Book review of ENCYCLOPEDIA OF NONLINEAR SCIENCE,edited by Alwyn Scott,Routledge, Taylor and Francis Group, 2005, VII +1053 pp., 135, $225 hardback (ISBN 1-57958-385-7).

We present three-dimensional (3D) solutions of the magnetohydrostatic equations in the co-rotating frame of reference outside a magnetized rigidly rotating cylinder. We make no symmetry assumption for the magnetic field, but to be able to make analytical progress we neglect outflows and specify a particular form for the current density. The magnetohydrostatic equations can then be reduced to a single linear partial differential equation for a pseudo-potential U, from which the magnetic field can be calculated by differentiation. The equation for U can be solved by standard methods. The solutions can also be used to determine the plasma pressure, density and temperature as functions of all three spatial coordinates. Despite the obvious limitations of this approach, it can, for example, be used as a simple tool to create 3D models for the closed field line regions of rotating magnetospheres without rotational symmetry.     

Experimental study of the K2ZrSi3O9 (wadeite)–K2TiSi3O9 and K2(Zr,Ti)Si3O9–phlogopite systems at 2–3 GPa

Experiments ranging from 2 to 3 GPa and 800 to 1300 °C and at 0.15 GPa and 770 °C were performed to investigate the stability and mutual solubility of the K₂ZrSi₃O₉ (wadeite) and K₂TiSi₃O₉ cyclosilicates under upper mantle conditions. The K₂ZrSi₃O₉–K₂TiSi₃O₉ join exhibits complete miscibility in the P–T interval investigated. With increasing degree of melting the solid solution becomes progressively enriched in Zr, indicating that K₂ZrSi₃O₉ is the more refractory end member. At 2 GPa, in the more complex K₂ZrSi₃O₉–K₂TiSi₃O₉–K₂Mg₆Al₂Si₆O₂₀(OH)₄ system, the presence of phlogopite clearly limits the extent of solid solution of the cyclosilicate to more Zr-rich compositions [Zr/(Zr + Ti) > 0.85], comparable to wadeite found in nature, with TiO₂ partitioning strongly into the coexisting mica and/or liquid. However, at 1200 °C, with increasing pressure from 2 to 3 GPa, the partitioning behaviour of TiO₂ changes in favour of the cyclosilicate, with Zr/(Zr + Ti) of the K₂(Zr,Ti)Si₃O₉ phase decreasing from ∼0.9 to ∼0.6. The variation in the Ti content of the coexisting phlogopite is related to its degree of melting to forsterite and liquid, following the major substitution ^VITi+^VI□=2^VIMg. Received: 26 January 1999 / Accepted: 10 January 2000     

Origin of spongy textures in clinopyroxene and spinel from mantle xenoliths, Hessian Depression, Germany

Summary Spongy textures are observed in anhydrous Group 1 mantle xenoliths (harzburgite, lherzolite and wehrlite) hosted in Tertiary alkali basaltic lavas from the Hessian Depression, Germany. These textures are developed only on clinopyroxene and spinel, and occur as rims or cross-cutting veinlets and patches showing optical continuity with the host grain. They are often associated with pools of amorphous glassy material. There is no preferential development of spongy domains against the xenolith-lava contact suggesting that the host magma did not play any significant role in their formation. Spongy clinopyroxene and spinel occur in all rock types, but, are more pervasive in wehrlite. Chemically, spongy domains of clinopyroxene and spinel are more refractory than unaffected areas, which is consistent with their formation through a partial melting event. The associated glassy material shows chemical characteristics which suggest that the melt pools are genetically related to the development of the spongy textures. The partial melting event was probably triggered by the infiltration of a low-density fluid. The fluid may have evolved from a silicate melt responsible for the metasomatic Fe-enrichment recorded in wehrlite. In this context, the more pervasive development of spongy clinopyroxene in wehrlite may be explained by a higher concentration of the evolved fluid phase at proximity to its silicate melt source. Received March 15, 2000; revised version accepted September 6, 2001     

Field spectroscopy and radiative transfer modelling to assess impacts of petroleum pollution on biophysical and biochemical parameters of the Amazon rainforest

Biophysical and biochemical plant foliage parameters play a key role in assessing vegetation health. Those plant parameters determine the spectral reflectance and transmittance properties of vegetation; therefore, hyperspectral remote sensing, particularly imaging spectroscopy, can provide estimates of leaf and canopy chemical properties. Based on the relationship between spectral response and biochemical/biophysical properties of the leaves and canopies, the PROSPECT radiative transfer model simulates the interaction of light with leaves. In this study, more than 1100 leaf samples from the Amazon forest of Ecuador were collected at several study sites, some of which are affected by petroleum pollution, and across the vertical profile of the forest. For every sample, field spectroscopy at leaf level was conducted with a spectroradiometer. The goal of this study was to assess leaf optical properties of polluted and unpolluted rainforest canopies across the vertical profile and identify vegetation stress expressed in changes of biophysical and biochemical properties of vegetation. An ANOVA followed by Holme’s multiple comparisons of means and a principal component analysis showed that photosynthetic pigments, chlorophyll and carotenoids have significantly lower levels across the vertical profile of the forest, particularly in sites affected by petroleum pollution. On the other hand, foliar water content showed significantly higher levels in the polluted site. Those findings are symptoms of vegetation stress caused by reduced photosynthetic activity and consequently decreased transpiration and water-use efficiency of the plants. Cross-comparison between SPAD-502 chlorophyll content meter index and chlorophyll content showed strong positive correlation coefficients (r = 0.71 and r ² = 0.51) which suggests that using the SPAD-502 chlorophyll index itself is sensitive enough to detect vegetation stress in a multispecies tropical forest. Therefore, the SPAD-502 can be used to assess chlorophyll content of vegetation across polluted and non-polluted sites at different canopy layers. The results presented in this paper contribute to the very limited literature on field spectroscopy and radiative transfer models applied to the vertical profile of the Amazon forest.     

Application of DARLAM to Regional Haze Modeling

— The CSIRO Division of Atmospheric Research limited area model (DARLAM) is applied to atmospheric transport modeling of haze in southeast Asia. The 1998 haze episode is simulated using an emission inventory derived from hotspot information and adopting removal processes based on SO₂.¶Results show that the model is able to simulate the transport of haze in the region. The model images closely resemble the plumes of NASA Total Ozone Mapping Spectrometer and Meteorological Service Singapore haze maps. Despite the limitation of input data, particularly for haze emissions, the three-month average pattern correlation obtained for the whole episode is 0.61. The model has also been able to reproduce the general features of transboundary air pollution over a long period of time. Predicted total particulate matter concentration also agrees reasonably well with observation.¶The difference in the model results from the satellite images may be attributed to the large uncertainties of emission, simplification of haze deposition and transformation mechanisms and the relatively coarse horizontal and vertical resolution adopted for this particular simulation.     

The vertical structure of planet-induced gaps in protoplanetary discs

Giant planets embedded in circumstellar discs are expected to open gaps in these discs. We examine the vertical structure of the gap edges. We find that the planet excites spiral arms with significant (Mach number of a half) vertical motion of the gas, and discuss the implications of these motions. In particular, the spiral arms will make the edge appear 'puffed up' relative to the bulk of the disc. Infrared observations (sensitive to dust) would be dominated by the light from the thick inner edge of the disc. Submillimetre observations (sensitive to gas velocities) would appear to be hot in 'turbulent' motions (actually the ordered motion caused by the passage of the spiral arms), but cold in chemistry. Resolved submillimetre maps of circumstellar discs might even be able to detect the spiral arms directly.     

Chemistry,mineralogy and petrology of an eclogite from the type locality (Saualpe,Austria)

An eclogite and five of its coexisting minerals (omphacite, garnet, carinthine, kyanite and zoisite) from the probable type locality of eclogites (Kupplerbrunn, Saualpe, Austria) described by Haüy (1822) have been analysed. Optical and X-ray data for these minerals are also given. Comparison of the Kupplerbrunn rock with those of other eclogites from the Saualpe region indicates they all have roughly similar compositions. When plotted on an A-C-F diagram the majority of these analyses fall in the region of kyanite-bearing eclogites suggested by Tilley (1936) although the Kupplerbrunn rock is the only sample containing kyanite; the others containing zoisite. The garnet and omphacite compositions of the Kupplerbrunn rock differ markedly from those of other Saualpe eclogites, possibly due to different metamorphic conditions of their formation. Carinthine analyses are all very similar for eclogites from Saualpe. On the basis of geological, analytical and limited experimental evidence, it is postulated that the Kupplerbrunn eclogite was derived from an original gabbroic rock low in water content such that amphibole and zoisite formed from plagioclase, pyroxene and water; omphacite, garnet and kyanite formed from plagioclase and pyroxene, once all the water was used up in the form of amphibole and zoisite. These reactions are believed to have taken place at 5–8 kb pressure at around 600° C; a value close to that suggested by Lodemann (1966) from field data.     

Molecular H2O in armenite, BaCa2Al6Si9O30·2H2O, and epididymite, Na2Be2Si6O15·H2O: Heat capacity, entropy and local-bonding behavior of confined H2O in microporous silicates

Armenite, ideal formula BaCa₂Al₆Si₉O₃₀·2H₂O, and its dehydrated analog BaCa₂Al₆Si₉O₃₀ and epididymite, ideal formula Na₂Be₂Si₆O₁₅·H₂O, and its dehydrated analog Na₂Be₂Si₆O₁₅ were studied by low-temperature relaxation calorimetry between 5 and 300 K to determine the heat capacity, C_p, behavior of their confined H₂O. Differential thermal analysis and thermogravimetry measurements, FTIR spectroscopy, electron microprobe analysis and powder Rietveld refinements were undertaken to characterize the phases and the local environment around the H₂O molecule.The determined structural formula for armenite is Ba_0.88(0.01)Ca_1.99(0.02)Na_0.04(0.01)Al_5.89(0.03)Si_9.12(0.02)O₃₀·2H₂O and for epididymite Na_1.88(0.03)K_0.05(0.004)Na_0.01(0.004)Be_2.02(0.008)Si_6.00(0.01)O₁₅·H₂O. The infrared (IR) spectra give information on the nature of the H₂O molecules in the natural phases via their H₂O stretching and bending vibrations, which in the case of epididymite only could be assigned. The powder X-ray diffraction data show that armenite and its dehydrated analog have similar structures, whereas in the case of epididymite there are structural differences between the natural and dehydrated phases. This is also reflected in the lattice IR mode behavior, as observed for the natural phases and the H₂O-free phases. The standard entropy at 298 K for armenite is S° = 795.7 ± 6.2 J/mol K and its dehydrated analog is S° = 737.0 ± 6.2 J/mol K. For epididymite S° = 425.7 ± 4.1 J/mol K was obtained and its dehydrated analog has S° = 372.5 ± 5.0 J/mol K. The heat capacity and entropy of dehydration at 298 K are Δ = 3.4 J/mol K and ΔS^rxn = 319.1 J/mol K and Δ = −14.3 J/mol K and ΔS^rxn = 135.7 J/mol K for armenite and epididymite, respectively. The H₂O molecules in both phases appear to be ordered. They are held in place via an ion-dipole interaction between the H₂O molecule and a Ca cation in the case of armenite and a Na cation in epididymite and through hydrogen-bonding between the H₂O molecule and oxygen atoms of the respective silicate frameworks. Of the three different H₂O phases ice, liquid water and steam, the C_p behavior of confined H₂O in both armenite and epididymite is most similar to that of ice, but there are differences between the two silicates and from the C_p behavior of ice. Hydrogen-bonding behavior and its relation to the entropy of confined H₂O at 298 K is analyzed for various microporous silicates.The entropy of confined H₂O at 298 K in various silicates increases approximately linearly with increasing average wavenumber of the OH-stretching vibrations. The interpretation is that decreased hydrogen-bonding strength between a H₂O molecule and the silicate framework, as well as weak ion-dipole interactions, results in increased entropy of H₂O. This results in increased amplitudes of external H₂O vibrations, especially translations of the molecule, and they contribute strongly to the entropy of confined H₂O at T < 298 K.     

An experimental study of partitioning of fluorine between K-richterite,apatite, phlogopite,and melt at 20 kbar

Phase relations have been determined at 20 kbar and primarily under suprasolidus conditions in the Fe−Ti-free F-bearing K-richterite—phlogopite and K-richterite—apatite systems in order to assess the partitioning of F among phlogopite, K-richterite, apatite, and melt under upper-mantle conditions. Both systems are pseudoternary because they contain forsterite, enstatite and a diopside-rich clinopyroxene from the breakdown of the mica and K-richterite. The F-bearing K-richterite systems have lower minimum melting temperatures than the F-bearing phlogopite —apatite system at the same pressure. However in the systems studied, F in phlogopite appears the most effective component in altering minimum liquid compositions whereas comparison between the present study and previous systems suggests that the presence of P₂O₅ during melting may result in more K-enriched melts. Variations in the compositions of the F-bearing phases are primarily controlled by the bulk compositions of the end-member minerals and by temperature, although buffering by non-F bearing minerals (e.g. clinopyroxene) may be effective. Distribution coefficients (as wt% ratios) between F-bearing minerals and coexisting liquids have been determined as functions of bulk composition and temperature for products of experiments. Distribution coefficients between K-richterite—liquid, apatite—liquid, and phlogopite—liquid are ≥1 to slightly <1 for most bulk compositions, indicating thatF is generally a compatible element. This conclusion is in agreement with the sequence ofF distribution for similar phases in ultrapotassic rocks. These results preclude F-bearing mineral reservoirs in the mantle, at depths corresponding to 20 kbar, being capable of producing F-enrichment in ultrapotassic magmas, or being effective in redox melting processes. Editorial responsibility: K. Hodges