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Journal articles on the topic 'Phase Transitions and Multiphase Systems'
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Lebedev V. G. "Phase transformations in single-component multiphase systems: phase-field approach." Technical Physics 92, no. 2 (2022): 155. http://dx.doi.org/10.21883/tp.2022.02.52941.215-21.
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The problems of constructing a multiphase model of the phase field for the processes of phase transitions of the first kind are considered. Based on the Gibbs energy of the complete system expressed in terms of antisymmetrized combinations of phase fields, it is shown that the equations of dissipative dynamics of a locally nonequilibrium system follow from the condition of its monotonic decrease, preserving the normalization of the sum of variables by one and the following properties of the previously known two-phase model. Keywords: multiphase systems, phase transformations, locally nonequilibrium processes, dissipative systems with constraints.
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Ge, Guanglong, Chukai Chen, Cheng Shi, Jing Yang, Jinfeng Lin, Jin Qian, Yongqi Wei, Bo Shen, and Jiwei Zhai. "Alkali-earth metal ion inducing multiphase transition of lanthanum-free Pb(Zr0.5Sn0.5)O3 ceramics improves the energy storage properties." Applied Physics Letters 122, no. 12 (March 20, 2023): 123903. http://dx.doi.org/10.1063/5.0140020.
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Constructing the stepwise phase transition can delay the polarization process of antiferroelectric ceramics, possessing certain significance for improving the energy storage density. However, the common multiphase transitions are obtained in the rare-earth ions doped PbZrO3-based systems. In the present work, the multiphase transition can also be induced in the lanthanum-free Pb(Zr0.5Sn0.5)O3 matrix with mere doping of the alkali-earth metal ion Sr. The introduction of Sr endows the matrix with a higher lattice distortion and the reduced phase-transition temperature. Moreover, related to the induced stepwise electric field-induced phase transition, the energy storage properties are remarkably enhanced to 10.5 J/cm3 and 83.2% when the substitution content of Sr is 3 mol. %. Sr modification can adjust the phase structure by regulating the phase stability of the matrix and suppress the leakage current originating from the structural changes. This work provides a successful attempt that the phase structure and energy storage performance of antiferroelectric ceramics can also be effectively controlled through cheaper and simpler element modification. The optimized energy storage performance provides a new material selection for pulsed power devices.
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Sun, Yujian, Sean G. Mueller, Boung W. Lee, and Milorad P. Dudukovic. "Optical Fiber Reflectance Probe for Detection of Phase Transitions in Multiphase Systems." Industrial & Engineering Chemistry Research 53, no. 2 (December 24, 2013): 999–1003. http://dx.doi.org/10.1021/ie403253c.
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Mamedov, Gasim A., and Natiq M. Abbasov. "Mathematical models of hydromechanics of multiphase flow with varying mass." Nafta-Gaz 79, no. 11 (November 2023): 709–15. http://dx.doi.org/10.18668/ng.2023.11.02.
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The paper discusses the mathematical model of hydromechanics of multiphase flows with varying mass. A multiphase flow is considered a continuum consisting of a set of a large number of different groups of particles. The derivation of motion equations and similarity criteria are given taking into account both the externally attached (or detached) mass and phase transitions within the medium. The equations of mass, momentum and energy transfer for individual phases and the medium as a whole are derived based on fundamental conservation laws. It was demonstrated that in the absence of sources (or flow-offs) of mass, momentum and energy, the known equations of single- and multi-phase flow hydromechanics follow as a special case from the obtained systems of motion equations and similarity criteria. The obtained motion equations are valid for the description of an ingredient of mixture and the medium as a whole, regardless of their physical and mechanical properties. Thermodynamic and rheological state equations, as well as expressions for heat flow, interfacial mass forces phase transitions, and heat exchange between phases can be used to close them. The implemented models make it possible to simulate both the stationary distribution of parameters along the wellbore during production and non-stationary processes that occur, for example, when the pump shaft speed changes during oil production. The developed approaches were implemented in the DataFlow software tool for analysis of the hydrodynamics of multiphase hydrocarbon flows, taking into account heat exchange with the rocks surrounding the well, and phase transitions in the fluid. Using the software package, test calculations were carried out to demonstrate the performance of the proposed and implemented models.
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Popović, Stanko. "Quantitative Phase Analysis by X-ray Diffraction—Doping Methods and Applications." Crystals 10, no. 1 (January 7, 2020): 27. http://dx.doi.org/10.3390/cryst10010027.
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X-ray powder diffraction is an ideal technique for the quantitative analysis of a multiphase sample. The intensities of diffraction lines of a phase in a multiphase sample are proportional to the phase fraction and the quantitative analysis can be obtained if the correction for the absorption of X-rays in the sample is performed. Simple procedures of quantitative X-ray diffraction phase analysis of a multiphase sample are presented. The matrix-flushing method, with the application of reference intensities, yields the relationship between the intensity and phase fraction free from the absorption effect, thus, shunting calibration curves or internal standard procedures. Special attention is paid to the doping methods: (i) simultaneous determination of the fractions of several phases using a single doping and (ii) determination of the fraction of the dominant phase. The conditions to minimize systematic errors are discussed. The problem of overlapping of diffraction lines can be overcome by combining the doping method (i) and the individual profile fitting method, thus performing the quantitative phase analysis without the reference to structural models of particular phases. Recent suggestions in quantitative phase analysis are quoted, e.g., in study of the decomposition of supersaturated solid solutions—intermetallic alloys. Round Robin on Quantitative Phase Analysis, organized by the IUCr Commission on Powder Diffraction, is discussed shortly. The doping methods have been applied in various studies, e.g., phase transitions in titanium dioxide, biomineralization processes, and phases in intermetallic oxide systems and intermetallic alloys.
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Sameer, Jane C. Charlton, Jackson M. Norris, Matthew Gebhardt, Christopher W. Churchill, Glenn G. Kacprzak, Sowgat Muzahid, et al. "Cloud-by-cloud, multiphase, Bayesian modelling: application to four weak, low-ionization absorbers." Monthly Notices of the Royal Astronomical Society 501, no. 2 (December 3, 2020): 2112–39. http://dx.doi.org/10.1093/mnras/staa3754.
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ABSTRACT We present a new method aimed at improving the efficiency of component by component ionization modelling of intervening quasar absorption-line systems. We carry out cloud-by-cloud, multiphase modelling making use of cloudy and Bayesian methods to extract physical properties from an ensemble of absorption profiles. Here, as a demonstration of method, we focus on four weak, low-ionization absorbers at low redshift, because they are multiphase but relatively simple to constrain. We place errors on the inferred metallicities and ionization parameters for individual clouds, and show that the values differ from component to component across the absorption profile. Our method requires user input on the number of phases and relies on an optimized transition for each phase, one observed with high resolution and signal-to-noise ratio. The measured Doppler parameter of the optimized transition provides a constraint on the Doppler parameter of H i, thus providing leverage in metallicity measurements even when hydrogen lines are saturated. We present several tests of our methodology, demonstrating that we can recover the input parameters from simulated profiles. We also consider how our model results are affected by which radiative transitions are covered by observations (for example, how many H i transitions) and by uncertainties in the b parameters of optimized transitions. We discuss the successes and limitations of the method, and consider its potential for large statistical studies. This improved methodology will help to establish direct connections between the diverse properties derived from characterizing the absorbers and the multiple physical processes at play in the circumgalactic medium.
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Marlton, Frederick, Stefano Checchia, and John Daniels. "Revealing phase boundaries by weighted parametric structural refinement." Journal of Synchrotron Radiation 26, no. 5 (August 1, 2019): 1638–43. http://dx.doi.org/10.1107/s1600577519007902.
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Parametric Rietveld refinement from powder diffraction data has been utilized in a variety of situations to understand structural phase transitions of materials in situ. However, when analysing data from lower-resolution two-dimensional detectors or from samples with overlapping Bragg peaks, such transitions become difficult to observe. In this study, a weighted parametric method is demonstrated whereby the scale factor is restrained via an inverse tan function, making the phase boundary composition a refinable parameter. This is demonstrated using compositionally graded samples within the lead-free piezoelectric (BiFeO3) x (Bi0.5K0.5TiO3) y (Bi0.5Na0.5TiO3)1–x–y and (Bi0.5Na0.5TiO3) x (BaTiO3)1–x systems. This has proven to be an effective method for diffraction experiments with relatively low resolution, weak peak splitting or compositionally complex multiphase samples.
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Schmitz, G. J., and B. Nestler. "Simulation of phase transitions in multiphase systems: peritectic solidification of (RE)Ba2Cu3O7-x superconductors." Materials Science and Engineering: B 53, no. 1-2 (May 1998): 23–27. http://dx.doi.org/10.1016/s0921-5107(97)00296-1.
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Roy, Priyatanu, Shihao Liu, and Cari S. Dutcher. "Droplet Interfacial Tensions and Phase Transitions Measured in Microfluidic Channels." Annual Review of Physical Chemistry 72, no. 1 (April 20, 2021): 73–97. http://dx.doi.org/10.1146/annurev-physchem-090419-105522.
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Measurements of droplet phase and interfacial tension (IFT) are important in the fields of atmospheric aerosols and emulsion science. Bulk macroscale property measurements with similar constituents cannot capture the effect of microscopic length scales and highly curved surfaces on the transport characteristics and heterogeneous chemistry typical in these applications. Instead, microscale droplet measurements ensure properties are measured at the relevant length scale. With recent advances in microfluidics, customized multiphase fluid flows can be created in channels for the manipulation and observation of microscale droplets in an enclosed setting without the need for large and expensive control systems. In this review, we discuss the applications of different physical principles at the microscale and corresponding microfluidic approaches for the measurement of droplet phase state, viscosity, and IFT.
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Qu, Danqi, and Hui-Chia Yu. "Multiphysics Electrochemical Impedance Simulations of Complex Multiphase Electrodes." ECS Meeting Abstracts MA2023-02, no. 54 (December 22, 2023): 2548. http://dx.doi.org/10.1149/ma2023-02542548mtgabs.
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Electrochemical impedance spectroscopy (EIS) is a widely used technique for characterizing materials in electrochemical systems. However, directly connecting the obtained quantities to microstructure-level phenomena is challenging. In this work, we performed detailed electrochemical microstructure simulations to investigate the EIS behavior of phase-separating graphite electrodes. We employed the Cahn-Hilliard phase-field equation to model Li transport and phase transitions in the graphite particles. In single-phase graphite particles, the charge-transfer resistance reflected the total active surface areas. In two-phase coexistence graphite particles with phase boundaries present on the particle surfaces, the simulations exhibited an inductive loop on the EIS curve. In core-shell phase-morphology cases, the EIS measurements reflected only the properties of the shells. The resulting EIS curves were indistinguishable from those in the single-phase cases. While Fick's law of diffusion has been mistakenly employed to model Li transport in phase-separating graphite electrodes, our simulations showed that the EIS curves obtained using the Fickian diffusion model were very similar to those obtained using the Cahn-Hilliard phase-field model. This tool provides unprecedentedly detailed simulations to connect the intrinsic material properties, electrochemical processes in the microstructures, and resulting EIS behavior. Figure 1
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Wang, Qian, Hong-Ze Yan, Xian Zhao, and Chun-Ming Wang. "Polymorphic Phase Transition and Piezoelectric Performance of BaTiO3-CaSnO3 Solid Solutions." Actuators 10, no. 6 (June 13, 2021): 129. http://dx.doi.org/10.3390/act10060129.
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BaTiO3-based piezoelectric ceramics have attracted considerable attention in recent years due to their tunable phase structures and good piezoelectric properties. In this work, the (1 − x)BaTiO3−xCaSnO3 (0.00 ≤ x ≤ 0.16, abbreviated as BT−xCS) solid solutions, were prepared by traditional solid-state reaction methods. The phase transitions, microstructure, dielectric, piezoelectric, and ferroelectric properties of BT-xCS have been investigated in detail. The coexistence of rhombohedral, orthorhombic, and tetragonal phases near room temperature, i.e., polymorphic phase transition (PPT), has been confirmed by X-ray diffraction and temperature-dependent dielectric measurements in the compositions range of 0.06 ≤ x ≤ 0.10. The multiphase coexistence near room temperature provides more spontaneous polarization vectors and facilitates the process of polarization rotation and extension by an external electric field, which is conducive to the enhancement of piezoelectric response. Remarkably, the composition of BT-0.08CS exhibits optimized piezoelectric properties with a piezoelectric coefficient d33 of 620 pC/N, electromechanical coupling factors kp of 58%, kt of 40%, and a piezoelectric strain coefficient d33* of 950 pm/V.
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Ayala, Luis F., and Michael A. Adewumi. "Low-Liquid Loading Multiphase Flow in Natural Gas Pipelines." Journal of Energy Resources Technology 125, no. 4 (November 18, 2003): 284–93. http://dx.doi.org/10.1115/1.1616584.
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Pressure and temperature variations of natural gas flows in a pipeline may cause partial gas condensation. Fluid phase behavior and prevailing conditions often make liquid appearance inevitable, which subjects the pipe flow to a higher pressure loss. This study focuses on the hydrodynamic behavior of the common scenarios that may occur in natural gas pipelines. For this purpose, a two-fluid model is used. The expected flow patterns as well as their transitions are modeled with emphasis on the low-liquid loading character of such systems. In addition, the work re-examines previous implementations of two-flow model for gas-condensate flow.
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Dinariev, Oleg, Nikolay Evseev, and Denis Klemin. "The Problem of Stability of Gas-Condensate Mixture at Pore-Scale: The Study by Density Functional Hydrodynamics." E3S Web of Conferences 366 (2023): 01005. http://dx.doi.org/10.1051/e3sconf/202336601005.
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The method of the density functional hydrodynamics (DFH) is used to model compositional gas-condensate systems in natural cores at pore-scale. In previous publications, it has been demonstrated by the authors that DFH covers many diverse multiphase pore-scale phenomena, including fluid transport in RCA and SCAL measurements and complex EOR processes. The pore-scale modeling of multiphase flow scenarios is performed by means of the direct hydrodynamic (DHD) simulator, which is a numerical implementation of the DFH. In the present work, we consider the problem of pore-scale numerical modeling of three-phase system: residual water, hydrocarbon gas and hydrocarbon liquid with phase transitions between the two latter phases. Such situations happen in case of gas-condensate or volatile oil deposits, in oil deposits with gas caps or in EOR methods with gas injection. The corresponding field development modeling by the conventional reservoir simulators rely on phase permeabilities and capillary pressures, which are provided by laboratory core analysis experiments. But the problem with gas-liquid hydrocarbon mixtures is that in laboratory procedures it may be difficult or even impossible to achieve full thermodynamic equilibrium between phases as it must be under the reservoir conditions of the initial reservoir state. However, reaching the said equilibrium is quite possible in numerical simulation. In this work, the gas-liquid mixture, after being injected into core sample, would slowly undergo the rearrangement of the phases and chemical components in pores converging to the minimum of the Helmholtz energy functional. This process is adequately described by DFH with consequent impact on phase permeabilities and capillary pressure. We give pore-scale numerical examples of the described phenomena in a micro-CT porous rock model for a realistic gas-condensate mixture with quantitative characterization of phase transition kinetic effects.
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Zaripov, Farkhat. "Oscillating Cosmological Solutions in the Modified Theory of Induced Gravity." Advances in Astronomy 2019 (April 24, 2019): 1–15. http://dx.doi.org/10.1155/2019/1502453.
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This work is the extension of author’s research, where the modified theory of induced gravity (MTIG) is proposed. In the framework of the MTIG, the mechanism of phase transitions and the description of multiphase behavior of the cosmological scenario are proposed. The theory describes two systems (stages): Einstein (ES) and “restructuring” (RS). This process resembles the phenomenon of a phase transition, where different phases (Einstein’s gravitational systems, but with different constants) pass into each other. The hypothesis that such transitions are random and lead to stochastic behavior of cosmological parameters is considered. In our model, effective gravitational and cosmological “constants” arise, which are defined by the “mean square” of the scalar fields. These parameters can be compared with observations related to the phenomenon of dark energy. The aim of the work is to solve equations of MTIG for the case of a quadratic potential and compare them with observational cosmology data. The interaction of fundamental scalar fields and matter in the form of an ideal fluid is introduced and investigated. For the case of Friedmann-Robertson-Walker space-time, numerical solutions of nonlinear MTIG equations are obtained using the qualitative theory of dynamical systems and mathematical computer programs. For the case of a linear potential, examples joining of solutions, the ES and RS stages, of the evolution of the cosmological model are given. It is shown that the values of such parameters as “Hubble parameter” and gravitational and cosmological “constants” in the RS stage contain solutions oscillating near monotonically developing averages or have stochastic behavior due to random transitions to different stages (RS or ES). Such a stochastic behavior might be at the origin of the tension between CMB measurements of the value of the Hubble parameter today and its local measurements.
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Chen, Yueling, Xiangyu Pei, Huichao Liu, Yikan Meng, Zhengning Xu, Fei Zhang, Chun Xiong, Thomas C. Preston, and Zhibin Wang. "Influence of acidity on liquid–liquid phase transitions of mixed secondary organic aerosol (SOA) proxy–inorganic aerosol droplets." Atmospheric Chemistry and Physics 23, no. 17 (September 14, 2023): 10255–65. http://dx.doi.org/10.5194/acp-23-10255-2023.
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Abstract. The phase state and morphology of aerosol particles play a critical role in determining their effect on climate. While aerosol acidity has been identified as a key factor affecting multiphase chemistry and phase transitions, the impact of acidity on the phase transition of multicomponent aerosol particles has not been extensively studied in situ. In this work, we employed aerosol optical tweezers (AOT) to probe the impact of acidity on the phase transition behavior of levitated aerosol particles. Our results revealed that higher acidity decreases the separation relative humidity (SRH) of aerosol droplets mixed with ammonium sulfate (AS) and secondary organic aerosol (SOA) proxy, such as 3-methylglutaric acid (3-MGA), 1,2,6-hexanetriol (HEXT) and 2,5-hexanediol (HEXD) across aerosol pH in atmospheric conditions. Phase separation of organic acids was more sensitive to acidity compared to organic alcohols. We found the mixing relative humidity (MRH) was consistently higher than the SRH in several systems. Phase-separating systems, including 3-MGA / AS, HEXT / AS and HEXD / AS, exhibited oxygen-to-carbon ratios (O:C) of 0.67, 0.50 and 0.33, respectively. In contrast, liquid–liquid phase separation (LLPS) did not occur in the high-O:C system of glycerol / AS, which had an O:C ratio of 1.00. Additionally, the morphology of 42 out of the 46 aerosol particles that underwent LLPS was observed to be a core–shell structure. Our findings provide a comprehensive understanding of the pH-dependent LLPS in individual suspended aerosol droplets and pave the way for future research on phase separation of atmospheric aerosol particles.
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Son, Seongmin, and Seong Jun Bae. "The Development of a Transient Analysis Platform of Near-Critical CO2 Thermodynamic Systems via an Enthalpy-Based Implicit Continuous Eulerian Approach." Energies 17, no. 5 (February 27, 2024): 1126. http://dx.doi.org/10.3390/en17051126.
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This work presents the development and validation of an enthalpy-based implicit continuous Eulerian (ICE) solver, termed the near-critical ICE solver (NICES), for the analysis of near-critical CO2 thermodynamic systems. Traditional approaches relying on pressure and temperature as main inputs for the analysis have limitations in handling CO2 near the critical point, which exhibits unique characteristics and frequent phase changes. To overcome these limitations, this study proposes using enthalpy as a more suitable mathematical modeling approach. The NICES methodology employs the homogeneous equilibrium model and the Span and Wagner equations of state for CO2. This solver demonstrates improved numerical stability and computational speed compared to explicit calculation methods, as validated by frictionless heated pipe scenarios involving phase transitions near the critical point. The enthalpy-based NICES platform can predict thermohydraulics, including multiphase flows, without requiring specialized two-phase flow models.
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Golubev, A. N., and V. G. Belonogov. "The development of multi-channel control system for a multi-phase synchronous electric drive with improved vibration noise characteristics." Vestnik IGEU, no. 3 (June 30, 2020): 43–50. http://dx.doi.org/10.17588/2072-2672.2020.3.043-050.
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Constantly increasing requirements for the performance of electromechanical systems include the task of improving the vibration and noise characteristics of the electric drive. Currently, this problem is solved mainly by using traditional three-phase systems. The transition to a multiphase version of the electric drive construction opens up new opportunities for its solution. The aim of the study is to improve the vibration and noise characteristics of the electric drive through the development of a multiphase control system that provides targeted formation of the field configuration in the gap of a multiphase electric machine. To conduct the research, the model of a multiphase synchronous motor proposed by the authors was used. The model considers the spatial non-sinusoidality of the field distribution in the gap and enables to represent the engine as a set of parallel substructures, the number of which depends on the number of phases. The technique to design a synchronous motor with an arbitrary number of winding phases based on the field model of the machine has been proposed. The correctness of the results obtained is ensured by the real geometry of the magnetic circuit and steel saturation. The multi-channel control system of the electric drive, characterized by the targeted formation of field configuration in the gap of a multiphase electric machine has been proposed. The calculation model of the electric drive has been developed. The model combines the field model of the engine and the control system. The engine model is implemented in the ElСut software package, the control system model is implemented in the MatLab (Simulink) complex. Compared to the traditional three-phase design of the electric drive with a sinusoidal supply voltage, the options for forming a field in the gap of a synchronous motor considered in the article provide a reduction in ponderomotive force by 8–14 %. The engineering methodology for designing an m-phase synchronous permanent magnet motor with permanent magnets and the structure of the multi-channel control system can be applied when developing electric drives with improved vibration and noise characteristics.
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Shi, Hongwei, Feng Li, Wei Liu, Cen Liang, Xiaoli Ji, Mingsheng Long, Weiping Gong, Chunchang Wang, and Lei Shan. "Composition dependent phase structure, dielectric and electrostrain properties in (Sr0.7Bi0.2□0.1)TiO3–PbTiO3–Bi(Mg0.5Ti0.5)O3 systems." Journal of Physics D: Applied Physics 55, no. 18 (February 4, 2022): 185301. http://dx.doi.org/10.1088/1361-6463/ac4ec4.
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Abstract Composition dependent transitions from normal ferroelectrics to nonergodic and finally to ergodic relaxor phase are observed in 0.7(Sr0.7Bi0.2□0.1)TiO3–(0.3 − x)PbTiO3–xBi(Mg0.5Ti0.5)O3 system (SBT–PT–xBMT, □ represents A–site vacancy). Rietveld refinement results show that with increasing BMT content, the system experiences a gradual transition from coexistence of pseudocubic and tetragonal (P c + T) to P c phase. The ferroelectric–relaxor phase transition and freezing temperature gradually decreases with addition of BMT content accompanied by an enhanced relaxor degree, which produces local disorder and polar nanodomains. This is also verified by Raman spectra and piezoelectric force microscopic analysis. The P–E loops transform from square to slant and finally to slim shape with increasing BMT component and an electric field-induced strain of ∼0.21% with ultralow hysteresis of ∼3.7% is obtained for x = 0.04 composition. The underlying mechanism for the large strain with low hysteresis lies in the existence of nonergodic and ergodic relaxor phase boundary and polar nanodomains at room temperature. Additionally, the multiphase coexistence contributes to a flatten free energy profile and thus contributing to such superior performances, as explained by a modified phenomenological model. High electrostrain with ultralow hysteresis in SBT–PT–xBMT systems are promising candidates in high–precision actuator applications.
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Xu, Jian Xin, Hua Wang, Jian Jun Wang, Shi Bo Wang, Dao Fei Zhu, and Guo Feng Fan. "CFD Simulation of Mixing Effects in Gas-Liquid-Solid Stirred Reactor." Advanced Materials Research 383-390 (November 2011): 5778–84. http://dx.doi.org/10.4028/www.scientific.net/amr.383-390.5778.
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In order to analyze the complex phase transition in the gas-liquid-solid three-phase mixing systems and to predict gas-liquid-solid multiphase mixing time, a novel method combined image processing technology, computational homology and CFD (Computational Fluid Dynamics) numerical simulation is introduced in this study. Firstly, the volume of fluid (VOF) multiphase flow model in FLUENT software is used for the simulation of fluid characteristics. Secondly the patterns produced by phase transition in the stirred tank are binaryzed. Finally evolution profile of the zeroth dimensional Betti numbers and the first dimensional Betti numbers in time series are obtained separately. In fact,some aggregates still remain in the tank after the homogeneous mixing.Comparing with the fractal method to characterize the mixing time, the result shows that this method not only can predict the gas-liquid-solid mixing time by the zeroth dimenstional Betti numbers, but also can predict the amount of these aggregates in the stired tank by the first dimenstional Betti numbers, leading to a useful parameter to characterize the non-uniformity of gas-liquid-solid mixing.
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Filimonov, M. Yu, and N. A. Vaganova. "Some problems of heat and mass transfer during the operation of engineering systems in multiphase environments." Diagnostics, Resource and Mechanics of materials and structures, no. 4 (August 2023): 15–28. http://dx.doi.org/10.17804/2410-9908.2023.4.015-028.
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Three types of problems related to problems of heat and mass transfer in the soil are considered. The first class of problems deals with the diagnostics of damage of underground pipelines by thermal fields on the soil surface. The second type studies the dynamics of changes in the temperature of a geothermal reservoir depending on the temperature of the water entering this reservoir and the pressure gap between injection and production wells. The third-type problems consider the propagation of non-stationary thermal fields in the soil from operated engineering systems in the permafrost. The main attention is paid to long-term forecasting of the propagation of non-stationary thermal fields in the frozen soil between operating production wells of northern oil and gas fields. In problems of the first two classes, which served as a basis for the development of problems of the third type, water filtration in the soil is considered, and thermal fields propagate in single-phase media. The third-class problems take into account possible phase transitions in the soil when describing non-stationary thermal fields in permafrost soils, leading to Stefan-type problems. Accounting for water migration for the specific third-type problems on the determination of the radius of frozen soil thawing from production wells in northern oil and gas fields does not significantly affect this process since lateral water migration above the groundwater level is minimal. Therefore, only the latent heat of the initial water content is taken into consideration. This paper discusses a mathematical model containing the most significant physical and climatic data affecting the distribution of thermal fields in permafrost rocks and presents the results of numerical calculations.
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Cristea, Iuliana, Beghenci Silapov, Iulian Nistor, and Timur Chis. "Numerical Modeling of Two-Phase Liquid-Solid Movement through Pipes." Journal of Advances in Mathematics and Computer Science 39, no. 4 (March 30, 2024): 90–99. http://dx.doi.org/10.9734/jamcs/2024/v39i41884.
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The oil industry is that branch of the world economy that provides energy resources for humanity and the transition to energy produced from renewable resources. That is precisely why the study of mass transfer (the transport of petroleum fluids through pipelines) represents one of the primary activities in scientific research; the role of this discipline is to provide theoretical support to understand the phenomena that govern these technological processes. One of the industrial applications of multiphase transport is the movement of multiphase fluids (liquid-solid) through pipes and especially the phenomena of separation of these phases. Due to the depletion of oil and gas resources associated with deposits discovered before 1990, the extraction of these petroleum fluids faces the presence in the composition of large amounts of sand, salt or paraffin (solid phase), dissolved solids, and present in the liquid phase, which makes the activity of separating, removing and cleaning petroleum fluids from associated sediments, an increasingly present and functional industrial activity for the development of oil and gas exploitations. That is precisely why a work that analyzes the numerical modeling of the separation process and the simulation of the solid-liquid transport processes through the central pipeline systems is necessary for the economic and detailed design of the machines associated with this industry. This paper analyzes the behavior of various solid substances in the flow of petroleum liquids. As a result of the laboratory data, we created a numerical model associated with these two-phase flows.
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McCollum, Gin. "Sensorimotor coordination and the structure of space." Journal of Vestibular Research 13, no. 4-6 (December 28, 2003): 157–72. http://dx.doi.org/10.3233/ves-2003-134-602.
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Embedded in neural and behavioral organization is a structure of sensorimotor space. Both this embedded spatial structure and the structure of physical space inform sensorimotor control. This paper reviews studies in which the gravitational vertical and horizontal are crucial. The mathematical expressions of spatial geometry in these studies indicate methods for investigating sensorimotor control in freefall. In freefall, the spatial structure introduced by gravitation – the distinction between vertical and horizontal – does not exist. However, an astronaut arriving in space carries the physiologically-embedded distinction between horizontal and vertical learned on earth. The physiological organization based on this distinction collapses when the strong otolith activity and other gravitational cues for sensorimotor behavior become unavailable. The mathematical methods in this review are applicable in understanding the changes in physiological organization as an astronaut adapts to sensorimotor control in freefall. Many mathematical languages are available for characterizing the logical structures in physiological organization. Here, group theory is used to characterize basic structure of physical and physiological spaces. Dynamics and topology allow the grouping of trajectory ranges according to the outcomes or attractors. The mathematics of ordered structures express complex orderings, such as in multiphase movements in which different parts of the body are moving in different phase sequences. Conditional dynamics, which combines dynamics with the mathematics of ordered structures, accommodates the parsing of movement sequences into trajectories and transitions. Studies reviewed include those of the sit-to-stand movement and early locomotion, because of the salience of gravitation in those behaviors. Sensorimotor transitions and the conditions leading to them are characterized in conditional dynamic control structures that do not require thinking of an organism as an input-output device. Conditions leading to sensorimotor transitions on earth assume the presence of a gravitational vertical which is lacking in space. Thus, conditions used on earth for sensorimotor transitions may become ambiguous in space. A platform study in which sensorimotor transition conditions are ambiguous and are related to motion sickness is reviewed.
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Spiridigliozzi, Luca, Claudio Ferone, Raffaele Cioffi, Grazia Accardo, Domenico Frattini, and Gianfranco Dell’Agli. "Entropy-Stabilized Oxides owning Fluorite Structure obtained by Hydrothermal Treatment." Materials 13, no. 3 (January 24, 2020): 558. http://dx.doi.org/10.3390/ma13030558.
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Entropy-Stabilized Oxides (ESO) is a modern class of multicomponent advanced ceramic materials with attractive functional properties. Through a five-component oxide formulation, the configurational entropy is used to drive the phase stabilization over a reversible solid-state transformation from a multiphase to a single-phase state. In this paper, a new transition metal/rare earth entropy-stabilized oxide, with composition Ce0.2Zr0.2Y0.2Gd0.2La0.2O2−δ, was found after several investigations on alternative candidate systems. X-Ray Diffraction (XRD) analyses of calcined powders pointed out different behavior as a function of the composition and a single-phase fluorite structure was obtained after a specific thermal treatment at 1500 °C. Powders presented the absence of agglomeration, so that the sintered specimen exhibited sufficient densification with a small porosity, uniformly distributed in the sample.
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Liu, Weiling, Chao Tan, and Feng Dong. "Local characteristic of horizontal air–water two-phase flow by wire-mesh sensor." Transactions of the Institute of Measurement and Control 40, no. 3 (September 8, 2016): 746–61. http://dx.doi.org/10.1177/0142331216665689.
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Two-phase flow widely exists in many industries. Understanding local characteristics of two-phase flow under different flow conditions in piping systems is important to design and optimize the industrial process for higher productivity and lower cost. Air–water two-phase flow experiments were conducted with a 16×16 conductivity wire-mesh sensor (WMS) in a horizontal pipe of a multiphase flow facility. The cross-sectional void fraction time series was analysed by the probability density function (PDF), which described the void fraction fluctuation at different flow conditions. The changes and causes of PDFs during a flow regime transition were analysed. The local structure and flow behaviour were characterized by the local flow spectrum energy analysis and the local void fraction distribution (horizontal, vertical and radial direction) analysis. Finally, three-dimensional transient flow fluctuation energy evolution and characteristic scale distribution based on wavelet analysis of air–water two-phase flow were presented, which revealed the structural features of each phase in two-phase flow.
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Avis, Samuel J., Jack R. Panter, and Halim Kusumaatmaja. "A robust and memory-efficient transition state search method for complex energy landscapes." Journal of Chemical Physics 157, no. 12 (September 28, 2022): 124107. http://dx.doi.org/10.1063/5.0102145.
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Locating transition states is crucial for investigating transition mechanisms in wide-ranging phenomena, from atomistic to macroscale systems. Existing methods, however, can struggle in problems with a large number of degrees of freedom, on-the-fly adaptive remeshing and coarse-graining, and energy landscapes that are locally flat or discontinuous. To resolve these challenges, we introduce a new double-ended method, the Binary-Image Transition State Search (BITSS). It uses just two states that converge to the transition state, resulting in a fast, flexible, and memory-efficient method. We also show that it is more robust compared to existing bracketing methods that use only two states. We demonstrate its versatility by applying BITSS to three very different classes of problems: Lennard-Jones clusters, shell buckling, and multiphase phase-field models.
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Pliss, Evgenii M., and Mikhail E. Soloviev. "Magnetic Field Effect on the Oxidation of Unsaturated Compounds by Molecular Oxygen." Magnetochemistry 8, no. 4 (April 11, 2022): 44. http://dx.doi.org/10.3390/magnetochemistry8040044.
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A quantum-chemical analysis of the effect of a constant magnetic field on radical formation in the processes of chain oxidation of organic compounds by molecular oxygen is presented. The calculation of the total electronic energies and thermodynamic functions of the compounds involved in the reactions was performed by the density functional method with the hybrid exchange-correlation functional of Becke, Lee, Yang and Parr DFT B3LYP/6-311G** using the NWChem software package. The effect of the magnetic field on the individual stages of chain oxidation is associated with the evolution of radical pairs. It is assumed that the dipole–dipole interaction in a radical pair is not averaged by the diffusion of radicals and should be taken into account. To a large extent, the magnetic field effect (MFE) value is influenced by the ratio between the relaxation time of the oscillatory-excited state in the radical pair (tvib) and the relaxation time of the inter-combination transitions (tst). Although the developed technique refers to liquid-phase reactions, it can be used to study the MFE for oxidation of biologically significant compounds in multiphase systems, such as micelles, liposomes and membranes.
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Xiao, Yao, Tao Wang, Yan-Fang Zhu, Hai-Yan Hu, Shuang-Jie Tan, Shi Li, Peng-Fei Wang, et al. "Large-Scale Synthesis of the Stable Co-Free Layered Oxide Cathode by the Synergetic Contribution of Multielement Chemical Substitution for Practical Sodium-Ion Battery." Research 2020 (October 19, 2020): 1–16. http://dx.doi.org/10.34133/2020/1469301.
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The O3-type layered oxide cathodes for sodium-ion batteries (SIBs) are considered as one of the most promising systems to fully meet the requirement for future practical application. However, fatal issues in several respects such as poor air stability, irreversible complex multiphase evolution, inferior cycling lifespan, and poor industrial feasibility are restricting their commercialization development. Here, a stable Co-free O3-type NaNi0.4Cu0.05Mg0.05Mn0.4Ti0.1O2 cathode material with large-scale production could solve these problems for practical SIBs. Owing to the synergetic contribution of the multielement chemical substitution strategy, this novel cathode not only shows excellent air stability and thermal stability as well as a simple phase-transition process but also delivers outstanding battery performance in half-cell and full-cell systems. Meanwhile, various advanced characterization techniques are utilized to accurately decipher the crystalline formation process, atomic arrangement, structural evolution, and inherent effect mechanisms. Surprisingly, apart from restraining the unfavorable multiphase transformation and enhancing air stability, the accurate multielement chemical substitution engineering also shows a pinning effect to alleviate the lattice strains for the high structural reversibility and enlarges the interlayer spacing reasonably to enhance Na+ diffusion, resulting in excellent comprehensive performance. Overall, this study explores the fundamental scientific understandings of multielement chemical substitution strategy and opens up a new field for increasing the practicality to commercialization.
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Zahedy, Fakhri S., Hsiao-Wen Chen, Thomas M. Cooper, Erin Boettcher, Sean D. Johnson, Gwen C. Rudie, Mandy C. Chen, et al. "The cosmic ultraviolet baryon survey (CUBS) – III. Physical properties and elemental abundances of Lyman-limit systems at z < 1." Monthly Notices of the Royal Astronomical Society 506, no. 1 (June 22, 2021): 877–902. http://dx.doi.org/10.1093/mnras/stab1661.
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ABSTRACT We present a systematic investigation of physical conditions and elemental abundances in four optically thick Lyman-limit systems (LLSs) at z = 0.36–0.6 discovered within the cosmic ultraviolet baryon survey (CUBS). Because intervening LLSs at z < 1 suppress far-UV (ultraviolet) light from background QSOs, an unbiased search of these absorbers requires a near-UV-selected QSO sample, as achieved by CUBS. CUBS LLSs exhibit multicomponent kinematic structure and a complex mix of multiphase gas, with associated metal transitions from multiple ionization states such as C ii, C iii, N iii, Mg ii, Si ii, Si iii, O ii, O iii, O vi, and Fe ii absorption that span several hundred km s−1 in line-of-sight velocity. Specifically, higher column density components (log N(H i)/cm−2≳ 16) in all four absorbers comprise dynamically cool gas with $\langle T \rangle =(2\pm 1) \times 10^4\,$K and modest non-thermal broadening of $\langle b_\mathrm{nt} \rangle =5\pm 3\,$km s−1. The high quality of the QSO absorption spectra allows us to infer the physical conditions of the gas, using a detailed ionization modelling that takes into account the resolved component structures of H i and metal transitions. The range of inferred gas densities indicates that these absorbers consist of spatially compact clouds with a median line-of-sight thickness of $160^{+140}_{-50}$ pc. While obtaining robust metallicity constraints for the low density, highly ionized phase remains challenging due to the uncertain $N\mathrm{(H\, {\small I})}$, we demonstrate that the cool-phase gas in LLSs has a median metallicity of $\mathrm{[\alpha /H]_{1/2}}=-0.7^{+0.1}_{-0.2}$, with a 16–84 percentile range of [α/H] = (−1.3, −0.1). Furthermore, the wide range of inferred elemental abundance ratios ([C/α], [N/α], and [Fe/α]) indicate a diversity of chemical enrichment histories. Combining the absorption data with deep galaxy survey data characterizing the galaxy environment of these absorbers, we discuss the physical connection between star-forming regions in galaxies and diffuse gas associated with optically thick absorption systems in the z < 1 circumgalactic medium.
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Ishimoto, Jun, and Kenjiro Kamijo. "Numerical Analysis of Cavitating Flow of Liquid Helium in a Converging-Diverging Nozzle." Journal of Fluids Engineering 125, no. 5 (September 1, 2003): 749–57. http://dx.doi.org/10.1115/1.1601253.
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The fundamental characteristics of the two-dimensional cavitating flow of liquid helium through a horizontal converging-diverging nozzle near the lambda point are numerically investigated to realize the further development and high performance of new multiphase superfluid cooling systems. First, the governing equations of the cavitating flow of liquid helium based on the unsteady thermal nonequilibrium multifluid model with generalized curvilinear coordinates system are presented, and several flow characteristics are numerically calculated, taking into account the effect of superfluidity. Based on the numerical results, the two-dimensional structure of the cavitating flow of liquid helium though a horizontal converging-diverging nozzle is shown in detail, and it is also found that the generation of superfluid counterflow against normal fluid flow based on the thermomechanical effect is conspicuous in the large gas phase volume fraction region where the liquid to gas phase change actively occurs. Furthermore, it is clarified that the mechanism of the He I to He II phase transition caused by the temperature decrease is due to the deprivation of latent heat for vaporization from the liquid phase.
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Barochkin, Alexey. "Matrix Method for Modelling of Multicomponent and Multistream Energy Systems and Installations of Thermal Power Plants." Problems of the Regional Energetics, no. 4(52) (November 2021): 59–67. http://dx.doi.org/10.52254/1857-0070.2021.4-52.06.
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The aim of this work is to increase the operational efficiency of the multicomponent multithreaded power units and systems of the TPP using modeling, calculation and optimization. The goal is achieved by solving the following tasks: development of the tasks’ classification system and a unified methodology for the mathematical description of energy formation and mass flows’ processes in multicomponent and multithreaded power units of the TPP; development of a model of a steam turbine power unit; development of a model of heat and mass transfer processes in multi-stage multistream multiphase systems. The most significant results obtained were: the developed unified methodology for the matrix description of the processes of energy and mass flows’ formation in multicomponent multistream energy systems of the TPP. Within the framework of the proposed methodology, a model of a steam turbine power was developed; model solutions were obtained and analyzed in order to calculate the energy characteristics of a heating turbine unit, the reliability and validity of the proposed approach was shown, a mathematical model of multistream multi-stage heat exchange systems were developed. The significance of the results obtained consisted in the development of a simple but informative mathematical model of a thermal power plant turbine generator and a model of multistream multi-stage heat exchange systems, each stage of which can have an arbitrary number of input and output flows with a possible phase transition in heat carriers.ave an arbitrary number of input and output flows with a possible phase transition in heat carriers.
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Pradeep, Jayadev, Sriram Sankar, T. M. Umasree, Anand Narayanan, Vikram Khaire, Matthew Gebhardt, Sameer, and Jane C. Charlton. "Solar-metallicity gas in the extended halo of a galaxy at z ∼ 0.12." Monthly Notices of the Royal Astronomical Society 493, no. 1 (January 22, 2020): 250–66. http://dx.doi.org/10.1093/mnras/staa184.
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ABSTRACT We present the detection and analysis of a weak low-ionization absorber at z = 0.121 22 along the sightline of the blazar PG 1424+240, using spectroscopic data from both HST/COS and STIS. The absorber is a weak Mg ii analogue, with an incidence of weak C ii and Si ii, along with multicomponent C iv and O vi. The low ions are tracing a dense (nH ∼ 10−3 cm−3) parsec-scale cloud of solar or higher metallicity. The kinematically coincident higher ions are either from a more diffuse (nH ∼ 10−5–10−4 cm−3) photoionized phase of kiloparsec-scale dimensions or are tracing a warm (T ∼ 2 × 105 K) collisionally ionized transition temperature plasma layer. The absorber resides in a galaxy overdense region, with 18 luminous (>L*) galaxies within a projected radius of 5 Mpc and velocity of 750 km s−1. The multiphase properties, high metallicity, and proximity to a 1.4L* galaxy, at ρ ∼ 200 kpc and separation |Δv| = 11 km s−1, favour the possibility of the absorption tracing circumgalactic gas. The absorber serves as an example of weak Mg ii–O vi systems as a means to study multiphase high-velocity clouds in external galaxies.
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Anufriev, Dmitrii, and Artem Holodov. "Description of approaches to the study of decentralized complex systems in the management of the regional construction cluster." MATEC Web of Conferences 251 (2018): 05008. http://dx.doi.org/10.1051/matecconf/201825105008.
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Regional construction cluster, which is considered as a decentralized socio-economic system, territorially localized within the region, consisting of interconnected enterprises of construction and related industries. Development of a method for centralized management of a complex socio-economic system based on the integration of simulation approaches. Approaches are considered that allow the transition from consideration of a decentralized complex system to the management of a centralized structure through the introduction of image agents and the formation of a multiphase queuing network, where the four-channel queuing system with expectations is considered as the phase. The structure of the simulation model is presented, which makes it possible to model the functionality of the regional construction cluster. The approaches to integration of the agent approach with modules of system dynamics and modules implementing the discrete-event approach for simulation of business pro-cesses in a complex socio-economic system that take into account the probabilistic structure of the emerging processes are considered in the article.
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Pei, Yuxin, Nanlin Zhang, Huaxing Zhou, Shengchuan Zhang, Wei Zhang, and Jinhong Zhang. "Simulation of multiphase flow pattern, effective distance and filling ratio in hydraulic fracture." Journal of Petroleum Exploration and Production Technology 10, no. 3 (November 23, 2019): 933–42. http://dx.doi.org/10.1007/s13202-019-00799-y.
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AbstractHydraulic fracturing is a key measure to increase production and transform oil and gas reservoirs, which plays an important role in oil and gas field development. Common hydraulic fracturing is of inevitable bottlenecks such as difficulty in sand adding, sand plugging, equipment wearing and fracturing fluid damage. To solve these problems, a new type of fracturing technology, i.e., the self-propping fracturing technology is currently under development. Technically, the principle is to inject a self-propping fracturing liquid system constituting a self-propping fracturing liquid and a channel fracturing liquid into the formation. Self-propping fracturing liquid changes from liquid to solid through phase transition under the formation temperature, replacing proppants such as ceramic particles and quartz sand to achieve the purpose of propping hydraulic fractures. The flow pattern, effective distance and filling ratio of the self-propping fracturing liquid system in the hydraulic fracture are greatly affected by the parameters such as the fluid leak-off rate, surface tension and injection velocity. In this paper, a set of mathematical models for the flow distribution of self-propping fracturing liquid system considering fluid leak-off was established to simulate the flow pattern, effective distance, as well as filling ratio under different leak-off rates, surface tensions and injection velocities. The mathematical model was verified by physical experiments, proving that the mathematical model established herein could simulate the flow of self-propping fracturing liquid systems in hydraulic fractures. In the meantime, these results have positive impacts on the research of interface distribution of liquid–liquid two-phase flow.
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Ahoranta, Jussi, Alexis Finoguenov, Massimiliano Bonamente, Evan Tilton, Nastasha Wijers, Sowgat Muzahid, and Joop Schaye. "Discovery of a multiphase O VI and O VII absorber in the circumgalactic/intergalactic transition region." Astronomy & Astrophysics 656 (December 2021): A107. http://dx.doi.org/10.1051/0004-6361/202038021.
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Aims. The observational constraints on the baryon content of the warm-hot intergalactic medium (WHIM) rely almost entirely on far ultraviolet (FUV) measurements. However, cosmological, hydrodynamical simulations predict strong correlations between the spatial distributions of FUV and X-ray absorbing WHIM. We investigate this prediction by analyzing XMM-Newton X-ray counterparts of FUV-detected intergalactic O VI absorbers known from FUSE and HST/STIS data, thereby aiming to gain understanding on the properties of the hot component of FUV absorbers and to compare this information to the predictions of simulations. Methods. We study the X-ray absorption at the redshift of the only significantly detected O VI absorber in the Ton S 180 sightline’s FUV spectrum, found at zOVI = 0.04579 ± 0.00001. We characterize the spectral properties of the O VI-O VIII absorbers and explore the ionization processes behind the measured absorption. The observational results are compared to the predicted warm-hot gas properties in the EAGLE simulation to infer the physical conditions of the absorber. Results. We detect both O VI and O VII absorption at a 5σ confidence level, whereas O VIII absorption is not significantly detected. Collisional ionization equilibrium (CIE) modeling constrains the X-ray absorbing gas temperature to log TCIE (K) = 6.22 ± 0.05 with a total hydrogen column density NH = 5.8−2.2+3.0 × Z⊙/Zabs × 1019 cm−2. This model predicts an O VI column density consistent with that measured in the FUV, but our limits on the O VI line width indicate > 90% likelihood that the FUV-detected O VI arises from a different, cooler phase. We find that the observed absorber lies about a factor of two further away from the detected galaxies than is the case for similar systems in EAGLE Conclusions. The analysis suggests that the detected O VI and O VII trace two different – warm and hot – gas phases of the absorbing structure at z ≈ 0.046, of which the hot component is likely in collisional ionization equilibrium. As the baryon content information of the studied absorber is primarily imprinted in the X-ray band, understanding the abundance of similar systems helps to define the landscape for WHIM searches with future X-ray telescopes. Our results highlight the crucial role of line widths for the interpretation and detectability of WHIM absorbers.
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Ling, Y., D. Fuster, G. Tryggvason, and S. Zaleski. "A two-phase mixing layer between parallel gas and liquid streams: multiphase turbulence statistics and influence of interfacial instability." Journal of Fluid Mechanics 859 (November 16, 2018): 268–307. http://dx.doi.org/10.1017/jfm.2018.825.
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The two-phase mixing layer formed between parallel gas and liquid streams is an important fundamental problem in turbulent multiphase flows. The problem is relevant to many industrial applications and natural phenomena, such as air-blast atomizers in fuel injection systems and breaking waves in the ocean. The velocity difference between the gas and liquid streams triggers an interfacial instability which can be convective or absolute depending on the stream properties and injection parameters. In the present study, a direct numerical simulation of a two-phase gas–liquid mixing layer that lie in the absolute instability regime is conducted. A dominant frequency is observed in the simulation and the numerical result agrees well with the prediction from viscous stability theory. As the interfacial wave plays a critical role in turbulence transition and development, the temporal evolution of turbulent fluctuations (such as the enstrophy) also exhibits a similar frequency. To investigate the statistical response of the multiphase turbulence flow, the simulation has been run for a long physical time so that time-averaging can be performed to yield the statistically converged results for Reynolds stresses and the turbulent kinetic energy (TKE) budget. An extensive mesh refinement study using from 8 million to about 4 billions cells has been performed. The turbulent dissipation is shown to be highly demanding on mesh resolution compared with other terms in TKE budget. The results obtained with the finest mesh are shown to be close to converged results of turbulent dissipation which allow us to obtain estimations of the Kolmogorov and Hinze scales. The estimated Kolmogorov scale is found to be similar to the cell size of the finest mesh used here. The computed Hinze scale is significantly larger than the size of droplets observed and does not seem to be a relevant length scale to describe the smallest size of droplets formed in atomization.
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Gahleitner, Markus, Tung Pham, and Doris Machl. "Polyolefin Blends with Selectively Crosslinked Disperse Phase Based on Silane-Modified Polyethylene." Polymers 15, no. 24 (December 13, 2023): 4692. http://dx.doi.org/10.3390/polym15244692.
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Polypropylene-based multiphase compositions with a disperse elastomer phase provide superior impact strength. Making this property indifferent to processing steps requires stabilization of the morphology of these materials. Various approaches have been tested over time, each of which shows limitations in terms of performance or applicability. Using polyethylene (PE) homo- and copolymers capable of silane-based crosslinking as modifiers was explored in the present study, which allows decoupling of the mixing and crosslinking processes. Commercial silane-copolymerized low-density PE (LD-PEX) from a high-pressure process and silane-grafted high-density PE (HD-PEX) were studied as impact modifiers for different types of PP copolymers, including non-modified reference PE grades, LDPE and HDPE. Blends based on ethylene–propylene random copolymers (PPR) and based on impact- (PPI) and random-impact (PPRI) copolymers show improvements of the stiffness–impact balance; however, to different degrees. While the absolute softest and most ductile compositions are achieved with the already soft PPRI copolymer base, the strongest relative effects are found for the PPR based blends. Modifiers with lower density are clearly superior in the toughening effect, with the LD-PEX including acrylate as second comonomer sticking out due to its glass transition around −40 °C. The impact strength improvement found in most compositions (except at very high content) results, however, not from the expected phase stabilization. For comparable systems, particle sizes are normally higher with crosslinking, probably because the process already starts during mixing. Thermoplastic processability could be retained in all cases, but the drop in melt flow rate limits the practical applicability of such systems.
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KIERZKOWSKA-PAWLAK, Hanna, Lucyna BILIŃSKA, and Jacek TYCZKOWSKI. "Perspective Applications of Plasma-Deposited Thin Film Nanocatalysts on Structured Supports: From CO2 Capture to Wastewater Treatment." Ecological Chemistry and Engineering S 30, no. 4 (December 1, 2023): 489–504. http://dx.doi.org/10.2478/eces-2023-0044.
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Abstract The urgent need for sustainable solutions to environmental challenges has led to significant research efforts towards innovative processes and technologies capable of addressing global issues such as carbon dioxide (CO2) capture and valorisation as well as efficient water-reuse cycles. The majority of processes involved in CO2 conversion require highly active catalysts for practical implementation. Concurrently, wastewater treatment technologies, critical for achieving sustainable water reuse, often rely on complex multi-stage systems that incorporate advanced oxidation processes (AOPs). Optimising reaction conditions and exploring unconventional approaches to catalytic system design are crucial for enhancing the efficiency of these processes. Among the emerging solutions, the application of thin-film catalysts deposited by cold plasma onto various structured supports has shown promising potential for improving process performance to meet environmental goals. This paper discusses recent advancements in the development of thin-film nanocatalysts based on cost-effective transition metals. It highlights their application in gas-phase reactions, such as CO2 hydrogenation to value-added products, as well as innovative uses in multiphase gas-liquid systems, including CO2 capture in aqueous solvents and the ozonation of wastewater.
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Gao, Zhong-Ke, Dong-Mei Lv, Wei-Dong Dang, Ming-Xu Liu, and Xiao-Lin Hong. "Multilayer Network from Multiple Entropies for Characterizing Gas-Liquid Nonlinear Flow Behavior." International Journal of Bifurcation and Chaos 30, no. 01 (January 2020): 2050014. http://dx.doi.org/10.1142/s0218127420500145.
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Characterizing nonlinear dynamic behaviors underlying multiphase flow has attracted considerable attention from the nonlinear research field. In this paper, the authors develop a novel multiple entropy-based multilayer network (MEMN) for exploring the complex gas-liquid two-phase flow. At first, we carry out the gas-liquid flow experiments to get the multichannel measurements. Then, MEMN is constructed based on the fusion of three nonlinear entropies, namely weighted permutation entropy (WPE), wavelet packet energy entropy (WPEE), and amplitude entropy (AE). For each derived projection network of MEMN, spectral radius and global clustering coefficient are both calculated and they allow effectively uncovering the nonlinear flow behaviors in the transition of different gas-liquid flow patterns. In addition, we perform wavelet time-frequency representation for the two typical flow patterns and the results support our findings well. All these demonstrate that our MEMN framework can effectively characterize the nonlinear evolution of gas-liquid flow from the perspective of complex network theory. And this also provides a novel idea for studying nonlinear complex systems from the observed multivariate time series.
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Yu, Jidu, Jidong Zhao, Shiwei Zhao, and Weijian Liang. "Multiphysics simulation of freezing and thawing granular media using material point method." IOP Conference Series: Earth and Environmental Science 1330, no. 1 (May 1, 2024): 012035. http://dx.doi.org/10.1088/1755-1315/1330/1/012035.
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Abstract In this paper, a fully coupled thermo-hydro-mechanical material point method, applicable to liquid-saturated porous systems undergoing large deformations and phase transitions, is presented. A mathematical framework was established based on multiphasic mixture theory and fundamental physical conservation laws, rather than using phenomenological or semi-empirical equations. A fractional-step-based semi-implicit solution scheme was proposed to solve the coupled formulations within the framework of the generalized interpolation material point method. The proposed method was validated using several benchmark examples, including the talik closure and thaw consolidation. Its performance in simulating climate-driven large deformation problems was further demonstrated by simulating the settlement of a rigid footing on thawing ground. This paper presents an innovative and rigorous framework for predicting the impact of climate change on engineering practices.
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Sparre, Martin, Christoph Pfrommer, and Kristian Ehlert. "Interaction of a cold cloud with a hot wind: the regimes of cloud growth and destruction and the impact of magnetic fields." Monthly Notices of the Royal Astronomical Society 499, no. 3 (October 14, 2020): 4261–81. http://dx.doi.org/10.1093/mnras/staa3177.
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ABSTRACT Multiphase galaxy winds, the accretion of cold gas through galaxy haloes, and gas stripping from jellyfish galaxies are examples of interactions between cold and hot gaseous phases. There are two important regimes in such systems. A sufficiently small cold cloud is destroyed by the hot wind as a result of Kelvin–Helmholtz instabilities, which shatter the cloud into small pieces that eventually mix and dissolve in the hot wind. In contrast, stripped cold gas from a large cloud mixes with the hot wind to intermediate temperatures, and then becomes thermally unstable and cools, causing a net accretion of hot gas to the cold tail. Using the magneto-hydrodynamical code arepo, we perform cloud crushing simulations and test analytical criteria for the transition between the growth and destruction regimes to clarify a current debate in the literature. We find that the hot-wind cooling time sets the transition radius and not the cooling time of the mixed phase. Magnetic fields modify the wind–cloud interaction. Draping of wind magnetic field enhances the field upstream of the cloud, and fluid instabilities are suppressed by a turbulently magnetized wind beyond what is seen for a wind with a uniform magnetic field. We furthermore predict jellyfish galaxies to have ordered magnetic fields aligned with their tails. We finally discuss how the results of idealized simulations can be used to provide input to subgrid models in cosmological (magneto-)hydrodynamical simulations, which cannot resolve the detailed small-scale structure of cold gas clouds in the circumgalactic medium.
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Pruess, Karsten. "A Practical Method for Modeling Fluid and Heat Flow in Fractured Porous Media." Society of Petroleum Engineers Journal 25, no. 01 (February 1, 1985): 14–26. http://dx.doi.org/10.2118/10509-pa.
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Abstract A multiple interacting continua (MINC) method is presented, which is applicable for numerical simulation presented, which is applicable for numerical simulation of heat and multiphase fluid flow in multidimensional, fractured porous media. This method is a generalization of the double-porosity concept. The partitioning of the flow domain into computational volume elements is based on the criterion of approximate thermodynamic equilibrium at all times within each element. The thermodynamic conditions in the rock matrix are assumed to be controlled primarily by the distance from the fractures, which leads to the use of nested gridblocks. The MINC concept is implemented through the integral finite difference (IFD) method. No analytical approximations are made for coupling between the fracture and matrix continua. Instead, the transient flow of fluid and heat between matrix and fractures is treated by a numerical method. The geometric parameters needed in simulation are preprocessed from a specification of fracture spacings and apertures and geometry of the matrix blocks. The numerical implementation of the MINC method is verified by comparison with the analytical solution of Warren and Root. Illustrative applications are given for several geothermal reservoir engineering problems. Introduction In this paper, we present a numerical method for simulating transient nonisothermal, two-phase flow of water in fractured porous medium. The method is base on a generalization of a concept originally proposed by Barenblatt et al. and introduced into the petroleum literature by Warren and Root, Odeh, and others in the form of what has been termed the "double-porosity" model. The essence of this approach is that in a fractured porous medium, fractures are characterized by much porous medium, fractures are characterized by much larger diffusivities (and hence, much smaller response times) than the rock matrix. Therefore, the early system response is influenced by the matrix. In seeking to analytically solve such a system, all fractures were grouped into one continuum and all the matrix blocks into another, resulting in two interacting continua coupled through a mass transfer function determined by the size and shape of the blocks, as well as the local difference in potentials between the two continua. Later, Kazemi and Duguid and Lee incorporated the double-porosity concept into a numerical model. For a more detailed description of the concept and its application, see Refs. 6 through 8. Very little work has been done in investigating nonisothermal, two-phase fluid flow in fractured porous media. Moench and coworkers used the discrete fracture approach to study the behavior of fissured, vapor-dominated geothermal reservoirs. The purpose of our work is first to generalize the double-porosity concept into one of many interacting continua. We then incorporate the MINC model into a simulator for nonisothermal transport of a homogeneous two-phase fluid (water and steam) in multidimensional systems. Our approach is considerably broader in scope and more general than any previous models discussed in the literature. The MINC previous models discussed in the literature. The MINC method permits treatment of multiphase fluids with large and variable compressibility and allows for phase transitions with latent heat effects, as well as for coupling between fluid and heat flow. The transient interaction between matrix and fractures is treated in a realistic way. Although the model can permit alternative formulations for the equation of motion, we shall assume that, macroscopically, each continuum obeys Darcy's law; in particular, we shall use the "cubic law" for the flow of particular, we shall use the "cubic law" for the flow of fluids in fracture. While the methodology presented in this paper is generally applicable to multiphase compositional thermal systems, our illustrative calculations were restricted to geothermal reservoir problems. The numerical method chosen to implement the MINC concept is the IFD method. In this method, all thermophysical and thermodynamic properties are represented by averages over explicitly defined finite subdomains, while fluxes of mass or energy across surface segments are evaluated through finite difference approximations. An important aspect of this method is that the geometric quantities required to evaluate the conductance between two communicating volume elements are provided directly as input data rather than having them generated from data on nodal arrangements and nodal coordinates. Thus, a remarkable flexibility is attained by which one can allow a volume element in any one continuum to communicate with another element in its own or any other continuum. Inasmuch as the interaction between volume elements of different continua is handled as a geometric feature, the IFD methodology does not distinguish between the MINC method and the conventional porous-medium type approaches to modeling. porous-medium type approaches to modeling. SPEJ p. 14
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Wong, Joseph. "Architectural Organization of Dinoflagellate Liquid Crystalline Chromosomes." Microorganisms 7, no. 2 (January 22, 2019): 27. http://dx.doi.org/10.3390/microorganisms7020027.
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Dinoflagellates have some of the largest genome sizes, but lack architectural nucleosomes. Their liquid crystalline chromosomes (LCCs) are the only non-architectural protein-mediated chromosome packaging systems, having high degrees of DNA superhelicity, liquid crystalline condensation and high levels of chromosomal divalent cations. Recent observations on the reversible decompaction–recompaction of higher-order structures implicated that LCCs are composed of superhelical modules (SPMs) comprising highly supercoiled DNA. Orientated polarizing light photomicrography suggested the presence of three compartments with different packaging DNA density in LCCs. Recent and previous biophysical data suggest that LCCs are composed of: (a) the highly birefringent inner core compartment (i) with a high-density columnar-hexagonal mesophase (CH-m); (b) the lower-density core surface compartment (ii.1) consisting of a spiraling chromonema; (c) the birefringent-negative periphery compartment (ii.2) comprising peripheral chromosomal loops. C(ii.1) and C(ii.2) are in dynamic equilibrium, and can merge into a single compartment during dinomitosis, regulated through multiphasic reversible soft-matter phase transitions.
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Prehal, Christian, Aleksej Samojlov, Manfred Nachtnebel, Ludek Lovicar, Manfred Kriechbaum, Heinz Amenitsch, and Stefan A. Freunberger. "In situ small-angle X-ray scattering reveals solution phase discharge of Li–O2 batteries with weakly solvating electrolytes." Proceedings of the National Academy of Sciences 118, no. 14 (March 30, 2021): e2021893118. http://dx.doi.org/10.1073/pnas.2021893118.
Full textAbstract:
Electrodepositing insulating lithium peroxide (Li2O2) is the key process during discharge of aprotic Li–O2 batteries and determines rate, capacity, and reversibility. Current understanding states that the partition between surface adsorbed and dissolved lithium superoxide governs whether Li2O2 grows as a conformal surface film or larger particles, leading to low or high capacities, respectively. However, better understanding governing factors for Li2O2 packing density and capacity requires structural sensitive in situ metrologies. Here, we establish in situ small- and wide-angle X-ray scattering (SAXS/WAXS) as a suitable method to record the Li2O2 phase evolution with atomic to submicrometer resolution during cycling a custom-built in situ Li–O2 cell. Combined with sophisticated data analysis, SAXS allows retrieving rich quantitative structural information from complex multiphase systems. Surprisingly, we find that features are absent that would point at a Li2O2 surface film formed via two consecutive electron transfers, even in poorly solvating electrolytes thought to be prototypical for surface growth. All scattering data can be modeled by stacks of thin Li2O2 platelets potentially forming large toroidal particles. Li2O2 solution growth is further justified by rotating ring-disk electrode measurements and electron microscopy. Higher discharge overpotentials lead to smaller Li2O2 particles, but there is no transition to an electronically passivating, conformal Li2O2 coating. Hence, mass transport of reactive species rather than electronic transport through a Li2O2 film limits the discharge capacity. Provided that species mobilities and carbon surface areas are high, this allows for high discharge capacities even in weakly solvating electrolytes. The currently accepted Li–O2 reaction mechanism ought to be reconsidered.
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Zhong, Mingjun, Yankai Li, Meng Lin, Minghao Yuan, and Yanhua Yang. "A Numerical Analysis Research on Earlier Behavior of Molten Droplet Covered with Vapor Film at the Stage of Triggering and Propagation in Steam Explosion." Science and Technology of Nuclear Installations 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/301262.
Full textAbstract:
When the molten fuel with high temperature falls into the cavity water, it will be dispersed into droplets which are covered with vapor films due to the rapid heat transfer with phase transition. This situation cannot be simply described by liquid-liquid or gas-liquid systems. And there are no sufficient experimental studies on the behavior of droplet covered with vapor film because of the rapid reaction and the difficulty in capture of the film configuration. In this paper, a multiphase code with the volume of fluid (VOF) method is used to simulate the earlier behavior of droplet when vapor film exits. The earlier behavior is defined as behavior of the droplet before its disintegration. Thermal effect and pure hydrodynamic effect are, respectively, considered. The simulation results indicate that the film thickness and material density have significant effect on the earlier behavior of droplet. The situation assumed in Ciccarelli and Frost’s model (1994) is observed in current simulation of earlier thermal droplet behavior. The effect of triggering pressure pulse on earlier hydrodynamic behavior is also discussed and it indicates that vapor film has little effect on the hydrodynamic droplet deformation when the intensity of the pressure pulse is very high.
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Sankar, Sriram, Anand Narayanan, Blair D. Savage, Vikram Khaire, Benjamin E. Rosenwasser, Jane Charlton, and Bart P. Wakker. "Physical conditions of five O vi absorption systems towards PG 1522+101." Monthly Notices of the Royal Astronomical Society 498, no. 4 (September 4, 2020): 4864–86. http://dx.doi.org/10.1093/mnras/staa2671.
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ABSTRACT We present the analysis of five O vi absorbers identified across a redshift path of z ∼ (0.6−1.3) towards the background quasar PG 1522+101 with information on five consecutive ionization stages of oxygen from O ii to O vi. The combined HST and Keck spectra cover UV, redshifted extreme-UV, and optical transitions from a multitude of ions spanning ionization energies in the range of ∼(13−300) eV. Low-ionization (C ii, O ii, Si ii, Mg ii) and very high-ionization species (Ne viii, Mg x) are non-detections in all the absorbers. Three of the absorbers have coverage of He i, in one of which it is a >3σ detection. The kinematic structures of these absorbers are extracted from C iv detected in HIRES spectra. The farthest absorber in our sample also contains the detections of Ne v and Ne vi. Assuming co-spatial absorbing components, the ionization models show the medium to be multiphased with small-scale density–temperature inhomogeneities that are sometimes kinematically unresolved. In two of the absorbers, there is an explicit indication of the presence of a warm gas phase (T ≳ 105 K) traced by O vi. In the remaining absorbers, the column densities of the ions are consistent with a non-uniform photoionized medium. The subsolar [C/O] relative abundances inferred for the absorbers point at enrichment from massive Type II supernovae. Despite metal enrichment, the inferred wide range for [O/H] ∼ [−2.1, +0.2] amongst the absorbers along with their anticorrelation with the observed H i suggest poor small-scale mixing of metals with hydrogen in the regions surrounding galaxies and the IGM.
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Trukhanov, K. A. "DYNAMICS OF PNEUMATIC DRIVE. LECTURE CYCLE. THE EQUATION OF MOTION OF THE WORKING MEDIUM. MULTIPHASE GAS-LIQUID MIXTURES. CAVITATION AND HYDRATES IN THE DRIVE. TRANSMISSION OF INFORMATION VIA A HYDRAULIC COMMUNICATION CHANNEL." Spravochnik. Inzhenernyi zhurnal, no. 306 (September 2022): 1–24. http://dx.doi.org/10.14489/hb.supp.2022.09.pp.001-024.
Full textAbstract:
The paper presents the derivation of a mathematical model of the movement of the working environment; the application of the compiled system of equations of motion of the working medium in a cylindrical coordinate system is shown. The validity and possibility of using a rotary rheometer to determine the rheological characteristics of liquids are mathematically proved. An equation is obtained for the moment of resistance during the movement of Newtonian and non-Newtonian fluids in a coaxially cylindrical developed measuring system, taking into account the rheological parameters of the fluid: “k” is measures of fluid consistency and «n» is characteristics of the degree of non-Newtonian behavior of the material. Verification of the obtained results on the example of two liquids is given, and the corresponding conclusions are drawn. The issues of phase transition in gas-liquid mixtures of adjustable chokes are considered. The criteria for the occurrence of cavitation and hydrate formation in liquid and gaseous media are presented. Equations are described that make it possible to determine the condition for a phase transition from a liquid to a gas-liquid state. The paper presents a modern method of protecting the design of an adjustable throttle from the cavitation phenomenon, which consists in the use of throttle cells or throttling stages. The result of using throttle cells is given. An example of the formation of hydrates in a gas-liquid mixture during its flow through an adjustable throttle is considered. The criterion and method for determining the conditions of hydrate formation in the flow channel of an adjustable throttle are given, which consists in constructing an operating curve of an adjustable throttle, an envelope curve and their intersection with the curve of hydrate formation of a gas-liquid mixture to determine the conditions and areas of hydrate formation. The paper gives an example of the use of a hydraulic communication channel for information transfer. The main mathematical dependences of the mathematical model of the hydraulic communication channel, boundary and initial conditions are given. The form of the pressure pulse is obtained, and one of the main methods of encoding information for a hydraulic communication channel is considered. The condition for ensuring the required purity class of the working fluid for hydraulic systems is determined. The scientific novelty of the work includes the relations obtained, which make it possible to study the hydrodynamics of a fluid with variable viscosity, predict and evaluate the values of the shear stress in the fluid during its movement, the shear strain rate, the moment of friction forces, etc., with known rheological characteristics of the fluid. In addition, the scientific novelty of the work is the formulated criteria for the conditions of the phase transition, as well as the provision of practical recommendations to specialists involved in the design and operation of adjustable chokes. This work is based and is implemented as a course of lectures of the course “Dynamics of Pneumatic drive”, is red by the author at the Bauman Moscow State Technical University at the Department of “Hydromechanics, Hydraulic Machines and Hydropneumoautomatics” (E10), as part of the preparation of masters in the specialty 05.04.13 “Hydraulic machines and hydropneumatic drives”.
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Tang, Xiaochu, and Yuan Li. "Phase division and transition modeling based on the dominant phase identification for multiphase batch process quality prediction." Transactions of the Institute of Measurement and Control 42, no. 5 (November 4, 2019): 1022–36. http://dx.doi.org/10.1177/0142331219881343.
Full textAbstract:
Batch processes are carried out from one steady phase to another one, which may have multiphase and transitions. Modeling in transitions besides in the steady phases should also be taken into consideration for quality prediction. In this paper, a quality prediction strategy is proposed for multiphase batch processes. First, a new repeatability factor is introduced to divide batch process into different steady phases and transitions. Then, the different local cumulative models that considered the cumulative effect of process variables on quality are established for steady phases and transitions. Compared with the reported modeling methods in transitions, a novel just-in-time model can be established based on the dominant phase identification. The proposed method can not only consider the dynamic characteristic in the transition but also improve the accuracy and the efficiency of transitional models. Finally, online quality prediction is performed by accumulating the prediction results from different phases and transitions. The effectiveness of the proposed method is demonstrated by penicillin fermentation process.
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Trukhanov, K. A. "DYNAMICS OF PNEUMATIC DRIVE. LECTURE CYCLE THE EQUATION OF MOTION OF THE WORKING MEDIUM. MULTIPHASE GAS-LIQUID MIXTURES. CAVITATION AND HYDRATES IN THE DRIVE. TRANSMISSION OF INFORMATION VIA A HYDRAULIC COMMUNICATION CHANNEL Continuation." Spravochnik. Inzhenernyi zhurnal, no. 307 (October 2022): 1–28. http://dx.doi.org/10.14489/hb.supp.2022.10.pp.001-028.
Full textAbstract:
The paper presents the derivation of a mathematical model of the movement of the working environment; the application of the compiled system of equations of motion of the working medium in a cylindrical coordinate system is shown. The validity and possibility of using a rotary rheometer to determine the rheological characteristics of liquids are mathematically proved. An equation is obtained for the moment of resistance during the movement of Newtonian and non-Newtonian fluids in a coaxially cylindrical developed measuring system, taking into account the rheological parameters of the fluid: “k” is measures of fluid consistency and «n» is characteristics of the degree of non-Newtonian behavior of the material. Verification of the obtained results on the example of two liquids is given, and the corresponding conclusions are drawn. The issues of phase transition in gas-liquid mixtures of adjustable chokes are considered. The criteria for the occurrence of cavitation and hydrate formation in liquid and gaseous media are presented. Equations are described that make it possible to determine the condition for a phase transition from a liquid to a gas-liquid state. The paper presents a modern method of protecting the design of an adjustable throttle from the cavitation phenomenon, which consists in the use of throttle cells or throttling stages. The result of using throttle cells is given. An example of the formation of hydrates in a gas-liquid mixture during its flow through an adjustable throttle is considered. The criterion and method for determining the conditions of hydrate formation in the flow channel of an adjustable throttle are given, which consists in constructing an operating curve of an adjustable throttle, an envelope curve and their intersection with the curve of hydrate formation of a gas-liquid mixture to determine the conditions and areas of hydrate formation. The paper gives an example of the use of a hydraulic communication channel for information transfer. The main mathematical dependences of the mathematical model of the hydraulic communication channel, boundary and initial conditions are given. The form of the pressure pulse is obtained, and one of the main methods of encoding information for a hydraulic communication channel is considered. The condition for ensuring the required purity class of the working fluid for hydraulic systems is determined. The scientific novelty of the work includes the relations obtained, which make it possible to study the hydrodynamics of a fluid with variable viscosity, predict and evaluate the values of the shear stress in the fluid during its movement, the shear strain rate, the moment of friction forces, etc., with known rheological characteristics of the fluid. In addition, the scientific novelty of the work is the formulated criteria for the conditions of the phase transition, as well as the provision of practical recommendations to specialists involved in the design and operation of adjustable chokes. This work is based and is implemented as a course of lectures of the course “Dynamics of Pneumatic drive”, is red by the author at the Bauman Moscow State Technical University at the Department of “Hydromechanics, Hydraulic Machines and Hydropneumoautomatics” (E10), as part of the preparation of masters in the specialty 05.04.13 “Hydraulic machines and hydropneumatic drives”.
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Sandrakov, G. V. "COMPUTATIONAL ALGORITHMS FOR MULTIPHASE HYDRODYNAMICS MODELS AND FILTRATION." Journal of Numerical and Applied Mathematics, no. 1 (2022): 46–61. http://dx.doi.org/10.17721/2706-9699.2022.1.04.
Full textAbstract:
Computational algorithms for modeling of multiphase hydrodynamics processes with take of phase transitions will be discussed. The algorithms are based on discretization of conservation laws for mass, momentum, and energy in integral and differential forms. The time and spatial discretization is natural and numerical simulations are realized as direct computer experiments. The experiments are implemented as a computer simulation of the dynamics of a multiphase carrier fluid containing particles that can undergo, for example, graphite–diamond phase transitions and calculations are given. Modification of the algorithms have also been developed to take into account the influence of viscosity when simulating the dynamics of a multiphase fluid in porous media.
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Rothman, Daniel H., and Stéphane Zaleski. "Lattice-gas models of phase separation: interfaces, phase transitions, and multiphase flow." Reviews of Modern Physics 66, no. 4 (October 1, 1994): 1417–79. http://dx.doi.org/10.1103/revmodphys.66.1417.
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