PreprintarXiv licencearXiv
Constituent-Tagged Transfer Linking Cluster Dynamics to Static Scaling
Abstract
Clusters that merge and split have no unique genealogy. Tracking the host size of a conserved constituent defines q* by ⟨(St+τ/St)q*⟩=1, with q*≠0. Across coupled map networks, coagulation-fragmentation dynamics, and Vicsek systems, q*≃α−2 without fitting, where c(s)∝ s−α on the same size window. Radius scans locate the known Vicsek interaction radius and recover an independently specified clustering scale in experimental active rods. Local scale covariance yields the relation, while a tent map counterexample shows when reducing the stationary balance at each parent size to one moment fails.
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BibTeX
@misc{shinoda2026constituenttagged,
title = {{Constituent-Tagged Transfer Linking Cluster Dynamics to Static Scaling}},
author = {Kenji Shinoda},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02960},
eprint = {2609.02960},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02960},
}
RIS
TY - UNPB
TI - Constituent-Tagged Transfer Linking Cluster Dynamics to Static Scaling
AU - Kenji Shinoda
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02960
UR - https://arxiv.org/abs/2609.02960
AB - Clusters that merge and split have no unique genealogy. Tracking the host size of a conserved constituent defines q_* by ⟨(S_t+τ/S_t)^q_*⟩=1, with q_*≠0. Across coupled map networks, coagulation-fragmentation dynamics, and Vicsek systems, q_*≃α−2 without fitting, where c(s)∝ s^−α on the same size window. Radius scans locate the known Vicsek interaction radius and recover an independently specified clustering scale in experimental active rods. Local scale covariance yields the relation, while a tent map counterexample shows when reducing the stationary balance at each parent size to one moment fails.
ER -