Efficient determination of the nonlinear Burnett coefficients

Rk, Standish; Dj, Evans

doi:10.1103/physreve.48.3478

Cited by 2 publications

(3 citation statements)

References 6 publications

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“…There is a considerable system size dependence, indicating that the nonlinear Burnett coefficients diverge in the thermodynamic limit, although the individual TTCFs remain finite. It can be shown, using the lemma proved in the appendix of [9], that the inverse nonlinear Burnett coefficients given by equation ( 2) should be intensive. As well as this, the 32 particle simulation shows strong evidence of a long time tail (Fig 2 and 3) when Q λ is increased (softening the currentstatting), leading to a divergence in the integrals as t → ∞.…”

Section: Resultsmentioning

confidence: 99%

“…In a previous paper [8] we show that this method can be applied to the situation of an arbitrary thermodynamic flux. Later, [9] we showed that this transient time correlation expression can be expressed in terms of an average over an equilibrium simulation, reducing the calculation required by two orders of magnitude. At the time, computational resources were not sufficient to establish whether this expression is finite in the limit as t → ∞, or in the thermodynamic limit.…”

Section: Introductionmentioning

confidence: 99%

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Numerical evidence for divergent Burnett coefficients

Standish

1999

Phys. Rev. E

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In previous papers [Phys. Rev. A 41, 4501 (1990); Phys. Rev. E 18, 3178 (1993)], simple equilibrium expressions were obtained for nonlinear Burnett coefficients. A preliminary calculation of a 32-particle Lennard-Jones fluid was presented in the previous papers. Now, sufficient resources have become available to address the question of whether nonlinear Burnett coefficients are finite for soft spheres. The hard sphere case is known to have infinite nonlinear Burnett coefficients (i.e., a nonanalytic constitutive relation) from mode-coupling theory. This paper reports a molecular dynamics caclulation of the third order nonlinear Burnett coefficient of a Lennard-Jones fluid undergoing color flow, which indicates that this term diverges in the thermodynamic limit.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical evidence for divergent Burnett coefficients

Standish

1999

Phys. Rev. E

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“…Gases with internal degrees of freedom have been examined in [95]. Other analyses of second-order constitutive equations are based on numerical simulations [15,172,201], on information-theoretical methods [52,87,133,134,[186][187][188][190][191] or on generalizations of the fluctuation-dissipation theorem [15,77,88]. Special attention to some of the subtleties related to the definition of the entropy may be found in [6][7][8][46][47][48][49].…”

Section: G) Kinetic Theory Molecular Simulations and Information Theorymentioning

confidence: 99%

Recent Bibliography On Extended Irreversible Thermodynamics and Related Topics (1992-1995)

Jou¹,

Casas-Vázquez²,

Lebon³

1996

Journal of Non-Equilibrium Thermodynamics

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We present a list of the references on extended irreversible thermodynamics and closely related topics published between May 1992 and May 1995, and we provide some general comments about the main open problems, applications and prospects in this field. This list complements our previous bibliographical review on this topic published in by several researchers working in this field. Since 1993, four books have appeared which are closely related to extended irreversible thermodynamics [45,83,126,164]. These books are rather different in their aims and scopes, but they rest on the same basic idea to extend the space of variables by including the fluxes as independent variables. Two of the books [83,126] are directly concerned with extended irreversible thermodynamics and provide global and systematic approaches to this subject. The book by Jou, Casas-Vazquez and Lebon [83] is based on techniques which are similar to those used in classical irreversible thermodynamics; the microscopic foundations of the theory are discussed from the points of view of kinetic theory of ideal and real gases, fluctuation and information theory, and applications to hyperbolic heat transport and phonon hydrodynamics, rheology, ultrasounds and shock waves in gases, generalized hydrodynamics, numerical simulations, multicomponent systems (including the analysis of phase diagrams of polymer solutions under shear and electrical systems), are also proposed as well as a relativistic approach with applications to cosmological models. Furthermore, each chapter includes several proposed problems, some of them based on recent research literature. The monograph by Müller and Ruggeri [126] uses methods similar to those of rational thermodynamics (in the formalism of Lagrange multipliers devised by Shi-Liu), and has a more mathematical character than the previous book [83]: it relates the macroscopic theory to the kinetic theory of ideal gases, it pays much attention to the properties of wave propagation and shock waves in solids (phonon system) and in radiation; one can also find an analysis of generalized hydrodynamics, and a relativistic formulation of the theory. Though the approaches followed in [83] and [126] differ, they yield rather similar conclusions concerning the essential points.The two other mentioned monographs are not centered on extended thermodynamics but they refer to it in a substantial part of the text. The book by Eu [45] starts from the kinetic theory and presents his generalized moment method, with a wide range of applications. This book reserves the name of entropy to the Boltzmann entropy, rather than to the macroscopic, phenomenological entropy used in extended thermodynamics, which receives in this book a different name. Therefore, it may be surprising for the reader to learn that the entropy is no longer function of state, in contrast to the assumptions introduced in [83] and [126]. In fact, as it has been recognised by the author of the book [48,49], there is not an unsurmountable contradiction between the different points...

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Efficient determination of the nonlinear Burnett coefficients

Cited by 2 publications

References 6 publications

Numerical evidence for divergent Burnett coefficients

Numerical evidence for divergent Burnett coefficients

Recent Bibliography On Extended Irreversible Thermodynamics and Related Topics (1992-1995)

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