Year: 2019
Type: preprint
Abstract: Adaptive flow networks may require changes not only in routing but also in local graphresolution. We study a reversible flow-conditioned elastic split–merge response: a local flowfunctional triggers refinement of a vertex into daughter vertices above an upper threshold andtheir reaggregation below a lower threshold.For a conservative binary split, any partition of the original external incident edges can becompleted conservatively, without changing those external flows, by adding at most one internaltransfer edge. If a single non-negative transfer is allowed, its magnitude and direction are fixedby the partition imbalance. For a split into k daughter vertices, at most k−1 non-zero internaltransfers suffice. Conversely, a conservatively completed daughter set can be reaggregated intoits parent while preserving conservation and all external flows at the transformation instant.Distinct split and merge thresholds introduce hysteresis; a fluctuation whose oscillation issmaller than the hysteresis width cannot generate a complete local split–merge cycle.The operator is formulated as a local building block for adaptive flow-network models.Here elastic refers only to reversible refinement and reaggregation, not to the establishednotion of an elastic graph
Source: arXiv (Cornell University)
Authors: Abu-Khzam, Faisal N., Arrighi, Emmanuel, Bentert, Matthias, Drange, Pål Grønås, Egan, Judith, Gaspers, Serge, Shaw, Alexis, Shaw, Peter, Sullivan, Blair D., Wolf, Petra
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G5916756760, G6774542772
OpenAlex ID: W4289005966