BIG-B8: Boundary Anisotropy and Finite-Time Separatrix Thresholds in Degenerate Mixed-Gradient Dissipative Fields

This dataset provides numerical results for the BIG-B8 series, studying finite-time runaway thresholds in a degenerate mixed-gradient dissipative field.

The model equation is

∂t φ = ∇·(φ^m ∇φ) − μφ − γ∇·(|∇φ|²∇φ),

with representative parameters m = 1.0, μ = 0.3, γ = 0.8735, and finite observation time T = 0.4. Initial conditions are compact elliptical profiles of the form

φ₀ = A(1 − x²/a² − y²/b²)²₊.

The main quantity is A_c, a finite-time amplitude threshold separating survival up to T = 0.4 from runaway under the stated numerical criterion.

The central finding is that the finite-time threshold A_c depends monotonically on the ellipse ratio b/a. More anisotropic boundaries have lower critical amplitudes. At N = 96, the eccentricity scan shows an approximately linear relation between A_c and b/a. Regression analysis further indicates that the same critical points can be smoothly reparametrized by the critical boundary-gradient energy E24_c = E2_c + E4_c, with an approximate square-root-like scaling.

A three-point N = 120 validation at b/a = 1.00, 0.70, and 0.40 confirms that the monotone ordering of A_c with respect to boundary anisotropy is preserved under resolution refinement, although the absolute threshold values decrease. Therefore, the geometry-dependent separatrix shift is not merely a coarse-grid artifact, while its quantitative location remains resolution-dependent.

Important caution: all reported thresholds should be interpreted as finite-time thresholds at T = 0.4 under the stated numerical criterion. They are not asymptotic stability thresholds.