Averaging method and adiabatic invariants

2008 ◽  
pp. 53-66 ◽  
Author(s):  
Anatoly Neishtadt
Keyword(s):  
Averaging Method ◽  
Adiabatic Invariants

scholarly journals Semi-analytical solutions of seismo-electromagnetic signals arising from the motional induction in 3-D multi-layered media: part II—numerical investigations

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Hengxin Ren ◽  
Ling Zeng ◽  
Yao-Chong Sun ◽  
Ken’ichi Yamazaki ◽  
Qinghua Huang ◽  
...  
Keyword(s):  
Point Source ◽  
Numerical Computation ◽  
Wave Velocity ◽  
Excellent Agreement ◽  
Seismic Waves ◽  
Averaging Method ◽  
Ground Surface ◽  
Induction Effect ◽  
Motional Induction ◽  
Electromagnetic Signals

AbstractIn this paper, numerical computations are carried out to investigate the seismo-electromagnetic signals arising from the motional induction effect due to an earthquake source embedded in 3-D multi-layered media. First, our numerical computation approach that combines discrete wavenumber method, peak-trough averaging method, and point source stacking method is introduced in detail. The peak-trough averaging method helps overcome the slow convergence problem, which occurs when the source–receiver depth difference is small, allowing us to consider any focus depth. The point source stacking method is used to deal with a finite fault. Later, an excellent agreement between our method and the curvilinear grid finite-difference method for the seismic wave solutions is found, which to a certain degree verifies the validity of our method. Thereafter, numerical computation results of an air–solid two-layer model show that both a receiver below and another one above the ground surface will record electromagnetic (EM) signals showing up at the same time as seismic waves, that is, the so-called coseismic EM signals. These results suggest that the in-air coseismic magnetic signals reported previously, which were recorded by induction coils hung on trees, can be explained by the motional induction effect or maybe other seismo-electromagnetic coupling mechanisms. Further investigations of wave-field snapshots and theoretical analysis suggest that the seismic-to-EM conversion caused by the motional induction effect will give birth to evanescent EM waves when seismic waves arrive at an interface with an incident angle greater than the critical angle θc = arcsin(Vsei/Vem), where Vsei and Vem are seismic wave velocity and EM wave velocity, respectively. The computed EM signals in air are found to have an excellent agreement with the theoretically predicted amplitude decay characteristic for a single frequency and single wavenumber. The evanescent EM waves originating from a subsurface interface of conductivity contrast will contribute to the coseismic EM signals. Thus, the conductivity at depth will affect the coseismic EM signals recorded nearby the ground surface. Finally, a fault rupture spreading to the ground surface, an unexamined case in previous numerical computations of seismo-electromagnetic signals, is considered. The computation results once again indicate the motional induction effect can contribute to the coseismic EM signals.

scholarly journals Why homogenization should be the averaging method of choice in hydrodynamic lubrication

2021 ◽  
pp. 100055
Author(s):  
Michael Rom ◽  
Florian König ◽  
Siegfried Müller ◽  
Georg Jacobs
Keyword(s):  
Averaging Method ◽  
Hydrodynamic Lubrication

scholarly journals Applications of the generalized state-space averaging method to modelling of DC–DC power converters

2012 ◽  
Vol 18 (3) ◽  
pp. 243-260 ◽  
Author(s):  
Phurich Ngamkong ◽  
Pijit Kochcha ◽  
Kongpan Areerak ◽  
Sarawut Sujitjorn ◽  
Kongpol Areerak
Keyword(s):  
State Space ◽  
Power Converters ◽  
Averaging Method ◽  
Dc Power ◽  
Generalized State Space ◽  
Generalized State

Study on Sliding Mode Control in Bidirectional DC/DC Converter Based on State Space Averaging Method

2014 ◽  
Vol 678 ◽  
pp. 399-405
Author(s):  
Yan Mei
Keyword(s):  
Sliding Mode Control ◽  
State Space ◽  
Averaging Method ◽  
Sliding Mode ◽  
Good Stability ◽  
Sliding Mode Controller ◽  
Battery Charging ◽  
Mode Control ◽  
Logic Diagram

Bidirectional DC/DC converter is used for the battery charging and discharging. The sliding mode controller based on state space averaging algorithm is used for controlling bidirectional DC/DC converter. Two kinds of working modes, buck mode and boost mode, have been analyzed and three kinds of working states which are consisted by two working modes have been deeply discussed, and the automatic switch logic diagram when battery charging and discharging through the bidirectional DC/DC converter has been presented. Situation of system based on S1, S2 conducting alternately has been studied, and the simulations were also presented. According to the results, the characteristics of good stability and transient can be confirmed.

Defining the elastic properties and the tensor of the pore-pressure transfer in rocks using the averaging method

2015 ◽  
Vol 70 (4) ◽  
pp. 354-361 ◽  
Author(s):  
S. V. Sheshenin ◽  
N. B. Artamonova ◽  
Yu. V. Frolova ◽  
V. M. Ladygin
Keyword(s):  
Pore Pressure ◽  
Elastic Properties ◽  
Averaging Method

Averaging method in multipoint problems of the theory of nonlinear oscillations

1996 ◽  
Vol 48 (8) ◽  
pp. 1241-1250
Author(s):  
A. M. Samoilenko ◽  
Ya. R. Petryshyn
Keyword(s):  
Averaging Method ◽  
Nonlinear Oscillations
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