Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term

In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Finally, some numerical examples are given and the results demonstrate the effectiveness of theoretical analysis. Keywords: The variable-order Galilei invariant advection diffusion equation with a nonlinear source term; The variable-order Riemann–Liouville fractional partial derivative; Stability; Convergence; Numerical scheme improving temporal accuracy

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.

Preferences of first-time expectant mothers for care of their child : 'I wouldn't leave them somewhere that made me feel insecure'

Australia has witnessed a continual increase in maternal employment over the past two decades, which places focus on both supply of childcare and a demand for high quality care. This study examined childcare preferences regarding the return to paid work of 124 Australian women who were expecting their first child. In contrast with most studies that have retrospective designs, the design of this study presents the perspectives of women prior to the birth of their first child-that is, before they have made a final decision about child care. This study found that the majority (78 per cent) of the women intended to re-commence work within the 12 months after the birth of their child. There were two factors that were the most salient features in their decision making-the quality of care and the personal satisfaction of engaging in paid work. The findings suggest that family friendly employment practices and access to secure, high-quality child care are key to women's secure participation in the paid workforce.

Towards automated and in-situ, near-real time 3-D reconstruction of coral reef environments

Coral reefs are biologically complex ecosystems that support a wide variety of marine organisms. These are fragile communities under enormous threat from natural and human-based influences. Properly assessing and measuring the growth and health of reefs is essential to understanding impacts of ocean acidification, coastal urbanisation and global warming. In this paper, we present an innovative 3-D reconstruction technique based on visual imagery as a non-intrusive, repeatable, in situ method for estimating physical parameters, such as surface area and volume for efficient assessment of long-term variability. The reconstruction algorithms are presented, and benchmarked using an existing data set. We validate the technique underwater, utilising a commercial-off-the-shelf camera and a piece of staghorn coral, Acropora cervicornis. The resulting reconstruction is compared with a laser scan of the coral piece for assessment and validation. The comparison shows that 77% of the pixels in the reconstruction are within 0.3 mm of the ground truth laser scan. Reconstruction results from an unknown video camera are also presented as a segue to future applications of this research.