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.

Brownian Motion on Cantor Sets

2020 ◽  
Vol 21 (3-4) ◽  
pp. 275-281
Author(s):  
Ali Khalili Golmankhaneh ◽  
Saleh Ashrafi ◽  
Dumitru Baleanu ◽  
Arran Fernandez
Keyword(s):  
Brownian Motion ◽  
Classical Method ◽  
Mean Square Displacement ◽  
Planck Equation ◽  
Cantor Sets ◽  
Mean Square ◽  
Fokker Planck Equation ◽  
Fractal Time ◽  
The Mean ◽  
Fokker Planck

AbstractIn this paper, we have investigated the Langevin and Brownian equations on fractal time sets using Fα-calculus and shown that the mean square displacement is not varied linearly with time. We have also generalized the classical method of deriving the Fokker–Planck equation in order to obtain the Fokker–Planck equation on fractal time sets.

scholarly journals Modeling Anomalous Diffusion by a Subordinated Integrated Brownian Motion

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Long Shi ◽  
Aiguo Xiao
Keyword(s):  
Brownian Motion ◽  
Continuous Time ◽  
Waiting Times ◽  
Mean Square Displacement ◽  
Mean Square ◽  
Weak Ergodicity ◽  
Normal Diffusion ◽  
Weak Ergodicity Breaking ◽  
The Mean ◽  
Ergodicity Breaking

We consider a particular type of continuous time random walk where the jump lengths between subsequent waiting times are correlated. In a continuum limit, the process can be defined by an integrated Brownian motion subordinated by an inverse α-stable subordinator. We compute the mean square displacement of the proposed process and show that the process exhibits subdiffusion when 0<α<1/3, normal diffusion when α=1/3, and superdiffusion when 1/3<α<1. The time-averaged mean square displacement is also employed to show weak ergodicity breaking occurring in the proposed process. An extension to the fractional case is also considered.

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.

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.

Numerics for the fractional Langevin equation driven by the fractional Brownian motion

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Peng Guo ◽  
Caibin Zeng ◽  
Changpin Li ◽  
YangQuan Chen
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Fractional Order ◽  
Langevin Equation ◽  
Mean Square Displacement ◽  
Hurst Parameter ◽  
Mean Square ◽  
Fractional Langevin Equation ◽  
Normal Diffusion ◽  
The Mean

AbstractWe study analytically and numerically the fractional Langevin equation driven by the fractional Brownian motion. The fractional derivative is in Caputo’s sense and the fractional order in this paper is α = 2 − 2H, where H ∈ ($\tfrac{1} {2} $, 1) is the Hurst parameter (or, index). We give numerical schemes for the fractional Langevin equation with or without an external force. From the figures we can find that the mean square displacement of the fractional Langevin equation has the property of the anomalous diffusion. When the fractional order tends to an integer, the diffusion reduces to the normal diffusion.

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.

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