scholarly journals THE BARE DIFFUSION COEFFICIENT AND THE PECULIAR VELOCITY AUTO-CORRELATION FUNCTION

2006 ◽  
Vol 06 (02) ◽  
pp. L179-L199
Author(s):  
RODNEY L. VARLEY
Keyword(s):  
Diffusion Coefficient ◽  
General Characteristic ◽  
Velocity Autocorrelation Function ◽  
Disk System ◽  
Peculiar Velocity ◽  
Time Integral ◽  
Velocity Autocorrelation ◽  
Auto Correlation Function ◽  
Dynamics Simulations ◽  
The Einstein Formula

The bare diffusion coefficient is given as the time integral of the peculiar velocity autocorrelation function or PVACF and this result is different from the well known Green-Kubo formula. The bare diffusion coefficient characterizes the diffusion process on a length scale lambda. The PVACF is given here for the first time in terms of the positions and velocities of the N particles of the system so the PVACF is in a form suitable for evaluation by molecular dynamics simulations. The computer simulations show that for the two dimensional hard disk system, the PVACF decays increasingly rapidly in time as lambda is reduced and this is probably a general characteristic. Finally, the Einstein formula for Brownian motion is a bit different for the bare diffusion coefficient.

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.

scholarly journals Frenkel line crossover of confined supercritical fluids

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Kanka Ghosh ◽  
C. V. Krishnamurthy
Keyword(s):  
Supercritical Fluids ◽  
Excess Entropy ◽  
Shear Mode ◽  
Velocity Autocorrelation Function ◽  
Crossover Point ◽  
Density Profiles ◽  
Velocity Autocorrelation ◽  
Supercritical Phase ◽  
Dynamics Simulations ◽  
T Phase

Abstract We investigate the temperature evolution of dynamics and structure of partially confined Lennard Jones (LJ) fluids in supercritical phase along an isobaric line in the P-T phase diagram using molecular dynamics simulations. We compare the Frenkel line (FL) crossover features of partially confined LJ fluids to that of the bulk LJ fluids in supercritical phase. Five different spacings have been chosen in this study and the FL crossover characteristics have been monitored for each of these spacings for temperatures ranging from 240 K to 1500 K keeping the pressure fixed at 5000 bar. We characterize the FL crossover using density of states (DoS) function and find that partially confined supercritical fluids (SCF) exhibit a progressive shift of FL crossover point to higher temperatures for smaller spacings. While the DoS perpendicular to the walls shows persistent oscillatory modes, the parallel component exhibits a smooth crossover from an oscillatory to non-oscillatory characteristics representative of FL crossover. We find that the vanishing of peaks in DoS parallel to the walls indicates that the SCF no longer supports shear mode excitations and could serve as an identifier of the FL crossover for confined systems just as is done for the bulk. Layer heights of density profiles, self-diffusivity and the peak heights of radial distribution function parallel to the walls also feature the FL crossover consistent with the DoS criteria. Surprisingly, self-diffusivity undergoes an Arrhenius to super-Arrhenius crossover at low temperatures for smaller spacings as a result of enhanced structural order evidenced via pair-excess entropy. This feature, typical of glass-forming liquids and binary supercooled liquids, is found to develop from the glass-like characteristic slowdown and strong caging in confined supercritical fluid, evidenced via mean squared displacement and velocity autocorrelation function respectively, over intermediate timescales.

DETERMINATION OF THE MASS DIFFUSION COEFFICIENT OF H2O DILUTED IN N2 USING CLASSICAL MOLECULAR DYNAMIC SIMULATION

2020 ◽  
Vol 65 (6) ◽  
pp. 75-81
Author(s):  
Hoa Ngo Ngoc ◽  
Thu Le Minh ◽  
Trang Nguyen Huyen ◽  
Tuong Le Cong
Keyword(s):  
Diffusion Coefficient ◽  
Center Of Mass ◽  
Mass Diffusion ◽  
Auto Correlation ◽  
Classical Molecular Dynamic Simulation ◽  
Decay Times ◽  
Auto Correlation Function ◽  
Dynamics Simulations ◽  
Decay Behavior

In this work, the auto-correlation function of the center of mass velocity has been used to deduce the mass diffusion coefficient (D) of water diluted in nitrogen using the Classical Molecular Dynamics Simulations (CMDS). The calculations have been performed at room temperature (296 K) for different mixtures of H2O in N2 and 2.107 molecules from a five-sites potential. The results show that the auto-correlation functions expected exponential decay behavior [i.e. v v t exp( ) τ      ] and from the decay times τv , the mass diffusion coefficient and the velocity changing collisions frequency have been determined. The comparison between the CMDS results and experimental results are presented and discussed.

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