Application of Fokker-Planck-Kramers equation treatment for short-time dynamics of diffusion-controlled reaction in supercritical Lennard-Jones fluids over a wide density range

2006 ◽  
Vol 124 (13) ◽  
pp. 134506 ◽  
Author(s):  
Kazuyasu Ibuki ◽  
Masakatsu Ueno
Keyword(s):  
Density Range ◽  
Time Dynamics ◽  
Lennard Jones ◽  
Diffusion Controlled ◽  
Kramers Equation ◽  
Short Time ◽  
Diffusion Controlled Reaction ◽  
Fokker Planck

scholarly journals Multipoint reconstruction of wind speeds

2020 ◽  
Vol 5 (3) ◽  
pp. 1211-1223
Author(s):  
Christian Behnken ◽  
Matthias Wächter ◽  
Joachim Peinke
Keyword(s):  
Wind Speed ◽  
Numerical Solutions ◽  
Mean Value ◽  
Wind Data ◽  
Conditional Probability Density ◽  
Time Dynamics ◽  
Fokker Planck Equations ◽  
Short Time ◽  
Speed Fluctuations ◽  
Fokker Planck

Abstract. The most intermittent behaviour of atmospheric turbulence is found for very short timescales. Based on a concatenation of conditional probability density functions (cpdf's) of nested wind speed increments, inspired by a Markov process in scale, we derive a short-time predictor for wind speed fluctuations around a non-stationary mean value and with a corresponding non-stationary variance. As a new quality this short-time predictor enables a multipoint reconstruction of wind data. The used cpdf's are (1) directly estimated from historical data from the offshore research platform FINO1 and (2) obtained from numerical solutions of a family of Fokker–Planck equations in the scale domain. The explicit forms of the Fokker–Planck equations are estimated from the given wind data. A good agreement between the statistics of the generated and measured synthetic wind speed fluctuations is found even on timescales below 1 s. This shows that our approach captures the short-time dynamics of real wind speed fluctuations very well. Our method is extended by taking the non-stationarity of the mean wind speed and its non-stationary variance into account.

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