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Journal articles on the topic 'Phase equilibria forward modelling'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Carnero, M., Jose Olmo, and Lorenzo Pascual. "Modelling the Dynamics of Fuel and EU Allowance Prices during Phase 3 of the EU ETS." Energies 11, no. 11 (November 14, 2018): 3148. http://dx.doi.org/10.3390/en11113148.

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This article studies the relationship between the prices of fuel and EU Allowances (EUA) for carbon emissions during Phase 3 of the European Union Emissions Trading System. We find that the forward prices of EUA, coal, gas and Brent oil are jointly determined in equilibrium. The existence of such a long-run relationship entails a permanent-transitory decomposition for the series of EUA and fuel prices that reveals the short- and long-term causal influence of the EUA market in shaping the joint dynamics of fuel prices. This result complements the literature that suggests that EUA prices are driven by the dynamics of fuel prices. Interestingly, we do not find an equilibrium relationship in the spot market. EUA and fuel spot prices are driven by independent unit root processes. The differences between spot and forward markets are attributed to the tradability of forward prices that are used for speculation and hedging in financial markets. In contrast, spot prices are mainly driven by supply and demand in energy markets.

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2

Wang, Hui, Xiaoli Chen, and Jinqiao Duan. "A Stochastic Pitchfork Bifurcation in Most Probable Phase Portraits." International Journal of Bifurcation and Chaos 28, no. 01 (January 2018): 1850017. http://dx.doi.org/10.1142/s0218127418500177.

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We study stochastic bifurcation for a system under multiplicative stable Lévy noise (an important class of non-Gaussian noise), by examining the qualitative changes of equilibrium states with its most probable phase portraits. We have found some peculiar bifurcation phenomena in contrast to the deterministic counterpart: (i) When the non-Gaussianity parameter in Lévy noise varies, there is either one, two or no backward pitchfork type bifurcations; (ii) When a parameter in the vector field varies, there are two or three forward pitchfork bifurcations; (iii) The non-Gaussian Lévy noise clearly leads to fundamentally more complex bifurcation scenarios, since in the special case of Gaussian noise, there is only one pitchfork bifurcation which is reminiscent of the deterministic situation.

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3

Williams, Megan A., David E. Kelsey, Martin Hand, Tom Raimondo, Laura J. Morrissey, Naomi M. Tucker, and Rian A. Dutch. "Further evidence for two metamorphic events in the Mawson Continent." Antarctic Science 30, no. 1 (December 4, 2017): 44–65. http://dx.doi.org/10.1017/s0954102017000451.

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AbstractIn this study,in situand erratic samples from George V Coast (East Antarctica) and southern Eyre Peninsula (Australia) have been used to characterize the microstructural, pressure–temperature and geochronological record of upper amphibolite and granulite facies polymetamorphism in the Mawson Continent to provide insight into the spatial distribution of reworking and the subice geology of the Mawson Continent. Monazite U-Pb data shows thatin situsamples from the George V Coast record exclusively 2450–2400 Ma ages, whereas most erratic samples from glacial moraines at Cape Denison and the Red Banks Charnockite record only 1720–1690 Ma ages, consistent with known ages of the Sleaford and Kimban events, respectively. Phase equilibria forward modelling reveals considerable overlap of the thermal character of these two events. Samples with unimodal 1720–1690 Ma Kimban ages reflect either formation after the Sleaford event or complete metamorphic overprinting. Rocks recording only 2450–2400 Ma ages were unaffected by the younger Kimban event, perhaps as a result of unreactive rock compositions inherited from the Sleaford event. Our results suggest the subice geology of the Mawson Continent is a pre-Sleaford-aged terrane with a cover sequence reworked during the Kimban event.

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Stewart, Ian. "Spontaneous Symmetry-Breaking in a Network Model for Quadruped Locomotion." International Journal of Bifurcation and Chaos 27, no. 14 (December 30, 2017): 1730049. http://dx.doi.org/10.1142/s021812741730049x.

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Spontaneous symmetry-breaking proves a mechanism for pattern generation in legged locomotion of animals. The basic timing patterns of animal gaits are produced by a network of spinal neurons known as a Central Pattern Generator (CPG). Animal gaits are primarily characterized by phase differences between leg movements in a periodic gait cycle. Many different gaits occur, often having spatial or spatiotemporal symmetries. A natural way to explain gait patterns is to assume that the CPG is symmetric, and to classify the possible symmetry-breaking periodic motions. Pinto and Golubitsky have discussed a four-node model CPG network for biped gaits with [Formula: see text] symmetry, classifying the possible periodic states that can arise. A more specific rate model with this structure has been analyzed in detail by Stewart. Here we extend these methods to quadruped gaits, using an eight-node network with [Formula: see text] symmetry proposed by Golubitsky and coworkers. We formulate a rate model and calculate how the first steady or Hopf bifurcation depends on its parameters, which represent four connection strengths. The calculations involve a distinction between “real” gaits with one or two phase shifts (pronk, bound, pace, trot) and “complex” gaits with four phase shifts (forward and reverse walk, forward and reverse buck). The former correspond to real eigenvalues of the connection matrix, the latter to complex conjugate pairs. The partition of parameter space according to the first bifurcation, ignoring complex gaits, is described explicitly. The complex gaits introduce further complications, not yet fully understood. All eight gaits can occur as the first bifurcation from a fully synchronous equilibrium, for suitable parameters, and numerical simulations indicate that they can be asymptotically stable.

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5

Mehdizadeh, N. S., and P. Sinaei. "Modelling methane-air turbulent diffusion flame in a gas turbine combustor with artifical neural network." Aeronautical Journal 113, no. 1146 (August 2009): 541–47. http://dx.doi.org/10.1017/s0001924000003195.

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Abstract The present paper reports a way of using an artificial neural network (ANN) for modelling methane-air jet diffusion turbulent flame characteristics, such as temperature and chemical species mass fractions in a gas turbine combustion chamber. Since the neural network needs sets of examples to adapt its synaptic weights in the training phase, we used pre-assumed probability density function (PDF) method and considered chemical equilibrium chemistry model to compute the flame characteristics for generating the examples of input-output data sets. In this approach, flow and mixing field results are presented with a non-linear first order k-ε model. The turbulence model is applied in combination with preassumed β-PDF modelling for turbulence-chemistry interaction. The training algorithm for the neural network is based on a back-propagation supervised learning procedure, and the feed-forward multilayer network is incorporated as neural network architecture. The ability of ANN model to represent a highly non-linear system, such as a turbulent non-premixed flame is illustrated, and it can be summarized that the results of modelling of the combustion characteristics using ANN model are satisfactory, and the CPU-time and memory savings encouraging.

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6

Boothby, Peter G., Ratih Puspitasari, Sanjay Thakur, Zachariah John Pallikathekathil, and Chris Walton. "Integrating multi-disciplinary data for building fit-for-purpose 3D mechanical earth model." APPEA Journal 59, no. 2 (2019): 856. http://dx.doi.org/10.1071/aj18153.

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Understanding the influence of geomechanics early in the field development phase facilitates reservoir management planning. To capture complex geology and associated field development, a 3D mechanical earth model (3D MEM) with finite element method (FEM) approach was selected to analyse the geomechanical-related risks associated with two fields in the North West Shelf, Australia. The 3D MEMs were constructed using geological static models, and seismic-derived horizons and faults. The 3D properties were propagated based on core-calibrated 1D properties and controlled by stratigraphy, 3D facies and seismic inversion volumes. The FEM was used to calculate the equilibrium of stresses and strains within the 3D MEMs. The 3D properties and pre-production stresses were validated in blind test wells before forward modelling. The 3D MEMs were linked to the dynamic reservoir models to capture the pressure evolution throughout the field lifecycle. The results were used to analyse the risks associated with compaction, subsidence, fault instability, completion integrity and drilling stability of infill wells through depleted reservoirs. The results provided insight in managing the risk early in field development stage. The study’s largest challenge was integrating a large volume of data to ensure that the structural complexity and rock heterogeneity were captured and consistent with the geological understanding of the field. A multi-disciplinary team of earth scientists and reservoir and geomechanics engineers worked together, and the value of data integration, good communication and teamwork were key success factors. Lessons learned and best practices were captured throughout the study and provided valuable feedback for future works.

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7

Henriques, Vasco M. J., Chris J. Nelson, Luc H. M. Rouppe van der Voort, and Mihalis Mathioudakis. "Umbral chromospheric fine structure and umbral flashes modelled as one: The corrugated umbra." Astronomy & Astrophysics 642 (October 2020): A215. http://dx.doi.org/10.1051/0004-6361/202038538.

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Context. The chromosphere of the umbra of sunspots features an assortment of dynamic fine structures that are poorly understood and often studied separately. Small-scale umbral brightenings (SSUBs), umbral microjets, spikes or short dynamic fibrils (SDFs), and umbral dark fibrils are found in any observation of the chromosphere with sufficient spatial resolution performed at the correct umbral flash stage and passband. Understanding these features means understanding the dynamics of the umbral chromosphere. Aims. We aim to fully understand the dynamics of umbral chromosphere through analysis of the relationships between distinct observed fine features and to produce complete models that explain both spectral profiles and the temporal evolution of the features. We seek to relate such understanding to umbral flashes. Methods. We studied the spatial and spectral co-evolution of SDFs, SSUBs, and umbral flashes in Ca II 8542 Å spectral profiles. We produced models that generate the spectral profiles for all classes of features using non-local thermodynamic equilibrium radiative transfer with a recent version of the NICOLE inversion code. Results. We find that both bright SSUBs and dark SDF structures are described with a continuous feature in the parameter space that is distinct from the surroundings even in pixel-by-pixel inversions. We find a phase difference between such features and umbral flashes in both inverted line-of-sight velocities and timing of the brightenings. For umbral flashes themselves we resolve, for the first time in inversion-based semi-empirical modelling, the pre-flash downflows, post-flash upflows, and the counter-flows present during the umbral flash phase. We further present a simple time-dependent cartoon model that explains the dynamics and spectral profiles of both fine structure, dark and bright, and umbral flashes in umbral chromospheres. Conclusions. The similarity of the profiles between the brightenings and umbral flashes, the pattern of velocities obtained from the inversions, and the phase relationships between the structures all lead us to put forward that all dynamic umbral chromospheric structures observed to this date are a locally delayed or locally early portion of the oscillatory flow pattern that generates flashes, secondary to the steepening large-scale acoustic waves at its source. Essentially, SSUBs are part of the same shock or merely compression front responsible for the spatially larger umbral flash phenomenon, but out of phase with the broader oscillation.

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8

Deiters, Ulrich K. "Modelling Supercritical Phase Equilibria: Problems and Pitfalls." Periodica Polytechnica Chemical Engineering 63, no. 2 (March 18, 2019): 261–69. http://dx.doi.org/10.3311/ppch.12757.

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This article addresses some recurring difficulties and problems of computing phase equilibria involving supercritical fluid phases. These difficulties prevent a full automatization of thermodynamic calculations and require human interference. Examples are the wrong interpretation of experimental data, phase inversion phenomena, or overlooking phases. While none of these insights are knew, publications dealing with them are scattered and sometimes hard to obtain. This article gives a short overview over some of the most common difficulties and pitfalls.

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9

Shubin, A. B., and K. Y. Shunyaev. "MnO-C Interaction – Thermodynamic Modelling of Phase Equilibria." Defect and Diffusion Forum 273-276 (February 2008): 632–36. http://dx.doi.org/10.4028/www.scientific.net/ddf.273-276.632.

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The interaction between manganese(II) oxide and carbon in powder mixtures may give manganese carbides, condensed(c) and gaseous(g) manganese at different temperatures and pressures. The initial assumptions and results of thermodynamic modelling of this interaction in the temperature range 1600-2100 K at the pressures 0.1-1.0 MPa are presented in this paper.

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10

Lototsky, M. V., V. A. Yartys, V. S. Marinin, and N. M. Lototsky. "Modelling of phase equilibria in metal–hydrogen systems." Journal of Alloys and Compounds 356-357 (August 2003): 27–31. http://dx.doi.org/10.1016/s0925-8388(03)00095-1.

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11

Achar, D. R. G., R. Munoz-Arroyo, L. Singheiser, and W. J. Quadakkers. "Modelling of phase equilibria in MCrAlY coating systems." Surface and Coatings Technology 187, no. 2-3 (October 2004): 272–83. http://dx.doi.org/10.1016/j.surfcoat.2004.02.018.

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12

Teja, Amyn S. "Modelling phase equilibria: thermodynamic background and practical tools." Chemical Engineering Science 48, no. 18 (September 1993): 3321. http://dx.doi.org/10.1016/0009-2509(93)80216-d.

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13

Yakymchuk, C., M. Brown, C. Clark, F. J. Korhonen, P. M. Piccoli, C. S. Siddoway, R. J. M. Taylor, and J. D. Vervoort. "Decoding polyphase migmatites using geochronology and phase equilibria modelling." Journal of Metamorphic Geology 33, no. 2 (December 29, 2014): 203–30. http://dx.doi.org/10.1111/jmg.12117.

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14

Cassel, E., M. Matt, M. Rogalski, and R. Solimando. "Phase equilibria modelling for binary systems that contain CO2." Fluid Phase Equilibria 134, no. 1-2 (June 1997): 63–75. http://dx.doi.org/10.1016/s0378-3812(97)00050-2.

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15

Das, Susanta K., and Alejandro D. Rey. "Computational modelling of multi-phase equilibria of mesogenic mixtures." Computational Materials Science 29, no. 2 (February 2004): 152–64. http://dx.doi.org/10.1016/j.commatsci.2003.06.007.

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16

Rodríguez-Palmeiro, Iago, Oscar Rodríguez, Ana Soto, and Christoph Held. "Measurement and PC-SAFT modelling of three-phase behaviour." Physical Chemistry Chemical Physics 17, no. 3 (2015): 1800–1810. http://dx.doi.org/10.1039/c4cp04336g.

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Liquid–liquid–liquid phase equilibria of ternary systems (water + surfactant ionic liquid + n-dodecane) were measured experimentally. Phase behaviour was accurately predicted by PC-SAFT using only pure-component parameters.

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17

Hoffmeister, Hans. "Heterogeneous phase equilibria as a basis for crevice corrosion modelling." Steel Research 70, no. 12 (December 1999): 519–23. http://dx.doi.org/10.1002/srin.199905678.

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18

Anderko, Andrzej. "Equation-of-state methods for the modelling of phase equilibria." Fluid Phase Equilibria 61, no. 1-2 (January 1990): 145–225. http://dx.doi.org/10.1016/0378-3812(90)90011-b.

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19

Durelle, Jeremy, Jesse R. Vanderveen, and Philip G. Jessop. "Modelling the behaviour of switchable-hydrophilicity solvents." Phys. Chem. Chem. Phys. 16, no. 11 (2014): 5270–75. http://dx.doi.org/10.1039/c3cp55391d.

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20

Acharya, S., and J. P. Hajra. "Thermodynamic modelling of phase equilibria in Al-Ga-P-As system." Bulletin of Materials Science 28, no. 2 (April 2005): 179–85. http://dx.doi.org/10.1007/bf02704238.

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21

Bogatu, Cristina, Anca Duţă, Theo W. de Loos, and Dan Geană. "Modelling fluid phase equilibria in the binary system trifluoromethane + 1-phenylpropane." Fluid Phase Equilibria 428 (November 2016): 190–202. http://dx.doi.org/10.1016/j.fluid.2016.06.027.

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22

Gürth, M., A. Grytsiv, J. Vrestal, V. V. Romaka, G. Giester, E. Bauer, and P. Rogl. "On the constitution and thermodynamic modelling of the system Ti–Ni–Sn." RSC Advances 5, no. 112 (2015): 92270–91. http://dx.doi.org/10.1039/c5ra16074j.

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23

Ghazi, Hala, Francois James, and Hélène Mathis. "Vapour-liquid phase transition and metastability." ESAIM: Proceedings and Surveys 66 (2019): 22–41. http://dx.doi.org/10.1051/proc/201966002.

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The paper deals with the modelling of the relaxation processes towards thermodynamic equilibrium in a liquid-vapour isothermal mixture. Focusing on the van der Waals equation of state, we construct a constrained optimization problem using Gibbs' formalism and characterize all possible equilibria: coexistence states, pure phases and metastable states. Coupling with time evolution, we develop a dynamical system whose equilibria coincide with the minimizers of the optimization problem. Eventually we consider the coupling with hydrodynamics and use the dynamical system as a relaxation source terms in an Euler-type system. Numerical results illustrate the ability of the whole model to depict coexistence and metastable states as well.

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24

MEDRAJ, M., R. HAMMOND, W. T. THOMPSON, and R. A. L. DREW. "PHASE EQUILIBRIA, THERMODYNAMIC MODELLING AND NEUTRON DIFFRACTION OF THE AlN-Al2O3-Y2O3SYSTEM." Canadian Metallurgical Quarterly 42, no. 4 (January 2003): 495–507. http://dx.doi.org/10.1179/cmq.2003.42.4.495.

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25

Guevara, V. E., and M. J. Caddick. "Shooting at a moving target: phase equilibria modelling of high-temperature metamorphism." Journal of Metamorphic Geology 34, no. 3 (February 10, 2016): 209–35. http://dx.doi.org/10.1111/jmg.12179.

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26

Garrido, Nuno M., Georgios K. Folas, and Georgios M. Kontogeorgis. "Modelling of phase equilibria of glycol ethers mixtures using an association model." Fluid Phase Equilibria 273, no. 1-2 (November 2008): 11–20. http://dx.doi.org/10.1016/j.fluid.2008.08.006.

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27

Li, Jun, Zhigang Zhang, Xiaorong Luo, and Xiaochun Li. "Modelling of phase equilibria in CH4–C2H6–C3H8–nC4H10–NaCl–H2O systems." Applied Geochemistry 56 (May 2015): 23–36. http://dx.doi.org/10.1016/j.apgeochem.2015.02.006.

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28

Vřesťál, J., J. Pavlů, U. D. Wdowik, and M. Sob. "Modelling of phase equilibria in the Hf-V system below room temperature." Journal of Mining and Metallurgy, Section B: Metallurgy 53, no. 3 (2017): 239–47. http://dx.doi.org/10.2298/jmmb170704032v.

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Phase transformation from orthorhombic HfV2 structure to cubic C15 Laves phase structure, which occurs during heating at about 114 K, is well known. In this contribution, a thermodynamic description of this phenomenon is provided supported by ab initio calculations. We utilize the third generation of thermodynamic database extending the Scientific Group Thermodata Europe (SGTE) unary data to zero Kelvin and demonstrate that it may be also applied to intermetallic phases. The data from a recent thermodynamic assessment of the Hf-V system (valid for temperatures above 298.15 K) were used and extended to zero Kelvin by the same method as it was used for unary data. Under the assumption of validity of harmonic approximation and electronic contribution to the heat capacity, the thermodynamics of C15 and orthorhombic phase were described. With the help of ab initio approach, we demonstrate that the HfV2 orthorhombic phase and C15 Laves phase are mechanically stable at 0 K and thanks to entropy stabilization they are in equilibrium with pure element phases in the temperature region of structural change.

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29

Ferreira, Olga, Esteban A. Brignole, and Eugénia A. Macedo. "Modelling of phase equilibria for associating mixtures using an equation of state." Journal of Chemical Thermodynamics 36, no. 12 (December 2004): 1105–17. http://dx.doi.org/10.1016/j.jct.2004.07.001.

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30

Gabas, N., and C. Laguerie. "Modelling of liquid-solid phase equilibria with UNIFAC. Application to sugar systems." Computers & Chemical Engineering 17 (January 1993): S239—S244. http://dx.doi.org/10.1016/0098-1354(93)80236-g.

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Gabas, N. "Modelling of liquid-solid phase equilibria with UNIFAC. Application to sugar systems." Computers & Chemical Engineering 17, no. 1 (1993): S239—S244. http://dx.doi.org/10.1016/0098-1354(93)85037-m.

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32

Bostan, Mihaï, and José Antonio Carrillo. "Fluid models with phase transition for kinetic equations in swarming." Mathematical Models and Methods in Applied Sciences 30, no. 10 (August 7, 2020): 2023–65. http://dx.doi.org/10.1142/s0218202520400163.

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We concentrate on kinetic models for swarming with individuals interacting through self-propelling and friction forces, alignment and noise. We assume that the velocity of each individual relaxes to the mean velocity. In our present case, the equilibria depend on the density and the orientation of the mean velocity, whereas the mean speed is not anymore a free parameter and a phase transition occurs in the homogeneous kinetic equation. We analyze the profile of equilibria for general potentials identifying a family of potentials leading to phase transitions. Finally, we derive the fluid equations when the interaction frequency becomes very large.

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Yakymchuk, Chris. "Applying Phase Equilibria Modelling to Metamorphic and Geological Processes: Recent Developments and Future Potential." Geoscience Canada 44, no. 1 (April 20, 2017): 27. http://dx.doi.org/10.12789/geocanj.2017.44.114.

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Phase equilibria modelling has played a key role in enhancing our understanding of metamorphic processes. An important breakthrough in the last three decades has been the ability to construct phase diagrams by integrating internally consistent datasets of the thermodynamic properties of minerals, fluids and melts with activity–composition models for mixed phases that calculate end-member activities from end-member proportions. A major advance in applying phase equilibria modelling to natural rocks is using isochemical phase diagrams to explore the phase assemblages and reaction sequences applicable for a particular sample. The chemical systems used for modelling phase equilibria are continually evolving to provide closer approximations to the natural compositions of rocks and allow wider varieties of compositions to be modelled. Phase diagrams are now routinely applied to metasedimentary rocks, metabasites and intermediate to felsic intrusive rocks and more recently to ultramafic rocks and meteorites. While the principal application of these phase diagrams is quantifying the pressure and temperature evolution of metamorphic rocks, workers are now applying them to other fields across the geosciences. For example, phase equilibria modelling of hydrothermal alteration and the metamorphism of hydrothermally altered rocks can be used to determine ‘alteration vectors’ to hydrothermal mineral deposits. Combining the results of phase equilibria of rock-forming minerals with solubility equations of accessory minerals has provided new insights into the geological significance of U–Pb ages of accessory minerals commonly used in geochronology (e.g. zircon and monazite). Rheological models based on the results of phase equilibria modelling can be used to evaluate how the strength of the crust and mantle can change through metamorphic and metasomatic processes, which has implications for a range of orogenic processes, including the localization of earthquakes. Finally, phase equilibria modelling of fluid generation and consumption during metamorphism can be used to explore links between metamorphism and global geochemical cycles of carbon and sulphur, which may provide new insights into the secular change of the lithosphere, hydrosphere and atmosphere.RÉSUMÉLa modélisation des équilibres de phases a joué un rôle clé dans l’amélioration de notre compréhension des processus métamorphiques. Une percée importante au cours des trois dernières décennies a été la capacité de construire des diagrammes de phase en y intégrant des ensembles de données cohérentes des propriétés thermodynamiques des minéraux, des fluides et des bains magmatiques avec des modèles d'activité-composition pour des phases mixtes qui déduisent l’activité des membres extrêmes à partir des proportions des membres extrêmes. Une avancée majeure dans l'application de la modélisation d'équilibre de phase aux roches naturelles consiste à utiliser des diagrammes de phases isochimiques pour étudier les assemblages de phase et les séquences de réaction applicables pour un échantillon particulier. Les systèmes chimiques utilisés pour la modélisation des équilibres de phase évoluent continuellement pour fournir des approximations plus proches des compositions naturelles des roches et permettent de modéliser de plus grandes variétés de compositions. Les diagrammes de phase sont maintenant appliqués de façon routinière aux roches métasédimentaires, aux métabasites et aux roches intrusives intermédiaires à felsiques et plus récemment aux roches ultramafiques et aux météorites. Bien que l'application principale de ces diagrammes de phase consiste à quantifier l'évolution de la pression et de la température des roches métamorphiques, les utilisateurs les appliquent maintenant à d'autres spécialités des géosciences. Par exemple, la modélisation des équilibres de phase de l'altération hydrothermale et du métamorphisme des roches d’altération hydrothermale peut être utilisée pour déterminer les « vecteurs d'altération » des gisements minéraux hydrothermaux. La combinaison des résultats des équilibres de phase des minéraux constitutifs des roches avec des équations de solubilité des minéraux accessoires a permis d’en savoir davantage sur la signification géologique des âges U–Pb des minéraux accessoires couramment utilisés en géochronologie (par exemple zircon et monazite). Les modèles rhéologiques basés sur les résultats de la modélisation des équilibres de phase peuvent être utilisés pour évaluer comment la résistance de la croûte et du manteau peut changer à travers des processus métamorphiques et métasomatiques, ce qui a des implications sur une gamme de processus orogéniques, y compris la localisation des séismes. Enfin, la modélisation des équilibres de phase de la génération et de l’absorption des fluides pendant le métamorphisme peut être utilisée pour explorer les liens entre le métamorphisme et les cycles géochimiques globaux du carbone et du soufre, ce qui peut fournir de nouvelles perspectives sur le changement séculaire de la lithosphère, de l'hydrosphère et de l'atmosphère.

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34

Guo, Feng. "Global Analysis of a Liénard System with Quadratic Damping." Discrete Dynamics in Nature and Society 2018 (September 2, 2018): 1–9. http://dx.doi.org/10.1155/2018/1249620.

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In this paper, the global analysis of a Liénard equation with quadratic damping is studied. There are 22 different global phase portraits in the Poincaré disc. Every global phase portrait is given as well as the complete global bifurcation diagram. Firstly, the equilibria at finite and infinite of the Liénard system are discussed. The properties of the equilibria are studied. Then, the sufficient and necessary conditions of the system with closed orbits are obtained. The degenerate Bogdanov-Takens bifurcation is studied and the bifurcation diagrams of the system are given.

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35

Rybka, Piotr. "Dynamical modelling of phase transitions by means of viscoelasticity in many dimensions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 121, no. 1-2 (1992): 101–38. http://dx.doi.org/10.1017/s0308210500014177.

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SynopsisWe study the equations of viscoelasticity in a multidimensional setting for the ‘no-traction’ boundary data. For the sake of modelling phase transitions we do not assume elliptieity of the stored energy function W. We construct dynamics in W1,2(Ωℝn) globally in time. Next, we study the question of stability for a class of equilibria. Moreover, we show a certain kind of decay in time of solutions for arbitrary initial conditions.

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Chen, Yuqiu, Xiaodong Liang, John M. Woodley, and Georgios M. Kontogeorgis. "Modelling study on phase equilibria behavior of ionic liquid-based aqueous biphasic systems." Chemical Engineering Science 247 (January 2022): 116904. http://dx.doi.org/10.1016/j.ces.2021.116904.

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INDARES, A., R. W. WHITE, and R. POWELL. "Phase equilibria modelling of kyanite-bearing anatectic paragneisses from the central Grenville Province." Journal of Metamorphic Geology 26, no. 8 (October 2008): 815–36. http://dx.doi.org/10.1111/j.1525-1314.2008.00788.x.

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38

Al Ghafri, Saif ZS, and J. P. Martin Trusler. "Phase equilibria of (Methylbenzene + Carbon dioxide + Methane) at elevated pressure: Experiment and modelling." Journal of Supercritical Fluids 145 (March 2019): 1–9. http://dx.doi.org/10.1016/j.supflu.2018.11.012.

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Perederic, Olivia A., Larissa P. Cunico, Sawitree Kalakul, Bent Sarup, John M. Woodley, Georgios M. Kontogeorgis, and Rafiqul Gani. "Systematic identification method for data analysis and phase equilibria modelling for lipids systems." Journal of Chemical Thermodynamics 121 (June 2018): 153–69. http://dx.doi.org/10.1016/j.jct.2018.02.007.

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Alavianmehr, M. M., F. Akbari, and R. Behjatmanesh-Ardakani. "Modelling phase equilibria of pure ionic liquids from a new equation of state." Ionics 22, no. 12 (July 14, 2016): 2447–59. http://dx.doi.org/10.1007/s11581-016-1769-z.

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Meng, Xin-You, Ni-Ni Qin, and Hai-Feng Huo. "Dynamics of a Food Chain Model with Two Infected Predators." International Journal of Bifurcation and Chaos 31, no. 02 (February 2021): 2150019. http://dx.doi.org/10.1142/s021812742150019x.

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In this paper, the dynamics of a three-species food chain model with two predators infected by an infectious disease is investigated. The positivity and boundedness of the system, the existence of the equilibria and the basic reproductive number are given. Sufficient conditions for the local stability of all equilibria are obtained by analyzing the corresponding characteristic equations. By constructing suitable Lyapunov functions and taking the geometric approach, the global stability of all equilibria is proved. According to the center manifold theory, this model undergoes the phenomenon of backward and forward bifurcations in a certain range of the basic reproductive number [Formula: see text]. By taking the disease transmission coefficient of predator as bifurcation parameter, Hopf bifurcation emerges in the neighborhood of the endemic equilibrium. Furthermore, the optimal control of the disease is discussed by the Pontryagin’s maximum principle. Various simulations are given to support the analytical results.

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Baidakov, V. G., and S. P. Protsenko. "Metastable phase equilibria in a Lennard-Jones system." Journal of Engineering Thermophysics 16, no. 4 (December 2007): 249–58. http://dx.doi.org/10.1134/s1810232807040066.

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Onderka, B., A. Dębski, and W. Gąsior. "Thermodynamic Assessment Of The Bi-In-Zn System." Archives of Metallurgy and Materials 60, no. 2 (June 1, 2015): 567–75. http://dx.doi.org/10.1515/amm-2015-0175.

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Abstract A thermodynamic description of the entire ternary Bi-In-Zn system was obtained by the CALPHAD modelling of the Gibbs energy of the liquid phase. The experimental data on the phase equilibria and the thermodynamic properties published and complemented by the authors’ own experiments were taken into account. In order to verify the phase equilibria in the Bi-In-Zn system, 15 different samples were studied in the temperature range of 300-900 K by the DTA technique during heating and cooling cycles. Coexisting phases and their composition were analyzed by the SEM and EDX techniques for 9 distinct samples after their thermal equilibration at 373 K and 473 K. Assessment and selected phase equilibrium calculations were performed with ThermoCalc and Pandat softwares, and compared with experimental data. The obtained results reproduce well the experimental data on both the phase equilibria and the thermodynamic properties in the optimized system.

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Drápala, Jaromír, Petr Kubíček, J. Vřeštál, and Monika Losertová. "Study of Reaction Diffusivity in the Copper–Indium–Tin Ternary System." Defect and Diffusion Forum 263 (March 2007): 231–36. http://dx.doi.org/10.4028/www.scientific.net/ddf.263.231.

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Interaction of lead-free solders with copper substrate represents an important phenomenon in the issue of reliability of solder joints. New experimental data describing phase equilibria in the Cu-In-Sn system after long-time diffusion annealing at the 400 °C/50 hours, 600 °C/310 hours and 600 °C/48 hours will be presented. The composition of solders was: 100 % Sn, 75 % Sn + 25 % In, 50 % Sn + 50 % In, 25 % Sn + 75 % In, 100 % In. The fast quenching method was employed to freeze thermodynamic equilibrium after annealing, followed by metallography, microhardness measurements, SEM (Scanning Electron Microscope) and WDX (Wave Dispersive X-ray) analysis. New phase equilibrium data, together with the data from literature, represent the best existing experimental description of phase equilibria in the system in question. The obtained experimental results of the phase equilibria were compared with the thermodynamic modelling by the CALPHAD (Calculation of Phase Diagrams) method and with other authors.

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Eltekova, N. A., and Yu A. Eltekov. "Adsorption Equilibria in Carbon/Hydrocarbon/Water Systems." Adsorption Science & Technology 15, no. 2 (January 1997): 109–14. http://dx.doi.org/10.1177/026361749701500204.

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Two equations derived from the theory of volume filling of micropores (the DR and DS equations) were used for the description of the liquid-phase adsorption of benzene, toluene and p-xylene from aqueous solution on to two commercial microporous activated carbons. Comparison of the experimental and calculated adsorption isotherms showed good accord between the theoretical and experimental values. The results of this work indicate that the parameters of these equations can be used for modelling a water purification process based on the activated carbons.

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Cornish, L. A., and M. J. Witcomb. "Data Collection for the Calculation of Phase Equilibria." Molecular Simulation 22, no. 1 (February 1999): 57–80. http://dx.doi.org/10.1080/08927029908022087.

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Gourgouillon, Didier, and Manuel Nunes da Ponte. "High pressure phase equilibria for poly(ethylene glycol)s + CO2: experimental results and modelling." Physical Chemistry Chemical Physics 1, no. 23 (1999): 5369–75. http://dx.doi.org/10.1039/a906927e.

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Tork, Thomas, Gabriele Sadowski, Wolfgang Arlt, André de Haan, and Gerard Krooshof. "Modelling of high-pressure phase equilibria using the Sako–Wu–Prausnitz equation of state." Fluid Phase Equilibria 163, no. 1 (September 1999): 61–77. http://dx.doi.org/10.1016/s0378-3812(99)00219-8.

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Tork, Thomas, Gabriele Sadowski, Wolfgang Arlt, André de Haan, and Gerard Krooshof. "Modelling of high-pressure phase equilibria using the Sako–Wu–Prausnitz equation of state." Fluid Phase Equilibria 163, no. 1 (September 1999): 79–98. http://dx.doi.org/10.1016/s0378-3812(99)00220-4.

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Fourie, Frederick Christiaan van Niekerk, Cara Elsbeth Schwarz, and Johannes Hendrik Knoetze. "CO2 + n-dodecane + 1-decanol: High pressure experimental phase equilibria data and thermodynamic modelling." Journal of Supercritical Fluids 151 (September 2019): 49–62. http://dx.doi.org/10.1016/j.supflu.2019.04.019.

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