Critical Phenomena in Filtration Processes of Real Gases

Lychagin, Valentin; Roop, Mikhail

doi:10.1134/s1995080220030129

Cited by 20 publications

(12 citation statements)

References 10 publications

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“…Note that this curve is of the similar form as that separating domains where

and

. This means that we get a more accurate applicability condition for van der Waals model, and it may be a considerable contribution to the theory of phase transitions, since, as we know, it is the sign changing of

that forces the first order phase transitions in van der Waals model [ 4 , 5 , 7 ].…”

Section: Discussionmentioning

confidence: 99%

“…The geometrical interpretation of thermodynamic systems in equilibrium goes back already to the 19th century [ 1 ] and is reflected recently in Reference [ 2 ]. In modern terms, it is clear that thermodynamic states are Legendrian submanifolds, i.e., maximal integral manifolds of the structure contact form (for more details, see Reference [ 3 , 4 , 5 ]) in the contact space where the mentioned structure form is the first law of thermodynamics. Additional structures, such as Riemannian structures on these Legendrian manifolds, were studied in, for example, Reference [ 6 ].…”

Section: Introductionmentioning

confidence: 99%

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On Higher Order Structures in Thermodynamics

Lychagin

Roop

2020

Entropy

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We present the development of the approach to thermodynamics based on measurement. First of all, we recall that considering classical thermodynamics as a theory of measurement of extensive variables one gets the description of thermodynamic states as Legendrian or Lagrangian manifolds representing the average of measurable quantities and extremal measures. Secondly, the variance of random vectors induces the Riemannian structures on the corresponding manifolds. Computing higher order central moments, one drives to the corresponding higher order structures, namely the cubic and the fourth order forms. The cubic form is responsible for the skewness of the extremal distribution. The condition for it to be zero gives us so-called symmetric processes. The positivity of the fourth order structure gives us an additional requirement to thermodynamic state.

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“…Note that this curve is of the similar form as that separating domains where

and

that forces the first order phase transitions in van der Waals model [ 4 , 5 , 7 ].…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Higher Order Structures in Thermodynamics

Lychagin

Roop

2020

Entropy

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“…here p and s are expressed in terms of Planck potential Φ(ρ, θ) [6] p(ρ, θ) = −Rρ 2 θΦ ρ , s(ρ, θ) = R(Φ + θΦ θ ), and R is a specific gas constant.…”

Section: Euler Equations On a Curvementioning

confidence: 99%

Quotient of the Euler system on one class of curves

Duyunova,

Lychagin,

Tychkov

2021

Preprint

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We consider the Euler system describing a one-dimensional inviscid flows in space along curves of a certain class. Using differential invariants for the Euler system, we obtain its quotient equation. The solutions of the quotient equation that are constant along characteristic vector field provide some solutions of the Euler system. We discuss solving the quotient using asymptotic expansions of unknown functions and virial expansion of thermodynamic state equations. Thus the quotient is reduced to a series of ODE systems.

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“…In this section, we describe Legendrian and Lagrangian manifolds for gases (see also [ 14 , 15 , 16 ]). We pay special attention to ideal gases and virial model of real gases [ 17 ], which are used further in optimal control problem.…”

Section: Legendrian Manifolds For Gasesmentioning

confidence: 99%

Optimal Thermodynamic Processes For Gases

Kushner

Lychagin

Roop

2020

Entropy

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In this paper, we consider an optimal control problem in equilibrium thermodynamics of gases. Thermodynamic state of the gas is given by a Legendrian submanifold in a contact thermodynamic space. Using Pontryagin's maximum principle we find a thermodynamic process on this submanifold such that the gas maximizes the work functional. For ideal gases, this problem is shown to be integrable in Liouville's sense and its solution is given by means of action-angle variables. For real gases considered as a perturbation of ideal ones, the integrals are given asymptotically. *

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Critical Phenomena in Filtration Processes of Real Gases

Cited by 20 publications

References 10 publications

On Higher Order Structures in Thermodynamics

On Higher Order Structures in Thermodynamics

Quotient of the Euler system on one class of curves

Optimal Thermodynamic Processes For Gases

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