Geodesic
Analytical derivation of time spectral rigidity for thermodynamic traffic gas
Kybernetika, Tome 46 (2010) no. 6, pp. 1108-1121 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We introduce an one-dimensional thermodynamical particle model which is efficient in predictions about a microscopical structure of animal/human groups. For such a model we present analytical calculations leading to formulae for time clearance distribution as well as for time spectral rigidity. Furthermore, the results obtained are reformulated in terms of vehicular traffic theory and consecutively compared to experimental traffic data.
We introduce an one-dimensional thermodynamical particle model which is efficient in predictions about a microscopical structure of animal/human groups. For such a model we present analytical calculations leading to formulae for time clearance distribution as well as for time spectral rigidity. Furthermore, the results obtained are reformulated in terms of vehicular traffic theory and consecutively compared to experimental traffic data.
Classification : 37L99, 70F45, 82B21
Keywords: thermodynamic traffic gas; clearance distribution; spectral rigidity 
@article{KYB_2010_46_6_a14,
     author = {Krb\'alek, Milan},
     title = {Analytical derivation of time spectral rigidity for thermodynamic traffic gas},
     journal = {Kybernetika},
     pages = {1108--1121},
     year = {2010},
     volume = {46},
     number = {6},
     mrnumber = {2797431},
     zbl = {1208.82015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2010_46_6_a14/}
}
TY  - JOUR
AU  - Krbálek, Milan
TI  - Analytical derivation of time spectral rigidity for thermodynamic traffic gas
JO  - Kybernetika
PY  - 2010
SP  - 1108
EP  - 1121
VL  - 46
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/KYB_2010_46_6_a14/
LA  - en
ID  - KYB_2010_46_6_a14
ER  - 
%0 Journal Article
%A Krbálek, Milan
%T Analytical derivation of time spectral rigidity for thermodynamic traffic gas
%J Kybernetika
%D 2010
%P 1108-1121
%V 46
%N 6
%U http://geodesic.mathdoc.fr/item/KYB_2010_46_6_a14/
%G en
%F KYB_2010_46_6_a14
Krbálek, Milan. Analytical derivation of time spectral rigidity for thermodynamic traffic gas. Kybernetika, Tome 46 (2010) no. 6, pp. 1108-1121. http://geodesic.mathdoc.fr/item/KYB_2010_46_6_a14/

[1] Appert-Rolland, C.: Experimental study of short-range interactions in vehicular traffic. Phys. Rev. E 80 (2009), 036102(1)–036102(5). | DOI

[2] Baik, J., Borodin, A., Deift, P., Suidan, T.: A model for the bus system in Cuernavaca (Mexico). J. Phys. A: Math. Gen. 39 (2006), 8965–8975. | DOI | MR | Zbl

[3] Barabási, A. L.: The origin of bursts and heavy tails in human dynamics. Nature (London) 435 (2005), 207–211. | DOI

[4] Helbing, D.: Traffic and related self-driven many-particle systems. Rev. Mod. Phys. 73 (2001), 1067–1141. | DOI

[5] Helbing, D., Treiber, M., Kesting, A.: Understanding interarrival and interdeparture time statistics from interactions in queuing systems. Physica A 363 (2006), 62–72. | DOI

[6] Chowdhury, D., Santen, L., Schadschneider, A.: Statistical Physics of Vehicular Traffic and Some Related Systems. Physics Reports 329 (2000), 199–369. | DOI | MR

[7] Krbálek, M., Helbing, D.: Determination of interaction potentials in freeway traffic from steady-state statistics. Physica A 333 (2004), 370–378. | DOI | MR

[8] Jezbera, D., Kordek, D., Křiž, J., Šeba, P., Šroll, P.: Walkers on the circle. J. Stat. Mech. (2010), L01001(1)–L01001(6). | DOI

[9] Krbálek, M.: Equilibrium distributions in a thermodynamical traffic gas. J. Phys. A: Math. Theor. 40 (2007), 5813–5821. | DOI | MR | Zbl

[10] Krbálek, M.: Inter-vehicle gap statistics on signal-controlled crossroads. J. Phys. A: Math. Theor. 41 (2008), 205004(1)–205004(8). | DOI | MR | Zbl

[11] Krbálek, M., Šeba, P.: Spectral rigidity of vehicular streams (random matrix theory approach). J. Phys. A: Math. Theor. 42 (2009), 345001(1)–345001(10). | DOI | MR | Zbl

[12] Mehta, M. L.: Random Matrices (revised and enlarged). Academic Press, New York 1991. | MR

[13] Moon, H., Conlon, D. E., Humphrey, S. E., Quigley, N., Devers, C. E., Nowakowski, J. M.: Group decision process and incrementalism in organizational decision making. Organizational Behavior and Human Decision Processes 92 (2003), 67–79.

[14] Oliveira, J. G., Barabási, A. L.: Human dynamics: Darwin and Einstein correspondence patterns. Nature (London) 437 (2005), 1251–1253. | DOI

[15] Oliveira, J. G., Vazquez, A.: Impact of interactions on human dynamics. Physica A 388 (2009), 187–192. | DOI

[16] Orosz, G., Wilson, R. E., Szalai, R., Stépán, G.: Exciting traffic jams: Nonlinear phenomena behind traffic jam formation on highways. Phys. Rev. E 80 (2009), 046205(1)–046205(12). | DOI

[17] Smith, D., Marklof, J., Wilson, R. E.: Improved power law potentials for highway traffic flow. Submitted to Eur. Phys. J. B (2008), preprint http://rose.bris.ac.uk/dspace/bitstream/1983/1061/1/dasmith.pdf

[18] Sopasakis, A.: Stochastic noise approach to traffic flow modeling. Physica A 342 (2004), 741–754. | DOI

[19] Sugiyama, Y., Fukui, M., Kikuchi, M., Hasebe, K., Nakayama, A., Nishinari, K., Tadaki, S., Yukawa, S.: Traffic jams without bottlenecks–experimental evidence for the physical mechanism of the formation of a jam. New Journal of Physics, 10 (2008), 033001(1)–033001(8). | DOI