Geometry-Controlled Initial-Density Dependence in Branching-Merging Exclusion Processes
Abstract
We study geometry-controlled, initial-density-dependent stationary states in exclusion processes with branching-merging structures. We consider two boundary geometries for connecting the parallel branches to the reservoirs: the 1-n-1 model, in which a single lane branches into n parallel lanes and then merges back into a single lane, and the 0-n-0 model, in which particles directly enter and leave the n parallel lanes. For both models, we derive critical initial densities separating the low-density, shock-wave, and high-density regimes, and show that the theoretical predictions reproduce the phase diagrams and branch-averaged densities observed in simulations. In the 1-n-1 geometry, the critical initial densities depend on both the number of branches and the lengths of the upstream and downstream single-lane segments, whereas in the 0-n-0 geometry the corresponding estimates depend only on the number of branches. These results show that initial-condition dependence can arise from the global geometry of a branching-merging exclusion process, even without an explicit friction rule at the merging point.
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BibTeX
@misc{yamamoto2026geometrycontrolled,
title = {{Geometry-Controlled Initial-Density Dependence in Branching-Merging Exclusion Processes}},
author = {Hiroki Yamamoto and Daichi Yanagisawa and Katsuhiro Nishinari},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15333},
eprint = {2610.15333},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15333},
note = {CC0},
}
RIS
TY - UNPB
TI - Geometry-Controlled Initial-Density Dependence in Branching-Merging Exclusion Processes
AU - Hiroki Yamamoto
AU - Daichi Yanagisawa
AU - Katsuhiro Nishinari
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15333
UR - https://arxiv.org/abs/2610.15333
AB - We study geometry-controlled, initial-density-dependent stationary states in exclusion processes with branching-merging structures. We consider two boundary geometries for connecting the parallel branches to the reservoirs: the 1-n-1 model, in which a single lane branches into n parallel lanes and then merges back into a single lane, and the 0-n-0 model, in which particles directly enter and leave the n parallel lanes. For both models, we derive critical initial densities separating the low-density, shock-wave, and high-density regimes, and show that the theoretical predictions reproduce the phase diagrams and branch-averaged densities observed in simulations. In the 1-n-1 geometry, the critical initial densities depend on both the number of branches and the lengths of the upstream and downstream single-lane segments, whereas in the 0-n-0 geometry the corresponding estimates depend only on the number of branches. These results show that initial-condition dependence can arise from the global geometry of a branching-merging exclusion process, even without an explicit friction rule at the merging point.
ER -