Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions

We consider time-space fractional reaction diffusion equations in two dimensions. This equation is obtained from the standard reaction diffusion equation by replacing the first order time derivative with the Caputo fractional derivative, and the second order space derivatives with the fractional Laplacian. Using the matrix transfer technique proposed by Ilic, Liu, Turner and Anh [Fract. Calc. Appl. Anal., 9:333--349, 2006] and the numerical solution strategy used by Yang, Turner, Liu, and Ilic [SIAM J. Scientific Computing, 33:1159--1180, 2011], the solution of the time-space fractional reaction diffusion equations in two dimensions can be written in terms of a matrix function vector product $f(A)b$ at each time step, where $A$ is an approximate matrix representation of the standard Laplacian. We use the finite volume method over unstructured triangular meshes to generate the matrix $A$, which is therefore non-symmetric. However, the standard Lanczos method for approximating $f(A)b$ requires that $A$ is symmetric. We propose a simple and novel transformation in which the standard Lanczos method is still applicable to find $f(A)b$, despite the loss of symmetry. Numerical results are presented to verify the accuracy and efficiency of our newly proposed numerical solution strategy.

Practical improvements to simultaneous computation of multi-view geometry and radial lens distortion

This paper discusses practical issues related to the use of the division model for lens distortion in multi-view geometry computation. A data normalisation strategy is presented, which has been absent from previous discussions on the topic. The convergence properties of the Rectangular Quadric Eigenvalue Problem solution for computing division model distortion are examined. It is shown that the existing method can require more than 1000 iterations when dealing with severe distortion. A method is presented for accelerating convergence to less than 10 iterations for any amount of distortion. The new method is shown to produce equivalent or better results than the existing method with up to two orders of magnitude reduction in iterations. Through detailed simulation it is found that the number of data points used to compute geometry and lens distortion has a strong influence on convergence speed and solution accuracy. It is recommended that more than the minimal number of data points be used when computing geometry using a robust estimator such as RANSAC. Adding two to four extra samples improves the convergence rate and accuracy sufficiently to compensate for the increased number of samples required by the RANSAC process.

New percentage body fat prediction equations for Japanese females

Anthropometry is a simple and cost-efficient method for the assessment of body composition. However prediction equations to estimate body composition using anthropometry should be ‘population-specific’. Most popular body composition prediction equations for Japanese females were proposed more than 40 years ago and there is some concern regarding their usefulness in Japanese females living today. The aim of this study was to compare percentage body fat (%BF) estimated from anthropometry and dual energy x-ray absorptiometry (DXA) to examine the applicability of commonly used prediction equations in young Japanese females. Body composition of 139 Japanese females aged between 18 and 27 years of age (BMI range: 15.1–29.1 kg/m2) was measured using whole-body DXA (Lunar DPX-LIQ) scans. From anthropometric measurements %BF was estimated using four equations developed from Japanese females. The results showed that the traditionally employed prediction equations for anthropometry significantly (p<0.01) underestimate %BF of young Japanese females and therefore are not valid for the precise estimation of body composition. New %BF prediction equations were proposed from the DXA and anthropometry results. Application of the proposed equations may assist in more accurate assessment of body fatness in Japanese females living today.

Simultaneous voltammetric determination of three herbicides in food and water samples with the aid of chemometrics

Differential pulse stripping voltammetry method(DPSV) was applied to the determination of three herbicides, ametryn, cyanatryn, and dimethametryn. It was found that their voltammograms overlapped strongly, and it is difficult to determine these compounds individually from their mixtures. With the aid of chemometrics, classical least squares(CLS), principal component regression(PCR) and partial least squares(PLS), voltammogram resolution and quantitative analysis of the synthetic mixtures of the three compounds were successfully performed. The proposed method was also applied to the analysis of some real samples with satisfactory results.

Outdoor simultaneous localisation and mapping using RatSLAM

In this paper an existing method for indoor Simultaneous Localisation and Mapping (SLAM) is extended to operate in large outdoor environments using an omnidirectional camera as its principal external sensor. The method, RatSLAM, is based upon computational models of the area in the rat brain that maintains the rodent’s idea of its position in the world. The system uses the visual appearance of different locations to build hybrid spatial-topological maps of places it has experienced that facilitate relocalisation and path planning. A large dataset was acquired from a dynamic campus environment and used to verify the system’s ability to construct representations of the world and simultaneously use these representations to maintain localisation.

On the relationships between self-reported bicycling injuries and perceived risk among cyclists in Queensland, Australia

The focus of governments on increasing active travel has motivated renewed interest in cycling safety. Bicyclists are up to 20 times more likely to be involved in serious injury crashes than drivers so understanding the relationship among factors in bicyclist crash risk is critically important for identifying effective policy tools, for informing bicycle infrastructure investments, and for identifying high risk bicycling contexts. This study aims to better understand the complex relationships between bicyclist self reported injuries resulting from crashes (e.g. hitting a car) and non-crashes (e.g. spraining an ankle) and perceived risk of cycling as a function of cyclist exposure, rider conspicuity, riding environment, rider risk aversion, and rider ability. Self reported data from 2,500 Queensland cyclists are used to estimate a series of seemingly unrelated regressions to examine the relationships among factors. The major findings suggest that perceived risk does not appear to influence injury rates, nor do injury rates influence perceived risks of cycling. Riders who perceive cycling as risky tend not to be commuters, do not engage in group riding, tend to always wear mandatory helmets and front lights, and lower their perception of risk by increasing days per week of riding and by increasing riding proportion on bicycle paths. Riders who always wear helmets have lower crash injury risk. Increasing the number of days per week riding tends to decrease both crash injury and non crash injury risk (e.g. a sprain). Further work is needed to replicate some of the findings in this study.

Numerical Modelling of LiteSteel Beams Subject to Shear

Abstract: LiteSteel beam (LSB) is a new cold-formed steel hollow flange channel beam produced using a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. It has the beneficial characteristics of torsionally rigid closed rectangular flanges combined with economical fabrication processes from a single strip of high strength steel. Although the LSB sections are commonly used as flexural members, no research has been undertaken on the shear behaviour of LSBs. Therefore experimental and numerical studies were undertaken to investigate the shear behaviour and strength of LSBs. In this research finite element models of LSBs were developed to investigate their nonlinear shear behaviour including their buckling characteristics and ultimate shear strength. They were validated by comparing their results with available experimental results. The models provided full details of the shear buckling and strength characteristics of LSBs, and showed the presence of considerable improvements to web shear buckling in LSBs and associated post-buckling strength. This paper presents the details of the finite element models of LSBs and the results. Both finite element analysis and experimental results showed that the current design rules in cold-formed steel codes are very conservative for the shear design of LSBs. The ultimate shear capacities from finite element analyses confirmed the accuracy of proposed shear strength equations for LSBs based on the North American specification and DSM design equations. Developed finite element models were used to investigate the reduction to shear capacity of LSBs when full height web side plates were not used or when only one web side plate was used, and these results are also presented in this paper.

New design rules for the shear strength of LiteSteel Beams with web openings

Abstract: LiteSteel beam (LSB) is a new cold-formed steel hollow flange channel section produced using a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. The LSBs are commonly used as floor joists and bearers with web openings in residential, industrial and commercial buildings. Their shear strengths are considerably reduced when web openings are included for the purpose of locating building services. However, no research has been undertaken on the shear behaviour and strength of LSBs with web openings. Therefore experimental and numerical studies were undertaken to investigate the shear behaviour and strength of LSBs with web openings. In this research, finite element models of LSBs with web openings in shear were developed to simulate the shear behaviour and strength of LSBs including their buckling characteristics. They were then validated by comparing their results with available experimental test results and used in a detailed parametric study. The results showed that the current design rules in cold-formed steel structures design codes are very conservative for the shear design of LSBs with web openings. Improved design equations have been proposed for the shear capacity of LSBs with web openings based on both experimental and parametric study results. An alternative shear design method based on an equivalent reduced web thickness was also proposed. It was found that the same shear strength design rules developed for LSBs without web openings can be used for LSBs with web openings provided the equivalent reduced web thickness equation developed in this paper is used. This is a significant advancement as it simplifies the shear design methods of LSBs with web openings considerably.

Numerical modelling and design of LiteSteel Beams subject to lateral buckling

The LiteSteel Beam (LSB) is a new hollow flange channel section developed using a patented dual electric resistance welding and cold-forming process. It has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a slender web, and is commonly used as flexural members. However, the LSB flexural members are subjected to a relatively new lateral distortional buckling mode, which reduces their moment capacities. Unlike lateral torsional buckling, the lateral distortional buckling of LSBs is characterised by simultaneous lateral deflection, twist and cross sectional change due to web distortion. Therefore a detailed investigation into the lateral buckling behaviour of LSB flexural members was undertaken using experiments and finite element analyses. This paper presents the details of suitable finite element models developed to simulate the behaviour and capacity of LSB flexural members subject to lateral buckling. The models included all significant effects that influence the ultimate moment capacities of such members, including material inelasticity, lateral distortional buckling deformations, web distortion, residual stresses, and geometric imperfections. Comparison of elastic buckling and ultimate moment capacity results with predictions from other numerical analyses and available buckling moment equations, and experimental results showed that the developed finite element models accurately predict the behaviour and moment capacities of LSBs. The validated model was then used in a detailed parametric study that produced accurate moment capacity data for all the LSB sections and improved design rules for LSB flexural members subject to lateral distortional buckling.

Efficient preconditioning of the method of lines for solving nonlinear two-sided space-fractional diffusion equations

A standard method for the numerical solution of partial differential equations (PDEs) is the method of lines. In this approach the PDE is discretised in space using �finite di�fferences or similar techniques, and the resulting semidiscrete problem in time is integrated using an initial value problem solver. A significant challenge when applying the method of lines to fractional PDEs is that the non-local nature of the fractional derivatives results in a discretised system where each equation involves contributions from many (possibly every) spatial node(s). This has important consequences for the effi�ciency of the numerical solver. First, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. Second, since the Jacobian matrix of the system is dense (partially or fully), methods that avoid the need to form and factorise this matrix are preferred. In this paper, we consider a nonlinear two-sided space-fractional di�ffusion equation in one spatial dimension. A key contribution of this paper is to demonstrate how an eff�ective preconditioner is crucial for improving the effi�ciency of the method of lines for solving this equation. In particular, we show how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

On the significance of omitted variables in intersection crash modeling

Advances in safety research—trying to improve the collective understanding of motor vehicle crash causes and contributing factors—rest upon the pursuit of numerous lines of research inquiry. The research community has focused considerable attention on analytical methods development (negative binomial models, simultaneous equations, etc.), on better experimental designs (before-after studies, comparison sites, etc.), on improving exposure measures, and on model specification improvements (additive terms, non-linear relations, etc.). One might logically seek to know which lines of inquiry might provide the most significant improvements in understanding crash causation and/or prediction. It is the contention of this paper that the exclusion of important variables (causal or surrogate measures of causal variables) cause omitted variable bias in model estimation and is an important and neglected line of inquiry in safety research. In particular, spatially related variables are often difficult to collect and omitted from crash models—but offer significant opportunities to better understand contributing factors and/or causes of crashes. This study examines the role of important variables (other than Average Annual Daily Traffic (AADT)) that are generally omitted from intersection crash prediction models. In addition to the geometric and traffic regulatory information of intersection, the proposed model includes many spatial factors such as local influences of weather, sun glare, proximity to drinking establishments, and proximity to schools—representing a mix of potential environmental and human factors that are theoretically important, but rarely used. Results suggest that these variables in addition to AADT have significant explanatory power, and their exclusion leads to omitted variable bias. Provided is evidence that variable exclusion overstates the effect of minor road AADT by as much as 40% and major road AADT by 14%.

Modeling ion channel dynamics through reflected stochastic differential equations

Ion channels are membrane proteins that open and close at random and play a vital role in the electrical dynamics of excitable cells. The stochastic nature of the conformational changes these proteins undergo can be significant, however current stochastic modeling methodologies limit the ability to study such systems. Discrete-state Markov chain models are seen as the "gold standard," but are computationally intensive, restricting investigation of stochastic effects to the single-cell level. Continuous stochastic methods that use stochastic differential equations (SDEs) to model the system are more efficient but can lead to simulations that have no biological meaning. In this paper we show that modeling the behavior of ion channel dynamics by a reflected SDE ensures biologically realistic simulations, and we argue that this model follows from the continuous approximation of the discrete-state Markov chain model. Open channel and action potential statistics from simulations of ion channel dynamics using the reflected SDE are compared with those of a discrete-state Markov chain method. Results show that the reflected SDE simulations are in good agreement with the discrete-state approach. The reflected SDE model therefore provides a computationally efficient method to simulate ion channel dynamics while preserving the distributional properties of the discrete-state Markov chain model and also ensuring biologically realistic solutions. This framework could easily be extended to other biochemical reaction networks. © 2012 American Physical Society.

A biphasic scaffold design combined with cell sheet technology for simultaneous regeneration of alveolar bone/periodontal ligament complex

This study describes the design of a biphasic scaffold composed of a Fused Deposition Modeling scaffold (bone compartment) and an electrospun membrane (periodontal compartment) for periodontal regeneration. In order to achieve simultaneous alveolar bone and periodontal ligament regeneration a cell-based strategy was carried out by combining osteoblast culture in the bone compartment and placement of multiple periodontal ligament (PDL) cell sheets on the electrospun membrane. In vitro data showed that the osteoblasts formed mineralized matrix in the bone compartment after 21 days in culture and that the PDL cell sheet harvesting did not induce significant cell death. The cell-seeded biphasic scaffolds were placed onto a dentin block and implanted for 8 weeks in an athymic rat subcutaneous model. The scaffolds were analyzed by μCT, immunohistochemistry and histology. In the bone compartment, a more intense ALP staining was obtained following seeding with osteoblasts, confirming the μCT results which showed higher mineralization density for these scaffolds. A thin mineralized cementum-like tissue was deposited on the dentin surface for the scaffolds incorporating the multiple PDL cell sheets, as observed by H&E and Azan staining. These scaffolds also demonstrated better attachment onto the dentin surface compared to no attachment when no cell sheets were used. In addition, immunohistochemistry revealed the presence of CEMP1 protein at the interface with the dentine. These results demonstrated that the combination of multiple PDL cell sheets and a biphasic scaffold allows the simultaneous delivery of the cells necessary for in vivo regeneration of alveolar bone, periodontal ligament and cementum. © 2012 Elsevier Ltd.

Anomalous subdiffusion equations by the meshless collocation method

This paper aims to develop an implicit meshless collocation technique based on the moving least squares approximation for numerical simulation of the anomalous subdiffusion equation(ASDE). The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach related to the time discretization are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling of ASDEs.