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ZENODO
Dataset . 2026
License: CC BY
Data sources: ZENODO
ZENODO
Dataset . 2026
License: CC BY
Data sources: Datacite
ZENODO
Dataset . 2026
License: CC BY
Data sources: Datacite
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BIG-B8: Boundary Anisotropy and Finite-Time Separatrix Thresholds in Degenerate Mixed-Gradient Dissipative Fields

Authors: Lucis, Jun;

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

Abstract

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.

Keywords

nonlinear dynamics, numerical simulation, compact support, separatrix, quartic gradient; mixed-gradient field, boundary anisotropy, finite-time threshold, Boundary Information Geometry, degenerate diffusion, runaway transition, free boundary

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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