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

Projected changes in mineral soil carbon of European croplands and grasslands, 1990-2080

We present the most comprehensive pan-European assessment of future changes in cropland and grassland soil organic carbon (SOC) stocks to date, using a dedicated process-based SOC model and state-of-the-art databases of soil, climate change, land-use change and technology change. Soil carbon change was calculated using the Rothamsted carbon model on a European 10 × 10' grid using climate data from four global climate models implementing four Intergovernmental Panel on Climate Change (IPCC) emissions scenarios (SRES). Changes in net primary production (NPP) were calculated by the Lund¿Potsdam¿Jena model. Land-use change scenarios, interpreted from the narratives of the IPCC SRES story lines, were used to project changes in cropland and grassland areas. Projections for 1990¿2080 are presented for mineral soil only. Climate effects (soil temperature and moisture) will tend to speed decomposition and cause soil carbon stocks to decrease, whereas increases in carbon input because of increasing NPP will slow the loss. Technological improvement may further increase carbon inputs to the soil. Changes in cropland and grassland areas will further affect the total soil carbon stock of European croplands and grasslands. While climate change will be a key driver of change in soil carbon over the 21st Century, changes in technology and land-use change are estimated to have very significant effects. When incorporating all factors, cropland and grassland soils show a small increase in soil carbon on a per area basis under future climate (1¿7 t C ha1 for cropland and 3¿6 t C ha1 for grassland), but when the greatly decreasing area of cropland and grassland are accounted for, total European cropland stocks decline in all scenarios, and grassland stocks decline in all but one scenario. Different trends are seen in different regions. For Europe (the EU25 plus Norway and Switzerland), the cropland SOC stock decreases from 11 Pg in 1990 by 4¿6 Pg (39¿54%) by 2080, and the grassland SOC stock increases from 6 Pg in 1990 to 1.5 Pg (25%) under the B1 scenario, but decreases to 1¿3 Pg (20¿44%) under the other scenarios. Uncertainty associated with the land-use and technology scenarios remains unquantified, but worst-case quantified uncertainties are 22.5% for croplands and 16% for grasslands, equivalent to potential errors of 2.5 and 1 Pg SOC, respectively. This is equivalent to 42¿63% of the predicted SOC stock change for croplands and 33¿100% of the predicted SOC stock change for grasslands. Implications for accounting for SOC changes under the Kyoto Protocol are discussed

Integrated treatment vs. treatment-as-usual for recent onset schizophrenia; 12 year follow-up on a randomized controlled trial

Background: The aim of this study is to compare the 12-year follow-up effects on in- and outpatient services of 2 years of integrated treatment for recent-onset schizophrenia versus treatment as usual in a randomized controlled trial. Methods: 50 patients aged 18–35 years were randomized to Integrated Treatment (IT) (N = 30) or Treatment-as-Usual (TAU) (N = 20) for two years. TAU comprised optimal pharmacotherapy and outreach assertive treatment, while IT also included cognitive-behavioural family treatment, skills training, strategies for residual psychotic and non-psychotic problems and home-based crisis management. Results: There were no differences in number of days in hospital, time to readmission, number of admittances to psychiatric wards, number of involuntarily psychiatric admissions or number of outpatient contacts over a period of 12 years following the initial 2-year treatment trial. Fewer patients in the IT group were, however, involuntary admitted to hospital in the period. Conclusions: The intensive two-year psychosocial intervention seemed to have little long-term effects on use of in- and outpatient services.<p>© 2013 Sigrúnarson et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</p