Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 40 min ago
PreprintarXiv licencearXiv

Analytical derivation of a three-dimensional fundamental diagram for a real-valued max-plus particle system

  • Daisuke Takahashi
  • Junta Matsukidaira
  • Kazuya Okamoto
Open at sourcePDFDOICite

Abstract

We study a real-valued max-plus particle system on a finite periodic lattice. Its three-dimensional fundamental diagram relates the mean flow to two densities: the conserved particle density and a second density defined by a local state function. We prove that the deviation from the diagram tends to zero for arbitrary initial data with all state values in [0,1]. The proof uses two nonnegative local quantities and their evolution relations. For rational initial data with all state values in [0,1], the orbit is eventually periodic, and the fundamental-diagram relation holds exactly on the periodic orbit.

Related

  1. Hamiltonian dynamics with nonconservative forces on extended phase space: An analytical mechanics derivation
    Joseph T. A Peterson, Manoranjan Majji, John L. Junkins
    arXivPreprintCC BY 4.0Full textGeometry & topologyMathematical physicsarXiv
  2. Derivation of OH sum rules without Rayleigh--Jeans approximation: a powerful tool for measuring the variation of fundamental physical constants
    Renzhi Su, Minfeng Gu
    arXivPreprintCC BY-NC-ND 4.0Full textCosmologyAtomic, molecular & optical physicsarXiv
  3. Breaking Behavioral Uniformity in Traffic Flow: Analytical Derivation and Numerical Verification of Optimal Cooperative Buffering
    Raphael Korbmacher, Antoine Tordeux
    arXivPreprintarXiv licenceFull textStatistical & nonlinear physicsarXiv
  4. Second-Order Rayleigh-Schrödinger Perturbation Theory for the GRASP2018 Package: Three-Particle Feynman Diagram Contribution to Valence-Valence Correlations
    G. Gaigalas, P. Rynkun, L. Kitovienė
    arXivPreprintCC BY-NC-ND 4.0Full textAtomic, molecular & optical physicsarXiv
  5. Second-Order Rayleigh-Schrödinger Perturbation Theory for the GRASP2018 Package: Three-Particle Feynman Diagram Contribution to Core-Valence Correlations
    G. Gaigalas, P. Rynkun, L. Kitovienė
    arXivPreprintCC BY-NC-ND 4.0Full textAtomic, molecular & optical physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{takahashi2026analytical,
  title = {{Analytical derivation of a three-dimensional fundamental diagram for a real-valued max-plus particle system}},
  author = {Daisuke Takahashi and Junta Matsukidaira and Kazuya Okamoto},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.00957},
  eprint = {2610.00957},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.00957},
}
RIS
TY  - UNPB
TI  - Analytical derivation of a three-dimensional fundamental diagram for a real-valued max-plus particle system
AU  - Daisuke Takahashi
AU  - Junta Matsukidaira
AU  - Kazuya Okamoto
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.00957
UR  - https://arxiv.org/abs/2610.00957
AB  - We study a real-valued max-plus particle system on a finite periodic lattice. Its three-dimensional fundamental diagram relates the mean flow to two densities: the conserved particle density and a second density defined by a local state function. We prove that the deviation from the diagram tends to zero for arbitrary initial data with all state values in [0,1]. The proof uses two nonnegative local quantities and their evolution relations. For rational initial data with all state values in [0,1], the orbit is eventually periodic, and the fundamental-diagram relation holds exactly on the periodic orbit.
ER  -