Anomalous subdiffusion equations by the meshless collocation method

This paper aims to develop an implicit meshless collocation technique based on the moving least squares approximation for numerical simulation of the anomalous subdiffusion equation(ASDE). The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach related to the time discretization are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling of ASDEs.

Design of flight avoidance manoeuvre alphabets for mixed centralised-decentralised separation management

This paper investigates a mixed centralised-decentralised air traffic separation management system, which combines the best features of the centralised and decentralised systems whilst ensuring the reliability of the air traffic management system during degraded conditions. To overcome communication band limits, we propose a mixed separation manager on the basis of a robust decision (or min-max) problem that is posed on a reduced set of admissible flight avoidance manoeuvres (or a FAM alphabet). We also present a design method for selecting an appropriate FAM alphabet for use in the mixed separation management system. Simulation studies are presented to illustrate the benefits of our proposed FAM alphabet based mixed separation manager.

Biodiversity–productivity relationships in small-scale mixed-species plantations using native species in Leyte province, Philippines

In this study, we investigate the relationship between tree species diversity and production in 18 mixed-species plantations established under the Rainforestation Farming system in Leyte province, the Philippines. The aim was to quantify productivity in the mixed-species plantations in comparison to the monocultures, and identify key drivers of productivity including environmental conditions, stand structural characteristics and surrogate measures of biodiversity, i.e. species richness, Shannon’s diversity index and functional groups. We found that monocultures had a much higher productivity than mixtures of the same and other species. In the mixtures, biodiversity and productivity did not have a simple relationship. Instead the proportion of exotic and native species, and the proportion of fast-growing species had a marginally significant positive effect on stand productivity, but no significant relationship was found with species richness or Shannon’s diversity. Instead stand structural characteristics such as density and age were the strongest drivers of increased productivity. Production levels within the mixed-species plantations varied significantly between sites. Overall, we found that the productivity of mixed species plantations was driven more by the characteristics of species present and stand structural characteristics then by simply the number and abundance of species, which suggests management practices are key for balancing multiple objectives to meet sustainable development needs.

The influence of vegetation and soil type on the speciation of iron in soil water

Soluble organic matter derived from exotic Pinus species has been shown to form stronger complexes with iron (Fe) than that derived from most native Australian species. It has also been proposed that the establishment of exotic Pinus plantations in coastal southeast Queensland may have enhanced the solubility of Fe in soils by increasing the amount of organically complexed Fe, but this remains inconclusive. In this study we test whether the concentration and speciation of Fe in soil water from Pinus plantations differs significantly from soil water from native vegetation areas. Both Fe redox speciation and the interaction between Fe and dissolved organic matter (DOM) were considered; Fe - DOM interaction was assessed using the Stockholm Humic Model. Iron concentrations (mainly Fe 2+) were greatest in the soil waters with the greatest DOM content collected from sandy podosols (Podzols), where they are largely controlled by redox potential. Iron concentrations were small in soil waters from clay and iron oxide-rich soils, in spite of similar redox potentials. This condition is related to stronger sorption on to the reactive clay and iron oxide mineral surfaces in these soils, which reduces the amount of DOM available for electron shuttling and microbial metabolism, restricting reductive dissolution of Fe. Vegetation type had no significant influence on the concentration and speciation of iron in soil waters, although DOM from Pinus sites had greater acidic functional group site densities than DOM from native vegetation sites. This is because Fe is mainly in the ferrous form, even in samples from the relatively well-drained podosols. However, modelling suggests that Pinus DOM can significantly increase the amount of truly dissolved ferric iron remaining in solution in oxic conditions. Therefore, the input of ferrous iron together with Pinus DOM to surface waters may reduce precipitation of hydrous ferric oxides (ferrihydrite) and increase the flux of dissolved Fe out of the catchment. Such inputs of iron are most probably derived from podosols planted with Pinus.

Analytical solutions of the multi-term modified power law wave equations in a finite domain

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n) (n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko’s Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi term time-space fractional models including fractional Laplacian.

Numerical methods for solving the multi-term time-fractional wave-diffusion equations

In this paper, the multi-term time-fractional wave diffusion equations are considered. The multiterm time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

Analytical solutions for the two- and three-dimensional time-fractional telegraph equations by the method of separating variables

In this paper, a method of separating variables is effectively implemented for solving a time-fractional telegraph equation (TFTE) in two and three dimensions. We discuss and derive the analytical solution of the TFTE in two and three dimensions with nonhomogeneous Dirichlet boundary condition. This method can be extended to other kinds of the boundary conditions.

Numerical techniques for the variable order time fractional diffusion equation

In this paper we consider the variable order time fractional diffusion equation. We adopt the Coimbra variable order (VO) time fractional operator, which defines a consistent method for VO differentiation of physical variables. The Coimbra variable order fractional operator also can be viewed as a Caputo-type definition. Although this definition is the most appropriate definition having fundamental characteristics that are desirable for physical modeling, numerical methods for fractional partial differential equations using this definition have not yet appeared in the literature. Here an approximate scheme is first proposed. The stability, convergence and solvability of this numerical scheme are discussed via the technique of Fourier analysis. Numerical examples are provided to show that the numerical method is computationally efficient. Crown Copyright © 2012 Published by Elsevier Inc. All rights reserved.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

Assessment of tumor prevention in Type 1 Neurofibromatosis using a nitroxide compound

Background Type 1 Neurofibromatosis (NF1) is a genetic disorder linked to mutations of the NF1 gene. Clinical symptoms are varied, but hallmark features of the disease include skin pigmentation anomalies (café au lait macules, skinfold freckling) and dermal neurofibromas. Method These dermal manifestations of NF1 have previously been reported in a mouse model where Nf1+/− mice are topically treated with dimethylbenz[a]anthracene (DMBA) and 12-O-tetradecanoylphorbol-13-acetate (TPA). We adopted this mouse model to test the protective effects of a nitroxide antioxidant, 5-carboxy-1,1,3,3-tetramethylisoindolin-2-yloxyl (CTMIO). Antioxidants have previously been shown to increase longevity in nf1-deficient fruitflies. Doses of 4 μM and 40 μM CTMIO provided ad libitum in drinking water were given to Nf1-deficient mice. Results Consistent with previous reports, Nf1-deficient mice showed a 4.7-fold increase in papilloma formation (P < 0.036). However, neither dose of CTMIO had any significant affect on papilloma formation. A non-significant decrease in skin pigmentation abnormalities was seen with 4 μM but not 40 μM CTMIO. Subsequent analysis of genomic DNA isolated from papillomas indicated that DMBA/TPA induced tumors did not exhibit a local loss of heterozygosity (LOH) at the Nf1 locus. Conclusion These data reveal that oral antioxidant therapy with CTMIO does not reduce tumor formation in a multistage cancer model, but also that this model does not feature LOH for Nf1.