Connection of the velocity autocorrelation function to the mean-square-displacement and to the memory function of generalized master equations

1981 ◽  
Vol 41 (2) ◽  
pp. 177-180 ◽  
Author(s):  
V. M. Kenkre ◽  
R. K�hne ◽  
P. Reineker
Keyword(s):  
Autocorrelation Function ◽  
Memory Function ◽  
Mean Square Displacement ◽  
Master Equations ◽  
Velocity Autocorrelation Function ◽  
Mean Square ◽  
Velocity Autocorrelation ◽  
Generalized Master Equations ◽  
The Mean

scholarly journals Impulse response function for Brownian motion

Soft Matter ◽  
2021 ◽  
Author(s):  
Nicos Makris
Keyword(s):  
Brownian Motion ◽  
Time Derivative ◽  
Mean Square Displacement ◽  
Impulse Response Function ◽  
Velocity Autocorrelation Function ◽  
Mean Square ◽  
Velocity Autocorrelation ◽  
The Mean ◽  
First Time

Motivated from the central role of the mean-square displacement and its second time-derivative – that is the velocity autocorrelation function in the description of Brownian motion, we revisit the physical meaning of its first time-derivative.

Velocity and force correlations in H2–He mixtures

1968 ◽  
Vol 46 (20) ◽  
pp. 2315-2319 ◽  
Author(s):  
V. F. Sears
Keyword(s):  
Autocorrelation Function ◽  
Room Temperature ◽  
Mean Square Displacement ◽  
Intermolecular Potential ◽  
Repulsive Core ◽  
Velocity Autocorrelation Function ◽  
Velocity Autocorrelation ◽  
A Value ◽  
Helium Gas ◽  
The Mean

The fundamental vibrational band of the pressure-induced infrared spectrum of hydrogen in room-temperature helium gas (compressed to twice the density of the normal liquid) is analyzed to determine the force autocorrelation function and, hence, the velocity autocorrelation function and the mean square displacement of a hydrogen molecule as a function of time. The initial curvature of the force autocorrelation function, extrapolated to zero density, yields a value 0.087 for the ratio ρ/σ where ρ is the range of the repulsive core of the intermolecular potential and σ is the diameter of this core. Moment relations, which enable one to determine the parameters in a model introduced recently by Van Kranen-donk, are derived for the force autocorrelation function.

scholarly journals Lecture on the anomalous diffusion in Condensed Matter Physics

2018 ◽  
Vol 3 (2) ◽  
Author(s):  
M. Benhamou ◽  
Keyword(s):  
Anomalous Diffusion ◽  
Condensed Matter ◽  
Mean Square Displacement ◽  
Continuous Phase ◽  
Generalized Langevin Equation ◽  
Velocity Autocorrelation Function ◽  
Condensed Matter Physics ◽  
Mean Square ◽  
Pickering Emulsions ◽  
The Mean

Diffusion is a natural or artificial process that governs many phenomena in nature. The most known diffusion is the Brownian or normal motion, where the mean-square-displacement of the tracer (diffusive particle among others) increases as the square-root of time. It is not the case, however, for complex systems, where the diffusion is rather slow, because at small-scales, these media present an heterogenous structure. This kind of slow motion is called subdiffusion, where the associated mean-square-displacement increases in time, with a non trivial exponent, alpha, whose value is between 0 and 1. In this review paper, we report on new trends dealing with the study of the anomalous diffusion in Condensed Matter Physics. The study is achieved using a theoretical approach that is based on a Generalized Langevin Equation. As particular crowded systems, we choose the so-called Pickering emulsions (oil-in-water), and we are interested in how the dispersed droplets (protected by small solid charged nanoparticles) can diffuse in the continuous phase (water). Dynamic study is accomplished through the mean-square-displacement and the velocity-autocorrelation-function. Finally, a comparison with Molecular Dynamics data is made.

A Titanium-Decorated Fullerene Cluster – A Molecular Dynamics Simulation

2008 ◽  
Vol 140 ◽  
pp. 109-116 ◽  
Author(s):  
A. Piątek ◽  
Roman Nowak ◽  
Z. Gburski
Keyword(s):  
Solid State ◽  
Md Simulation ◽  
Mean Square Displacement ◽  
Dynamics Simulation ◽  
Pentagonal Bipyramid ◽  
Velocity Autocorrelation Function ◽  
Translational Diffusion Coefficient ◽  
Velocity Autocorrelation ◽  
Wide Range ◽  
The Mean

A small titanium-decorated fullerene cluster (C60[TiH2]6)7 was studied by MD simulation over a wide range of energy, from the solid state to the vaporization of the nanosystem. The low energy, solid state structure of the cluster was obtained as a deformed pentagonal bipyramid. Several physical characteristics: the radial distribution function, the mean square displacement, the translational velocity autocorrelation function, translational diffusion coefficient, Lindemann index, etc., were calculated for a wide range of energy in the system.

The Influence of Graphene Sheet on the Dynamics of Cholesterol Molecules in the Lodgment Located near a Transmembrane Protein – MD Study

2008 ◽  
Vol 140 ◽  
pp. 141-146
Author(s):  
P. Raczynski ◽  
A. Dawid ◽  
Z. Gburski
Keyword(s):  
Molecular Dynamics ◽  
Distribution Function ◽  
Graphene Sheet ◽  
Transmembrane Protein ◽  
Mean Square Displacement ◽  
Md Simulations ◽  
Mean Square ◽  
Velocity Autocorrelation ◽  
The Mean ◽  
Velocity Autocorrelation Functions

Molecular dynamics (MD) simulations have been made for a cluster of cholesterols localized near the transmembrane protein at the physiological temperature of 310 K. It was observed that the cholesterol molecules form a lodgment on the surface of protein. Additional studies were made of the influence of graphene sheet on several physical observables of cholesterol molecules including: the radial distribution function, the mean square displacement, diffusion coefficient and the linear and angular velocity autocorrelation functions.

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