2105.00169
ASYMPTOTIC BEHAVIOR OF FRONTS AND PULSES OF THE BIDOMAIN MODEL
Hiroshi Matano, Yoichiro Mori, Mitsunori Nara, Koya Sakakibara
uncertainmedium confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
Key statements about bidomain Allen–Cahn (long-wave instability via Frank-plot nonconvexity) are summarized from prior analytic work and used correctly; the paper’s new claims on zigzag-facet selection and Wulff-shape spreading are posed as conjectures with numerical support, not proofs. The candidate solution mirrors this: it correctly cites the known spectral criterion, reproduces the geometric speed formula, and treats Wulff-shape convergence for the bidomain operator as expected but (as of 2021-05-01) unproven. Hence the central parts remain open at the stated cutoff, with both paper and model aligned on what is proven versus conjectural.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
A solid computational study grounded in prior analysis that clarifies phenomena unique to the bidomain operator (zigzag fronts/pulses, Hopf bifurcations, coarsening, spreading). It advances understanding and suggests mechanisms relevant to arrhythmias. Some statements are conjectural (as clearly indicated) and supported numerically. Minor revisions focused on clarity and reproducibility would improve the paper.