Error propagation in numerical approximations near relative equilibria

AbstractWe study the propagation of errors in the numerical integration of perturbations of relative equilibrium solutions of Hamiltonian differential equations with symmetries. First it is shown that taking an initial perturbation of a relative equilibrium, the corresponding solution is related, in a first approximation, to another relative equilibrium, with the parameters perturbed from the original. Then, this is used to prove that, for stable relative equilibria, error growth with respect to the perturbed solution is in general quadratic, but only linear for schemes that preserve the invariant quantities of the problem. In this sense, the conclusion is similar to the one obtained when integrating unperturbed relative equilibria. Numerical experiments illustrate the results

Influence of legumes on N cycling in a heathland in northwest Spain

Nitrogen availability frequently limits plant growth in natural ecosystems. N-fixers should have a substantial competitive advantage in N-limited systems, and as a byproduct of their activity they should increase the quantity and availability of N in the system as a whole. However, this effect has rarely been quantified in natural ecosystems. Heathlands in northwest Spain are frequently occupied by legume scrubs. We tested whether the presence of these legumes affected the N cycle in these communities. Specifically, we addressed the following questions: is nitrogen availability higher beneath legume canopies than beneath non-legume canopies? Is soil microbial biomass acting as a sink of extra N mineralized beneath legume canopies? Does the presence of legume scrubs change the soil pools of labile N and P? Is N plant uptake different under N-fixer scrubs than under non-N-fixer scrubs? <br><br> To answer these questions, we sampled soil beneath the canopy of randomly selected individuals of <i>Erica umbellata</i>, <i>Ulex gallii</i>, and <i>Genista tridentata</i> twice during the growing season. Soil samples were analyzed for organic matter, NH<sub>4</sub>-N, NO<sub>3</sub>-N, DON, PO<sub>4</sub>-P, N mineralization and nitrification rates, and soil microbial biomass-N. In addition, we estimated N uptake by plants and the N concentration in green tissue to compare internal N cycles between legume and non-legume scrubs. Nitrification rates, DON (dissolved organic nitrogen), soil NO<sub>3</sub> concentration, and N uptake were significantly higher beneath legume canopies. However, soil microbial biomass-N and extractable-P were significantly lower under legumes. Our results showed that the presence of legume scrubs modify the size of N pools and the dominant form of available N for plants, increasing spatial heterogeneity in mixed stands

Hercynian Metamorphism in the Catalonian Coastel Ranges

Paleozoic rocks in the Catalonian Coastal Ranges are in their largest part affectedby alow- tovery-low grade Hercynian metamorphism. Amphibolite facies conditions are only found in restricted areas such as the southwestern part of the Guilleries massif where upper amphibolite facies conditions are reached. Metamorphic grade increases from top to bottom of the Paleozoic stratigraphic sequence and the metamorphic peak is diachronous, being progressively older in the lower grade metamorphic zones. The isograd pattern, mineral assemblages, mineral chemistry and preserved reaction textures are consistent with a low pressure metamorphism possibly evolving from a previous Barrovian type event. The metamorphic climax in the high grade zone was reached after the seconddeformational phase. Calculatedpeak P-Tconditions are 620-640 OC and around 3.5 Kb . A latter episode of decompression from the maximum conditions to 1-2 Kb, with an associated temperature decrease to 530-550 OC, is recognized. The intrusion of late Hercynian granitoids produced contact metamorphic aureoles where the pyroxene-hornfels facies is locally reached

Towards relativistic simulations of magneto-rotational core collapse

We present a new general relativistic hydrodynamics code specifically designed to study magneto-rotational, relativistic, stellar core collapse. The code is an extension of an existing (and thoroughly tested) hydrodynamics code, which has been applied in the recent past to study relativistic rotational core collapse. It is based on the conformally-flat approximation of Einstein's field equations and conservative formulations for the magneto-hydrodynamics equations. As a first step towards magneto-rotational core collapse simulations the code assumes a passive (test) magnetic field. The paper is focused on the description of the technical details of the numerical implementation, with emphasis on the magnetic field module. A number of code tests are presented and discussed, along with a representative core collapse simulation