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.

Excess power circulation in distribution networks containing distributed energy resources

The presence of large number of single-phase distributed energy resources (DERs) can cause severe power quality problems in distribution networks. The DERs can be installed in random locations. This may cause the generation in a particular phase exceeds the load demand in that phase. Therefore the excess power in that phase will be fed back to the transmission network. To avoid this problem, the paper proposes the use of distribution static compensator (DSTATCOM) that needs to be connected at the first bus following a substation. When operated properly, the DSTATCOM can facilitate a set of balanced current flow from the substation, even when excess power is generated by DERs. The proposals are validated through extensive digital computer simulation studies using PSCAD and MATLAB.

An approach for current balancing in distribution networks with rooftop PVs

Current unbalance is a significant power quality problem in distribution networks. This problem increases further with the increased penetration of single-phase photovoltaic cells. In this paper, a new approach is developed for current unbalance reduction in medium voltage distribution networks. The method is based on utilization of three single-phase voltage source converters connected in delta configuration between the phases. Each converter is controlled to function as a varying capacitor. The combination of the load and the compensator will result in a balanced load with unity power factor. The efficacy of the proposed current unbalance reduction concept is verified through dynamic simulations in PSCAD/EMTDC.

Distribution feeder loads classification and decomposition

Load in distribution networks is normally measured at the 11kV supply points; little or no information is known about the type of customers and their contributions to the load. This paper proposes statistical methods to decompose an unknown distribution feeder load to its customer load sector/subsector profiles. The approach used in this paper should assist electricity suppliers in economic load management, strategic planning and future network reinforcements.

The spatial distribution of rodent damage in Australian macadamia (Macadamia integrifolia) orchards

The Black Rat (Rattus rattus), a global pest within the macadamia production industry, causes up to 30% crop damage in Australian orchards. During early stages of production in Australia, research demonstrated the importance of non crop adjacent habitats as significant in affecting the patterns of crop damage seen throughout orchards. Where once rodent damage was limited to the outside edges of orchard blocks, growers are now reporting finding crop damage throughout entire orchards. This study therefore aims to explore the spatial patterns of rodent distribution and damage now occurring in Australian macadamia orchards. We show that rodent damage and rodent distribution in these newer production regions differ from that shown in previous Australian research. Previous Australian research has shown damage patterns which were associated with the edges of orchard blocks however this study demonstrates a more widespread damage distribution. In the current study there is no relationship between rodent damage and the orchard edge. Arboreal rodent nests were identified within these newer orchard systems, suggesting rodents are residing within the tree component of the orchard system and not dependent on adjacent non-crop habitat for shelter. Results from this study confirm that rodents have modified their nesting and foraging behaviour in newer orchards systems in Australia. We suggest that this is a response of increased and prolonged availability of macadamia nuts in newer production regions enabling populations to be maintained throughout the year. Management strategies will require modification if control is to be achieved.

Smart grid-demand side response model for optimization air conditioning

The growing demand of air-conditioning is one of the largest contributors to Australia’s overall electricity consumption. This has started to create peak load supply problems for some electricity utilities particularly in Queensland. This research aimed to develop consumer demand side response model to assist electricity consumers to mitigate peak demand on the electrical network. The model developed demand side response model to allow consumers to manage and control air conditioning for every period, it is called intelligent control. This research investigates optimal response of end-user toward electricity price for several cases in the near future, such as: no spike, spike and probability spike price cases. The results indicate the potential of the scheme to achieve energy savings, reducing electricity bills (costs) to the consumer and targeting best economic performance for electrical generation distribution and transmission.

Probability analysis of machine angle stability with non-gaussian wind power input

The security of power transfer across a given transmission link is typically a steady state assessment. This paper develops tools to assess machine angle stability as affected by a combination of faults and uncertainty of wind power using probability analysis. The paper elaborates on the development of the theoretical assessment tool and demonstrates its efficacy using single machine infinite bus system.

A quantum probability perspective on borderline vagueness

The term “vagueness” describes a property of natural concepts, which normally have fuzzy boundaries, admit borderline cases, and are susceptible to Zeno’s sorites paradox. We will discuss the psychology of vagueness, especially experiments investigating the judgment of borderline cases and contradictions. In the theoretical part, we will propose a probabilistic model that describes the quantitative characteristics of the experimental finding and extends Alxatib’s and Pelletier’s (2011) theoretical analysis. The model is based on a Hopfield network for predicting truth values. Powerful as this classical perspective is, we show that it falls short of providing an adequate coverage of the relevant empirical results. In the final part, we will argue that a substan- tial modification of the analysis put forward by Alxatib and Pelletier and its probabilistic pendant is needed. The proposed modification replaces the standard notion of probabilities by quantum probabilities. The crucial phenomenon of borderline contradictions can be explained then as a quantum interference phenomenon.

Return distribution predictability and its implications for portfolio selection

The inquiries to return predictability are traditionally limited to conditional mean, while literature on portfolio selection is replete with moment-based analysis with up to the fourth moment being considered. This paper develops a distribution-based framework for both return prediction and portfolio selection. More specifically, a time-varying return distribution is modeled through quantile regressions and copulas, using quantile regressions to extract information in marginal distributions and copulas to capture dependence structure. A preference function which captures higher moments is proposed for portfolio selection. An empirical application highlights the additional information provided by the distributional approach which cannot be captured by the traditional moment-based methods.

Expression and distribution of cell-surface proteoglycans in the normal Lewis rat molar periodontium

Cell-surface proteoglycans participate in several biological functions such as cell cell and cell-matrix interactions, cell adhesion, the binding to various growth factors as co-receptors and repair. To understand better the expression and distribution of cell-surface proteoglycans in the periodontal tissues, an immunohistochemical evaluation of the normal Lewis rat molar periodontium using panels of antibodies for syndecan-1, -2, -4, glypican and betaglycan was carried out. Our results demonstrated the expression and distribution of all proteoglycans in the suprabasal gingival epithelium, soft and hard connective tissues. Both cellular and matrix localization was evident within the various periodontal compartments. The presence of these cell-surface proteoglycans indicates the potential for roles in the process of tissue homeostasis, repair or regeneration in periodontium of which each function requires further study.

Differential expression and distribution of syndecan-1 and -2 in periodontal wound healing of the rat

Cell-surface proteoglycans participate in several biological functions including interactions with adhesion molecules, growth factors and a variety of other effector molecules. Accordingly, these molecules play a central role in various aspects of cell–cell and cell–matrix interactions. To investigate the expression and distribution of the cell surface proteoglycans, syndecan-1 and -2, during periodontal wound healing, immunohistochemical analyses were carried out using monoclonal antibodies against syndecan-1, or -2 core proteins. Both syndecan-1 and -2 were expressed and distributed differentially at various stages of early inflammatory cell infiltration, granulation tissue formation, and tissue remodeling in periodontal wound healing. Expression of syndecan-1 was noted in inflammatory cells within and around the fibrin clots during the earliest stages of inflammatory cell infiltration. During granulation tissue formation it was noted in fibroblast-like cells and newly formed blood vessels. Syndecan-1 was not seen in newly formed bone or cementum matrix at any of the time periods studied. Syndecan-1 expression was generally less during the late stages of wound healing but was markedly expressed in cells that were close to the repairing junctional epithelium. In contrast, syndecan-2 expression and distribution was not evident at the early stages of inflammatory cell infiltration. During the formation of granulation tissue and subsequent tissue remodeling, syndecan-2 was expressed extracellularly in the newly formed fibrils which were oriented toward the root surface. Syndecan-2 was found to be significantly expressed on cells that were close to the root surface and within the matrix of repaired cementum covering root dentin as well as at the alveolar bone edge. These findings indicate that syndecan-1 and -2 may have distinctive functions during wound healing of the periodontium. The appearance of syndecan-1 may involve both cell–cell and cell–matrix interactions, while syndecan-2 showed a predilection to associate with cell–matrix interactions during hard tissue formation.