scholarly journals Chemical Heterogeneities in the Mantle: Progress Towards a General Quantitative Description

2018 ◽  
Author(s):  
Massimiliano Tirone
Keyword(s):  
Mass Transfer ◽  
Numerical Models ◽  
Quantitative Description ◽  
Transient State ◽  
Real Data ◽  
Initial State ◽  
Initial Size ◽  
Simple Diffusion ◽  
Chemical Equilibration ◽  
The Difference

Abstract. Chemical equilibration between two different assemblages (peridotite-type and gabbro/eclogite-type) of variable initial size assuming few different initial compositions has been determined using certain mass and reactions constraints and thermodynamic principles. The pattern that emerges suggests that mass transfer between the two sub-systems defines two petrological assemblages that separately are maintained in local thermodynamic equilibrium. In addition, when two assemblages previously equilibrated together in a certain mass ratio are rearranged assuming a different initial ratio, no mass transfer occurs and the two sub-systems remain unmodified. By modeling the chemical equilibration results of several systems it is possible to provide a quantitative framework to determine the chemical and petrological evolution of two assemblages from an initial state, in which the two are separately in chemical equilibrium, to a state of equilibration of the whole system (sum of the two sub-systems). Assuming that the local Gibbs energy variation follows a simple diffusion couple model, a complete petrological description of the two systems can be determined over time and space. Since there are no data to constrain the kinetic of the processes involved, the temporal and spatial scale is arbitrary. Nevertheless a 1-D static model shows how chemical equilibration is controlled by the size of the two sub-systems. As the initial size of the first assemblage (peridotite-like) increases, the differences between the initial and the final equilibrated stage becomes smaller, while on the opposite side the difference increases. A simplified 2-D dynamic model in which either one of the two sub-systems is allowed to move with a prescribed velocity, shows that after an initial transient state, the moving sub-system tends to preserve its original composition defined at the entry side. The other sub-system instead evolves towards a large compositional difference from the starting assemblage. The results appear to be the same varying the initial proportion of the two assemblages, which simplify somehow the development of potential tools for predicting the chemical equilibration process from real data and geodynamic applications. Four animations and data sets of three 1-D and two 2-D numerical models are available following the instructions in the supplementary material.

scholarly journals Chemical heterogeneities in the mantle: progress towards a general quantitative description

Solid Earth ◽  
2019 ◽  
Vol 10 (4) ◽  
pp. 1409-1428 ◽  
Author(s):  
Massimiliano Tirone
Keyword(s):  
Mass Transfer ◽  
Chemical Equilibrium ◽  
Transport Model ◽  
Numerical Models ◽  
Quantitative Description ◽  
Transient State ◽  
Real Data ◽  
Initial State ◽  
Initial Size ◽  
Chemical Equilibration

Abstract. Chemical equilibration between two different assemblages (peridotite type and gabbro–eclogite type) has been determined using basic thermodynamic principles and certain constraints and assumptions regarding mass and reaction exchange. When the whole system (defined by the sum of the two subsystems) is in chemical equilibrium the two assemblages will not be homogenized, but they will preserve distinctive chemical and mineralogical differences. Furthermore, the mass transfer between the two subsystems defines two petrological assemblages that separately are also in local thermodynamic equilibrium. In addition, when two assemblages previously equilibrated as a whole in a certain initial mass ratio are held together assuming a different proportion, no mass transfer occurs and the two subsystems remain unmodified. By modeling the chemical equilibration results of several systems of variable initial size and different initial composition it is possible to provide a quantitative framework to determine the chemical and petrological evolution of two assemblages from an initial state, in which the two are separately in chemical equilibrium, to a state of equilibration of the whole system. Assuming that the local Gibbs energy variation follows a simple transport model with an energy source at the interface, a complete petrological description of the two systems can be determined over time and space. Since there are no data to constrain the kinetics of the processes involved, the temporal and spatial scale is arbitrary. The evolution model should be considered only a semiempirical tool that shows how the initial assemblages evolve while preserving distinct chemical and petrological features. Nevertheless, despite the necessary simplification, a 1-D model illustrates how chemical equilibration is controlled by the size of the two subsystems. By increasing the initial size of the first assemblage (peridotite like), the compositional differences between the initial and the final equilibrated stage become smaller, while on the eclogite-type side the differences tend to be larger. A simplified 2-D dynamic model in which one of the two subsystems is allowed to move with a prescribed velocity shows that after an initial transient state, the moving subsystem tends to preserve its original composition defined at the influx side. The composition of the static subsystem instead progressively diverges from the composition defining the starting assemblage. The observation appears to be consistent for various initial proportions of the two assemblages, which somehow simplify the development of potential tools for predicting the chemical equilibration process from real data and geodynamic applications. Four animation files and the data files of three 1-D and two 2-D numerical models are available following the instructions in the Supplement.

Melting of ice in a porous medium saturated with ice and gas while injecting warm water

2019 ◽  
Vol 13 (4) ◽  
pp. 112-117 ◽  
Author(s):  
V.Sh. Shagapov ◽  
M.N. Zapivakhina
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Low Temperature ◽  
Numerical Models ◽  
Warm Water ◽  
Temperature Fields ◽  
Initial State ◽  
Simplified Models ◽  
Frozen Soils ◽  
Porous Formation

The numerical models for the injection of warm water (in the temperature range from 300 to 340 K) into a cold porous formation are considered. Simplified models describing the processes of heat and mass transfer are proposed. The influence of the parameters determining the initial state of the porous medium, the boundary pressure, temperature and moisture content on the rate of propagation of hydrodynamic and temperature fields in the porous medium is investigated. It has been established that it is economically feasible to melt frozen soils saturated with ice and gas (air) at a sufficiently low temperature of the injected water (about 300 K).

Consolidating rock-physics classics: A practical take on granular effective medium models

2019 ◽  
Vol 38 (5) ◽  
pp. 334-340 ◽  
Author(s):  
Fabien Allo
Keyword(s):  
Numerical Models ◽  
Quantitative Description ◽  
Rock Physics ◽  
Real Data ◽  
Analytical Form ◽  
Effective Medium ◽  
Seismic Exploration ◽  
Stiffness Index ◽  
Rock Composition ◽  
Rock Types

Granular effective medium (GEM) models rely on the physics of a random packing of spheres. Although the relative simplicity of these models contrasts with the complex texture of most grain-based sedimentary rocks, their analytical form makes them easier to apply than numerical models designed to simulate more complex rock structures. Also, unlike empirical models, they do not rely on data acquired under specific physical conditions and can therefore be used to extrapolate beyond available observations. In addition to these practical considerations, the appeal of GEM models lies in their parameterization, which is suited for a quantitative description of the rock texture. As a result, they have significantly helped promote the use of rock physics in the context of seismic exploration for hydrocarbon resources by providing geoscientists with tools to infer rock composition and microstructure from sonic velocities. Over the years, several classic GEM models have emerged to address modeling needs for different rock types such as unconsolidated, cemented, and clay-rich sandstones. We describe how these rock-physics models, pivotal links between geology and seismic data, can be combined into extended models through the introduction of a few additional parameters (matrix stiffness index, cement cohesion coefficient, contact-cement fraction, and laminated clays fraction), each associated with a compositional or textural property of the rock. A variety of real data sets are used to illustrate how these parameters expand the realm of seismic rock-physics diagnostics by increasing the versatility of the extended models and facilitating the simulation of plausible geologic variations away from the wells.

Analysis and calculation of the process of low-pressure reverse osmosis during recycling of hygienic water

2019 ◽  
pp. 28-36
Author(s):  
Leonid S. Bobe ◽  
Nikolay A. Salnikov
Keyword(s):  
Mass Transfer ◽  
Reverse Osmosis ◽  
Life Support ◽  
Space Station ◽  
Low Pressure ◽  
Operating Pressure ◽  
Life Support System ◽  
Cleaning Agent ◽  
The Difference ◽  
Pressure Channel

Analysis and calculation have been conducted of the process of low-pressure reverse osmosis in the membrane apparatus of the system for recycling hygiene water for the space station. The paper describes the physics of the reverse osmosis treatment and determines the motive force of the process, which is the difference of effective pressures (operating pressure minus osmotic pressure) in the solution near the surface of the membrane and in the purified water. It is demonstrated that the membrane scrubbing action is accompanied by diffusion outflow of the cleaning agent components away from the membrane. The mass transfer coefficient and the difference of concentrations (and, accordingly, the difference of osmotic pressures) in the boundary layer of the pressure channel can be determined using an extended analogy between mass transfer and heat transfer. A procedure has been proposed and proven in an experiment for calculating the throughput of a reverse osmosis apparatus purifying the hygiene water obtained through the use of a cleaning agent used in sanitation and housekeeping procedures on Earth. Key words: life support system, hygiene water, water processing, low-pressure reverse osmosis, space station.

Possible application of approximate models for calculation of selectivity of consecutive reactions under the effect of mass transfer

1982 ◽  
Vol 47 (5) ◽  
pp. 1301-1309 ◽  
Author(s):  
František Kaštánek ◽  
Marie Fialová
Keyword(s):  
Mass Transfer ◽  
Numerical Method ◽  
Analytical Method ◽  
Approximate Analytical Method ◽  
Approximate Models ◽  
Consecutive Reactions ◽  
The Difference

The possibility of use of approximate models for calculation of selectivity of consecutive reactions is critically analysed. Simple empirical criteria are proposed which enable safer application of approximate analytical reactions. A more universal modification has been formulated by use of which the difference of selectivity calculated by the exact numerical method and by the approximate analytical method is at maximum 12%.

scholarly journals A Semi-Theoretical Model for Water Condensation: Dew Used in Conservation of Earthen Heritage Sites

Water ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 52
Author(s):  
Xiang He ◽  
Sijia Wang ◽  
Bingjian Zhang
Keyword(s):  
Mass Transfer ◽  
Theoretical Model ◽  
Field Experiments ◽  
Environmental Control ◽  
Mass Transfer Process ◽  
Formation Processes ◽  
Heritage Sites ◽  
Dew Formation ◽  
The Difference ◽  
Two Parameter

Dew is a common but important phenomenon. Though water is previously considered to be a threat to earthen heritage sites, artificial dew is showing potential in relic preservation. A model of dew prediction on earthen sites will be essential for developing preventive protection methods, but studies of dew formation processes on relics are limited. In this study, a two parameter model is proposed. It makes approximations according to the features of earthen heritage sites, assuming that a thin and steady air layer exists close to the air–solid interface. This semi-theoretical model was based on calculations of the mass transfer process in the air layer, and was validated by simulations of laboratory experiments (R > 0.9) as well as field experiments. Additionally, a numerical simulation, performed by the commercial software COMSOL, confirmed that the difference between fitting parameter δ and the thickness of assumed mass transfer field was not significant. This model will be helpful in developing automatic environmental control systems for stabilizing water and soluble salts, thus enhancing preventive protection of earthen heritage sites.

scholarly journals Estimating Differential Latent Variable Graphical Models with Applications to Brain Connectivity

Biometrika ◽  
2020 ◽  
Author(s):  
S Na ◽  
M Kolar ◽  
O Koyejo
Keyword(s):  
Graphical Models ◽  
Latent Variable ◽  
Graphical Model ◽  
Brain Connectivity ◽  
Statistical Error ◽  
Real Data ◽  
Low Rank ◽  
Conditional Dependence ◽  
Gradient Descent Algorithm ◽  
The Difference

Abstract Differential graphical models are designed to represent the difference between the conditional dependence structures of two groups, thus are of particular interest for scientific investigation. Motivated by modern applications, this manuscript considers an extended setting where each group is generated by a latent variable Gaussian graphical model. Due to the existence of latent factors, the differential network is decomposed into sparse and low-rank components, both of which are symmetric indefinite matrices. We estimate these two components simultaneously using a two-stage procedure: (i) an initialization stage, which computes a simple, consistent estimator, and (ii) a convergence stage, implemented using a projected alternating gradient descent algorithm applied to a nonconvex objective, initialized using the output of the first stage. We prove that given the initialization, the estimator converges linearly with a nontrivial, minimax optimal statistical error. Experiments on synthetic and real data illustrate that the proposed nonconvex procedure outperforms existing methods.

Numerical Model of Current Speed in Bojong Salawe Beach, Pangandaran West Java Province

2021 ◽  
Vol 2 (1) ◽  
pp. 17-23
Author(s):  
Subiyanto Subiyanto ◽  
Nira na Nirwa ◽  
Yuniarti Yuniarti ◽  
Yudi Nurul Ihsan ◽  
Eddy Afrianto
Keyword(s):  
Numerical Models ◽  
High Tide ◽  
Movement Pattern ◽  
Numerical Data ◽  
Current Speed ◽  
The West ◽  
Instantaneous Speed ◽  
The Difference ◽  
West Monsoon ◽  
Current Movement

The purpose of this study was to determine the hydrodynamic conditions at Bojong Salawe beach. The method used in this research is a quantitative method, where numerical data is collected to support the formation of numerical models such as wind, bathymetry, and tide data. The hydrodynamic model will be made using Mike 21 with the Flow Model FM module to determine the current movement pattern based on the data used. In the west monsoon with a maximum instantaneous speed of 0.04 - 0.08 m/s, while in the east monsoon it moves with a maximum instantaneous speed of 0,4 – 0,44 m/s. The dominant direction of current movement tends to the northeast. The results indicate the current speed during the east monsoon is higher than the west monsoon. The difference in the current speed is also influenced by the tide conditions; higher during high tide and lower during low tide. Monsoons also have a role in the current movements, though the effect is not very significant.

Principles of Metal Refining and Recycling

2021 ◽  
Author(s):  
Thorvald Abel Engh ◽  
Geoffrey K. Sigworth ◽  
Anne Kvithyld
Keyword(s):  
Mass Transfer ◽  
Transport Properties ◽  
Numerical Models ◽  
Impurity Elements

Covers the field of recycling and refining of metals. An important point the book stresses is that the principles are the same in the treatment of various different metals. The book answerd why it is important to have a clean and properly alloyed metal from recycling and refined metal? The text covers basic thermodynamics, physical and transport properties, mixing, mass transfer and numerical models. Further it identifies problems and described methods for removal of dissolved impurity elements, particles and inclusions, also during solidification. And lastly applications remelting and addition of alloys, recycling and challenges and specific processes for each metal are included. The book is self-contained.

scholarly journals A Robust Rerank Approach for Feature Selection and Its Application to Pooling-Based GWA Studies

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jia-Rou Liu ◽  
Po-Hsiu Kuo ◽  
Hung Hung
Keyword(s):  
Characteristic Curve ◽  
Real Data ◽  
Tuning Parameter ◽  
Practical Implementation ◽  
Tuning Parameters ◽  
Genome Wide ◽  
Feature Based ◽  
The Difference ◽  
Gwa Studies ◽  
Selection Of

Large-p-small-ndatasets are commonly encountered in modern biomedical studies. To detect the difference between two groups, conventional methods would fail to apply due to the instability in estimating variances int-test and a high proportion of tied values in AUC (area under the receiver operating characteristic curve) estimates. The significance analysis of microarrays (SAM) may also not be satisfactory, since its performance is sensitive to the tuning parameter, and its selection is not straightforward. In this work, we propose a robust rerank approach to overcome the above-mentioned diffculties. In particular, we obtain a rank-based statistic for each feature based on the concept of “rank-over-variable.” Techniques of “random subset” and “rerank” are then iteratively applied to rank features, and the leading features will be selected for further studies. The proposed re-rank approach is especially applicable for large-p-small-ndatasets. Moreover, it is insensitive to the selection of tuning parameters, which is an appealing property for practical implementation. Simulation studies and real data analysis of pooling-based genome wide association (GWA) studies demonstrate the usefulness of our method.

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