A fast semi-implicit difference method for a nonlinear two-sided space-fractional diffusion equation with variable diffusivity coefficients

In this paper, we derive a new nonlinear two-sided space-fractional diffusion equation with variable coefficients from the fractional Fick’s law. A semi-implicit difference method (SIDM) for this equation is proposed. The stability and convergence of the SIDM are discussed. For the implementation, we develop a fast accurate iterative method for the SIDM by decomposing the dense coefficient matrix into a combination of Toeplitz-like matrices. This fast iterative method significantly reduces the storage requirement of O(n2)O(n2) and computational cost of O(n3)O(n3) down to n and O(nlogn)O(nlogn), where n is the number of grid points. The method retains the same accuracy as the underlying SIDM solved with Gaussian elimination. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.

Novel non-linear elastic structural analysis with generalised transverse element loads using a refined finite element

In the finite element modelling of structural frames, external loads such as wind loads, dead loads and imposed loads usually act along the elements rather than at the nodes only. Conventionally, when an element is subjected to these general transverse element loads, they are usually converted to nodal forces acting at the ends of the elements by either lumping or consistent load approaches. In addition, it is especially important for an element subjected to the first- and second-order elastic behaviour, to which the steel structure is critically prone to; in particular the thin-walled steel structures, when the stocky element section may be generally critical to the inelastic behaviour. In this sense, the accurate first- and second-order elastic displacement solutions of element load effect along an element is vitally crucial, but cannot be simulated using neither numerical nodal nor consistent load methods alone, as long as no equilibrium condition is enforced in the finite element formulation, which can inevitably impair the structural safety of the steel structure particularly. It can be therefore regarded as a unique element load method to account for the element load nonlinearly. If accurate displacement solution is targeted for simulating the first- and second-order elastic behaviour on an element on the basis of sophisticated non-linear element stiffness formulation, the numerous prescribed stiffness matrices must indispensably be used for the plethora of specific transverse element loading patterns encountered. In order to circumvent this shortcoming, the present paper proposes a numerical technique to include the transverse element loading in the non-linear stiffness formulation without numerous prescribed stiffness matrices, and which is able to predict structural responses involving the effect of first-order element loads as well as the second-order coupling effect between the transverse load and axial force in the element. This paper shows that the principle of superposition can be applied to derive the generalized stiffness formulation for element load effect, so that the form of the stiffness matrix remains unchanged with respect to the specific loading patterns, but with only the magnitude of the loading (element load coefficients) being needed to be adjusted in the stiffness formulation, and subsequently the non-linear effect on element loadings can be commensurate by updating the magnitude of element load coefficients through the non-linear solution procedures. In principle, the element loading distribution is converted into a single loading magnitude at mid-span in order to provide the initial perturbation for triggering the member bowing effect due to its transverse element loads. This approach in turn sacrifices the effect of element loading distribution except at mid-span. Therefore, it can be foreseen that the load-deflection behaviour may not be as accurate as those at mid-span, but its discrepancy is still trivial as proved. This novelty allows for a very useful generalised stiffness formulation for a single higher-order element with arbitrary transverse loading patterns to be formulated. Moreover, another significance of this paper is placed on shifting the nodal response (system analysis) to both nodal and element response (sophisticated element formulation). For the conventional finite element method, such as the cubic element, all accurate solutions can be only found at node. It means no accurate and reliable structural safety can be ensured within an element, and as a result, it hinders the engineering applications. The results of the paper are verified using analytical stability function studies, as well as with numerical results reported by independent researchers on several simple frames.

Performance dispersion for evidence-based classification of stationary throwers

Background There is a need for better understanding of the dispersion of classification-related variable to develop an evidence-based classification of athletes with a disability participating in stationary throwing events. Objectives The purposes of this study are (A) to describe tools designed to comprehend and represent the dispersion of the performance between successive classes, and (B) to present this dispersion for the elite male and female stationary shot-putters who participated in Beijing 2008 Paralympic Games. Study design Retrospective study Methods This study analysed a total of 479 attempts performed by 114 male and female stationary shot-putters in three F30s (F32-F34) and six F50s (F52-F58) classes during the course of eight events during Beijing 2008 Paralympic Games. Results The average differences of best performance were 1.46±0.46 m for males between F54 and F58 classes as well as 1.06±1.18 m for females between F55 and F58 classes. The results demonstrated a linear relationship between best performance and classification while revealing two male Gold Medallists in F33 and F52 classes were outliers. Conclusions This study confirms the benefits of the comparative matrices, performance continuum and dispersion plots to comprehend classification-related variables. The work presented here represents a stepping stone into biomechanical analyses of stationary throwers, particularly on the eve of the London 2012 Paralympic Games where new evidences could be gathered.

Variable phenotype in 16p duplication within a family

Background More individuals are now being identified with very rare genetic syndromes. We present a family with an inherited duplication of 16p11.2 to 16q12.1 in ring formation. Three of the four children, (aged 15 months to 10 years), mother, uncle, and grandmother are affected. Our aim was to provide preliminary evidence of possible phenotypic patterns of learning and behaviour associated with this chromosome anomaly. Method Psychometric assessments were undertaken with all four children. The mother and uncle also agreed to participate in the study. Measures of development (Bayley or Mullen), intellectual ability (WISC-IV or WAIS-III), academic achievement (WIAT-II), adaptive behaviour (Vinelands), and other relevant aspects of functioning (e.g., Children’s Memory Scale) were administered. Results. The first-born child is the only one who is unaffected. Her intellectual ability was assessed as being within the superior range. The second child experienced early difficulties with speech and motor skills. Although his intelligence is average, he has learning difficulties and significant auditory memory problems. The third child’s speech and motor milestones were markedly delayed. He has a complex medical history that includes a vitamin B12 deficiency. On the Mullen Scales at age 4 his scores ranged from average to very low. The development of the youngest child (aged 15 months), who also had a B12 deficiency but was treated early, was assessed as being within typical limits. Conclusions There is considerable developmental variability among the three children with this inherited 16p duplication. We discuss the intriguing similarities and differences, considering common features that may reflect phenotypic patterns and speculating about possible explanations for the variable presentations.

Copula-based spatial modelling of geometallurgical variables

The most important aspect of modelling a geological variable, such as metal grade, is the spatial correlation. Spatial correlation describes the relationship between realisations of a geological variable sampled at different locations. Any method for spatially modelling such a variable should be capable of accurately estimating the true spatial correlation. Conventional kriged models are the most commonly used in mining for estimating grade or other variables at unsampled locations, and these models use the variogram or covariance function to model the spatial correlations in the process of estimation. However, this usage assumes the relationships of the observations of the variable of interest at nearby locations are only influenced by the vector distance between the locations. This means that these models assume linear spatial correlation of grade. In reality, the relationship with an observation of grade at a nearby location may be influenced by both distance between the locations and the value of the observations (ie non-linear spatial correlation, such as may exist for variables of interest in geometallurgy). Hence this may lead to inaccurate estimation of the ore reserve if a kriged model is used for estimating grade of unsampled locations when nonlinear spatial correlation is present. Copula-based methods, which are widely used in financial and actuarial modelling to quantify the non-linear dependence structures, may offer a solution. This method was introduced by Bárdossy and Li (2008) to geostatistical modelling to quantify the non-linear spatial dependence structure in a groundwater quality measurement network. Their copula-based spatial modelling is applied in this research paper to estimate the grade of 3D blocks. Furthermore, real-world mining data is used to validate this model. These copula-based grade estimates are compared with the results of conventional ordinary and lognormal kriging to present the reliability of this method.

Prior and posterior linear pooling for combining expert opinions: Uses and impact on Bayesian Networks

The use of expert knowledge to quantify a Bayesian Network (BN) is necessary when data is not available. This however raises questions regarding how opinions from multiple experts can be used in a BN. Linear pooling is a popular method for combining probability assessments from multiple experts. In particular, Prior Linear Pooling (PrLP), which pools opinions then places them into the BN is a common method. This paper firstly proposes an alternative pooling method, Posterior Linear Pooling (PoLP). This method constructs a BN for each expert, then pools the resulting probabilities at the nodes of interest. Secondly, it investigates the advantages and disadvantages of using these pooling methods to combine the opinions of multiple experts. Finally, the methods are applied to an existing BN, the Wayfinding Bayesian Network Model, to investigate the behaviour of different groups of people and how these different methods may be able to capture such differences. The paper focusses on 6 nodes Human Factors, Environmental Factors, Wayfinding, Communication, Visual Elements of Communication and Navigation Pathway, and three subgroups Gender (female, male),Travel Experience (experienced, inexperienced), and Travel Purpose (business, personal) and finds that different behaviors can indeed be captured by the different methods.

Wide-area damping control for inter-area oscillations using inverse filtering technique

In this study, a non-linear excitation controller using inverse filtering is proposed to damp inter-area oscillations. The proposed controller is based on determining generator flux value for the next sampling time which is obtained by maximising reduction rate of kinetic energy of the system after the fault. The desired flux for the next time interval is obtained using wide-area measurements and the equivalent area rotor angles and velocities are predicted using a non-linear Kalman filter. A supplementary control input for the excitation system, using inverse filtering approach, to track the desired flux is implemented. The inverse filtering approach ensures that the non-linearity introduced because of saturation is well compensated. The efficacy of the proposed controller with and without communication time delay is evaluated on different IEEE benchmark systems including Kundur's two area, Western System Coordinating Council three-area and 16-machine, 68-bus test systems.

A review on prognostic techniques for non-stationary and non-linear rotating systems

The field of prognostics has attracted significant interest from the research community in recent times. Prognostics enables the prediction of failures in machines resulting in benefits to plant operators such as shorter downtimes, higher operation reliability, reduced operations and maintenance cost, and more effective maintenance and logistics planning. Prognostic systems have been successfully deployed for the monitoring of relatively simple rotating machines. However, machines and associated systems today are increasingly complex. As such, there is an urgent need to develop prognostic techniques for such complex systems operating in the real world. This review paper focuses on prognostic techniques that can be applied to rotating machinery operating under non-linear and non-stationary conditions. The general concept of these techniques, the pros and cons of applying these methods, as well as their applications in the research field are discussed. Finally, the opportunities and challenges in implementing prognostic systems and developing effective techniques for monitoring machines operating under non-stationary and non-linear conditions are also discussed.

Numerical treatment of a two-dimensional variable-order fractional nonlinear reaction-diffusion model

A two-dimensional variable-order fractional nonlinear reaction-diffusion model is considered. A second-order spatial accurate semi-implicit alternating direction method for a two-dimensional variable-order fractional nonlinear reaction-diffusion model is proposed. Stability and convergence of the semi-implicit alternating direct method are established. Finally, some numerical examples are given to support our theoretical analysis. These numerical techniques can be used to simulate a two-dimensional variable order fractional FitzHugh-Nagumo model in a rectangular domain. This type of model can be used to describe how electrical currents flow through the heart, controlling its contractions, and are used to ascertain the effects of certain drugs designed to treat arrhythmia.

Improving PLDA speaker verification using WMFD and linear-weighted approaches in limited microphone data conditions

This paper proposes the addition of a weighted median Fisher discriminator (WMFD) projection prior to length-normalised Gaussian probabilistic linear discriminant analysis (GPLDA) modelling in order to compensate the additional session variation. In limited microphone data conditions, a linear-weighted approach is introduced to increase the influence of microphone speech dataset. The linear-weighted WMFD-projected GPLDA system shows improvements in EER and DCF values over the pooled LDA- and WMFD-projected GPLDA systems in inter-view-interview condition as WMFD projection extracts more speaker discriminant information with limited number of sessions/ speaker data, and linear-weighted GPLDA approach estimates reliable model parameters with limited microphone data.

Electromyography and sonomyography analysis of the tibialis anterior: a cross sectional study

Background Foot dorsiflexion plays an essential role in both controlling balance and human gait. Electromyography (EMG) and sonomyography (SMG) can provide information on several aspects of muscle function. The aim was to establish the relationship between the EMG and SMG variables during isotonic contractions of foot dorsiflexors. Methods Twenty-seven healthy young adults performed the foot dorsiflexion test on a device designed ad hoc. EMG variables were maximum peak and area under the curve. Muscular architecture variables were muscle thickness and pennation angle. Descriptive statistical analysis, inferential analysis and a multivariate linear regression model were carried out. The confidence level was established with a statistically significant p-value of less than 0.05. Results The correlation between EMG variables and SMG variables was r = 0.462 (p < 0.05). The linear regression model to the dependent variable “peak normalized tibialis anterior (TA)” from the independent variables “pennation angle and thickness”, was significant (p = 0.002) with an explained variance of R2 = 0.693 and SEE = 0.16. Conclusions There is a significant relationship and degree of contribution between EMG and SMG variables during isotonic contractions of the TA muscle. Our results suggest that EMG and SMG can be feasible tools for monitoring and assessment of foot dorsiflexors. TA muscle parameterization and assessment is relevant in order to know that increased strength accelerates the recovery of lower limb injuries.

Correlation between architectural variables and torque in the erector spinae muscle during maximal isometric contraction

This study analysed whether a significant relationship exists between the torque and muscle thickness and pennation angle of the erector spinae muscle during a maximal isometric lumbar extension with the lumbar spine in neutral position. This was a cross-sectional study in which 46 healthy adults performed three repetitions for 5 s of maximal isometric lumbar extension with rests of 90 s. During the lumbar extensions, bilateral ultrasound images of the erector spinae muscle (to measure pennation angle and muscle thickness) and torque were acquired. Reliability test analysis calculating the internal consistency (Cronbach's alpha) of the measure, correlation between pennation angle, muscle thickness and torque extensions were examined. Through a linear regression the contribution of each independent variable (muscle thickness and pennation angle) to the variation of the dependent variable (torque) was calculated. The results of the reliability test were: 0.976–0.979 (pennation angle), 0.980–0.980 (muscle thickness) and 0.994 (torque). The results show that pennation angle and muscle thickness were significantly related to each other with a range between 0.295 and 0.762. In addition, multiple regression analysis showed that the two variables considered in this study explained 68% of the variance in the torque. Pennation angle and muscle thickness have a moderate impact on the variance exerted on the torque during a maximal isometric lumbar extension with the lumbar spine in neutral position.

To sonicate or not to sonicate PM filters: Reactive Oxygen Species generation upon ultrasonic irradiation

In aerosol research, a common approach for the collection of particulate matter (PM) is the use of filters in order to obtain sufficient material to undertake analysis. For subsequent chemical and toxicological analyses, in most of cases the PM needs to be extracted from the filters. Sonication is commonly used to most efficiently extract the PM from the filters. Extraction protocols generally involve 10 - 60 min of sonication. The energy of ultrasonic waves causes the formation and collapse of cavitation bubbles in the solution. Inside the collapsing cavities the localised temperatures and pressures can reach extraordinary values. Although fleeting, such conditions can lead to pyrolysis of the molecules present inside the cavitation bubbles (gases dissolved in the liquid and solvent vapours), which results in the production of free radicals and the generation of new compounds formed by reactions with these free radicals. For example, simple sonication of pure water will result in the formation of detectable levels of hydroxyl radicals. As hydroxyl radicals are recognised as playing key roles as oxidants in the atmosphere the extraction of PM from filters using sonication is therefore problematic. Sonication can result in significant chemical and physical changes to PM through thermal degradation and other reactions. In this article, an overview of sonication technique as used in aerosol research is provided, the capacity for radical generation under these conditions is described and an analysis is given of the impact of sonication-derived free radicals on three molecular probes commonly used by researchers in this field to detect Reactive Oxygen Species in PM.

Design and fabrication of linear pixel arrays for organic photovoltaic modules to achieve scalable power output

We describe a design and fabrication method to enable simpler manufacturing of more efficient organic solar cell modules using a modified flat panel deposition technique. Many mini-cell pixels are individually connected to each other in parallel forming a macro-scale solar cell array. The pixel size of each array is optimized through experimentation to maximize the efficiency of the whole array. We demonstrate that integrated organic solar cell modules with a scalable current output can be fabricated in this fashion and can also be connected in series to generate a scalable voltage output.

Investigating the population structure of Queensland invasive Streptococcus pneumoniae isolates in children: Using a modified multi-locus variable number of tandem repeat analysis and a novel minimum SNPs capsular typing method

This research investigated the use of DNA fingerprinting to characterise the bacteria Streptococcus pneumoniae or pneumococcus, and hence gain insight into the development of new vaccines or antibiotics. Different bacterial DNA fingerprinting methods were studied, and a novel method was developed and validated, which characterises different cell coatings that pneumococci produce. This method was used to study the epidemiology of pneumococci in Queensland before and after the introduction of the current pneumococcal vaccine. This study demonstrated that pneumococcal disease is highly prevalent in children under four years, that the bacteria can `switch' its cell coating to evade the vaccine, and that some DNA fingerprinting methods are more discriminatory than others. This has an impact on understanding which strains are more prone to cause invasive disease. Evidence of the excellent research findings have been published in high impact internationally refereed journals.