Stochastic Complex Ginzburg-Landau

Implementation of the Stochastic Complex Ginzburg-Landau (SCGL) using pseudospectral method and Runge-Kuta-Fehlberg 4-5 method. The additive SCGL is: $$\partial_t A = (1+ib) \nabla^2 A + A - (1+ic) |A|^2A + \sigma \partial_t(\eta_\beta)$$ The multiplicative SCGL is:
$$\partial_t A = (1+ib) \nabla^2 A + A - (1+ic) |A|^2A + \sigma A \partial_t(\eta_\beta)$$ where $A$ is a complex number, and $\eta_\beta$ is a colored noise. This method was implemented for a multidimensional context, meaning 1D, 2D and 3D examples are presented.

Files

The implementation of SCGL is given by NCGL.py.

The noise generation algorithm is given by the cNoise.py

The examples are presented here.

The following video shows the traditional Complex Ginzburg-Landau:

CGL.2D.mp4

SCGL

An example of SCGL with additive noise is:

Additive.SCGL.mp4

An example of SCGL with multiplicative noise is:

Multiplicative.SCGL.mp4

GPA

We also present a Gradient Pattern Analysis (GPA) of the system. The implementation is public available here. The following video shows the real, imaginary and modulus at every snapshot, and the histogram of amplitudes. The series bellow the snapshot shows the second Gradient Moment metric ($G_2$), and the dashed line is the respective time.

GPA.Analysis.CGL.mp4

Multidimension CGL

The multidimensional case is under development. The solution for the simplest case is:

1D:

3D:

3D.Ginzburg-Landau.mp4

Paper link

Under submission