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Full-Text Articles in Physical Sciences and Mathematics
Hydrodynamic Description Of The Adiabatic Piston, Alejandro Garcia, M. M. Mansour
Hydrodynamic Description Of The Adiabatic Piston, Alejandro Garcia, M. M. Mansour
Faculty Publications
A closed macroscopic equation for the motion of the two-dimensional adiabatic piston is derived from standard hydrodynamics. It predicts a damped oscillatory motion of the piston towards a final rest position, which depends on the initial state. In the limit of large piston mass, the solution of this equation is in quantitative agreement with the results obtained from both hard disk molecular dynamics and hydrodynamics. The explicit forms of the basic characteristics of the piston’s dynamics, such as the period of oscillations and the relaxation time, are derived. The limitations of the theory’s validity, in terms of the main system …
Estimating Hydrodynamic Quantities In The Presence Of Microscopic Fluctuations, Alejandro Garcia
Estimating Hydrodynamic Quantities In The Presence Of Microscopic Fluctuations, Alejandro Garcia
Faculty Publications
This paper discusses the evaluation of hydrodynamic variables in the presence of spontaneous fluctuations, such as in molecular simulations of fluid flows. The principal point is that hydrodynamic variables such as fluid velocity and temperature must be defined in terms of mechanical variables such as momentum and energy density). Because these relations are nonlinear and because fluctuations of mechanical variables are correlated, care must be taken to avoid introducing a bias when evaluating means, variances, and correlations of hydrodynamic variables. The unbiased estimates are formulated; some alternative, incorrect approaches are presented as cautionary warnings. The expressions are verified by numerical …