Category: Nonlinear Dyn.

Summary: Measuring how the dominant Turing wavelength on finite domains deviates from the linear instability prediction in Schnakenberg pattern formation.

Linear stability theory predicts the most unstable wavelength for a Turing instability, but finite domains and nonlinear mode competition can shift the pattern that actually dominates after the system evolves. This experiment asks how the selected wavelength differs from the linear prediction and how that mismatch scales with domain size.

The script uses a GPU-aware pseudospectral solver for the Schnakenberg reaction-diffusion equations on periodic two-dimensional domains of varying size. It extracts the dominant wavenumber from the late-time Fourier spectrum and compares the measured value against the theoretical linear prediction.

That turns a standard pattern-forming model into a finite-size selection study. The interest is not only whether patterns emerge, but how nonlinear competition and box size bias the wavelength that ultimately wins.

Method: GPU-accelerated FFT pseudospectral integration of the Schnakenberg equations across multiple domain sizes, followed by spectral peak extraction.

What is measured: Dominant wavenumber, linear-prediction wavenumber, wavelength shift delta_k, peak spectral power, domain-size dependence, and trial variability.