform surface heat flux. This heat flux is a ramp function of time, where the temperature gradient on the surface increases with time up to some specific time and then remains constant. The growth of the boundary layer strongly depends on the ramp time. If the ramp time is sufficiently long, the boundary layer reaches a quasi steady mode before the growth of the temperature gradient is completed. In this mode, the thermal boundary layer at first grows in thickness and then contracts with increasing time. However, if the ramp time is sufficiently short, the boundary layer develops differently, but after the wall temperature gradient growth is completed, the boundary layer develops as though the startup had been instantaneous.

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.

The heart of quality teaching : a values-based pedagogy for pre-service teacher education

In an ever changing world the adults of the future will be faced with many challenges. To cope with these challenges it seems apparent that values education will need to become paramount within a child.s education. A considerable number of research studies have indicated that values education is a critical component within education (Lovat & Toomey, 2007b). Building on this research Lovat (2006) claimed that values education was the missing link in quality teaching The concept of quality teaching had risen to the fore within educational research literature in the late 20th century with the claim that it is the teacher who makes the difference in schooling (Hattie, 2004). Thus, if teachers make such a difference to student learning, achievement and well-being, then it must hold true that pre-service teacher education programmes are vital in ensuring the development of quality teachers for our schools. The gap that this current research programme addressed was to link the fields of values education, quality teaching and pre-service teacher education. This research programme aimed to determine the impact of a values-based pedagogy on the development of quality teaching dimensions within pre-service teacher education. The values-based pedagogy that was investigated in this research programme was Philosophy in the Classroom. The research programme adopted a nested case study design based on the constructivist-interpretative paradigm in examining a unit within a pre-service teacher education programme at a Queensland university. The methodology utilised was qualitative where the main source of data was via interviews. In total, 43 pre-service teachers participated in three studies in order to determine if their involvement in a unit where the focus was on introducing pre-service teachers to an explicit values-based pedagogy impacted on their knowledge, skills and confidence in terms of quality teaching dimensions. The research programme was divided into three separate studies in order to address the two research questions: 1. In what ways do pre-service teachers perceive they are being prepared to become quality teachers? 2. Is there a connection between an explicit values-based pedagogy in pre-service teacher education and the development of pre-service teachers. understanding of quality teaching? Study One provided insight into 21 pre-service teachers. understandings of quality teaching. These 21 participants had not engaged in an explicit values-based pedagogy. Study Two involved the interviewing of 22 pre-service teachers at two separate points in time . prior to exposure to a unit that employed a values-explicit pedagogy and post this subject.s lecture content delivery. Study Three reported on and analysed individual case studies of five pre-service teachers who had participated in Study Two Time 1 and Time 2, as well as a third time following their field experience where they had practice in teaching the values explicit pedagogy. The results of the research demonstrate that an explicit values-based pedagogy introduced into a teacher education programme has a positive impact on the development of pre-service teachers. understanding of quality teaching skills and knowledge. The teaching and practice of a values-based pedagogy positively impacted on pre-service teachers with increases of knowledge, skills and confidence demonstrated on the quality teaching dimensions of intellectual quality, a supportive classroom environment, recognition of difference, connectedness and values. These findings were reinforced through the comparison of pre-service teachers who had participated in the explicit values-based pedagogical approach, with a sample of pre-service teachers who had not engaged in this same values-based pedagogical approach. A solid values-based pedagogy and practice can and does enhance pre-service teachers. understanding of quality teaching. These findings surrounding the use of a values-based pedagogy in pre-service teacher education to enhance quality teaching knowledge and skills has contributed theoretically to the field of educational research, as well having practical implications for teacher education institutions and teacher educators.