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Local Equilibrium (local + equilibrium)
Selected AbstractsExhumation paths of high-pressure metapelites obtained from local equilibria for chlorite,phengite assemblagesGEOLOGICAL JOURNAL, Issue 3-4 2000O. Vidal Abstract The compositional variation of phengite and chlorite pairs in rocks sampled across the metamorphic zonation of three different blueschist belts (Cycladic, Sambagawa and Schistes Lustrés) is characterized from the regional to the thin-section scale. The different sample suites show different compositional trends, but similar trends are observed at the regional and thin-section scale in the same unit. At the thin-section scale, several local chlorite,phengite equilibria involving minerals of different compositions can be identified. These observations suggest that at temperature T <,,550°C, equilibration of chlorite and phengite compositions with varying pressure and temperature is controlled by crystallization/recrystallization processes rather than by changing the composition of older grains by lattice diffusion. In some instances, the relative time of growth of the different phyllosilicate generations can be determined using microstructural criteria. The observed compositional variations are interpreted and quantified in terms of pressure (P) and temperature (T) variations using new thermodynamic solution models accounting for the Tschermak, di/trioctahedral, and pyrophyllitic substitutions. Chlorite,phengite local equilibria constrain the shape of the exhumation P,T paths of the rocks under consideration. The assemblage chlorite,phengite,paragonite,albite,quartz,H2O can be used to constrain different P,T paths for Tinos and Sambagawa blueschists. Copyright © 2000 John Wiley & Sons, Ltd. [source] A mathematical model for steady-state regolith production at constant erosion rateEARTH SURFACE PROCESSES AND LANDFORMS, Issue 5 2010M.I. Lebedeva Abstract It has been hypothesized that many soil profiles reach a steady-state thickness. In this work, such profiles were simulated using a one-dimensional model of reaction with advective and diffusive solute transport. A model ,rock' is considered, consisting of albite that weathers to kaolinite in the presence of chemically inert quartz. The model yields three different steady-state regimes of weathering. At the lowest erosion rates, a local-equilibrium regime is established where albite is completely depleted in the weathering zone. This regime is equivalent to the transport-limited regime described in the literature. With an increase in erosion rate, transition and kinetic regimes are established. In the transition regime, both albite and kaolinite are present in the weathering zone, but albite does not persist to the soil,air interface. In the weathering-limited regime, here called the kinetic regime, albite persists to the soil,air interface. The steady-state thickness of regolith decreases with increasing erosion rate in the local equilibrium and transition regimes, but in the kinetic regime, this thickness is independent of erosion rate. Analytical expressions derived from the model are used to show that regolith production rates decrease exponentially with regolith thickness. The steady-state regolith thickness increases with the Darcy velocity of the pore fluid, and in the local equilibrium regime may vary markedly with small variations in this velocity and erosion rate. In the weathering-limited regime, the temperature dependences for chemical weathering rates are related to the activation energy for the rate constant for mineral reaction and to the ,H of dissolution, while for local equilibrium regimes they are related to the ,H only. The model illustrates how geochemical and geomorphological observations are related for a simple compositional system. The insights provided will be useful in interpreting natural regolith profiles. Copyright © 2010 John Wiley & Sons, Ltd. [source] Statistical sensitivity analysis of packed column reactors for contaminated wastewaterENVIRONMETRICS, Issue 8 2003A. Fassň Abstract In this article we consider the statistical sensitivity analysis of heavy metal biosorption in contaminated wastewater packed column reactors. In particular, the model describes the biosorption phenomenon using the Advection Dispersion Reaction equation under rapid local equilibrium. This allows computer simulation with random input parameters chosen from appropriate probability distributions. In order to have a statistical framework for analyzing the simulated data and assessing input importance, we introduce heteroskedastic and multivariate sensitivity analysis, which extends standard sensitivity analysis. Copyright © 2003 John Wiley & Sons, Ltd. [source] Scaling of water flow through porous media and soilsEUROPEAN JOURNAL OF SOIL SCIENCE, Issue 1 2008K. Roth Summary Scaling of fluid flow in general is outlined and contrasted to the scaling of water flow in porous media. It is then applied to deduce Darcy's law, thereby demonstrating that stationarity of the flow field at the scale of the representative elementary volume (REV) is a critical prerequisite. The focus is on the implications of the requirement of stationarity, or local equilibrium, in particular on the validity of the Richards equation for the description of water movement through soils. Failure to satisfy this essential requirement may occur at the scale of the REV or, particularly in numerical simulations, at the scale of the model discretization. The latter can be alleviated by allocation of more computational resources and by working on a finer-grained representation. In contrast, the former is fundamental and leads to an irrevocable failure of the Richards equation as is observed with infiltration instabilities that lead to fingered flow. [source] Bond rolling resistance and its effect on yielding of bonded granulates by DEM analysesINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 8 2006M. J. Jiang Abstract A discrete element modelling of bonded granulates and investigation on the bond effect on their behaviour are very important to geomechanics. This paper presents a two-dimensional (2-D) discrete element theory for bonded granulates with bond rolling resistance and provides a numerical investigation into the effect of bond rolling resistance on the yielding of bonded granulates. The model consists of mechanical contact models and equations governing the motion of bonded particles. The key point of the theory is that the assumption in the original bond contact model previously proposed by the authors (55th CSCE-ASCE Conference, Hamilton, Ont., Canada, 2002; 313,320; J. Eng. Mech. (ASCE) 2005; 131(11):1209,1213) that bonded particles are in contact at discrete points, is here replaced by a more reliable assumption that bonded particles are in contact over a width. By making the idealization that the bond contact width is continuously distributed with the normal/tangential basic elements (BE) (each BE is composed of spring, dashpot, bond, slider or divider), we establish a bond rolling contact model together with bond normal/tangential contact models, and also relate the governing equations to local equilibrium. Only one physical parameter , needs to be introduced in the theory in comparison to the original bond discrete element model. The model has been implemented into a 2-D distinct element method code, NS2D. Using the NS2D, a total of 86 1-D, constant stress ratio, and biaxial compressions tests have been carried out on the bonded granular samples of different densities, bonding strengths and rolling resistances. The numerical results show that: (i) the new theory predicts a larger internal friction angle, a larger yielding stress, more brittle behaviour and larger final broken contact ratio than the original bond model; (ii) the yielding stress increases nonlinearly with the increasing value of ,, and (iii) the first-yield curve (initiation of bond breakage), which define a zone of none bond breakage and which shape and size are affected by the material density, is amplified by the bond rolling resistance in analogous to that predicted by the original bond model. Copyright © 2006 John Wiley & Sons, Ltd. [source] Plagioclase replacement textures in partially eclogitised gabbros from the Sanddal mafic-ultramafic complex, Greenland CaledonidesJOURNAL OF METAMORPHIC GEOLOGY, Issue 5 2001H. M. Lang Abstract The Sanddal mafic-ultramafic complex (SMUK) is a cluster of variably eclogitised mafic and ultramafic bodies that comprise the westernmost known eclogite facies locality in the North-East Greenland eclogite province (NEGEP). Although there are no true eclogites in the SMUK, we interpret three distinct textural types of plagioclase replacement to record sequential stages in adjustment of SMUK olivine gabbro-norites to eclogite facies conditions. The earliest stage, in which plagioclase was replaced by omphacite/spinel symplectite before nucleation of garnet (Type 1A & 1B) has not previously been described. Documentation of this texture provides clear evidence that, at least in some cases, garnet nucleation is delayed relative to nucleation of omphacite and is a rate-limiting step for eclogitisation. Type 1C domains were produced by scattered nucleation of garnet in the same sample. In Type 2 domains, plagioclase was replaced by a layered corona with an outer layer of garnet, an inner layer of omphacite and an interior of inclusion-rich plagioclase. In Type 3 domains, the omphacite layer was overgrown by the garnet rim, and omphacite is preserved only as inclusions in garnet. In more coarse grained leucogabbros, recrystallization was more complete, plagioclase replacement textures were less localised, and could not be divided into distinct stages. Plagioclase replacement in SMUK samples was not isochemical, and required diffusion of at least Mg and Fe from replacement of mafic phases in the surroundings. Strong compositional gradients in garnet reflect disequilibrium and were controlled by the different diffusion rates of Mg/Fe and Ca, different local chemical environments, and progress of the plagioclase breakdown reaction. The presence of small amounts of hydrous minerals (amphibole, phlogopite and clinozoisite) in local equilibrium in plagioclase domains of most SMUK samples indicates that a small amount of H2O was present during high pressure metamorphism. [source] Time evolution of relativistic d + Au and Au + Au collisionsANNALEN DER PHYSIK, Issue 6 2006G. Wolschin Abstract The evolution of charged-particle production in collisions of heavy ions at relativistic energies is investigated as function of centrality in a nonequilibrium-statistical framework. Precise agreement with recent d + Au and Au + Au data at = 200 GeV is found in a Relativistic Diffusion Model with three sources for particle production. Only the midrapidity source comes very close to local equilibrium, whereas the analyses of the overall pseudorapidity distributions show that the systems remain far from statistical equilibrium. [source] Liouville and Fokker,Planck dynamics for classical plasmas and radiationANNALEN DER PHYSIK, Issue 6 2006R.F. Alvarez-Estrada Abstract We consider a nonequilibrium statistical system formed by many classical non-relativistic particles of opposite electric charges (plasma) and by the classical dynamical electromagnetic (EM) field. The charges interact with one another directly through instantaneous Coulomb potentials and with the dynamical degrees of freedom of the transverse EM field. The system may also be subject to external influences of: i) either static, but spatially inhomogeneous, electric and magnetic fields (case 1)), or ii) weak distributions of electric charges and currents (case 2)). The particles and the dynamical EM field are described, for any time t > 0, by the classical phase-space probability distribution functional (CPSPDF) f and, at the initial time (t = 0), by the initial CPSPDF fin. The CPSPDF f and fin, multiplied by suitable Hermite polynomials (for particles and field) and integrated over all canonical momenta, yield new moments. The Liouville equation and fin imply a new nonequilibrium linear infinite hierarchy for the moments. In case 1), fin describes local equilibrium but global nonequilibrium, and we propose a long-time approximation in the hierarchy, which introduces irreversibility and relaxation towards global thermal equilibrium. In case 2), the statistical system, having been at global thermal equilibrium, without external influences, for t , 0, is subject to weak external charge-current distributions: then, new hierarchies for moments and their long-time behaviours are discussed in outline. As examples, approximate mean-field (Vlasov) approximations are treated for both cases 1) and 2). [source] | ||||||||||