2404.01032
Gelation in input-driven aggregation
P. L. Krapivsky, S. A. Matveev
correcthigh confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s statements and derivations are correct and complete for the items audited (pre-gel M2(t)=tan t with tg=π/2; post-gel Flory parametric formula for g(t); Stockmayer steady state with μ=√2, explicit c_s and c; ternary Riccati/Airy result). The candidate solution reaches the same main results, but it mis-specifies the PDE for G=∂zF and briefly conflates G(0,t) with M1(t); nonetheless it proceeds via the same characteristics/energy route and arrives at the exact parametric representation for g(t) matching the paper.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
A careful, largely exact analysis of input-driven aggregation with product kernels is presented. The pre-gel, post-gel (Flory) parametric description of the giant component, and the Stockmayer steady state are all derived cleanly and verified numerically; the ternary extension is handled with Airy functions. The results provide valuable analytical benchmarks. Minor expository additions (derivation details for the Burgers-type PDE and characteristics, brief comments on Stockmayer consistency) would improve accessibility.