Velocity autocorrelation function and diffusion coefficient in a liquid

1971 ◽  
Vol 4 (12) ◽  
pp. 1466-1478 ◽  
Author(s):  
T Gaskell
Keyword(s):  
Diffusion Coefficient ◽  
Autocorrelation Function ◽  
Velocity Autocorrelation Function ◽  
Velocity Autocorrelation ◽  
And Diffusion

scholarly journals Velocity autocorrelation function and self-diffusion coefficient in large molecular dynamics models of liquid argon and water

2021 ◽  
Vol 13 (2) ◽  
pp. 149-156
Author(s):  
Yuri I. Naberukhin ◽  
◽  
Alexey V. Anikeenko ◽  
Vladimir P. Voloshin ◽  
◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Diffusion Coefficient ◽  
Autocorrelation Function ◽  
Liquid Argon ◽  
Time Interval ◽  
Velocity Autocorrelation Function ◽  
Self Diffusion ◽  
Velocity Autocorrelation ◽  
The Difference ◽  
Self Diffusion Coefficient

Autocorrelation function of the particle velocity Z(t) is calculated using the molecular dynamics method in the models of liquid argon and water. The large size of the models (more than a hundred thousand particles) allowed us to trace these functions up to 50 picoseconds in argon and up to 10 picoseconds in water, and to achieve a calculation accuracy sufficient for analytical analysis of their shape. The difference in the determination of the self-diffusion coefficient using Einstein's law and the integral of Z(t) (Green-Kubo integral) is analyzed and it is shown to be 3% at best when t is of the order of several picoseconds. The asymptote of the function Z(t) in argon is close to the power law αt–3/2 predicted by hydrodynamics, but with an amplitude that depends on the time interval under consideration. In water, the asymptote of Z(t) has nothing in common with that in argon: it has α < 0 and the exponent is close to -5/2, and not to -3/2.

Measuring the properties of liquids by counting

1994 ◽  
Vol 446 (1928) ◽  
pp. 429-439
Keyword(s):  
Computer Simulation ◽  
Diffusion Coefficient ◽  
Autocorrelation Function ◽  
Density Profile ◽  
Simulation Method ◽  
Computational Effort ◽  
Velocity Autocorrelation Function ◽  
Alternative Procedure ◽  
Velocity Autocorrelation ◽  
Inhomogeneous Systems

In the computer simulation method (NVE ensemble) of determining the properties of classical liquids there are well established procedures for determining the properties of the liquid. We suggest an alternative procedure, for many properties, based on counting the passage of particles through a notional plane in the liquid. This method is used in homogeneous liquids as an alternative way of determining the temperature, the diffusion coefficient and the velocity autocorrelation function. In inhomogeneous systems the new procedure is used to determine the density profile. For all properties, except the velocity autocorrelation function, the method proposed is more accurate for given computational effort than the coventional one.

Nondiffusive Brownian Motion Studied by Diffusing-Wave Spectroscopy

1989 ◽  
Vol 177 ◽  
Author(s):  
D. J. Pine ◽  
D. A. Weitz ◽  
D. J. Durian ◽  
P. N. Pusey ◽  
R. J. A. Tough
Keyword(s):  
Autocorrelation Function ◽  
Colloidal Particles ◽  
Scattered Light ◽  
Short Time Scale ◽  
Velocity Autocorrelation Function ◽  
Velocity Autocorrelation ◽  
Power Law Decay ◽  
Brownian Particles ◽  
Short Time ◽  
Surrounding Fluid

ABSTRACTOn a short time scale, Brownian particles undergo a transition from initially ballistic trajectories to diffusive motion. Hydrodynamic interactions with the surrounding fluid lead to a complex time dependence of this transition. We directly probe this transition for colloidal particles by measuring the autocorrelation function of multiply scattered light and observe the effects of the slow power-law decay of the velocity autocorrelation function.

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