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

How can soil monitoring networks be used to improve predictions of organic carbon pool dynamics and CO2 fluxes in agricultural soils?

Abstract As regional and continental carbon balances of terrestrial ecosystems become available, it becomes clear that the soils are the largest source of uncertainty. Repeated inventories of soil organic carbon (SOC) organized in soil monitoring networks (SMN) are being implemented in a number of countries. This paper reviews the concepts and design of SMNs in ten countries, and discusses the contribution of such networks to reducing the uncertainty of soil carbon balances. Some SMNs are designed to estimate country-specific land use or management effects on SOC stocks, while others collect soil carbon and ancillary data to provide a nationally consistent assessment of soil carbon condition across the major land-use/soil type combinations. The former use a single sampling campaign of paired sites, while for the latter both systematic (usually grid based) and stratified repeated sampling campaigns (5–10 years interval) are used with densities of one site per 10–1,040 km². For paired sites, multiple samples at each site are taken in order to allow statistical analysis, while for the single sites, composite samples are taken. In both cases, fixed depth increments together with samples for bulk density and stone content are recommended. Samples should be archived to allow for re-measurement purposes using updated techniques. Information on land management, and where possible, land use history should be systematically recorded for each site. A case study of the agricultural frontier in Brazil is presented in which land use effect factors are calculated in order to quantify the CO2 fluxes from national land use/management conversion matrices. Process-based SOC models can be run for the individual points of the SMN, provided detailed land management records are available. These studies are still rare, as most SMNs have been implemented recently or are in progress. Examples from the USA and Belgium show that uncertainties in SOC change range from 1.6–6.5 Mg C ha−1 for the prediction of SOC stock changes on individual sites to 11.72 Mg C ha−1 or 34% of the median SOC change for soil/land use/climate units. For national SOC monitoring, stratified sampling sites appears to be the most straightforward attribution of SOC values to units with similar soil/land use/climate conditions (i.e. a spatially implicit upscaling approach). Keywords Soil monitoring networks - Soil organic carbon - Modeling - Sampling design

Living well with diabetes: a randomized controlled trial of a telephone-delivered intervention for maintenance of weight loss, physical activity and glycaemic control in adults with type 2 diabetes

Background By 2025, it is estimated that approximately 1.8 million Australian adults (approximately 8.4% of the adult population) will have diabetes, with the majority having type 2 diabetes. Weight management via improved physical activity and diet is the cornerstone of type 2 diabetes management. However, the majority of weight loss trials in diabetes have evaluated short-term, intensive clinic-based interventions that, while producing short-term outcomes, have failed to address issues of maintenance and broad population reach. Telephone-delivered interventions have the potential to address these gaps. Methods/Design Using a two-arm randomised controlled design, this study will evaluate an 18-month, telephone-delivered, behavioural weight loss intervention focussing on physical activity, diet and behavioural therapy, versus usual care, with follow-up at 24 months. Three-hundred adult participants, aged 20-75 years, with type 2 diabetes, will be recruited from 10 general practices via electronic medical records search. The Social-Cognitive Theory driven intervention involves a six-month intensive phase (4 weekly calls and 11 fortnightly calls) and a 12-month maintenance phase (one call per month). Primary outcomes, assessed at 6, 18 and 24 months, are: weight loss, physical activity, and glycaemic control (HbA1c), with weight loss and physical activity also measured at 12 months. Incremental cost-effectiveness will also be examined. Study recruitment began in February 2009, with final data collection expected by February 2013. Discussion This is the first study to evaluate the telephone as the primary method of delivering a behavioural weight loss intervention in type 2 diabetes. The evaluation of maintenance outcomes (6 months following the end of intervention), the use of accelerometers to objectively measure physical activity, and the inclusion of a cost-effectiveness analysis will advance the science of broad reach approaches to weight control and health behaviour change, and will build the evidence base needed to advocate for the translation of this work into population health practice.