×

zbMATH — the first resource for mathematics

Hybrid two scales mathematical tools for active particles modelling complex systems with learning hiding dynamics. (English) Zbl 1142.82019
A mathematical hybrid approach is proposed to model large systems of interacting particles, with good examples of application.
Although the application is to simple system, this mathematical formulation is elegant and interesting and can be extended to more complicated cases with further mathematical development and promising perspectives.
The paper is well written.

MSC:
82C40 Kinetic theory of gases in time-dependent statistical mechanics
92D25 Population dynamics (general)
37H10 Generation, random and stochastic difference and differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1090/S0273-0979-04-01004-3 · Zbl 1151.82351 · doi:10.1090/S0273-0979-04-01004-3
[2] DOI: 10.1090/conm/353/06434 · doi:10.1090/conm/353/06434
[3] Cercignani C., Theory and Application of the Boltzmann Equation (1993) · Zbl 0803.35151
[4] Schweitzer F., Brownian Agents and Active Particles (2003) · Zbl 1140.91012
[5] Prigogine I., Kinetic Theory of Vehicular Traffic (1971) · Zbl 0226.90011
[6] DOI: 10.1137/0152083 · Zbl 0759.92011 · doi:10.1137/0152083
[7] DOI: 10.1016/0895-7177(94)90223-2 · Zbl 0811.92014 · doi:10.1016/0895-7177(94)90223-2
[8] DOI: 10.1007/978-1-4612-0513-5 · doi:10.1007/978-1-4612-0513-5
[9] Arlotti L., Math. Mod. Meth. Appl. Sci. 12 pp 579–
[10] DOI: 10.1142/S0218202505000923 · Zbl 1093.82016 · doi:10.1142/S0218202505000923
[11] DOI: 10.1142/S0218202504003799 · Zbl 1060.92029 · doi:10.1142/S0218202504003799
[12] Bellouquid A., Modelling Complex Multicellular Systems - A Kinetic Theory Approach (2005)
[13] DOI: 10.1016/S0895-7177(03)00005-0 · Zbl 1062.91062 · doi:10.1016/S0895-7177(03)00005-0
[14] Carbonaro B., Math. Mod. Meth. Appl. Sci. 12 pp 1463–
[15] DOI: 10.1016/j.mcm.2003.05.021 · Zbl 1116.91074 · doi:10.1016/j.mcm.2003.05.021
[16] DOI: 10.1142/S0218202504003702 · Zbl 1149.76654 · doi:10.1142/S0218202504003702
[17] DOI: 10.1142/S0217979204024100 · Zbl 1073.82034 · doi:10.1142/S0217979204024100
[18] Boccarra N., Modelling Complex Systems (2004)
[19] Bellomo N., Math. Mod. Meth. Appl. Sci. 15 pp iii–
[20] DOI: 10.1142/S0218202504003738 · Zbl 1057.92036 · doi:10.1142/S0218202504003738
[21] DOI: 10.1142/S0218202505000911 · Zbl 1077.92031 · doi:10.1142/S0218202505000911
[22] Novak M. A., Science 303 pp 793–
[23] DOI: 10.1016/j.physd.2005.06.032 · Zbl 1087.34028 · doi:10.1016/j.physd.2005.06.032
[24] DOI: 10.1016/j.mcm.2005.05.003 · Zbl 1080.92042 · doi:10.1016/j.mcm.2005.05.003
[25] DOI: 10.1016/j.mcm.2005.05.004 · Zbl 1085.92019 · doi:10.1016/j.mcm.2005.05.004
[26] DOI: 10.1080/1027336042000288633 · Zbl 1107.92020 · doi:10.1080/1027336042000288633
[27] DOI: 10.1142/S0218202506001443 · Zbl 1093.92002 · doi:10.1142/S0218202506001443
[28] DOI: 10.1016/j.ijnonlinmec.2005.07.006 · Zbl 1160.76403 · doi:10.1016/j.ijnonlinmec.2005.07.006
[29] DOI: 10.1142/S0218202505000935 · Zbl 1078.92036 · doi:10.1142/S0218202505000935
[30] DOI: 10.1016/0893-9659(96)00014-6 · Zbl 0853.35050 · doi:10.1016/0893-9659(96)00014-6
[31] DOI: 10.1142/S0218202504003544 · Zbl 1083.92032 · doi:10.1142/S0218202504003544
[32] El Ghordaf J., Math. Mod. Meth. Appl. Sci. 16 pp 374–
[33] DOI: 10.1016/S0895-7177(04)90529-8 · Zbl 1112.91011 · doi:10.1016/S0895-7177(04)90529-8
[34] Bellomo N., Diff. Eqns. Nonlinear Mech. 1 pp 1–
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.