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Startseite > Seminars > Séminaires théorie > Theory Club Mercredi 17 Février à 14h en salle 646A. Masato Itami: "Derivation of Stokes law without the hydrodynamic equations".

Theory Club Mercredi 17 Février à 14h en salle 646A. Masato Itami: "Derivation of Stokes law without the hydrodynamic equations"

Unless otherwise stated, seminars and defences take place at 11:30 in room 454A of Condorcet building.

Derivation of Stokes law without the hydrodynamic equations

Masato Itami (Kyoto University)

Abstract: In equilibrium systems, macroscopic behavior is phenomenologically well described by thermodynamics. On the basis of a microscopic description of equilibrium systems, the principle of equal a priori probabilities and Boltzmann’s principle reproduce thermodynamics, which is established as equilibrium statistical mechanics. By contrast, there is still no theory describing the general behavior of nonequilibrium systems beyond the linear response regime. Thus, much effort is devoted to investigate steady-state thermodynamics and nonequilibrium statistical mechanics.

When liquids and gases are out of equilibrium but still remain in local equilibrium, their macroscopic dynamical behavior is phenomenologically well described by the hydrodynamic equations. Microscopic understanding of the hydrodynamic equations is well established through the Boltzmann equation for the case of dilute gases, whereas it remains unclear for a general fluid.

In this presentation, we study the friction coefficient of a Brownian particle in a viscous incompressible fluid at low Reynolds number. According to Kirkwood’s formula [1], the friction coefficient is expressed in terms of the stress correlation on the surface of the Brownian particle. Then, with the aid of large deviation theory, we phenomenologically relate the surface stress correlation to the stress correlation in the bulk of the fluid, where the bulk stress correlation is characterized by the viscosity from the Green–Kubo formula [2]. By combining Kirkwood’s formula and the Green–Kubo formula in large deviation theory, we derive Stokes’ law [3] without explicitly employing the hydrodynamic equations [4].

REFERENCES 1. J. Kirkwood, J. Chem. Phys. 14, 180 (1946). 2. M.S. Green, J. Chem. Phys. 22, 398 (1954). 3. G.G. Stokes, Trans. Cambridge Philos. Soc. 9, 8 (1851). 4. M. Itami and S. Sasa, J. Stat. Phys. 161, 532-552 (2015).

Contact : Équipe séminaires / Seminar team - Published on / Publié le 15 February 2016

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