Saddle-node conjecture for the two-dimensional Ren–Wei branch

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Let χ\chi be the fissility parameter, let χ∗\chi_* be the bifurcation value, and let χ4≈0.904±0.001\chi_4\approx0.904\pm0.001. The Ren–Wei branch is the two-dimensional equilibrium branch emerging at χ=χ∗\chi=\chi_*. Ren–Wei saddle-node conjecture. The Ren–Wei branch does not continue to arbitrarily small χ\chi and disappears at χ=χ4\chi=\chi_4 through a saddle-node bifurcation. As χ\chi decreases from χ∗\chi_* to χ4\chi_4, the equilibrium on this branch changes shape from a disk to an ellipse-like shape to an eye mask. This claim is based on the paper's numerical results and remains unresolved in the supplied text.

References

Primary source

Zirui Xu and Qiang Du, “Bifurcation and fission in the liquid drop model: a phase-field approach”, arXiv:2302.14449 (2023).

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