A finite volume method with linearisation in time for the solution of advection-reaction-diffusion systems

The numerical solution in one space dimension of advection--reaction--diffusion systems with nonlinear source terms may invoke a high computational cost when the presently available methods are used. Numerous examples of finite volume schemes with high order spatial discretisations together with various techniques for the approximation of the advection term can be found in the literature. Almost all such techniques result in a nonlinear system of equations as a consequence of the finite volume discretisation especially when there are nonlinear source terms in the associated partial differential equation models. This work introduces a new technique that avoids having such nonlinear systems of equations generated by the spatial discretisation process when nonlinear source terms in the model equations can be expanded in positive powers of the dependent function of interest. The basis of this method is a new linearisation technique for the temporal integration of the nonlinear source terms as a supplementation of a more typical finite volume method. The resulting linear system of equations is shown to be both accurate and significantly faster than methods that necessitate the use of solvers for nonlinear system of equations.

Exploring pedestrian accessibility and walkability : insight from public place observations in inner-urban higher density Brisbane, Australia

As planners work to create more sustainable and liveable urban environments, a priority is to transition away from prioritising the automobile and towards enhancing the pedestrian experience. Thus, this research explores the experience of pedestrian accessibility in inner-urban higher-density Brisbane in Australia, drawing on findings from semi-structured in-depth interviews with 24 residents and over 100 hours of public place observations in three case-study neighbourhoods. The interviews took place in residents homes and explored their experience of higher density living and their neighbourhood, whilst observations were recorded through a combination of methods including photographs, sketch maps, recordings and field journals. Observation locations included retail and commercial space, roads, parkland and open space, with multiple observations at each location. A thematic analysis identified common themes in both interviews and the observations, with this paper focusing on residents’ lived experience in urban built environments. This analysis revealed that pedestrian accessibility is linked to access to local amenities and direct routes, aesthetics, sense of community, ownership of space and safety. In particular, observations revealed how pedestrian accessibility and route-taking works with, against or in spite of the design features of urban environments, as well as the importance of the social use of the built environment. Residents spoke about although walking quick and preferred for local amenities, the decision to walk was moderated by factors such as time of day and perceived safety. Measures to ensure and improve the pedestrian accessibility of urban areas needs to take into account the propensity for people to prefer and improvise direct routes (often to the detriment of traffic safety considerations), the importance of ongoing maintenance and upgrading of walking infrastructure and the importance of aesthetically pleasing and safe walking environments. By combining interviews and observations, this research highlights the current dominance of the automobile culture in Brisbane and the layers of meaning, experiences and complexity hidden within the pedestrian experience.

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

We present a finite volume method to solve the time-space two-sided fractional advection-dispersion equation on a one-dimensional domain. The spatial discretisation employs fractionally-shifted Grünwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes. We demonstrate how the finite volume formulation provides a natural, convenient and accurate means of discretising this equation in conservative form, compared to using a conventional finite difference approach. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

A comparison of finite difference and finite volume methods for solving the space-fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non- classical diffusion or dispersion which is not adequately described by the classical theory of Brownian motion and Fick’s law. We consider a space-fractional advection-dispersion equation based on a fractional Fick’s law. Zhang et al. [Water Resources Research, 43(5)(2007)] considered such an equation with variable coefficients, which they dis- cretised using the finite difference method proposed by Meerschaert and Tadjeran [Journal of Computational and Applied Mathematics, 172(1):65-77 (2004)]. For this method the presence of variable coef- ficients necessitates applying the product rule before discretising the Riemann–Liouville fractional derivatives using standard and shifted Gru ̈nwald formulas, depending on the fractional order. As an alternative, we propose using a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Gru ̈nwald formulas are used to discretise the Riemann–Liouville fractional derivatives at control volume faces, eliminating the need for product rule expansions. We compare the two methods for several case studies, highlighting the convenience of the finite volume approach.

The relationship between BCOM1 gene variants and macular pigment optical density in persons with and without age-related macular degeneration

Background: Recent evidence indicates that gene variants related to carotenoid metabolism play a role in the uptake of macular pigments lutein (L) and zeaxanthine (Z). Moreover, these pigments are proposed to reduce the risk for advanced age-related macular degeneration (AMD). This study provides the initial examination of the relationship between the gene variants related to carotenoid metabolism, macular pigment optical density (MPOD) and their combined expression in healthy humans and patients with AMD. Participants and Methods: Forty-four participants were enrolled from a general population and a private practice including 20 healthy participants and 24 patients with advanced (neovascular) AMD. Participants were genotyped for the three single nucleotide polymorphisms (SNPs) upstream from BCMO1, rs11645428, rs6420424 and rs6564851 that have been shown to either up or down regulate beta-carotene conversion efficiency in the plasma. MPOD was determined by heterochromatic flicker photometry. Results: Healthy participants with the rs11645428 GG genotype, rs6420424 AA genotype and rs6564851 GG genotype all had on average significantly lower MPOD compared to those with the other genotypes (p < 0.01 for all three comparisons). When combining BCMO1 genotypes reported to have “high” (rs11645428 AA/rs6420424 GG/rs6564851 TT) and “low” (rs11645428 GG/rs6420424 AA/rs6564851 GG) beta-carotene conversion efficiency, we demonstrate clear differences in MPOD values (p<0.01). In patients with AMD there were no significant differences in MPOD for any of the three BCMO1 gene variants. Conclusion: In healthy participants MPOD levels can be related to high and low beta-carotene conversion BCMO1 genotypes. Such relationships were not found in patients with advanced neovascular AMD, indicative of additional processes influencing carotenoid uptake, possibly related to other AMD susceptibility genes. Our findings indicate that specific BCMO1 SNPs should be determined when assessing the effects of carotenoid supplementation on macular pigment and that their expression may be influenced by retinal disease.

Biophilic urbanism : harnessing natural elements to enhance the performance of constructed assets

Creating climate resilient, low-carbon urban environments and assets is a policy goal of many governments and city planners today, and an important issue for constructed asset owners. Stakeholders and decision makers in urban environments are also responding to growing evidence that cities need to increase their densities to reduce their footprint in the face of growing urban populations. Meanwhile, research is highlighting the importance of balancing such density with urban nature, to provide a range of health and wellbeing benefits to residents as well as to mitigate the environmental and economic impacts of heavily built up, impervious urban areas. Concurrently achieving this suite of objectives requires the coordination and cooperation of multiple stakeholder groups, with urban development and investment increasingly involving many private and public actors. Strategies are needed that can provide ‘win-win’ outcomes to benefit these multiple stakeholders, and provide immediate benefits while also addressing the emerging challenges of climate change, resource shortages and urban population growth. Within this context, ‘biophilic urbanism’ is emerging as an important design principle for buildings and urban areas. Through the use of a suite of natural design elements, biophilic urbanism has the potential to address multiple pressures related to climate change, increasing urban populations, finite resources and human’s inherent need for contact with nature. The principle directs the creation of urban environments that are conducive to life, delivering a range of benefits to stakeholders including building owners, occupiers and the surrounding community. This paper introduces the principle of biophilic urbanism and discusses opportunities for improved building occupant experience and performance of constructed assets, as well as addressing other sustainability objectives including climate change mitigation and adaptation. The paper presents an emerging process for considering biophilic design opportunities at different scales and highlights implications for the built environment industry. This process draws on findings of a study of leading cities internationally and learnings related to economic and policy considerations. This included literature review, two stakeholder workshops, and extensive industry consultation, funded by the Sustainable Built Environment National Research Centre through core project partners Western Australian Department of Finance, Parsons Brinckerhoff, Townsville City Council CitySolar Program, Green Roofs Australasia, and PlantUp.

Nonlinear analysis of plastic ball grid array solder joints

A nonlinear finite element analysis was carried out to investigate the viscoplastic deformation of solder joints in a ball grid array (BGA) package under temperature cycle. The effects of constraint on print circuit board (PCB) and stiffness of substrate on the deformation behaviour of the solder joints were also studied. A relative damage stress was adopted to analyze the potential failure sites in the solder joints. The results indicated that high inelastic strain and strain energy density were developed in the joints close to the package center. On the other hand, high constraint and high relative damage stress were associated with the joint closest to the edge of the silicon chip. The joint closest to the edge of the silicon chip was regarded as the most susceptible failure site if cavitation instability is the dominant failure mechanism. Increase the external constraint on the print circuit board (PCB) causes a slight increase in stress triaxiality (m/eq) and relative damage stress in the joint closest to the edge of silicon die. The relative damage stress is not sensitive to the Young’s modulus of the substrate.

Geometric sensitivity of patient-specific finite element models of the spine to variability in user-selected anatomical landmarks

Software to create individualised finite element (FE) models of the osseoligamentous spine using pre-operative computed tomography (CT) data-sets for spinal surgery patients has recently been developed. This study presents a geometric sensitivity analysis of this software to assess the effect of intra-observer variability in user-selected anatomical landmarks. User-selected landmarks on the osseous anatomy were defined from CT data-sets for three scoliosis patients and these landmarks were used to reconstruct patient-specific anatomy of the spine and ribcage using parametric descriptions. The intra-observer errors in landmark co-ordinates for these anatomical landmarks were calculated. FE models of the spine and ribcage were created using the reconstructed anatomy for each patient and these models were analysed for a loadcase simulating clinical flexibility assessment. The intra-observer error in the anatomical measurements was low in comparison to the initial dimensions, with the exception of the angular measurements for disc wedge and zygapophyseal joint (z-joint) orientation and disc height. This variability suggested that CT resolution may influence such angular measurements, particularly for small anatomical features, such as the z-joints, and may also affect disc height. The results of the FE analysis showed low variation in the model predictions for spinal curvature with the mean intra-observer variability substantially less than the accepted error in clinical measurement. These findings demonstrate that intra-observer variability in landmark point selection has minimal effect on the subsequent FE predictions for a clinical loadcase.

Analysis of strain-rate dependent mechanical behavior of single chondrocyte : a finite element study

Various studies have been conducted to investigate the effects of impact loading on cartilage damage and chondrocyte death. These have shown that the rate and magnitude of the applied strain significantly influence chondrocyte death, and that cell death occurred mostly in the superficial zone of cartilage suggesting the need to further understand the fundamental mechanisms underlying the chondrocytes death induced at certain levels of strain-rate. To date there is no comprehensive study providing insight on this phenomenon. The aim of this study is to examine the strain-rate dependent behavior of a single chondrocyte using a computational approach based on Finite Element Method (FEM). An FEM model was developed using various mechanical models, which were Standard Neo-Hookean Solid (SnHS), porohyperelastic (PHE) and poroviscohyperelastic (PVHE) to simulate Atomic Force Microscopy (AFM) experiments of chondrocyte. The PVHE showed, it can capture both relaxation and loading rate dependent behaviors of chondrocytes, accurately compared to other models.

Second-order elastic finite element analysis of structures using a single element per member

Finite element frame analysis programs targeted for design office application necessitate algorithms which can deliver reliable numerical convergence in a practical timeframe with comparable degrees of accuracy, and a highly desirable attribute is the use of a single element per member to reduce computational storage, as well as data preparation and the interpretation of the results. To this end, a higher-order finite element method including geometric non-linearity is addressed in the paper for the analysis of elastic frames for which a single element is used to model each member. The geometric non-linearity in the structure is handled using an updated Lagrangian formulation, which takes the effects of the large translations and rotations that occur at the joints into consideration by accumulating their nodal coordinates. Rigid body movements are eliminated from the local member load-displacement relationship for which the total secant stiffness is formulated for evaluating the large member deformations of an element. The influences of the axial force on the member stiffness and the changes in the member chord length are taken into account using a modified bowing function which is formulated in the total secant stiffness relationship, for which the coupling of the axial strain and flexural bowing is included.

Non-linear refined finite element elastic analysis of steel frames with generalized transverse member loads

In the finite element modelling of steel frames, external loads usually act along the members rather than at the nodes only. Conventionally, when a member is subjected to these transverse loads, they are converted to nodal forces which act at the ends of the elements into which the member is discretised by either lumping or consistent nodal load approaches. For a contemporary geometrically non-linear analysis in which the axial force in the member is large, accurate solutions are achieved by discretising the member into many elements, which can produce unfavourable consequences on the efficacy of the method for analysing large steel frames. Herein, a numerical technique to include the transverse loading in the non-linear stiffness formulation for a single element is proposed, and which is able to predict the structural responses of steel frames involving the effects of first-order member loads as well as the second-order coupling effect between the transverse load and the axial force in the member. This allows for a minimal discretisation of a frame for second-order analysis. For those conventional analyses which do include transverse member loading, prescribed stiffness matrices must be used for the plethora of specific loading patterns encountered. This paper shows, however, that the principle of superposition can be applied to the equilibrium condition, so that the form of the stiffness matrix remains unchanged with only the magnitude of the loading being needed to be changed in the stiffness formulation. This novelty allows for a very useful generalised stiffness formulation for a single higher-order element with arbitrary transverse loading patterns to be formulated. The results are verified using analytical stability function studies, as well as with numerical results reported by independent researchers on several simple structural frames.

Performance-based structural fire design and testing of structures

Fire incident in buildings is common in Hong Kong and this could lead to heavy casualties due to its high population density, so the fire safety design of the framed structure is an important research topic. This paper describes a computer tool for determination of capacity of structural safety against various fire scenarios and the well-accepted second-order direct plastic analysis is adopted for simulation of material yielding and buckling. A computer method is developed to predict structural behaviour of bare steel framed structures at elevated temperatures but the work can be applied to structures made of other materials. These effects of thermal expansion and material degradation due to heating are required to be considered in order to capture the actual behavior of the structure under fire. Degradation of material strength with increasing temperature is included by a set of temperature-stress-strain curves according to BS5950 Part 8 mainly, which implicitly allows for creep deformation. Several numerical and experimental verifications of framed structures are presented and compared against solutions by other researchers. The proposed method allows us to adopt the truly performance-based structural fire analysis and design with significant saving in cost and time.

Mammographic density-a review on the current understanding of its association with breast cancer

There has been considerable recent interest in the genetic, biological and epidemiological basis of mammographic density (MD), and the search for causative links between MD and breast cancer (BC) risk. This report will critically review the current literature on MD and summarize the current evidence for its association with BC. Keywords 'mammographic dens*', 'dense mammary tissue' or 'percent dens*' were used to search the existing literature in English on PubMed and Medline. All reports were critically analyzed. The data were assigned to one of the following aspects of MD: general association with BC, its relationship with the breast hormonal milieu, the cellular basis of MD, the generic variations of MD, and its significance in the clinical setting. MD adjusted for age, and BMI is associated with increased risk of BC diagnosis, advanced tumour stage at diagnosis and increased risk of both local recurrence and second primary cancers. The MD measures that predict BC risk have high heritability, and to date several genetic markers associated with BC risk have been found to also be associated with these MD risk predictors. Change in MD could be a predictor of the extent of chemoprevention with tamoxifen. Although the biological and genetic pathways that determine and perhaps modulate MD remain largely unresolved, significant inroads are being made into the understanding of MD, which may lead to benefits in clinical screening, assessment and treatment strategies. This review provides a timely update on the current understanding of MD's association with BC risk.

Dynamic changes in high and low mammographic density human breast tissues maintained in murine tissue engineering chambers during various murine peripartum states and over time

Mammographic density (MD) is a strong heritable risk factor for breast cancer, and may decrease with increasing parity. However, the biomolecular basis for MD-associated breast cancer remains unclear, and systemic hormonal effects on MD-associated risk is poorly understood. This study assessed the effect of murine peripartum states on high and low MD tissue maintained in a xenograft model of human MD. Method High and low MD human breast tissues were precisely sampled under radiographic guidance from prophylactic mastectomy specimens of women. The high and low MD tissues were maintained in separate vascularised biochambers in nulliparous or pregnant SCID mice for 4 weeks, or mice undergoing postpartum involution or lactation for three additional weeks. High and low MD biochamber material was harvested for histologic and radiographic comparisons during various murine peripartum states. High and low MD biochamber tissues in nulliparous mice were harvested at different timepoints for histologic and radiographic comparisons. Results High MD biochamber tissues had decreased stromal (p = 0.0027), increased adipose (p = 0.0003) and a trend to increased glandular tissue areas (p = 0.076) after murine postpartum involution. Stromal areas decreased (p = 0.042), while glandular (p = 0.001) and adipose areas (p = 0.009) increased in high MD biochamber tissues during lactation. A difference in radiographic density was observed in high (p = 0.0021) or low MD biochamber tissues (p = 0.004) between nulliparous, pregnant and involution groups. No differences in tissue composition were observed in high or low MD biochamber tissues maintained for different durations, although radiographic density increased over time. Conclusion High MD biochamber tissues had measurable histologic changes after postpartum involution or lactation. Alterations in radiographic density occurred in biochamber tissues between different peripartum states and over time. These findings demonstrate the dynamic nature of the human MD xenograft model, providing a platform for studying the biomolecular basis of MD-associated cancer risk. © 2013 Springer Science+Business Media New York.

Electrical imaging and fluid modeling of convective fingering in a shallow water-table aquifer

Unstable density-driven flow can lead to enhanced solute transport in groundwater. Only recently has the complex fingering pattern associated with free convection been documented in field settings. Electrical resistivity (ER) tomography has been used to capture a snapshot of convective instabilities at a single point in time, but a thorough transient analysis is still lacking in the literature. We present the results of a 2 year experimental study at a shallow aquifer in the United Arab Emirates that was designed to specifically explore the transient nature of free convection. ER tomography data documented the presence of convective fingers following a significant rainfall event. We demonstrate that the complex fingering pattern had completely disappeared a year after the rainfall event. The observation is supported by an analysis of the aquifer halite budget and hydrodynamic modeling of the transient character of the fingering instabilities. Modeling results show that the transient dynamics of the gravitational instabilities (their initial development, infiltration into the underlying lower-density groundwater, and subsequent decay) are in agreement with the timing observed in the time-lapse ER measurements. All experimental observations and modeling results are consistent with the hypothesis that a dense brine that infiltrated into the aquifer from a surficial source was the cause of free convection at this site, and that the finite nature of the dense brine source and dispersive mixing led to the decay of instabilities with time. This study highlights the importance of the transience of free convection phenomena and suggests that these processes are more rapid than was previously understood.