Molecular Distribution Functions in a One‐Dimensional Fluid

1953 ◽  
Vol 21 (6) ◽  
pp. 1098-1107 ◽  
Author(s):  
Zevi W. Salsburg ◽  
Robert W. Zwanzig ◽  
John G. Kirkwood
Keyword(s):  
Distribution Functions ◽  
One Dimensional ◽  
Molecular Distribution

Asymptotic behavior of velocity process in the Smoluchowski–Kramers approximation for stochastic differential equations

1991 ◽  
Vol 23 (2) ◽  
pp. 317-326 ◽  
Author(s):  
Kiyomasa Narita
Keyword(s):  
Mean Field ◽  
Planck Equation ◽  
Equation Of Motion ◽  
Distribution Functions ◽  
Two Dimensional ◽  
Large Parameter ◽  
Uhlenbeck Process ◽  
One Dimensional ◽  
Kramers Equation ◽  
Non Linear Oscillator

Here a response of a non-linear oscillator of the Liénard type with a large parameter α ≥ 0 is formulated as a solution of a two-dimensional stochastic differential equation with mean-field of the McKean type. This solution is governed by a special form of the Fokker–Planck equation such as the Smoluchowski–Kramers equation, which is an equation of motion for distribution functions in position and velocity space describing the Brownian motion of particles in an external field. By a change of time and displacement we find that the velocity process converges to a one-dimensional Ornstein–Uhlenbeck process as α →∞.

Comparative Study of Probability Distribution Functions of Wind Power Variation

2014 ◽  
Vol 953-954 ◽  
pp. 414-418
Author(s):  
An Jue Dai ◽  
Qian Wang ◽  
Yan Nan Zhou
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Wind Power ◽  
Gaussian Distribution ◽  
Gaussian Mixture ◽  
Second Order ◽  
Distribution Functions ◽  
Normal Distribution Function ◽  
One Dimensional ◽  
Power Variation

This work focuses on the probability distribution function of wind power variation. After analyzing the characters of the power fluctuation data, normal distribution function, t location-scale distribution function and mixed second-order one-dimensional Gaussian distribution function are chosen to describe the wind power variation. Then K-S test(Kolmogorov-Smirnov) test and Pearson product-moment correlation coefficient are used to evaluate the fitting effect of the three distribution functions respectively, which indicates that the mixed second-order one-dimensional Gaussian distribution is the most appropriate one. At last, the factors affecting the parameters of Gaussian mixture distribution and to what degree they can achieve are investigated.

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