EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 58 / No 2 (March-April 2024) ESAIM: M2AN, 58 2 (2024) 515-544 References
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. [CrossRef] [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. [CrossRef] [PubMed] [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. [CrossRef] [PubMed] [Google Scholar]
  4. L. Carlitz, Some theorems on Bernoulli numbers of higher order. Pac. J. Math. 2 (1952) 127–139. [CrossRef] [Google Scholar]
  5. R.E. Chandler, R. Herman and E.W. Montroll, Traffic dynamics: studies in car following. Oper. Res. 6 (1958) 165–184. [CrossRef] [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. [CrossRef] [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. [CrossRef] [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. [CrossRef] [Google Scholar]
  9. F. Cordoni, L. Di Persio and R. Muradore, Stochastic port-Hamiltonian systems. J. Nonlinear Sci. 32 (2022) 1–53. [CrossRef] [Google Scholar]
  10. D. Cvijović and H.M. Srivastava, Closed-form summation of the Dowker and related sums. J. Math. Phys. 48 (2007) 043507. [CrossRef] [MathSciNet] [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. [CrossRef] [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. [CrossRef] [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. [CrossRef] [Google Scholar]
  14. R. De and D. Chakraborty, Collective motion: Influence of local behavioural interactions among individuals. J. Biosci. 47 (2022) 48. [CrossRef] [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. [CrossRef] [MathSciNet] [Google Scholar]
  16. J.S. Dowker, Casimir effect around a cone. Phys. Rev. D 36 (1987) 3095–3101. [CrossRef] [PubMed] [Google Scholar]
  17. J.S. Dowker, Heat kernel expansion on a generalized cone. J. Math. Phys. 30 (1989) 770–773. [CrossRef] [MathSciNet] [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. [CrossRef] [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. [CrossRef] [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. [CrossRef] [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. [CrossRef] [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. [CrossRef] [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. [CrossRef] [PubMed] [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. [CrossRef] [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. [CrossRef] [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. [CrossRef] [Google Scholar]
  33. A. Marrocco, Numerical simulation of chemotactic bacteria aggregation via mixed finite elements. ESAIM:M2AN 37 (2003) 617–630. [CrossRef] [EDP Sciences] [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. [CrossRef] [PubMed] [Google Scholar]
  35. B. Maury and J. Venel, A discrete contact model for crowd motion. ESAIM:M2AN 45 (2011) 145–168. [CrossRef] [EDP Sciences] [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. [CrossRef] [PubMed] [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. [CrossRef] [PubMed] [Google Scholar]
  38. G.A. Pavliotis, Stochastic Processes and Applications: Diffusion Processes, the Fokker-Planck and Langevin Equations, Vol. 60. Springer (2014). [CrossRef] [Google Scholar]
  39. L.A. Pipes, An operational analysis of traffic dynamics. J. Appl. Phys. 24 (1953) 274–281. [CrossRef] [MathSciNet] [Google Scholar]
  40. S. Ramaswamy, Active matter. J. Stat. Mech. Theory Exp. 2017 (2017) 054002. [CrossRef] [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. [CrossRef] [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. [CrossRef] [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. [CrossRef] [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. [CrossRef] [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. [CrossRef] [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. [CrossRef] [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. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  52. T. Vicsek and A. Zafeiris, Collective motion. Phys. Rep. 517 (2012) 71–140. [CrossRef] [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. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you