On the efficiency and accuracy of interpolation methods for spectral codes

In this paper a general theory for interpolation methods on a rectangular grid is introduced. By the use of this theory an efficient B-spline based interpolation method for spectral codes is presented. The theory links the order of the interpolation method with its spectral properties. In this way many properties like order of continuity, order of convergence and magnitude of errors can be explained. Furthermore, a fast implementation of the interpolation methods is given. We show that the B-spline based interpolation method has several advantages compared to other methods. First, the order of continuity of the interpolated field is higher than for other methods. Second, only one FFT is needed whereas e.g. Hermite interpolation needs multiple FFTs for computing the derivatives. Third, the interpolation error almost matches the one of Hermite interpolation, a property not reached by other methods investigated.Comment: 19 pages, 5 figure

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Early Developmental Responses to Seedling Environment Modulate Later Plasticity to Light Spectral Quality

Correlations between developmentally plastic traits may constrain the joint evolution of traits. In plants, both seedling de-etiolation and shade avoidance elongation responses to crowding and foliage shade are mediated by partially overlapping developmental pathways, suggesting the possibility of pleiotropic constraints. To test for such constraints, we exposed inbred lines of Impatiens capensis to factorial combinations of leaf litter (which affects de-etiolation) and simulated foliage shade (which affects phytochrome-mediated shade avoidance). Increased elongation of hypocotyls caused by leaf litter phenotypically enhanced subsequent elongation of the first internode in response to low red∶far red (R∶FR). Trait expression was correlated across litter and shade conditions, suggesting that phenotypic effects of early plasticity on later plasticity may affect variation in elongation traits available to selection in different light environments

Use of dynamic soil-vegetation models to assess impacts of nitrogen deposition on plant species composition: an overview

Field observations and experimental data of effects of nitrogen (N) deposition on plant species diversity have been used to derive empirical critical N loads for various ecosystems. The great advantage of such an approach is the inclusion of field evidence, but there are also restrictions, such as the absence of explicit criteria regarding significant effects on the vegetation, and the impossibility to predict future impacts when N deposition changes. Model approaches can account for this. In this paper, we review the possibilities of static and dynamic multispecies models in combination with dynamic soil–vegetation models to (1) predict plant species composition as a function of atmospheric N deposition and (2) calculate critical N loads in relation to a prescribed protection level of the species composition. The similarities between the models are presented, but also several important differences, including the use of different indicators for N and acidity and the prediction of individual plant species vs. plant communities. A summary of the strengths and weaknesses of the various models, including their validation status, is given. Furthermore, examples are given of critical load calculations with the model chains and their comparison with empirical critical N loads. We show that linked biogeochemistry–biodiversity models for N have potential for applications to support European policy to reduce N input, but the definition of damage thresholds for terrestrial biodiversity represents a major challenge. There is also a clear need for further testing and validation of the models against long-term monitoring or long-term experimental data sets and against large-scale survey data. This requires a focused data collection in Europe, combing vegetation descriptions with variables affecting the species diversity, such as soil acidity, nutrient status and water availability. Finally, there is a need for adaptation and upscaling of the models beyond the regions for which dose–response relationships have been parameterized, to make them generally applicable

Coherent Structures and Extreme Events in Rotating Multiphase Turbulent Flows

By using direct numerical simulations (DNS) at unprecedented resolution, we study turbulence under rotation in the presence of simultaneous direct and inverse cascades. The accumulation of energy at large scale leads to the formation of vertical coherent regions with high vorticity oriented along the rotation axis. By seeding the flow with millions of inertial particles, we quantify—for the first time—the effects of those coherent vertical structures on the preferential concentration of light and heavy particles. Furthermore, we quantitatively show that extreme fluctuations, leading to deviations from a normal-distributed statistics, result from the entangled interaction of the vertical structures with the turbulent background. Finally, we present the first-ever measurement of the relative importance between Stokes drag, Coriolis force, and centripetal force along the trajectories of inertial particles. We discover that vortical coherent structures lead to unexpected diffusion properties for heavy and light particles in the directions parallel and perpendicular to the rotation axis