Download From kinetic models to hydrodynamics : some novel results by Matteo Colangeli PDF
By Matteo Colangeli
Creation -- From the part area to the Boltzmann Equation -- equipment of diminished Description -- Hydrodynamic Spectrum of straightforward Fluids -- Hydrodynamic Fluctuations from the Boltzmann Equation -- Grad's 13-Moments procedure -- Conclusions
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From kinetic models to hydrodynamics : some novel results
Advent -- From the part area to the Boltzmann Equation -- tools of lowered Description -- Hydrodynamic Spectrum of easy Fluids -- Hydrodynamic Fluctuations from the Boltzmann Equation -- Grad's 13-Moments method -- Conclusions
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Yip, Molecular Hydrodynamics (Dover, 1991). 2. L. E. Reichl, A modern course in statistical physics (University of Texas Press, Austin, 1980). 3. U. Marini Bettolo Marconi, A. Puglisi, L. Rondoni and A. Vulpiani, Fluctuation-Dissipation: Response Theory in Statistical Physics, Phys. Rep. 461, 111 (2008). 4. V. Lucarini and M. Colangeli, beyond the linear fluctuation-dissipation theorem: the role of causality, J. Stat. Mech. P05013 (2012). 5. M. Colangeli, L. Rondoni and A. Vulpiani, Fluctuation-dissipation relation for chaotic nonhamiltonian systems, J.
E. Uhlenbeck, Fluctuation Theory for the Boltzmann Equation, Phys. Fluids 13, 2881 (1970). 11. L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon Press, 1959). 12. H. C. Öttinger, Betond Equilibrium Thermodynamics (Wiley, 2005). References 21 13. L. P. Gross and M. Krook, A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems, Phys. Rev. 94, 511 (1954). 14. V. Karlin, M. Colangeli and M. Kröger, Exact linear hydrodynamics from the Boltzmann Equation, Phys.
21) where we choose a reference frame in which the equilibrium bulk velocity u0 is zero. The response of the system to the small perturbations resulting from the spontaneous equilibrium fluctuations always present in the system can be described in terms of the linearized hydrodynamic equations. 22) ρ0 cv r α ρ0 ∂t u = η∇r2 u + where γ = c p /cv is the ratio of the specific heats at constant pressure and constant volume respectively, α = ρ (∂ V /∂ T ) p is the coefficient of thermal expansion, and c0 = (∂ p/∂ρ)s is the adiabatic speed of sound, with the subscript s denoting the entropy per unit mass.