Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term

In this paper, we consider a modified anomalous subdiffusion equation with a nonlinear source term for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. A new implicit difference method is constructed. The stability and convergence are discussed using a new energy method. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis

Modified alternating direction methods for solving a two-dimensional non-continuous seepage flow with fractional derivatives

In this paper, a two-dimensional non-continuous seepage flow with fractional derivatives (2D-NCSF-FD) in uniform media is considered, which has modified the well known Darcy law. Using the relationship between Riemann-Liouville and Grunwald-Letnikov fractional derivatives, two modified alternating direction methods: a modified alternating direction implicit Euler method and a modified Peaceman-Rachford method, are proposed for solving the 2D-NCSF-FD in uniform media. The stability and consistency, thus convergence of the two methods in a bounded domain are discussed. Finally, numerical results are given.

How useful is expert opinion for predicting the distribution of a species within and beyond the region of expertise? A case study using brush-tailed rock-wallabiesPetrogale penicillata

1. Species' distribution modelling relies on adequate data sets to build reliable statistical models with high predictive ability. However, the money spent collecting empirical data might be better spent on management. A less expensive source of species' distribution information is expert opinion. This study evaluates expert knowledge and its source. In particular, we determine whether models built on expert knowledge apply over multiple regions or only within the region where the knowledge was derived. 2. The case study focuses on the distribution of the brush-tailed rock-wallaby Petrogale penicillata in eastern Australia. We brought together from two biogeographically different regions substantial and well-designed field data and knowledge from nine experts. We used a novel elicitation tool within a geographical information system to systematically collect expert opinions. The tool utilized an indirect approach to elicitation, asking experts simpler questions about observable rather than abstract quantities, with measures in place to identify uncertainty and offer feedback. Bayesian analysis was used to combine field data and expert knowledge in each region to determine: (i) how expert opinion affected models based on field data and (ii) how similar expert-informed models were within regions and across regions. 3. The elicitation tool effectively captured the experts' opinions and their uncertainties. Experts were comfortable with the map-based elicitation approach used, especially with graphical feedback. Experts tended to predict lower values of species occurrence compared with field data. 4. Across experts, consensus on effect sizes occurred for several habitat variables. Expert opinion generally influenced predictions from field data. However, south-east Queensland and north-east New South Wales experts had different opinions on the influence of elevation and geology, with these differences attributable to geological differences between these regions. 5. Synthesis and applications. When formulated as priors in Bayesian analysis, expert opinion is useful for modifying or strengthening patterns exhibited by empirical data sets that are limited in size or scope. Nevertheless, the ability of an expert to extrapolate beyond their region of knowledge may be poor. Hence there is significant merit in obtaining information from local experts when compiling species' distribution models across several regions.

Elastic lateral buckling of simply supported LiteSteel beams subject to transverse loading

The buckling strength of a new cold-formed hollow flange channel section known as LiteSteel beam (LSB) is governed by lateral distortional buckling characterised by simultaneous lateral deflection, twist and web distortion for its intermediate spans. Recent research has developed a modified elastic lateral buckling moment equation to allow for lateral distortional buckling effects. However, it is limited to a uniform moment distribution condition that rarely exists in practice. Transverse loading introduces a non-uniform bending moment distribution, which is also often applied above or below the shear centre (load height). These loading conditions are known to have significant effects on the lateral buckling strength of beams. Many steel design codes have adopted equivalent uniform moment distribution and load height factors to allow for these effects. But they were derived mostly based on data for conventional hot-rolled, doubly symmetric I-beams subject to lateral torsional buckling. The moment distribution and load height effects of transverse loading for LSBs, and the suitability of the current design modification factors to accommodate these effects for LSBs is not known. This paper presents the details of a research study based on finite element analyses on the elastic lateral buckling strength of simply supported LSBs subject to transverse loading. It discusses the suitability of the current steel design code modification factors, and provides suitable recommendations for simply supported LSBs subject to transverse loading.

The distribution of the sample minimum-variance frontier

In this paper, we present a finite sample analysis of the sample minimum-variance frontier under the assumption that the returns are independent and multivariate normally distributed. We show that the sample minimum-variance frontier is a highly biased estimator of the population frontier, and we propose an improved estimator of the population frontier. In addition, we provide the exact distribution of the out-of-sample mean and variance of sample minimum-variance portfolios. This allows us to understand the impact of estimation error on the performance of in-sample optimal portfolios. Key Words: minimum-variance frontier; efficiency set constants; finite sample distribution

Sensitivity analysis of voltage imbalance in distribution networks with rooftop PVs

A comprehensive voltage imbalance sensitivity analysis and stochastic evaluation based on the rating and location of single-phase grid-connected rooftop photovoltaic cells (PVs) in a residential low voltage distribution network are presented. The voltage imbalance at different locations along a feeder is investigated. In addition, the sensitivity analysis is performed for voltage imbalance in one feeder when PVs are installed in other feeders of the network. A stochastic evaluation based on Monte Carlo method is carried out to investigate the risk index of the non-standard voltage imbalance in the network in the presence of PVs. The network voltage imbalance characteristic based on different criteria of PV rating and location and network conditions is generalized. Improvement methods are proposed for voltage imbalance reduction and their efficacy is verified by comparing their risk index using Monte Carlo simulations.

Optimal allocation and sizing of DGs in distribution networks

In this paper, the placement and sizing of Distributed Generators (DG) in distribution networks are determined optimally. The objective is to minimize the loss and to improve the reliability. The constraints are the bus voltage, feeder current and the reactive power flowing back to the source side. The placement and size of DGs are optimized using a combination of Discrete Particle Swarm Optimization (DPSO) and Genetic Algorithm (GA). This increases the diversity of the optimizing variables in DPSO not to be stuck in the local minima. To evaluate the proposed algorithm, the semi-urban 37-bus distribution system connected at bus 2 of the Roy Billinton Test System (RBTS), which is located at the secondary side of a 33/11 kV distribution substation, is used. The results finally illustrate the efficiency of the proposed method.

Smectite flocculation structure modified by AI13 macromolecules; as revealed by the Transmission X-ray Microscopy (TXM)

The aggregate structure which occurs in aqueous smectitic suspensions is responsible for poor water clarification, difficulties in sludge dewatering and the unusual rheological behaviour of smectite rich soils. These macroscopic properties are dictated by the 3-D structural arrangement of smectite finest fraction within flocculated aggregates. Here, we report results from a relatively new technique, Transmission X-ray Microscopy (TXM), which makes it possible to investigate the internal structure and 3-D tomographic reconstruction of the smectite clay aggregates modified by Al13 keggin macro-molecule [Al13(O)4(OH)24(H2O)12 ]7+. Three different treatment methods were shown resulted in three different micro-structural environments of the resulting flocculation.

Enhancing the Stability of an Autonomous Microgrid using DSTATCOM

This paper proposes a method enhancing stability of an autonomous microgrid with distribution static compensator (DSTATCOM) and power sharing with multiple distributed generators (DG). It is assumed that all the DGs are connected through voltage source converter (VSC) and all connected loads are passive, making the microgrid totally inertia less. The VSCs are controlled by either state feedback or current feedback mode to achieve desired voltage-current or power outputs respectively. A modified angle droop is used for DG voltage reference generation. Power sharing ratio of the proposed droop control is established through derivation and verified by simulation results. A DSTATCOM is connected in the microgrid to provide ride through capability during power imbalance in the microgrid, thereby enhancing the system stability. This is established through extensive simulation studies using PSCAD.

Delay distribution based robust H∞ control of networked control systems with uncertainties

Network induced delay in networked control systems (NCS) is inherently non-uniformly distributed and behaves with multifractal nature. However, such network characteristics have not been well considered in NCS analysis and synthesis. Making use of the information of the statistical distribution of NCS network induced delay, a delay distribution based stochastic model is adopted to link Quality-of-Control and network Quality-of-Service for NCS with uncertainties. From this model together with a tighter bounding technology for cross terms, H∞ NCS analysis is carried out with significantly improved stability results. Furthermore, a memoryless H∞ controller is designed to stabilize the NCS and to achieve the prescribed disturbance attenuation level. Numerical examples are given to demonstrate the effectiveness of the proposed method.

Structure–property relationships of silk-modified mesoporous bioglass scaffolds

Porous mesopore-bioglass (MBG) scaffolds have been proposed as a new class of bone regeneration materials due to their apatite-formation and drug-delivery properties; however, the material’s inherent brittleness and high degradation and surface instability are major disadvantages, which compromise its mechanical strength and cytocompatibility as a biological scaffold. Silk, on the other hand, is a native biomaterial and is well characterized with respect to biocompatibility and tensile strength. In this study we set out to investigate what effects blending silk with MBG had on the physiochemical, drug-delivery and biological properties of MBG scaffolds with a view to bone tissue engineering applications. Transmission electron microscopy (TEM), scanning electron microscopy (SEM) and Fourier transform infrared spectroscopy (FTIR) were the methods used to analyze the inner microstructure, pore size and morphology, and composition of MBG scaffolds, before and after addition of silk. The effect of silk modification on the mechanical property of MBG scaffolds was determined by testing the compressive strength of the scaffolds and also compressive strength after degradation over time. The drug-delivery potential was evaluated by the release of dexamethasone (DEX) from the scaffolds. Finally, the cytocompatibility of silk-modified scaffolds was investigated by the attachment, morphology, proliferation, differentiation and bone-relative gene expression of bone marrow stromal cells (BMSCs). The results showed that silk modification improved the uniformity and continuity of pore network of MBG scaffolds, and maintained high porosity (94%) and large-pore size (200–400 mm). There was a significant improvement in mechanical strength, mechanical stability, and control of burst release of DEX in silkmodified MBG scaffolds. Silk modification also appeared to provide a better environment for BMSC attachment, spreading, proliferation, and osteogenic differentiation on MBG scaffolds.

Hydrogen bonding in the water stabilized structure of the modified unsymmetrically substituted viologen chromophore, N-ethyl-N'-(2-phosphonomethyl)-4,4'-bipyridylium dichloride

The crystal structure of the modified unsymmetrically N, N'-substituted viologen chromophore, N-ethyl- N'-(2-phosphonoethyl)-4, 4'-bipyridinium dichloride 0.75 hydrate. (1) has been determined. Crystals are triclinic, space group P-1 with Z = 2 in a cell with a = 7.2550(1), b = 13.2038(5), c = 18.5752(7) Å, α = 86.495(3), β = 83.527(2), γ = 88.921(2)o. The two independent but pseudo-symmetrically related cations in the asymmetric unit form one-dimensional hydrogen-bonded chains through short homomeric phosphonic acid O-H...O links [2.455(4), 2.464(4)A] while two of the chloride anions are similarly strongly linked to phosphonic acid groups [O-H…Cl, 2.889(4), 2.896(4)Å]. The other two chloride anions together with the two water molecules of solvation (one with partial occupancy) form unusual cyclic hydrogen-bonded bis(Cl...water) dianion units which lie between the layers of bipyridylium rings of the cation chain structures with which they are weakly associated.

Technical note : modelling a complex micro-multileaf collimator using the standard BEAMnrc distribution

Purpose: The component modules in the standard BEAMnrc distribution may appear to be insufficient to model micro-multileaf collimators that have tri-faceted leaf ends and complex leaf profiles. This note indicates, however, that accurate Monte Carlo simulations of radiotherapy beams defined by a complex collimation device can be completed using BEAMnrc's standard VARMLC component module.---------- Methods: That this simple collimator model can produce spatially and dosimetrically accurate micro-collimated fields is illustrated using comparisons with ion chamber and film measurements of the dose deposited by square and irregular fields incident on planar, homogeneous water phantoms.---------- Results: Monte Carlo dose calculations for on- and off-axis fields are shown to produce good agreement with experimental values, even upon close examination of the penumbrae.--------- Conclusions: The use of a VARMLC model of the micro-multileaf collimator, along with a commissioned model of the associated linear accelerator, is therefore recommended as an alternative to the development or use of in-house or third-party component modules for simulating stereotactic radiotherapy and radiosurgery treatments. Simulation parameters for the VARMLC model are provided which should allow other researchers to adapt and use this model to study clinical stereotactic radiotherapy treatments.