Upwind solution of singular differential equations arising from steady channel flows

We study ordinary nonlinear singular differential equations which arise from steady conservation laws with source terms. An example of steady conservation laws which leads to those scalar equations is the Saint–Venant equations. The numerical solution of these scalar equations is sought by using the ideas of upwinding and discretisation of source terms. Both the Engquist–Osher scheme and the Roe scheme are used with different strategies for discretising the source terms.

Fast approximate calculation of multiply scattered lidar returns

An efficient method is described for the approximate calculation of the intensity of multiply scattered lidar returns. It divides the outgoing photons into three populations, representing those that have experienced zero, one, and more than one forward-scattering event. Each population is parameterized at each range gate by its total energy, its spatial variance, the variance of photon direction, and the covariance, of photon direction and position. The result is that for an N-point profile the calculation is O(N-2) efficient and implicitly includes up to N-order scattering, making it ideal for use in iterative retrieval algorithms for which speed is crucial. In contrast, models that explicitly consider each scattering order separately are at best O(N-m/m!) efficient for m-order scattering and often cannot be performed to more than the third or fourth order in retrieval algorithms. For typical cloud profiles and a wide range of lidar fields of view, the new algorithm is as accurate as an explicit calculation truncated at the fifth or sixth order but faster by several orders of magnitude. (C) 2006 Optical Society of America.

Projected gradient approach to the numerical solution of the SCoTLASS

The SCoTLASS problem-principal component analysis modified so that the components satisfy the Least Absolute Shrinkage and Selection Operator (LASSO) constraint-is reformulated as a dynamical system on the unit sphere. The LASSO inequality constraint is tackled by exterior penalty function. A globally convergent algorithm is developed based on the projected gradient approach. The algorithm is illustrated numerically and discussed on a well-known data set. (c) 2004 Elsevier B.V. All rights reserved.

Observational evidence of a coronal mass ejection distortion directly attributable to a structured solar wind

We present the first observational evidence of the near-Sun distortion of the leading edge of a coronal mass ejection (CME) by the ambient solar wind into a concave structure. On 2007 November 14, a CME was observed by coronagraphs onboard the STEREO-B spacecraft, possessing a circular cross section. Subsequently the CME passed through the field of view of the STEREO-B Heliospheric Imagers where the leading edge was observed to distort into an increasingly concave structure. The CME observations are compared to an analytical flux rope model constrained by a magnetohydrodynamic solar wind solution. The resultant bimodal speed profile is used to kinematically distort a circular structure that replicates the initial shape of the CME. The CME morphology is found to change rapidly over a relatively short distance. This indicates an approximate radial distance in the heliosphere where the solar wind forces begin to dominate over the magnetic forces of the CME influencing the shape of the CME.

The promotion of grassland forb abundance: A chemical or biological solution?

Techniques that increase the biodiversity value of species-poor grassland are required if conservation targets aimed at reversing the decline in species-rich grassland are to be met. This study investigated the diversification of swards dominated by Lolium perenne by testing the efficacies of two treatments applied to reduce competitive exclusion of species introduced as seed. The 'biological' treatment was the addition of the hemiparasitic plant species introduced as seed. The 'biological' treatment was the application of a selective graminicide, fluazifop-P-butyl (Fusilade 250EW). Changes in plant community composition were monitored for a period of 2 years. Values of plant species richness increased significantly between years regardless of treatment, but to a greater extent in plots sown with R. minor. The number of established sown species and their richness and tended to promote unsown species rather than those introduced as seed. Overall, the R. minor treatment was associated with the greatest impact on sward composition, facilitating establishment and development of the introduced species and promoting forb abundance. (c) 2007 Gessellschaft fur Okologie. Published by Elsevier GmbH. All rights reserved.

Adaptive approximate Bayesian computation

Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.'s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al. (2006), the application to approximate Bayesian computation results in a bias in the approximation to the posterior. An alternative version based on genuine importance sampling arguments bypasses this difficulty, in connection with the population Monte Carlo method of Cappe et al. (2004), and it includes an automatic scaling of the forward kernel. When applied to a population genetics example, it compares favourably with two other versions of the approximate algorithm.