Multiscale Thermo-Dynamics

Pavelka, Michal; Klika, Václav; Grmela, Miroslav

doi:10.1515/9783110350951

Cited by 112 publications

(219 citation statements)

References 80 publications

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“…1. When the calculation leads to a bracket in a closed form, the bracket is certainly Poisson and reversible in the sense of time-reversal [12]. Moreover, even without carrying out the calculation, it is sometimes possible to ensure that the projection will result in a Poisson bracket by relating Lie algebras of the two levels of description.…”

Section: Resultsmentioning

confidence: 99%

“…The Liouville-Poisson bracket generates reversible evolution in the sense of time-reversal transformation, see [12]. Are the brackets derived from a reversible Poisson bracket also reversible?…”

Section: Geometric Interpretationmentioning

confidence: 99%

“…Suppose, moreover, that the Poisson bracket on the higher level of description generates reversible evolution (as for example the Liouville Poisson bracket does), which means that 22) as shown in [12]. The Poisson bivector at the lower level evaluated at inverted coordinates (i.e.…”

Section: Geometric Interpretationmentioning

confidence: 99%

“…Various thermodynamically relevant models are shown to be part of the hierarchy. Some of the projections equation in [12] or it can be seen from compatibility of Liouville equation and Hamilton canonical equations.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A hierarchy of Poisson brackets in non-equilibrium thermodynamics

Pavelka

Klika

Esen

et al. 2016

Physica D: Nonlinear Phenomena

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Reversible evolution of macroscopic and mesoscopic systems can be conveniently constructed from two ingredients: an energy functional and a Poisson bracket. The goal of this paper is to elucidate how the Poisson brackets can be constructed and what additional features we also gain by the construction. In particular, the Poisson brackets governing reversible evolution in one-particle kinetic theory, kinetic theory of binary mixtures, binary fluid mixtures, classical irreversible thermodynamics and classical hydrodynamics are derived from Liouville equation. Although the construction is quite natural, a few examples where it does not work are included (e.g. the BBGKY hierarchy). Finally, a new infinite grand-canonical hierarchy of Poisson brackets is proposed, which leads to Poisson brackets expressing non-local phenomena such as turbulent motion or evolution of polymeric fluids. Eventually, Lie-Poisson structures standing behind some of the brackets are identified.

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Section: Resultsmentioning

confidence: 99%

Section: Geometric Interpretationmentioning

confidence: 99%

Section: Geometric Interpretationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A hierarchy of Poisson brackets in non-equilibrium thermodynamics

Pavelka

Klika

Esen

et al. 2016

Physica D: Nonlinear Phenomena

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“…Such a closure may depend on a particular application. This emphasizes an exceptional role of the energy potential in the formulation of the reversible equations, similar to the GENERIC formulation [18,19].…”

mentioning

confidence: 89%

A new continuum model for general relativistic viscous heat-conducting media

Romenski

Peshkov

Dumbser

et al. 2020

Phil. Trans. R. Soc. A.

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The lack of formulation of macroscopic equations for irreversible dynamics of viscous heat-conducting media compatible with the causality principle of Einstein’s special relativity and the Euler–Lagrange structure of general relativity is a long-lasting problem. In this paper, we propose a possible solution to this problem in the framework of SHTC equations. The approach does not rely on postulates of equilibrium irreversible thermodynamics but treats irreversible processes from the non-equilibrium point of view. Thus, each transfer process is characterized by a characteristic velocity of perturbation propagation in the non-equilibrium state, as well as by an intrinsic time/length scale of the dissipative dynamics. The resulting system of governing equations is formulated as a first-order system of hyperbolic equations with relaxation-type irreversible terms. Via a formal asymptotic analysis, we demonstrate that classical transport coefficients such as viscosity, heat conductivity, etc., are recovered in leading terms of our theory as effective transport coefficients. Some numerical examples are presented in order to demonstrate the viability of the approach. This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

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On the nonlinear stability and the existence of selective decay states of 3D quasi‐geostrophic potential vorticity equation

Esen

Han

Şengül

et al. 2019

Math Methods in App Sciences

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In this article, we study the dynamics of large scale motion in atmosphere and ocean governed by the 3D-quasi-geostrophic potential vorticity (QGPV) equation with a constant stratification. It is shown that for a Kolmogorov forcing on the first energy shell, there exist a family of exact solutions which are dissipative Rossby waves. The nonlinear stability of these exact solutions are analyzed based on the assumptions on the growth rate of the forcing. In the absence of forcing, we show the existence of selective decay states for the 3D-QGPV equation. The selective decay states are the 3D-Rossby waves traveling horizontally at a constant speed. All these results can be regarded as the expansion of that of the 2D-QGPV system and in the case of 3D-QGPV system with isotropic viscosity. Finally, we present a geometric foundation for the model as a general equation for non-equilibrium reversible-irreversible coupling.

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Multiscale Thermo-Dynamics

Abstract: This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Cited by 112 publications

References 80 publications

A hierarchy of Poisson brackets in non-equilibrium thermodynamics

A hierarchy of Poisson brackets in non-equilibrium thermodynamics

A new continuum model for general relativistic viscous heat-conducting media

On the nonlinear stability and the existence of selective decay states of 3D quasi‐geostrophic potential vorticity equation

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