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Hydrodynamic Spectrum of Simple Fluids

  • Matteo ColangeliEmail author
Chapter
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Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

In this chapter, we will focus on the statistical properties of a fluid from a macroscopic perspective. To this end, we will discuss the properties of the linearized version of the NSF equations of hydrodynamics and will introduce the correlation function formalism, which allows us to characterize the spectrum of fluctuations of the hydrodynamic variables.

Keywords

Hydrodynamic Regime Dynamic Structure Factor Static Structure Factor Hydrodynamic Variable Differential Scattering Cross Section 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    J.P. Boon and S. Yip, Molecular Hydrodynamics (Dover, 1991).Google Scholar
  2. 2.
    L. E. Reichl, A modern course in statistical physics (University of Texas Press, Austin, 1980).Google Scholar
  3. 3.
    U. Marini Bettolo Marconi, A. Puglisi, L. Rondoni and A. Vulpiani, Fluctuation-Dissipation: Response Theory in Statistical Physics, Phys. Rep. 461, 111 (2008).Google Scholar
  4. 4.
    V. Lucarini and M. Colangeli, beyond the linear fluctuation-dissipation theorem: the role of causality, J. Stat. Mech. P05013 (2012).Google Scholar
  5. 5.
    M. Colangeli, L. Rondoni and A. Vulpiani, Fluctuation-dissipation relation for chaotic non-hamiltonian systems, J. Stat. Mech. L04002 (2012).Google Scholar
  6. 6.
    L. Bertini, A.D. Sole, D. Gabrielli, G. Jona-Lasinio and C. Landim, Macroscopic fluctuation theory for stationary non-equilibrium states, J. Stat. Phys. 107, 635 (2002).Google Scholar
  7. 7.
    L. Onsager and S. Machlup, fluctuations and irreversible processes, Phys. Rev. 91, 1505 (1953).Google Scholar
  8. 8.
    R. Balescu, Equilibrium and nonequilibrium statistical mechanics (Wiley, 1975).Google Scholar
  9. 9.
    J.-P. Hansen and I.R. McDonald, Theory of Simple Liquids (Academic Press, 2006).Google Scholar
  10. 10.
    D. Forster, Hydrodynamic fluctuations, Broken Symmetry, and Correlation Functions (W. A. Benjamin, New York, 1975).Google Scholar
  11. 11.
    R. Kubo, The fluctuation-dissipation theorem, Rep. Prog. Phys. 29, 255 (1966).Google Scholar
  12. 12.
    R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Japan 12, 570 (1957).Google Scholar
  13. 13.
    M. Baiesi, C. Maes and B. Wynants, Nonequilibrium linear response for Markov dynamics: I. Jump Processes and Overdamped Diffusion, J. Stat. Phys. 137, 1094 (2009).Google Scholar
  14. 14.
    M. Baiesi, E. Boksenbojm, C. Maes and B. Wynants, Nonequilibrium linear response for Markov dynamics: II. Inertial dynamics, J. Stat. Phys. 139, 492 (2010).Google Scholar
  15. 15.
    M. Colangeli, C. Maes and B. Wynants, A meaningful expansion around detailed balance, J. Phys. A: Math. Theor. 44, 095001 (2011).Google Scholar
  16. 16.
    D. Ruelle, General linear response formula in statistical mechanics, and the fluctuation-dissipation theorem far from equilibrium, Phys. Lett. A 245, 220 (1998).Google Scholar

Copyright information

© Matteo Colangeli 2013

Authors and Affiliations

  1. 1.Department of MathematicsPolitecnico di TorinoTorinoItaly

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