Gaussian short-time propagators and electron kinetics: Numerical evaluation of path-sum solutions to Fokker–Planck equations for rf heating and current drive

1997 ◽  
Vol 4 (6) ◽  
pp. 2027-2030 ◽  
Author(s):  
João P. S. Bizarro ◽  
Jorge H. Belo ◽  
António C. Figueiredo
Keyword(s):  
Numerical Evaluation ◽  
Current Drive ◽  
Rf Heating ◽  
Electron Kinetics ◽  
Fokker Planck Equations ◽  
Short Time ◽  
Fokker Planck

scholarly journals Multipoint Reconstruction of Wind Speeds

2020 ◽  
Author(s):  
Christian Behnken ◽  
Matthias Wächter ◽  
Joachim Peinke
Keyword(s):  
Wind Speed ◽  
Time Scales ◽  
Numerical Solutions ◽  
Wind Data ◽  
Conditional Probability Density ◽  
Wind Speeds ◽  
Fokker Planck Equations ◽  
Short Time ◽  
Speed Fluctuations ◽  
Fokker Planck

Abstract. The most intermittent behavior of atmospheric turbulence is found for very short time scales. Based on a concatenation of conditional probability density functions (cpdfs) of nested wind speeds 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 cpdfs 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 synthetic wind speed fluctuations and the measured is found even on time scales 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.

Short-time propagators for nonlinear Fokker-Planck equations

1999 ◽  
Vol 32 (20) ◽  
pp. 3681-3695 ◽  
Author(s):  
J M Donoso ◽  
J J Salgado ◽  
M Soler
Keyword(s):  
Fokker Planck Equations ◽  
Short Time ◽  
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.

scholarly journals Fokker–Planck representations of non-Markov Langevin equations: application to delayed systems

2019 ◽  
Vol 377 (2153) ◽  
pp. 20180131 ◽  
Author(s):  
Luca Giuggioli ◽  
Zohar Neu
Keyword(s):  
Langevin Equation ◽  
Complex Dynamics ◽  
Probability Distributions ◽  
Delay Systems ◽  
Langevin Equations ◽  
Delayed Systems ◽  
Temporal Features ◽  
Fokker Planck Equations ◽  
Random Fluctuations ◽  
Fokker Planck

Noise and time delays, or history-dependent processes, play an integral part in many natural and man-made systems. The resulting interplay between random fluctuations and time non-locality are essential features of the emerging complex dynamics in non-Markov systems. While stochastic differential equations in the form of Langevin equations with additive noise for such systems exist, the corresponding probabilistic formalism is yet to be developed. Here we introduce such a framework via an infinite hierarchy of coupled Fokker–Planck equations for the n -time probability distribution. When the non-Markov Langevin equation is linear, we show how the hierarchy can be truncated at n  = 2 by converting the time non-local Langevin equation to a time-local one with additive coloured noise. We compare the resulting Fokker–Planck equations to an earlier version, solve them analytically and analyse the temporal features of the probability distributions that would allow to distinguish between Markov and non-Markov features. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.

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