Euler characteristic as a structural invariant of the phase diagrams of multicomponent multiphase systems

Фролкова, А. К.; Серафимов, Л. А.; Semin, G. A.

doi:10.1134/s0040579514020055

Cited by 2 publications

(2 citation statements)

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“…The Euler characteristic for the boundary space is determined, as previously mentioned, by Formula (8); for a sphere, using Formula (1), these values coincide. If a “hole” appears on a sphere of a certain dimension, then its Euler characteristic will decrease by one [ 11 , 14 ].…”

Section: Resultsmentioning

confidence: 99%

“…Such topological invariants include: the Euler characteristic, surface genus, connectivity, type and Poincaré index of a singular point. Topological properties of phase diagrams are considered in the literature [ 2 , 3 , 4 , 5 , 6 , 7 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 ]: vapor–liquid equilibrium [ 2 , 3 , 4 , 5 , 6 , 7 , 11 , 12 ], liquid–liquid equilibrium [ 13 , 14 , 15 ] and liquid–solid equilibrium (LSE) [ 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 ].…”

Section: Introductionmentioning

confidence: 99%

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Topological Invariants of Vapor–Liquid, Vapor–Liquid–Liquid and Liquid–Liquid Phase Diagrams

Фролкова

2021

Entropy

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The study of topological invariants of phase diagrams allows for the development of a qualitative theory of the processes being researched. Studies of the properties of objects in the same equivalence class may be carried out with the aim of predicting the properties of unexplored objects from this class, or predicting the behavior of a whole system. This paper describes a number of topological invariants in vapor–liquid, vapor–liquid–liquid and liquid–liquid equilibrium diagrams. The properties of some invariants are studied and illustrated. It is shown that the invariant of a diagram with a miscibility gap can be used to distinguish equivalence classes of phase diagrams, and that the balance equation of the singular-point indices, based on the Euler characteristic, may be used to analyze the binodal-surface structure of a quaternary system.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Topological Invariants of Vapor–Liquid, Vapor–Liquid–Liquid and Liquid–Liquid Phase Diagrams

Фролкова

2021

Entropy

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Multicomponent Systems With Three-Phase Splitting Region

Фролкова

Akishina

2016

Fine Chem. Tech.

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A review of scientific publications that describe systems with a three-phase splitting region is presented. Mechanisms of a three-phase splitting region formation are shown. All the suggested classifications of diagrams with a three-phase splitting region are presented. Methods for studying the evolution of a three-phase splitting region are described. Problems connected with the mathematical modeling of liquid - liquid - liquid equilibrium are considered. The ability of mixtures to form three-phase splitting regions and opportunities of separating such mixtures by special methods is analyzed. A list of known systems with three and more liquid phases is presented.

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Euler characteristic as a structural invariant of the phase diagrams of multicomponent multiphase systems

Cited by 2 publications

References 2 publications

Topological Invariants of Vapor–Liquid, Vapor–Liquid–Liquid and Liquid–Liquid Phase Diagrams

Topological Invariants of Vapor–Liquid, Vapor–Liquid–Liquid and Liquid–Liquid Phase Diagrams

Multicomponent Systems With Three-Phase Splitting Region

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