THERIA_G: a software program to numerically model prograde garnet growth

We present the software program THERIA_G, which allows for numerical simulation of garnet growth in a given volume of rock along any pressure-temperature-time (P-T-t) path. THERIA_G assumes thermodynamic equilibrium between the garnet rim and the rock matrix during growth and accounts for component fractionation associated with garnet formation as well as for intracrystalline diffusion within garnet. In addition, THERIA_G keeps track of changes in the equilibrium phase relations, which occur during garnet growth along the specified P-T-t trajectory. This is accomplished by the combination of two major modules: a Gibbs free energy minimization routine is used to calculate equilibrium phase relations including the volume and composition of successive garnet growth increments as P and T and the effective bulk rock composition change. With the second module intragranular multi-component diffusion is modelled for spherical garnet geometry. THERIA_G allows to simulate the formation of an entire garnet population, the nucleation and growth history of which is specified via the garnet crystal size frequency distribution. Garnet growth simulations with THERIA_G produce compositional profiles for the garnet porphyroblasts of each size class of a population and full information on equilibrium phase assemblages for any point along the specified P-T-t trajectory. The results of garnet growth simulation can be used to infer the P-T-t path of metamorphism from the chemical zoning of garnet porphyroblasts. With a hypothetical example of garnet growth in a pelitic rock we demonstrate that it is essential for the interpretation of the chemical zoning of garnet to account for the combined effects of the thermodynamic conditions of garnet growth, the nucleation history and intracrystalline diffusio

A Quaternary Solution Model for White Micas Based on Natural Coexisting Phengite-Paragonite Pairs

A thermodynamic model for the quaternary white mica solid solution with end-members muscovite-Mg-celadonite-paragonite-Fe-celadonite (Ms-MgCel-Pg-FeCel) is presented. The interaction energies for the MgCel-Pg join, the FeCel-Pg join and the ternary interactions were obtained from natural coexisting phengite-paragonite pairs. Phengite-paragonite pairs were selected based on the criteria that their chemical compositions may be represented as a linear combination of the model end-member compositions and that the respective formation conditions (350-650°C, 4-21 kbar) are accurately known. Previously published excess free energy expressions were used for the Ms-Pg, Ms-MgCel and Ms-FeCel binaries. The suggested mixing model was tested by calculating multicomponent equilibrium phase diagrams. This proved to be particularly well suited to reproduce compositional variations of white micas from amphibolite-facies metapelite

Modelling phase-assemblage diagrams for magnesian metapelites in the system K2O-FeO-MgO-Al2O3-SiO2-H2O: geodynamic consequences for the Monte Rosa nappe, Western Alps

Magnesian metamorphic rocks with metapelitic mineral assemblage and composition are of great interest in metamorphic petrology for their ability to constrain P-T conditions in terranes where metamorphism is not easily visible. Phase-assemblage diagrams for natural and model magnesian metapelites in the system KFMASH are presented to document how phase relationships respond to water activity, bulk composition, pressure and temperature. The phase assemblages displayed on these phase diagrams are consistent with natural mineral assemblages occurring in magnesian metapelites. It is shown that the equilibrium assemblages at high pressure conditions are very sensitive to a(H2O). Specifically, the appearance of the characteristic HP assemblage chloritoid-talc-phengite-quartz (with excess H2O) in the magnesian metapelites of the Monte Rosa nappe (Western Alps) is due to the reduction of a(H2O). Furthermore, the mineral assemblages are determined by the whole-rock FeO/(FeO+MgO) ratio and effective Al content X A as well as P and T. The predicted mineral associations for the low- and high-X A model bulk compositions of magnesian metapelites at high pressure are not dependent on the X A variations as they show a similar sequence of mineral assemblages. Above 20kbar, the prograde sequence of assemblages associated with phengite (with excess SiO2 and H2O) for low- and high-X A bulk compositions of magnesian metapelites is: carpholite-chlorite→chlorite-chloritoid→chloritoid-talc→chloritoid-talc-kyanite→ talc-garnet-kyanite→garnet-kyanite±biotite. At low to medium P-T conditions, a low-X A stabilises the phengite-bearing assemblages associated with chlorite, chlorite+K-feldspar and chlorite+biotite while a high-X A results in the chlorite-phengite bearing assemblages associated with pyrophyllite, andalusite, kyanite and carpholite. A high-X A magnesian metapelite with nearly iron-free content stabilises the talc-kyanite-phengite assemblage at moderate to high P-T conditions. Taking into account the effective bulk composition and a(H2O) involved in the metamorphic history, the phase-assemblage diagrams presented here may be applied to all magnesian metapelites that have compositions within the system KFMASH and therefore may contribute to gaining insights into the metamorphic evolution of terranes. As an example, the magnesian metapelites of the Monte Rosa nappe have been investigated, and an exhumation path with P-T conditions for the western roof of the Monte Rosa nappe has been derived for the first time. The exhumation shows first a near-isothermal decompression from the Alpine eclogite peak conditions around 24kbar and 505°C down to approximately 8kbar and 475°C followed by a second decompression with concomitant coolin

Data security issues in cloud scenarios

The amount of data created, stored, and processed has enormously increased in the last years. Today, millions of devices are connected to the Internet and generate a huge amount of (personal) data that need to be stored and processed using scalable, efficient, and reliable computing infrastructures. Cloud computing technology can be used to respond to these needs. Although cloud computing brings many benefits to users and companies, security concerns about the cloud still represent the major impediment for its wide adoption. We briefly survey the main challenges related to the storage and processing of data in the cloud. In particular, we focus on the problem of protecting data in storage, supporting fine-grained access, selectively sharing data, protecting query privacy, and verifying the integrity of computations

Power Corrections to Perturbative QCD and OPE in Gluon Green Functions

We show that QCD Green functions in Landau Gauge exhibit sizable $O(1/\mu^2)$ corrections to the expected perturbative behavior at energies as high as 10 GeV. We argue that these are due to a $$-condensate which does not vanish in Landau gauge.Comment: 3 pages 1 figure lattice2001 (gaugetheories

Prograde garnet growth along complex P-T-t paths: results from numerical experiments on polyphase garnet from the Wölz Complex (Austroalpine basement)

Garnet in metapelites from the Wölz Complex of the Austroalpine crystalline basement east of the Tauern Window characteristically consists of two growth phases, which preserve a comprehensive record of the geothermal history during polymetamorphism. From numerical modelling of garnet formation, detailed information on the pressure-temperature-time (P-T-t) evolution during prograde metamorphism is obtained. In that respect, the combined influences of chemical fractionation associated with garnet growth, modification of the original growth zoning through intragranular diffusion and the nucleation history on the chemical zoning of garnet as P and T change during growth are considered. The concentric chemical zoning observed in garnet and the homogenous rock matrix, which is devoid of chemical segregation, render the simulation of garnet growth through successive equilibrium states reliable. Whereas the first growth phase of garnet was formed at isobaric conditions of ∼3.8kbar at low heating/cooling rates, the second growth phase grew along a Barrovian P-T path marked with a thermal peak of ∼625°C at ∼10kbar and a maximum in P of ∼10.4kbar at ∼610°C. For the heating rate during the growth of the second phase of garnet, average rates faster than 50°CMa−1 are obtained. From geochronological investigations the first growth phase of garnet from the Wölz Complex pertains to the Permian metamorphic event. The second growth phase grew in the course of Eo-Alpine metamorphism during the Cretaceou

Quark bilinear step scaling functions and their continuum limit extrapolation

Some new results on nonperturbative renormalisation of quark bilinears in quenched QCD with Schroedinger Functional techniques are presented. Special emphasis is put on a study of the universality of the continuum limit for step scaling functions computed with different levels of O(a) improvement.Comment: Lattice2003(improve), 3 pages, 3 figure

Phase Relations and Chemical Composition of Phengite and Paragonite in Pelitic Schists During Decompression: a Case Study from the Monte Rosa Nappe and Camughera-Moncucco Unit, Western Alps

The metamorphic evolution of metapelites from the eastern part of the Monte Rosa nappe and the Camughera-Moncucco unit, both situated in the upper Penninic units SW of the Simplon line, were investigated using microstructural relationships and equilibrium phase diagrams. The units under consideration experienced pre-Alpine amphibolite-facies conditions and underwent a complex metamorphic evolution during the Alpine orogeny. Peak pressures during an early Alpine high-pressure stage of 12·5-16 kbar were similar in the Monte Rosa nappe and Camughera-Moncucco unit. A pronounced thermal gradient is indicated during decompression leading to an amphibolite-facies overprint, as the decompression paths went through the chlorite, biotite and plagioclase stability fields in most of the Monte Rosa nappe, through the staurolite field in the easternmost Monte Rosa nappe and in the Camughera-Moncucco unit, and through the sillimanite field in the easternmost Camughera-Moncucco unit. In high-Al metapelites the initial formation of staurolite is related to continuous paragonite breakdown and associated formation of biotite. In the course of this reaction phengite becomes successively sodium enriched. In low-Al metapelites, in contrast, the initial staurolite formation occurs via the continuous breakdown of sodium-rich phengite. In both low- and high-Al metapelites the largest volume of staurolite is formed during the continuous breakdown of sodium-rich phengite below P-T conditions of about 9·5 kbar at 600-650°C. During this reaction phengite becomes successively potassium enriched as sodium from phengite is used to form the albite component in plagioclase. For ‘normal' pelitic chemistries, phengite becomes Na enriched during decompression through the breakdown of paragonite along a near-isothermal decompression path. The Na content in phengite reaches its maximum when paragonite is entirely consumed. During further decompression the paragonite component in phengite decreases again because Na is preferentially incorporated into the albite component of plagioclas

The three-loop beta function of SU(N) lattice gauge theories with Wilson fermions

We calculate the third coefficient of the lattice beta function associated with the Wilson formulation for both gauge fields and fermions. This allows us to evaluate the three-loop correction (linear in $g_0^2$) to the relation between the lattice Lambda-parameter and the bare coupling $g_0$, which is important in order to verify asymptotic scaling predictions. Our calculation also leads to the two-loop relation between the coupling renormalized in the MSbar scheme and $g_0$. The original version of this paper contained a numerical error in one of the diagrams, which has now been corrected. The calculations, as well as the layout of the paper have remained identical, but there are some important changes in the numerical results.Comment: One 14-page LaTeX file, one PostScript file containing 2 figures. Corrected a numerical error in one of the diagrams. The calculations, as well as the layout of the paper have remained unaffected, but there are some important changes in the numerical result