Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access April 30, 2011

Spring-block model for a single-lane highway traffic

  • Ferenc Járai-Szabó EMAIL logo , Bulcsú Sándor and Zoltán Néda
From the journal Open Physics

Abstract

A simple one-dimensional spring-block chain with asymmetric interactions is considered to model an idealized single-lane highway traffic. The main elements of the system are blocks (modeling cars), springs with unidirectional interactions (modeling distance-keeping interactions between neighbors), static and kinetic friction (modeling inertia of drivers and cars) and spatiotemporal disorder in the values of these friction forces (modeling differences in the driving attitudes). The traveling chain of cars correspond to the dragged spring-block system. Contrary to most of the studies in the field of highway traffic here we focus on a measure characteristic for one car in the row. Our statistical analysis for the spring-block chain predicts a non-trivial and rich complex behavior. As a function of the disorder level in the system a dynamic phase-transition is observed. For low disorder levels uncorrelated slidings of blocks are revealed while for high disorder levels correlated avalanches dominates.

[1] B.D. Greenshields, Highway Research Board Proceedings 14, 448 (1935) Search in Google Scholar

[2] M.J. Lighthill, G.B. Whitham, P. Roy. Soc. A-Math. Phy. 229, 317 (1955) http://dx.doi.org/10.1098/rspa.1955.008910.1098/rspa.1955.0089Search in Google Scholar

[3] D. Chowdhury, L. Santen, A. Schadschneider, Phys. Rep. 329, 199 (2000) http://dx.doi.org/10.1016/S0370-1573(99)00117-910.1016/S0370-1573(99)00117-9Search in Google Scholar

[4] D. Helbing, Rev. Mod. Phys. 73, 1067 (2001) http://dx.doi.org/10.1103/RevModPhys.73.106710.1103/RevModPhys.73.1067Search in Google Scholar

[5] S. Maerivoet, B. De Moor, Phys. Rep. 419, 1 (2005) http://dx.doi.org/10.1016/j.physrep.2005.08.00510.1016/j.physrep.2005.08.005Search in Google Scholar

[6] S. Darbha, K.R. Rajagopal, V. Tyagi, Nonlinear Anal.-Theor. 69, 950 (2008) http://dx.doi.org/10.1016/j.na.2008.02.12310.1016/j.na.2008.02.123Search in Google Scholar

[7] R. Mahnke, J. Kaupuzs, I. Lubashevsky, Phys. Rep. pringer, Berlin, 408, 1 (2005) 10.1016/j.physrep.2004.12.001Search in Google Scholar

[8] T. Nagatani, Rep. Prog. Phys. 65, 1331 (2002) http://dx.doi.org/10.1088/0034-4885/65/9/20310.1088/0034-4885/65/9/203Search in Google Scholar

[9] B.S. Kerner, The physics of traffic (Spr New York, 2004) 10.1007/978-3-540-40986-1Search in Google Scholar

[10] Y. Sugiyama et al., New J. Phys. 10, 033001 (2008) http://dx.doi.org/10.1088/1367-2630/10/3/03300110.1088/1367-2630/10/3/033001Search in Google Scholar

[11] R. Burridge, L. Knopoff, B. Seismol. Soc. Am. 57, 341 (1967) 10.1785/BSSA0570030341Search in Google Scholar

[12] B. Gutenberg, C.F. Richter, Ann. Geophys. 9, 1 (1956) 10.1007/978-3-662-28668-5_1Search in Google Scholar

[13] J.M. Carlson, J.S. Langer, Phys. Rev. A 40, 6470 (1989) http://dx.doi.org/10.1103/PhysRevA.40.647010.1103/PhysRevA.40.6470Search in Google Scholar PubMed

[14] K.-t. Leung, Z. Néda, Phys. Rev. Lett. 85, 662 (2000) http://dx.doi.org/10.1103/PhysRevLett.85.66210.1103/PhysRevLett.85.662Search in Google Scholar PubMed

[15] K.-t. Leung, L. Jozsa, M. Ravasz, Z. Néda, Nature 410, 166 (2001) http://dx.doi.org/10.1038/3506551710.1038/35065517Search in Google Scholar PubMed

[16] F. Járai-Szabó, S. Astilean, Z. Néda, Chem. Phys. Lett. 408, 241 (2005) http://dx.doi.org/10.1016/j.cplett.2005.04.05110.1016/j.cplett.2005.04.051Search in Google Scholar

[17] F. Járai-Szabó et al., J. Optoelectron. Adv. M. 8, 1083 (2006) Search in Google Scholar

[18] F. Járai-Szabó, Z. Néda, S. Astilean, C. Farcau, A. Kuttesch, Eur. Phys. J. E 23, 153 (2007) http://dx.doi.org/10.1140/epje/i2006-10194-910.1140/epje/i2006-10194-9Search in Google Scholar PubMed

[19] K. Kovács, Z. Néda, Phys. Lett. A 361, 18 (2007) http://dx.doi.org/10.1016/j.physleta.2006.08.08610.1016/j.physleta.2006.08.086Search in Google Scholar

[20] E.-A. Horváth, F. Járai-Szabó, Z. Néda, J. Optoelectron. Adv. M. 10, 2433 (2008) Search in Google Scholar

Published Online: 2011-4-30
Published in Print: 2011-8-1

© 2011 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Downloaded on 26.2.2024 from https://www.degruyter.com/document/doi/10.2478/s11534-011-0007-6/html
Scroll to top button