Open Access
Issue
ESAIM: M2AN
Volume 58, Number 2, March-April 2024
Page(s) 515 - 544
DOI https://doi.org/10.1051/m2an/2024004
Published online 04 April 2024
  1. J.A. Acebrón, L.L. Bonilla, C.J.P. Vicente, F. Ritort and R. Spigler, The Kuramoto model: A simple paradigm for synchronization phenomena. Rev. Mod. Phys. 77 (2005) 137–185. [Google Scholar]
  2. M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, V. Lecomte, A. Orlandi, G. Parisi, A. Procaccini and V. Zdravkovic, Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study. Proc. Natl. Acad. Sci. 105 (2008) 1232–1237. [Google Scholar]
  3. L. Barberis and F. Peruani, Phase separation and emergence of collective motion in a one-dimensional system of active particles. J. Chem. Phys. 150 (2019) 144905. [Google Scholar]
  4. L. Carlitz, Some theorems on Bernoulli numbers of higher order. Pac. J. Math. 2 (1952) 127–139. [Google Scholar]
  5. R.E. Chandler, R. Herman and E.W. Montroll, Traffic dynamics: studies in car following. Oper. Res. 6 (1958) 165–184. [Google Scholar]
  6. H. Chaté, F. Ginelli, G. Grégoire, F. Peruani and F. Raynaud, Modeling collective motion: variations on the Vicsek model. Eur. Phys. J. B 64 (2008) 451–456. [Google Scholar]
  7. B. Ciuffo, K. Mattas, M. Makridis, G. Albano, A. Anesiadou, Y. He, S. Josvai, D. Komnos, M. Pataki, S. Vass and Z. Szalay, Requiem on the positive effects of commercial adaptive cruise control on motorway traffic and recommendations for future automated driving systems. Trans. Res. Part C: Emerg. Technol. 130 (2021) 103305. [Google Scholar]
  8. F. Cordoni, L. Di Persio and R. Muradore, Stabilization of bilateral teleoperators with asymmetric stochastic delay. Syst. Control Lett. 147 (2021) 104828. [Google Scholar]
  9. F. Cordoni, L. Di Persio and R. Muradore, Stochastic port-Hamiltonian systems. J. Nonlinear Sci. 32 (2022) 1–53. [Google Scholar]
  10. D. Cvijović and H.M. Srivastava, Closed-form summation of the Dowker and related sums. J. Math. Phys. 48 (2007) 043507. [Google Scholar]
  11. D. Cvijović and H.M. Srivastava, Closed-form summations of Dowker’s and related trigonometric sums. J. Phy. A Math. Theor. 45 (2012) 374015. [Google Scholar]
  12. A. Czirók, A.-L. Barabási and T. Vicsek, Collective motion of self-propelled particles: Kinetic phase transition in one dimension. Phys. Rev. Lett. 82 (1999) 209–212. [Google Scholar]
  13. C.M. da Fonseca, M.L. Glasser and V. Kowalenko, Generalized cosecant numbers and trigonometric inverse power sums. Appl. Anal. Discret. Math. 12 (2018) 70–109. [Google Scholar]
  14. R. De and D. Chakraborty, Collective motion: Influence of local behavioural interactions among individuals. J. Biosci. 47 (2022) 48. [Google Scholar]
  15. P. Degond, G. Dimarco and T.B.N. Mac, Hydrodynamics of the Kuramoto–Vicsek model of rotating self-propelled particles. Math. Models Methods Appl. Sci. 24 (2014) 277–325. [Google Scholar]
  16. J.S. Dowker, Casimir effect around a cone. Phys. Rev. D 36 (1987) 3095–3101. [Google Scholar]
  17. J.S. Dowker, Heat kernel expansion on a generalized cone. J. Math. Phys. 30 (1989) 770–773. [Google Scholar]
  18. J.S. Dowker, On Verlinde’s formula for the dimensions of vector bundles on moduli spaces. J. Phys. A Math. Gen. 25 (1992) 2641–2648. [Google Scholar]
  19. Z. Fang and C. Gao, Stabilization of input-disturbed stochastic port-Hamiltonian systems via passivity. IEEE Trans. Automat. Contr. 62 (2017) 4159–4166. [Google Scholar]
  20. C.K. Fong, Course Notes in Linear Algebra, MATH 2107, February (2008). [Google Scholar]
  21. C.W. Gardiner, Handbook of Stochastic Methods, Vol. 3. Springer Berlin (1985). [Google Scholar]
  22. J. Gautrais, F. Ginelli, R. Fournier, S. Blanco, M. Soria, H. Chat and G. Theraulaz, Deciphering interactions in moving animal groups. PLOS Comput. Biol. 8 (2012) 1–11. [Google Scholar]
  23. D.C. Gazis, R. Herman and R.W. Rothery, Nonlinear follow-the-leader models of traffic flow. Oper. Res. 9 (1961) 545–567. [Google Scholar]
  24. R. Großmann, I.S. Aranson and F. Peruani, A particle-field approach bridges phase separation and collective motion in active matter. Nat. Commun. 11 (2020) 5365. [Google Scholar]
  25. G. Gunter, D. Gloudemans, R.E. Stern, S. McQuade, R. Bhadani, M. Bunting, M.L. Delle Monache, R. Lysecky, B. Seibold, J. Sprinkle and B. Piccoli, Are commercially implemented adaptive cruise control systems string stable? IEEE Trans. Intell. Transp. Syst. 22 (2020) 6992–7003. [Google Scholar]
  26. R. Herman, E.W. Montroll, R.B. Potts and R.W. Rothery, Traffic dynamics: analysis of stability in car following. Oper. Res. 7 (1959) 86–106. [Google Scholar]
  27. Y.-E. Keta, R.L. Jack and L. Berthier, Disordered collective motion in dense assemblies of persistent particles. Phys. Rev. Lett. 129 (2022) 048002. [Google Scholar]
  28. P. Khound, P. Will, A. Tordeux and F. Gronwald, Extending the adaptive time gap car-following model to enhance local and string stability for adaptive cruise control systems. J. Intell. Transp. Syst. 27 (2023) 36–56. [Google Scholar]
  29. F. Lamoline and J.J. Winkin, On stochastic port-Hamiltonian systems with boundary control and observation. In 2017 IEEE 56th Annual Conference on Decision and Control (CDC). IEEE (2017) 2492–2497. [Google Scholar]
  30. F. Lamoline and A. Hastir, On Dirac structure of infinite-dimensional stochastic port-Hamiltonian systems. Preprint: arXiv:2210.06358 (2022). [Google Scholar]
  31. M. Makridis, K. Mattas, A. Anesiadou and B. Ciuffo, OpenACC an open database of car-following experiments to study the properties of commercial ACC systems. Transp. Res. Part C Emerg. Technol. 125 (2021) 103047. [Google Scholar]
  32. M.C. Marchetti, J.-F. Joanny, S. Ramaswamy, T.B. Liverpool, J. Prost, M. Rao and R.A. Simha, Hydrodynamics of soft active matter. Rev. Mod. Phys. 85 (2013) 1143–1189. [Google Scholar]
  33. A. Marrocco, Numerical simulation of chemotactic bacteria aggregation via mixed finite elements. ESAIM:M2AN 37 (2003) 617–630. [Google Scholar]
  34. D. Martin, H. Chaté, C. Nardini, A. Solon, J. Tailleur and F. Van Wijland, Fluctuation-induced phase separation in metric and topological models of collective motion. Phys. Rev. Lett. 126 (2021) 148001. [Google Scholar]
  35. B. Maury and J. Venel, A discrete contact model for crowd motion. ESAIM:M2AN 45 (2011) 145–168. [Google Scholar]
  36. J.C. Moreno, M.L.R. Puzzo and W. Paul, Collective dynamics of pedestrians in a corridor: An approach combining social force and Vicsek models. Phys. Rev. E 102 (2020) 022307. [Google Scholar]
  37. T. Nemoto, É. Fodor, M.E. Cates, R.L. Jack and J. Tailleur, Optimizing active work: Dynamical phase transitions, collective motion, and jamming. Phys. Rev. E 99 (2019) 022605. [Google Scholar]
  38. G.A. Pavliotis, Stochastic Processes and Applications: Diffusion Processes, the Fokker-Planck and Langevin Equations, Vol. 60. Springer (2014). [Google Scholar]
  39. L.A. Pipes, An operational analysis of traffic dynamics. J. Appl. Phys. 24 (1953) 274–281. [Google Scholar]
  40. S. Ramaswamy, Active matter. J. Stat. Mech. Theory Exp. 2017 (2017) 054002. [Google Scholar]
  41. R. Rashad, F. Califano, A.J. van der Schaft and S. Stramigioli, Twenty years of distributed port-Hamiltonian systems: a literature review. IMA J. Math. Control Inf. 37 (2020) 1400–1422. [Google Scholar]
  42. B. Rüdiger, A. Tordeux and B. Ugurcan, Stability analysis of a stochastic port-Hamiltonian car-following model. Preprint: arXiv:2212.05139 (2022). [Google Scholar]
  43. S. Satoh, Input-to-state stability of stochastic port-Hamiltonian systems using stochastic generalized canonical transformations. Int. J. Robust Nonlinear Control 27 (2017) 3862–3885. [Google Scholar]
  44. S. Satoh and K. Fujimoto, Passivity based control of stochastic port-Hamiltonian systems. IEEE Trans. Automat. Control 58 (2012) 1139–1153. [Google Scholar]
  45. M.R. Shaebani, A. Wysocki, R.G. Winkler, G. Gompper and H. Rieger, Computational models for active matter. Nat. Rev. Phys. 2 (2020) 181–199. [Google Scholar]
  46. R.E. Stern, S. Cui, M.L. Delle Monache, R. Bhadani, M. Bunting, M. Churchill, N. Hamilton, H. Pohlmann, F. Wu, B. Piccoli and B. Seibold, Dissipation of stop-and-go waves via control of autonomous vehicles: Field experiments. Trans. Res. Part C Emerg. Technol. 89 (2018) 205–221. [Google Scholar]
  47. A. Tordeux and C. Totzeck, Multi-scale description of pedestrian collective dynamics with port-Hamiltonian systems. Preprint: arXiv:2211.06503 (2022). [Google Scholar]
  48. M. Treiber, A. Kesting and D. Helbing, Delays, inaccuracies and anticipation in microscopic traffic models. Phys. A Stat. Mech. Appl. 360 (2006) 71–88. [Google Scholar]
  49. A. van der Schaft, Port-Hamiltonian systems: An introductory survey. In Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006 (2007) 1339–1365. [Google Scholar]
  50. A. van der Schaft and D. Jeltsema, Port-Hamiltonian systems theory: An introductory overview. Found. Trends Syst. Control 1 (2014) 173–378. [Google Scholar]
  51. T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen and O. Shochet, Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75 (1995) 1226–1229. [Google Scholar]
  52. T. Vicsek and A. Zafeiris, Collective motion. Phys. Rep. 517 (2012) 71–140. [Google Scholar]
  53. T. Wang, G. Li, J. Zhang, S. Li and T. Sun, The effect of headway variation tendency on traffic flow: Modeling and stabilization. Phys. A Stat. Mech. Appl. 525 (2019) 566–575. [Google Scholar]

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