Lattice Boltzmann method for the fractional advection-diffusion equation

Mass transport, such as movement of phosphorus in soils and solutes in rivers, is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or superdiffusion, and it is well described using a fractional advection-diffusion equation (FADE). The FADE finds a wide range of applications in various areas with great potential for studying complex mass transport in real hydrological systems. However, solution to the FADE is difficult, and the existing numerical methods are complicated and inefficient. In this study, a fresh lattice Boltzmann method is developed for solving the fractional advection-diffusion equation (LabFADE). The FADE is transformed into an equation similar to an advection-diffusion equation and solved using the lattice Boltzmann method. The LabFADE has all the advantages of the conventional lattice Boltzmann method and avoids a complex solution procedure, unlike other existing numerical methods. The method has been validated through simulations of several benchmark tests: a point-source diffusion, a boundary-value problem of steady diffusion, and an initial-boundary-value problem of unsteady diffusion with the coexistence of source and sink terms. In addition, by including the effects of the skewness β , the fractional order α , and the single relaxation time τ , the accuracy and convergence of the method have been assessed. The numerical predictions are compared with the analytical solutions, and they indicate that the method is second-order accurate. The method presented will allow the FADE to be more widely applied to complex mass transport problems in science and engineering

Major agricultural changes required to mitigate phosphorus losses under climate change

Phosphorus losses from land to water will be impacted by climate change and land management for food production, with detrimental impacts on aquatic ecosystems. Here we use a unique combination of methods to evaluate the impact of projected climate change on future phosphorus transfers, and to assess what scale of agricultural change would be needed to mitigate these transfers. We combine novel high-frequency phosphorus flux data from three representative catchments across the UK, a new high-spatial resolution climate model, uncertainty estimates from an ensemble of future climate simulations, two phosphorus transfer models of contrasting complexity and a simplified representation of the potential intensification of agriculture based on expert elicitation from land managers. We show that the effect of climate change on average winter phosphorus loads (predicted increase up to 30% by 2050s) will be limited only by large-scale agricultural changes (e.g., 20–80% reduction in phosphorus inputs)

Characterisation of myo-inositol hexakisphosphate deposits from larval Echinococcus granulosus

The abundant metabolite myo-inositol hexakisphosphate (InsP6) can form vesicular deposits with cations, a widespread phenomenon in plants also found in the cestode parasite, Echinococcus granulosus. In this organism, the deposits are exocytosed, accumulating in a host-exposed sheath of extracellular matrix termed the laminated layer. The formation and mobilization of InsP6 deposits, which involve precipitation and solubilization reactions, respectively, cannot yet be rationalized in quantitative chemical terms, as the solids involved have not been formally described. We report such a description for the InsP6 deposits from E. granulosus, purified as the solid residue left by mild alkaline digestion of the principal mucin component of the laminated layer. The deposits are largely composed of the compound Ca5H2L·16H2O (L representing fully deprotonated InsP6), and additionally contain Mg2+ (6–9% molar ratio with respect to Ca2+), but not K+. Calculations employing recently available chemical constants show that the precipitation of Ca5H2L·16H2O is predicted by thermodynamics in secretory vesicle-like conditions. The deposits appear to be similar to microcrystalline solids when analysed under the electron microscope; we estimate that each crystal comprises around 200 InsP6 molecules. We calculate that the deposits increase, by three orders of magnitude, the surface area available for adsorption of host proteins, a salient ability of the laminated layer. The major inositol phosphate in the deposits, other than InsP6, is myo-inositol (1,2,4,5,6) pentakisphosphate, or its enantiomer, inositol (2,3,4,5,6) pentakisphosphate. The compound appears to be a subproduct of the intracellular pathways leading to the synthesis and vesicular accumulation of InsP6, rather than arising from extracellular hydrolysis of InsP6