Multifractality of random walks in the theory of vehicular traffic

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 78, Issue 5, 2008, Pages

  Buendia G M ^a,b   Viswanathan, G M ^a,c   Kenkre, V M ^a  

^a UNIVERSITY OF NEW MEXICO   (United States)

^b UNIVERSIDAD SIMÓN BOLÍVAR   (Venezuela)

^c FEDERAL UNIVERSITY OF ALAGOAS   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

FLUID DYNAMICS; HYDRODYNAMICS; NUMERICAL ANALYSIS; RANDOM PROCESSES; TRAFFIC SURVEYS; WIRELESS TELECOMMUNICATION SYSTEMS;

BURGER'S EQUATIONS; DIFFUSION CONSTANTS; DIFFUSIVE PARTICLES; GENERALIZED HURST EXPONENTS; HYDRODYNAMIC MODELS; INITIAL CONDITIONS; MULTIFRACTAL SCALING; MULTIFRACTALITY; MULTISCALING; NONLINEAR CONVECTIONS; PROBABILITY DENSITIES; RANDOM WALKERS; RANDOM WALKS; REALISTIC SCENARIOS; SPEED LIMITS; TIME SCALES; TRANSIENT EFFECTS; VEHICULAR TRAFFIC FLOWS; VEHICULAR TRAFFICS;

PROBABILITY DENSITY FUNCTION;

EID: 57349099261     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.78.056110     Document Type: Article

References (61)

1. D. Helbing, Rev. Mod. Phys. 73, 1067 (2001). 10.1103/RevModPhys.73.1067
2. D. Chowdhury, L. Santen, and A. Schadschneider, Phys. Rep. 329, 199 (2000). 10.1016/S0370-1573(99)00117-9
3. M. J. Lighthill and G. B. Whitham, Proc. R. Soc. London, Ser. A 229, 317 (1955); 10.1098/rspa.1955.0089
4. P. I. Richards, Oper. Res. 4, 42 (1956). 10.1287/opre.4.1.42
5. D. Ngoduy and R. Liu, Physica A 385, 667 (2007); 10.1016/j.physa.2007.07. 041
6. J. B. Sheu, Physica A 367, 461 (2006); 10.1016/j.physa.2005.11.039
7. P. Nelson, Phys. Rev. E 61, R6052 (2000); 10.1103/PhysRevE.61.R6052
8. B. S. Kerner, S. L. Klenov, and P. Konhauser, Phys. Rev. E 56, 4200 (1997); 10.1103/PhysRevE.56.4200
9. D. Helbing, Physica A 219, 375 (1995); 10.1016/0378-4371(95)00174-6
10. D. Helbing, Phys. Rev. E 51, 3164 (1995). 10.1103/PhysRevE.51.3164
11. J. Ward, R. E. Wilson, and P. Bergh, Physica D 236, 1 (2007). 10.1016/j.physd.2007.07.008
12. X. W. Li and P. J. Shang, Chaos, Solitons Fractals 31, 1089 (2007). 10.1016/j.chaos.2005.10.109
13. P. J. Shang, Y. B. Lu, and S. Kamae, Chaos, Solitons Fractals 36, 82 (2008). 10.1016/j.chaos.2006.06.019
14. M. I. Bogachev, J. F. Eichner, and A. Bunde, Eur. Phys. J. Spec. Top. 161, 181 (2008). 10.1140/epjst/e2008-00760-5
15. J. Levy-Vehel and R. Vojak Rapport de Recherche No. 1943, INRIA, France, 1993 (unpublished).
16. A. Kudrolli, G. Lumay, D. Volfson, and L. S. Tsimring, Phys. Rev. Lett. 100, 058001 (2008); 10.1103/PhysRevLett.100.058001
17. F. Peruani and L. G. Morelli, Phys. Rev. Lett. 99, 010602 (2007); 10.1103/PhysRevLett.99.010602
18. A. Baskaran and M. C. Marchetti, Phys. Rev. E 77, 011920 (2008). 10.1103/PhysRevE.77.011920
19. H. E. Hurst, R. P. Black, and Y. M. Simaika, Long-Term Storage: An Experimental Study (Constable, London, 1965).
20. B. B. Mandelbrot, The Fractal Geometry of Nature (W. H. Freeman and Co., New York, 1982).
21. A. Bunde and S. Havlin, Fractals and Disordered Systems (Springer, Berlin, 1991).
22. Bruce J. West and William D. Deering, The Lure of Modern Science: Fractal Thinking (World Scientific, Singapore, 1995).
23. J. Feder, Fractals (Plenum Press, New York, 1988).
24. A. L. Barabási and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, U.K., 1995).
25. J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, and H. E. Stanley, Physica A 316, 87 (2002); 10.1016/S0378-4371(02)01383- 3
26. C. M. Nascimento, H. B. N. Junior, H. D. Jennings, M. Serva, I. Gleria, and G. M. Viswanathan, Europhys. Lett. 81, 18002 (2008). 10.1209/0295-5075/81/ 18002
27. G. B. Whitham, Linear and Nonlinear Waves, Pure and Applied Mathematics Vol. 1237 (Wiley, New York, 1974).
28. J. A. Shercliff, Rev. Mod. Phys. 32, 980 (1960). 10.1103/RevModPhys.32. 980
29. E. Ben-Naim, S. Y. Chen, G. D. Doolen, and S. Redner, Phys. Rev. Lett. 83, 4069 (1999); 10.1103/PhysRevLett.83.4069
30. P. Carbonaro, Phys. Rev. E 56, 2896 (1997). 10.1103/PhysRevE.56.2896
31. P. Constantin and C. Folias, Navier-Stokes Equations, Chicago Lectures in Mathematics Vol. 19 (University Of Chicago Press, Chicago, 1989).
32. W. A. Woyczynski, Burgers-KPZ Turbulence: Göttingen Lectures, Lecture Notes in Mathematics (Springer, Berlin, 1999).
33. Nonlinear Stochastic PDE's: Hydrodynamic Limit and Burgers' Turbulence, edited by, T. Funaki, and, W. A. Woyczynski, The IMA Volumes in Mathematics and its Applications (Springer, Berlin, 1995).
34. M. Kardar, G. Parisi, and Y. C. Zhang, Phys. Rev. Lett. 56, 889 (1986). 10.1103/PhysRevLett.56.889
35. E. Hopf, Pure Appl. Math. 3, 201 (1950); 10.1002/cpa.3160030302
36. J. D. Cole, Q. Appl. Math. 9, 225 (1951).
37. E. W. Montroll and G. Weiss, J. Math. Phys. 6, 167 (1965). 10.1063/1.1704269
38. H. Scher and M. Lax, Phys. Rev. B 7, 4491 (1973); 10.1103/PhysRevB.7.4491
39. H. Scher and E. W. Montroll, Phys. Rev. B 12, 2455 (1975). 10.1103/PhysRevB.12.2455
40. V. M. Kenkre, in Statistical Mechanics and Statistical Methods in Theory and Application, edited by, U. Landman, (Plenum, New York, 1977);
41. V. M. Kenkre, E. W. Montroll, and M. F. Shlesinger, J. Stat. Phys. 9, 45 (1973). 10.1007/BF01016796
42. V. M. Kenkre and F. J. Sevilla, in Contributions in Mathematical Physics, edited by, S. T. Ali, and, K. B. Sinha, (Hindustan Book Agency, New Delhi, 2007).
43. E. Barkai, R. Metzler and J. Klafter, Phys. Rev. E 61, 132 (2000). 10.1103/PhysRevE.61.132
44. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000); 10.1016/S0370- 1573(00)00070-3
45. R. Metzler and J. Klafter, J. Phys. A 37, R161 (2004). 10.1088/0305-4470/37/31/R01
46. Y. S. Ji, IEICE Trans. Commun. E89-B, 2125 (2006). 10.1093/ietcom/e89-b. 8.2125
47. R. L. Costa and G. L. Vasconcelos, Physica A 329, 231 (2003). 10.1016/S0378-4371(03)00607-1
48. G. M. Viswanathan, S. V. Buldyrev, S. Havlin, and H. E. Stanley, Physica A 249, 581 (1998); 10.1016/S0378-4371(97)00519-0
49. G. M. Viswanathan, S. V. Buldyrev, S. Havlin, and H. E. Stanley, Biophys. J. 72, 866 (1997);
50. G. M. Viswanathan, C. K. Peng, H. E. Stanley, and A. L. Goldberger, Phys. Rev. E 55, 845 (1997). 10.1103/PhysRevE.55.845
51. V. M. Kenkre, in Modern Challenges in Statistical Mechanics: Patterns, Noise and the Interplay of Nonlinearity and Complexity, Proceedings of the Pan American Advanced Studies Institute, Bariloche, Argentina, edited by, V. M. Kenkre, and, K. Lindenberg, (AIP, Melville, NY, 2003).
52. Katja Lindenberg and Bruce J. West, The Nonequilibrium Statistical Mechanics of Open and Closed Systems (VCH, New York, 1990).
53. D. L. Gerlough and M. J. Huber, Transportation Research Board Special Report No. 165, National Research Council, Washington, DC, 1975 (unpublished).
54. D. Forster, D. R. Nelson, and M. J. Stephen, Phys. Rev. A 16, 732 (1977); 10.1103/PhysRevA.16.732
55. T. Musha and H. Higuchi, Jpn. J. Appl. Phys. 17, 811 (1978). 10.1143/JJAP.17.811
56. K. Nagel, Phys. Rev. E 53, 4655 (1996); 10.1103/PhysRevE.53.4655
57. K. Nagel and M. Schreckenberg, J. Phys. I 2, 2221 (1992); 10.1051/jp1:1992277
58. K. Nagel, in Physics Computing '92, edited by, R. A. de Groot, and, J. Nadrchal, (World Scientific, Singapore, 1993) p. 419;
59. K. Nagel, Ph.D. thesis, University of Cologne, 1995.
60. H. C. Fogedby, Phys. Rev. E 68, 026132 (2003). 10.1103/PhysRevE.68.026132
61. A. Zoia, A. Rosso, and M. Kardar, Phys. Rev. E 76, 021116 (2007). 10.1103/PhysRevE.76.021116