Model Reduction of the Nonlinear Complex Ginzburg–Landau Equation

2010 ◽  
Vol 9 (4) ◽  
pp. 1284-1302 ◽  
Author(s):  
Miloš Ilak ◽  
Shervin Bagheri ◽  
Luca Brandt ◽  
Clarence W. Rowley ◽  
Dan S. Henningson
Keyword(s):  
Model Reduction ◽  
Landau Equation ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation

scholarly journals Input-Output Analysis and Control Design Applied to a Linear Model of Spatially Developing Flows

2009 ◽  
Vol 62 (2) ◽  
Author(s):  
S. Bagheri ◽  
D. S. Henningson ◽  
J. Hœpffner ◽  
P. J. Schmid
Keyword(s):  
Fluid Mechanics ◽  
Model Reduction ◽  
Landau Equation ◽  
Control Design ◽  
Input Output ◽  
Output Analysis ◽  
Ginzburg Landau ◽  
Input Output Analysis ◽  
Ginzburg Landau Equation ◽  
And Control

This review presents a framework for the input-output analysis, model reduction, and control design for fluid dynamical systems using examples applied to the linear complex Ginzburg–Landau equation. Major advances in hydrodynamics stability, such as global modes in spatially inhomogeneous systems and transient growth of non-normal systems, are reviewed. Input-output analysis generalizes hydrodynamic stability analysis by considering a finite-time horizon over which energy amplification, driven by a specific input (disturbances/actuator) and measured at a specific output (sensor), is observed. In the control design the loop is closed between the output and the input through a feedback gain. Model reduction approximates the system with a low-order model, making modern control design computationally tractable for systems of large dimensions. Methods from control theory are reviewed and applied to the Ginzburg–Landau equation in a manner that is readily generalized to fluid mechanics problems, thus giving a fluid mechanics audience an accessible introduction to the subject.

Spiral Solutions of the Two-Dimensional Complex Ginzburg–Landau Equation

2001 ◽  
Vol 35 (2) ◽  
pp. 159-161
Author(s):  
Liu Shi-Da ◽  
Liu Shi-Kuo ◽  
Fu Zun-Tao ◽  
Zhao Qiang
Keyword(s):  
Landau Equation ◽  
Two Dimensional ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation
Sign in / Sign up

Export Citation Format

Share Document