Subcritical pitchfork conjecture for the Ren–Wei branch

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Let χ\chi be the fissility parameter and let χ∗\chi_* be the bifurcation value. The Ren–Wei branch is the equilibrium branch emerging at this bifurcation. Subcritical pitchfork conjecture. The bifurcation at χ=χ∗\chi=\chi_* is of subcritical pitchfork type. The equilibrium on the Ren–Wei branch exists only for χ<χ∗\chi<\chi_* and is unstable. This conjecture is proposed in opposition to the supercritical scenario, based on the paper's numerical results; the supplied text gives no rigorous resolution.

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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