Decay of the Velocity Autocorrelation Function

by: BJ Alder, TE Wainwright

Physical Review A, Vol. 1, No. 1. (January 1970), 18.

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Abstract

Molecular-dynamic studies of the behavior of the diffusion coefficient after a long time s have shown that the velocity autocorrelation function decays as s -1 for hard disks and as s -3 / 2 for hard spheres; at least at intermediate fluid densities. A hydrodynamic similarity solution of the decay in velocity of an initially moving volume element in an otherwise stationary compressible viscous fluid agrees with a decay of (η s ) - d / 2 ; where η is the viscosity and d is the dimensionality of the system. The slow decay; which would lead to a divergent diffusion coefficient in two dimensions; is caused by a vortex flow pattern which has been quantitatively compared for the hydrodynamic and molecular-dynamic calculations.

@article{alder70, abstract = {Molecular-dynamic studies of the behavior of the diffusion coefficient after a long time s have shown that the velocity autocorrelation function decays as s -1 for hard disks and as s -3 / 2 for hard spheres; at least at intermediate fluid densities. A hydrodynamic similarity solution of the decay in velocity of an initially moving volume element in an otherwise stationary compressible viscous fluid agrees with a decay of (η s ) - d / 2 ; where η is the viscosity and d is the dimensionality of the system. The slow decay; which would lead to a divergent diffusion coefficient in two dimensions; is caused by a vortex flow pattern which has been quantitatively compared for the hydrodynamic and molecular-dynamic calculations.}, author = {Alder, B. J. and Wainwright, T. E. }, citeulike-article-id = {1299614}, doi = {10.1103/PhysRevA.1.18}, journal = {Physical Review A}, keywords = {classic, diffusion, hard-sphere, simulation}, month = {January}, number = {1}, pages = {18+}, posted-at = {2007-09-29 03:14:33}, priority = {0}, publisher = {American Physical Society}, title = {Decay of the Velocity Autocorrelation Function}, url = {http://dx.doi.org/10.1103/PhysRevA.1.18}, volume = {1}, year = {1970} }

RIS record

TY - JOUR ID - alder70 L3 - citeulike-article-id:1299614 TI - Decay of the Velocity Autocorrelation Function JF - Physical Review A VL - 1 IS - 1 SP - 18 PB - American Physical Society N2 - Molecular-dynamic studies of the behavior of the diffusion coefficient after a long time s have shown that the velocity autocorrelation function decays as s -1 for hard disks and as s -3 / 2 for hard spheres; at least at intermediate fluid densities. A hydrodynamic similarity solution of the decay in velocity of an initially moving volume element in an otherwise stationary compressible viscous fluid agrees with a decay of (η s ) - d / 2 ; where η is the viscosity and d is the dimensionality of the system. The slow decay; which would lead to a divergent diffusion coefficient in two dimensions; is caused by a vortex flow pattern which has been quantitatively compared for the hydrodynamic and molecular-dynamic calculations. KW - classic KW - diffusion KW - hard-sphere KW - simulation AU - Alder, BJ AU - Wainwright, TE PY - 1970/01// UR - http://dx.doi.org/10.1103/PhysRevA.1.18 ER -

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