Journal ArticleDOI
Nonanalytic dispersion relations for classical fluids. II. The general fluid
Matthieu H. Ernst,J. R. Dorfman +1 more
TLDR
The analytical structure of the hydrodynamic frequencies for the sound, heat, and shear modes and of hydrodynamics equations for a monatomic fluid are discussed in this article.Abstract:
The analytic structure of the hydrodynamic frequenciesz(k) for the sound, heat, and shear modes and of the hydrodynamic equations for a monatomic fluid are discussed on the basis of the mode-mode coupling theory. It is shown that the hydrodynamic frequencies depend on the wave numberk, for smallk, asz(k) = ak + bk
2 +
$$z(k) = ak + bk^2 + \sum\nolimits_{n = 1}^\infty {c_n k^{3 - 2^{ - n} } } $$
and that some of the correlation functions that appear in the Fourier-Laplace transforms of the hydrodynamic equations contain branch point singularities. The implications of these results for the derivation of linear hydrodynamic equations, such as the Burnett equations, and for the long-time behavior of time correlation functions are discussed.read more
Citations
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Kinetic theory representation of hydrodynamics: a way beyond the Navier–Stokes equation
TL;DR: The resulting discrete Boltzmann models are based on a kinetic representation of the fluid dynamics, hence the drawbacks in conventional higher-order hydrodynamic formulations can be avoided.
Journal ArticleDOI
Rapid granular flows
TL;DR: A recent avalanche of research activity in the field of granular hydrodynamics has yielded much progress as discussed by the authors, which has led to the discovery of new states and patterns and enabled detailed tests of theories and models.
Journal ArticleDOI
Mode-coupling theory and the glass transition in supercooled liquids
TL;DR: In this paper, the authors discuss the various methods used to obtain the model equations and illustrate the effects of structure on dynamics and scaling behavior over different time scales using a wave-vector-dependent model.
Journal ArticleDOI
Microscopic dynamics in liquid metals: The experimental point of view
TL;DR: In this article, the experimental results relevant for the understanding of the microscopic dynamics in liquid metals are reviewed, with special regard to the ones achieved in the last two decades, including the ones obtained in this article.
Journal ArticleDOI
Hydrodynamic fluctuations, long-time tails, and supersymmetry
Pavel Kovtun,Laurence G. Yaffe +1 more
TL;DR: In this article, the authors show that hydrodynamic fluctuations in supersymmetric theories generate essentially the same long-time power-law tails in real-time correlation functions that are known in simple fluids.
References
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Journal ArticleDOI
Lectures in Theoretical Physics
Journal ArticleDOI
Kinetic equations and time correlation functions of critical fluctuations.
Kyozi Kawasaki,Kyozi Kawasaki +1 more
TL;DR: In this paper, the Boltzmann equation of dilute gases was derived with the aid of a generalized Langevin equation due to Mori, which was then used to obtain selfconsistent closed equations to determine time correlation functions of critical fluctuations.
Journal ArticleDOI
Transport Coefficients near the Liquid-Gas Critical Point
Leo P. Kadanoff,Jack Swift +1 more
TL;DR: In this paper, a perturbation theory for the determination of transport coefficients near the critical point is presented, which is based upon processes in which one transport mode decays into several low-wave-number modes.
Journal ArticleDOI
Asymptotic Time Behavior of Correlation Functions
TL;DR: In this article, the asymptotic time behavior of the velocity autocorrelation function and of the kinetic parts of the correlation functions for the shear viscosity and the heat conductivity is derived.