Directional turnover towards larger-ranged plants over time and across habitats

Species turnover is ubiquitous. However, it remains unknown whether certain types of species are consistently gained or lost across different habitats. Here, we analysed the trajectories of 1827 plant species over time intervals of up to 78 years at 141 sites across mountain summits, forests, and lowland grasslands in Europe. We found, albeit with relatively small effect sizes, displacements of smaller- by larger-ranged species across habitats. Communities shifted in parallel towards more nutrient-demanding species, with species from nutrient-rich habitats having larger ranges. Because these species are typically strong competitors, declines of smaller-ranged species could reflect not only abiotic drivers of global change, but also biotic pressure from increased competition. The ubiquitous component of turnover based on species range size we found here may partially reconcile findings of no net loss in local diversity with global species loss, and link community-scale turnover to macroecological processes such as biotic homogenisation

Numerical integration of the three-dimensional Green kernel for an electromagnetic problem

In this paper, we present a method for the numerical integration of the three-dimensional Green kernel over two triangles. This method is compared with the results obtained by other algorithms. The comparison proves the efficiency of the technique in removing the numerical singularity. Furthermore, we provide a numerical algorithm for increasing the computation accuracy without refining the finite element mesh. (c) 2004 Elsevier Inc. All rights reserved

Numerical Modeling of Induction-Heating for 2-Dimensional Geometries

We present both a mathematical model and a numerical method for simulating induction heating processes. The geometry of the conductors is cylindrical and the magnetic field is assumed to be parallel to the invariance axis. The model equations have current tension as prescribed data rather than current intensity. In Particular, the formulation of the electromagnetic problem uses the magnetic field as the unknown function. The numerical method takes into account the time periodicity of the prescribed tension and deals with the two different time scales of electromagnetic and thermal phenomena

Numerical modeling of induction heating for two-dimensional geometries

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Modelling of Electromagnetic Heating, Cooling and Phase Transformations during Surface Hardening of Steels

A comprehensive micro-macroscopic model of the continuous hardening of 3d-axisymmetric steel components by induction heating has been developed. At the macroscopic scale, the Maxwell and heat flow equations are solved using a mixed numerical formulation : the inductor and the workpiece are enmeshed with finite elements (FE) but boundary elements (BE) are used for the solution of the electromagnetic equations in the ambient air. This method allows the inductor to be moved with respect to the workpiece without any remeshing procedure. The heat flow equation is solved for the workpiece using the same FE mesh. For the thermal boundary conditions, a net radiation method has been implemented to account for grey diffuse bodies and the viewing factors of the element facets are calculated using a "shooting" technique. The boundary condition associated with the water spraying below the inductor is deduced from the inverse modelling of temperatures measured at various locations of a test piece. These macroscopic calculations of induction heating have been coupled to a microscopic model describing the solid state transformations that occur during both heating and cooling. From the local thermal history, the evolutions of the various phase fractions are predicted from TTT-diagrams using an additivity principle. A micro-enthalpy method has been implemented in the heat flow calculations in order to account for the latent heat released by the various transformations. At each time step the local properties of the material, in particular its magnetic susceptibility, are updated according to the new temperatures and magnetic field. The results of the simulation are compared with experimental cooling curves and hardness profiles