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

Numerical modelling of light gauge cold-formed steel compression members subjected to distortional buckling at elevated temperatures

Fire safety design of building structures has received greater attention in recent times due to continuing loss of properties and lives during fires. However, fire performance of light gauge cold-formed steel structures is not well understood despite its increased usage in buildings. Cold-formed steel compression members are susceptible to various buckling modes such as local and distortional buckling and their ultimate strength behaviour is governed by these buckling modes. Therefore a research project based on experimental and numerical studies was undertaken to investigate the distortional buckling behaviour of light gauge cold-formed steel compression members under simulated fire conditions. Lipped channel sections with and without additional lips were selected with three thicknesses of 0.6, 0.8, and 0.95 mm and both low and high strength steels (G250 and G550 steels). More than 150 compression tests were undertaken first at ambient and elevated temperatures. Finite element models of the tested compression members were then developed by including the degradation of mechanical properties with increasing temperatures. Comparison of finite element analysis and experimental results showed that the developed finite element models were capable of simulating the distortional buckling and strength behaviour at ambient and elevated temperatures up to 800 °C. The validated model was used to determine the effects of mechanical properties, geometric imperfections and residual stresses on the distortional buckling behaviour and strength of cold-formed steel columns. This paper presents the details of the numerical study and the results. It demonstrated the importance of using accurate mechanical properties at elevated temperatures in order to obtain reliable strength characteristics of cold-formed steel columns under fire conditions.

Soil carbon sequestration rates and associated economic costs for farming systems of south-eastern Australia

Soil organic carbon (C) sequestration rates based on the Intergovernmental Panel for Climate Change (IPCC) methodology were combined with local economic data to simulate the economic potential for C sequestration in response to conservation tillage in the six agro-ecological zones within the Southern Region of the Australian grains industry. The net C sequestration rate over 20 years for the Southern Region (which includes discounting for associated greenhouse gases) is estimated to be 3.6 or 6.3 Mg C/ha after converting to either minimum or no-tillage practices, respectively, with no-till practices estimated to return 75% more carbon on average than minimum tillage. The highest net gains in C per ha are realised when converting from conventional to no-tillage practices in the high-activity clay soils of the High Rainfall and Wimmera agro-ecological zones. On the basis of total area available for change, the Slopes agro-ecological zone offers the highest net returns, potentially sequestering an additional 7.1 Mt C under no-tillage scenario over 20 years. The economic analysis was summarised as C supply curves for each of the 6 zones expressing the total additional C accumulated over 20 years for a price per t C sequestered ranging from zero to AU$200. For a price of $50/Mg C, a total of 427 000 Mg C would be sequestered over 20 years across the Southern Region, <5% of the simulated C sequestration potential of 9.1 Mt for the region. The Wimmera and Mid-North offer the largest gains in C under minimum tillage over 20 years of all zones for all C prices. For the no-tillage scenario, for a price of $50/Mg C, 1.74 Mt C would be sequestered over 20 years across the Southern Region, <10% of the simulated C sequestration potential of 18.6 Mt for the region over 20 years. The Slopes agro-ecological zone offers the best return in C over 20 years under no-tillage for all C prices. The Mallee offers the least return for both minimum and no-tillage scenarios. At a price of $200/Mg C, the transition from conventional tillage to minimum or no-tillage practices will only realise 19% and 33%, respectively, of the total biogeochemical sequestration potential of crop and pasture systems of the Southern Region over a 20-year period.

Critical gap estimation by numerical and statistical highest likelihood search

Many traffic situations require drivers to cross or merge into a stream having higher priority. Gap acceptance theory enables us to model such processes to analyse traffic operation. This discussion demonstrated that numerical search fine tuned by statistical analysis can be used to determine the most likely critical gap for a sample of drivers, based on their largest rejected gap and accepted gap. This method shares some common features with the Maximum Likelihood Estimation technique (Troutbeck 1992) but lends itself well to contemporary analysis tools such as spreadsheet and is particularly analytically transparent. This method is considered not to bias estimation of critical gap due to very small rejected gaps or very large rejected gaps. However, it requires a sufficiently large sample that there is reasonable representation of largest rejected gap/accepted gap pairs within a fairly narrow highest likelihood search band.

Asymptotic and numerical results for a model of solvent-dependent drug diffusion through polymeric spheres

A model for drug diffusion from a spherical polymeric drug delivery device is considered. The model contains two key features. The first is that solvent diffuses into the polymer, which then transitions from a glassy to a rubbery state. The interface between the two states of polymer is modelled as a moving boundary, whose speed is governed by a kinetic law; the same moving boundary problem arises in the one-phase limit of a Stefan problem with kinetic undercooling. The second feature is that drug diffuses only through the rubbery region, with a nonlinear diffusion coefficient that depends on the concentration of solvent. We analyse the model using both formal asymptotics and numerical computation, the latter by applying a front-fixing scheme with a finite volume method. Previous results are extended and comparisons are made with linear models that work well under certain parameter regimes. Finally, a model for a multi-layered drug delivery device is suggested, which allows for more flexible control of drug release.

Advanced numerical study of impact forces on railway sleepers under wheel flat

Wheel-rail interaction is one of the most important research topics in railway engineering. It includes track vibration, track impact response and safety of the track. Track structure failures caused by impact forces can lead to significant economic loss for track owners through damage to rails and to the sleepers beneath. The wheel-rail impact forces occur because of imperfections on the wheels or rails such as wheel flats, irregular wheel profile, rail corrugation and differences in the height of rails connected at a welded joint. In this paper, a finite element model for the wheel flat study is developed by use of the FEA software package ANSYS. The effect of the wheel flat to impact force on sleepers is investigated. It has found that the wheel flat significantly increases impact forces and maximum Von Mises stress, and also delays the peak position of dynamic variation for impact forces on both rail and sleeper.

Application of electrical resistivity method to detect deep cracks in unsaturated residual soil slope

Crack is a significant influential factor in soil slope that could leads to rainfall-induced slope instability. Existence of cracks at soil surface will decrease the shear strength and increase the hydraulic conductivity of soil slope. Although previous research has shown the effect of surface-cracks in soil stability, the influence of deep-cracks on soil stability is still unknown. The limited availability of deep crack data due to the difficulty of effective investigate methods could be one of the obstacles. Current technology in electrical resistivity can be used to detect deep-cracks in soil. This paper discusses deep cracks in unsaturated residual soil slopes in Indonesia using electrical resistivity method. The field investigation such as bore hole and SPT tests was carried out at multiple locations in the area where the electrical resistivity testing have been conducted. Subsequently, the results from bore-hole and SPT test were used to verify the results of the electrical resistivity test. This study demonstrates the benefits and limitations of the electrical resistivity in detecting deep-cracks in a residual soil slopes.