An advanced implicit meshless approach for fractional partial differential equation in computational mechanics

Recently, the numerical modelling and simulation for fractional partial differential equations (FPDE), which have been found with widely applications in modern engineering and sciences, are attracting increased attentions. The current dominant numerical method for modelling of FPDE is the explicit Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of time fractional diffusion equations. The discrete system of equations is obtained by using the RBF meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modelling and simulation for FPDE.

Multivariate Markov Process Models for the transmission of methicillin-resistant Staphylococcus Aureus in a hospital ward

Methicillin-resistant Staphylococcus Aureus (MRSA) is a pathogen that continues to be of major concern in hospitals. We develop models and computational schemes based on observed weekly incidence data to estimate MRSA transmission parameters. We extend the deterministic model of McBryde, Pettitt, and McElwain (2007, Journal of Theoretical Biology 245, 470–481) involving an underlying population of MRSA colonized patients and health-care workers that describes, among other processes, transmission between uncolonized patients and colonized health-care workers and vice versa. We develop new bivariate and trivariate Markov models to include incidence so that estimated transmission rates can be based directly on new colonizations rather than indirectly on prevalence. Imperfect sensitivity of pathogen detection is modeled using a hidden Markov process. The advantages of our approach include (i) a discrete valued assumption for the number of colonized health-care workers, (ii) two transmission parameters can be incorporated into the likelihood, (iii) the likelihood depends on the number of new cases to improve precision of inference, (iv) individual patient records are not required, and (v) the possibility of imperfect detection of colonization is incorporated. We compare our approach with that used by McBryde et al. (2007) based on an approximation that eliminates the health-care workers from the model, uses Markov chain Monte Carlo and individual patient data. We apply these models to MRSA colonization data collected in a small intensive care unit at the Princess Alexandra Hospital, Brisbane, Australia.

Patient-specific computational biomechanics for simulating adolescent scoliosis surgery : predicted vs clinical correction for a preliminary series of six patients

Scoliosis is a spinal deformity that requires surgical correction in progressive cases. In order to optimize surgical outcomes, patient-specific finite element models are being developed by our group. In this paper, a single rod anterior correction procedure is simulated for a group of six scoliosis patients. For each patient, personalised model geometry was derived from low-dose CT scans, and clinically measured intra-operative corrective forces were applied. However, tissue material properties were not patient-specific, being derived from existing literature. Clinically, the patient group had a mean initial Cobb angle of 47.3 degrees, which was corrected to 17.5 degrees after surgery. The mean simulated post-operative Cobb angle for the group was 18.1 degrees. Although this represents good agreement between clinical and simulated corrections, the discrepancy between clinical and simulated Cobb angle for individual patients varied between -10.3 and +8.6 degrees, with only three of the six patients matching the clinical result to within accepted Cobb measurement error of +-5 degrees. The results of this study suggest that spinal tissue material properties play an important role in governing the correction obtained during surgery, and that patient-specific modelling approaches must address the question of how to prescribe patient-specific soft tissue properties for spine surgery simulation.

Genome-wide identification and expression analysis of the NF-Y family of transcription factors in Triticum aestivum

Nuclear Factor Y (NF-Y) is a trimeric complex that binds to the CCAAT box, a ubiquitous eukaryotic promoter element. The three subunits NF-YA, NF-YB and NF-YC are represented by single genes in yeast and mammals. However, in model plant species (Arabidopsis and rice) multiple genes encode each subunit providing the impetus for the investigation of the NF-Y transcription factor family in wheat. A total of 37 NF-Y and Dr1 genes (10 NF-YA, 11 NF-YB, 14 NF-YC and 2 Dr1) in Triticum aestivum were identified in the global DNA databases by computational analysis in this study. Each of the wheat NF-Y subunit families could be further divided into 4-5 clades based on their conserved core region sequences. Several conserved motifs outside of the NF-Y core regions were also identified by comparison of NF-Y members from wheat, rice and Arabidopsis. Quantitative RT-PCR analysis revealed that some of the wheat NF-Y genes were expressed ubiquitously, while others were expressed in an organ-specific manner. In particular, each TaNF-Y subunit family had members that were expressed predominantly in the endosperm. The expression of nine NF-Y and two Dr1 genes in wheat leaves appeared to be responsive to drought stress. Three of these genes were up-regulated under drought conditions, indicating that these members of the NF-Y and Dr1 families are potentially involved in plant drought adaptation. The combined expression and phylogenetic analyses revealed that members within the same phylogenetic clade generally shared a similar expression profile. Organ-specific expression and differential response to drought indicate a plant-specific biological role for various members of this transcription factor family.

Evolutionary biology of Gondwanan non-biting midges (Diptera: Chironomidae)

The potential restriction to effective dispersal and gene flow caused by habitat fragmentation can apply to multiple levels of evolutionary scale; from the fragmentation of ancient supercontinents driving diversification and speciation on disjunct landmasses, to the isolation of proximate populations as a result of their inability to cross intervening unsuitable habitat. Investigating the role of habitat fragmentation in driving diversity within and among taxa can thus include inferences of phylogenetic relationships among taxa, assessments of intraspecific phylogeographic structure and analyses of gene flow among neighbouring populations. The proposed Gondwanan clade within the chironomid (non-biting midge) subfamily Orthocladiinae (Diptera: Chironomidae) represents a model system for investigating the role that population fragmentation and isolation has played at different evolutionary scales. A pilot study by Krosch et al (2009) indentified several highly divergent lineages restricted to ancient rainforest refugia and limited gene flow among proximate sites within a refuge for one member of this clade, Echinocladius martini Cranston. This study provided a framework for investigating the evolutionary history of this taxon and its relatives more thoroughly. Populations of E. martini were sampled in the Paluma bioregion of northeast Queensland to investigate patterns of fine-scale within- and among-stream dispersal and gene flow within a refuge more rigorously. Data was incorporated from Krosch et al (2009) and additional sites were sampled up- and downstream of the original sites. Analyses of genetic structure revealed strong natal site fidelity and high genetic structure among geographically proximate streams. Little evidence was found for regular headwater exchange among upstream sites, but there was distinct evidence for rare adult flight among sites on separate stream reaches. Overall, however, the distribution of shared haplotypes implied that both larval and adult dispersal was largely limited to the natal stream channel. Patterns of regional phylogeographic structure were examined in two related austral orthoclad taxa – Naonella forsythi Boothroyd from New Zealand and Ferringtonia patagonica Sæther and Andersen from southern South America – to provide a comparison with patterns revealed in their close relative E. martini. Both taxa inhabit tectonically active areas of the southern hemisphere that have also experienced several glaciation events throughout the Plio-Pleistocene that are thought to have affected population structure dramatically in many taxa. Four highly divergent lineages estimated to have diverged since the late Miocene were revealed in each taxon, mirroring patterns in E. martini; however, there was no evidence for local geographical endemism, implying substantial range expansion post-diversification. The differences in pattern evident among the three related taxa were suggested to have been influenced by variation in the responses of closed forest habitat to climatic fluctuations during interglacial periods across the three landmasses. Phylogeographic structure in E. martini was resolved at a continental scale by expanding upon the sampling design of Krosch et al (2009) to encompass populations in southeast Queensland, New South Wales and Victoria. Patterns of phylogeographic structure were consistent with expectations and several previously unrecognised lineages were revealed from central- and southern Australia that were geographically endemic to closed forest refugia. Estimated divergence times were congruent with the timing of Plio-Pleistocene rainforest contractions across the east coast of Australia. This suggested that dispersal and gene flow of E. martini among isolated refugia was highly restricted and that this taxon was susceptible to the impacts of habitat change. Broader phylogenetic relationships among taxa considered to be members of this Gondwanan orthoclad group were resolved in order to test expected patterns of evolutionary affinities across the austral continents. The inferred phylogeny and estimated divergence times did not accord with expected patterns based on the geological sequence of break-up of the Gondwanan supercontinent and implied instead several transoceanic dispersal events post-vicariance. Difficulties in appropriate taxonomic sampling and accurate calibration of molecular phylogenies notwithstanding, the sampling regime implemented in the current study has been the most intensive yet performed for austral members of the Orthocladiinae and unsurprisingly has revealed both novel taxa and phylogenetic relationships within and among described genera. Several novel associations between life stages are made here for both described and previously unknown taxa. Investigating evolutionary relationships within and among members of this clade of proposed Gondwanan orthoclad taxa has demonstrated that a complex interaction between historical population fragmentation and dispersal at several levels of evolutionary scale has been important in driving diversification in this group. While interruptions to migration, colonisation and gene flow driven by population fragmentation have clearly contributed to the development and maintenance of much of the diversity present in this group, long-distance dispersal has also played a role in influencing diversification of continental biotas and facilitating gene flow among disjunct populations.

Computational fluid dynamics analysis of a flat plate photocatalytic reactor for storm and wastewater reuse

A computational fluid dynamics (CFD) analysis has been performed for a flat plate photocatalytic reactor using CFD code FLUENT. Under the simulated conditions (Reynolds number, Re around 2650), a detailed time accurate computation shows the different stages of flow evolution and the effects of finite length of the reactor in creating flow instability, which is important to improve the performance of the reactor for storm and wastewater reuse. The efficiency of a photocatalytic reactor for pollutant decontamination depends on reactor hydrodynamics and configurations. This study aims to investigate the role of different parameters on the optimization of the reactor design for its improved performance. In this regard, more modelling and experimental efforts are ongoing to better understand the interplay of the parameters that influence the performance of the flat plate photocatalytic reactor.

Flow field investigation in a water treatment reactor using computational fluid dynamics

The hydrodynamic behaviour of a novel flat plate photocatalytic reactor for water treatment is investigated using CFD code FLUENT. The reactor consists of a reactive section that features negligible pressure drop and uniform illumination of the photocatalyst to ensure enhanced photocatalytic efficiency. The numerical simulations allowed the identification of several design issues in the original reactor, which include extensive boundary layer separation near the photocatalyst support and regions of flow recirculation that render a significant portion of the reactive area. The simulations reveal that this issue could be addressed by selecting the appropriate inlet positions and configurations. This modification can cause minimal pressure drop across the reactive zone and achieves significant uniformization of the tested pollutant on the photocatalyst surface. The influence of roughness elements type has also been studied with a view to identify their role on the distribution of pollutant concentration on the photocatalyst surface. The results presented here indicate that the flow and pollutant concentration field strongly depend on the geometric parameters and flow conditions.

Probability distributed time delays: integrating spatial effects into temporal models

Background In order to provide insights into the complex biochemical processes inside a cell, modelling approaches must find a balance between achieving an adequate representation of the physical phenomena and keeping the associated computational cost within reasonable limits. This issue is particularly stressed when spatial inhomogeneities have a significant effect on system's behaviour. In such cases, a spatially-resolved stochastic method can better portray the biological reality, but the corresponding computer simulations can in turn be prohibitively expensive. Results We present a method that incorporates spatial information by means of tailored, probability distributed time-delays. These distributions can be directly obtained by single in silico or a suitable set of in vitro experiments and are subsequently fed into a delay stochastic simulation algorithm (DSSA), achieving a good compromise between computational costs and a much more accurate representation of spatial processes such as molecular diffusion and translocation between cell compartments. Additionally, we present a novel alternative approach based on delay differential equations (DDE) that can be used in scenarios of high molecular concentrations and low noise propagation. Conclusions Our proposed methodologies accurately capture and incorporate certain spatial processes into temporal stochastic and deterministic simulations, increasing their accuracy at low computational costs. This is of particular importance given that time spans of cellular processes are generally larger (possibly by several orders of magnitude) than those achievable by current spatially-resolved stochastic simulators. Hence, our methodology allows users to explore cellular scenarios under the effects of diffusion and stochasticity in time spans that were, until now, simply unfeasible. Our methodologies are supported by theoretical considerations on the different modelling regimes, i.e. spatial vs. delay-temporal, as indicated by the corresponding Master Equations and presented elsewhere.

The waddlia genome: A window into chlamydial biology

Growing evidence suggests that a novel member of the Chlamydiales order, Waddlia chondrophila, is a potential agent of miscarriage in humans and abortion in ruminants. Due to the lack of genetic tools to manipulate chlamydia, genomic analysis is proving to be the most incisive tool in stimulating investigations into the biology of these obligate intracellular bacteria. 454/Roche and Solexa/Illumina technologies were thus used to sequence and assemble de novo the full genome of the first representative of the Waddliaceae family, W. chondrophila. The bacteria possesses a 2′116′312bp chromosome and a 15′593 bp low-copy number plasmid that might integrate into the bacterial chromosome. The Waddlia genome displays numerous repeated sequences indicating different genome dynamics from classical chlamydia which almost completely lack repetitive elements. Moreover, W. chondrophila exhibits many virulence factors also present in classical chlamydia, including a functional type III secretion system, but also a large complement of specific factors for resistance to host or environmental stresses. Large families of outer membrane proteins were identified indicating that these highly immunogenic proteins are not Chlamydiaceae specific and might have been present in their last common ancestor. Enhanced metabolic capability for the synthesis of nucleotides, amino acids, lipids and other co-factors suggests that the common ancestor of the modern Chlamydiales may have been less dependent on their eukaryotic host. The fine-detailed analysis of biosynthetic pathways brings us closer to possibly developing a synthetic medium to grow W. chondrophila, a critical step in the development of genetic tools. As a whole, the availability of the W. chondrophila genome opens new possibilities in Chlamydiales research, providing new insights into the evolution of members of the order Chlamydiales and the biology of the Waddliaceae.

Hybrid-Game Strategies for multi-objective design optimization in engineering

A number of Game Strategies (GS) have been developed in past decades. They have been used in the fields of economics, engineering, computer science and biology due to their efficiency in solving design optimization problems. In addition, research in multi-objective (MO) and multidisciplinary design optimization (MDO) has focused on developing robust and efficient optimization methods to produce a set of high quality solutions with low computational cost. In this paper, two optimization techniques are considered; the first optimization method uses multi-fidelity hierarchical Pareto optimality. The second optimization method uses the combination of two Game Strategies; Nash-equilibrium and Pareto optimality. The paper shows how Game Strategies can be hybridised and coupled to Multi-Objective Evolutionary Algorithms (MOEA) to accelerate convergence speed and to produce a set of high quality solutions. Numerical results obtained from both optimization methods are compared in terms of computational expense and model quality. The benefits of using Hybrid-Game Strategies are clearly demonstrated