Hybrid numerical methods for exponential models of growth

A series of novel numerical methods for the exponential models of growth are proposed. Based on these methods, hybrid predictor-corrector methods are constructed. The hybrid numerical methods can increase the accuracy and the computing speed obviously, as well as enlarge the stability domain greatly. (c) 2005 Published by Elsevier Inc.

Generation and evolution of magma beneath the East Pacific Rise: Constraints from U-series disequilibrium and plagioclase-hosted melt inclusions

Mid-ocean ridge basalt (MORB) samples from the East Pacific Rise (EPR 12 degrees 50'N) were analyzed for U-series isotopes and compositions of plagioclase-hosted melt inclusions. The Ra-226 and Th-230 excesses are negatively correlated; the Ra-226 excess is positively correlated with Mg# and Sm/Nd, and is negatively correlated with La/Sm and Fe-8; the Th-230 excess is positively correlated with Fe-8 and La/Sm and is negatively correlated with Mg# and Sm/Nd. Interpretation of these correlations is critical for understanding the magmatic process. There are two models (the dynamic model and the "two-porosity" model) for interpreting these correlations, however, some crucial parameters used in these models are not ascertained. We propose instead a model to explain the U-series isotopic compositions based on the control of melt density variation. For melting either peridotite or the "marble-cake" mantle, the FeOt content, Th-230 excess and La/Sm ratio increases and Sm/Nd decreases with increasing pressure. A deep melt will evolve to a higher density and lower Mg# than a shallow melt, the former corresponds to a long residence time, which lowers the Ra-226 excess significantly. This model is supported by the existence of low Ra-226 excesses and high Th-230 excesses in MORBs having a high Fe-8 content and high density. The positive correlation of Ra-226 excess and magma liquidus temperature implies that the shallow melt is cooled less than the deep melt due to its low density and short residence time. The correlations among Fe-8, Ti-8 and Ca-8/Al-8 in plagioclase-hosted melt inclusions further prove that MORBs are formed from melts having a negative correlation in melting depths and degrees. The negative correlation of Ra-226 excess vs. chemical diversity index (standard deviation of Fe-8, Ti-8 and Ca-8/Al-8) of the melt inclusions is in accordance with the influence of a density-controlled magma residence time. We conclude that the magma density variation exerts significant control on residence time and U-series isotopic compositions. (c) 2010 Elsevier B.V. All rights reserved.