jmframe/cgle

omplex Ginzburg-Landau Equation

Complex Ginzburg-Landau Equation (CGLE) Simulation

This repository contains a Jupyter Notebook (cgle.ipynb) that demonstrates a numerical simulation of the Complex Ginzburg-Landau Equation (CGLE), a nonlinear partial differential equation that describes a wide array of phenomena from fluid dynamics to quantum physics.

Overview

The CGLE is an equation of great interest in the study of pattern formation and turbulence in nonlinear, nonequilibrium systems. The equation takes the form of a partial differential equation with both linear and nonlinear terms that include complex coefficients.

$$\partial_t A = A + (1 + i\alpha) \nabla^2 A - (1 + i\beta)|A|^2 A$$

In this notebook, we present a numerical approach to solve this equation using a pseudo-spectral method and visualize the evolution of the complex field over time.

Dependencies

To run the notebook, you will need the following:

• Python 3.x
• Matplotlib (for plotting and animation)
• NumPy (for numerical operations)

You can install these dependencies via pip:

pip install matplotlib numpy

Running the Simulation

To view and run the simulation:

1. Clone this repository or download cgle.py and cgle.ipynb.
2. Ensure you have Jupyter installed, or use an online platform such as Google Colab.
3. Open the notebook and execute the cells in sequence.

Visualization

The notebook uses matplotlib to create snapshot plots that visualizes the dynamics of the complex field as they evolve in time according to the CGLE.