Category: Nonlinear Dyn.

Summary: Finding how much anisotropic shell-to-bulk mixing is needed to destroy a shell-localized unstable mode in a random Turing-like system.

Reaction-diffusion systems can form patterns when an unstable mode amplifies spatial structure, and heterogeneous media can localize that activity to particular regions. This experiment asks when anisotropic transport between a shell and a bulk region becomes strong enough to erase a mode that was previously concentrated on the shell.

The model builds dense random operators for coupled shell and bulk degrees of freedom, then uses GPU eigensolves to track the dominant unstable mode while anisotropy is varied. An iterative threshold search identifies the point where localization collapses and the mode is no longer confined to the shell geometry.

That makes the project a structural stability problem for pattern-forming systems. Instead of asking only whether an instability exists, it asks where that instability lives and when directional mixing destroys the spatial specialization that produced it.

Method: GPU dense symmetric eigensolves on random shell-bulk reaction-diffusion operators, with iterative deepening and bisection on anisotropic mixing.

What is measured: Critical anisotropy threshold, localization of the leading unstable mode, shell-versus-bulk weight, system size reached, and bracket width.