Swift-Hohenberg Equation - Ripple Pattern vs. Homogeneous State
Автор: Richters Finger
Загружено: 2021-06-27
Просмотров: 579
Описание:
The spatially two-dimensional Swift-Hohenberg equation with quadratic and cubic nonlinearity (SH23) finds application in the description of a broad spectrum of pattern forming systems. Hence, this equation is a well-investigated and often used paradigmatic model for pattern formation.
The visualization below shows the models dynamics for larger values of r = -2.5 and δ∈[4.05, 4.25]. If the system is initialized with high-amplitude noise, a competition between the formation of a ripple pattern and grains of a homogeneous state can be observed. Here, a set of three examples in this regime is given.
The numerical integration was done using a pseudo-spectral implementation of the standard Runge-Kutta scheme.
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