zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Non-lane-based lattice hydrodynamic model of traffic flow considering the lateral effects of the lane width. (English) Zbl 1250.90023
Summary: A new non-lane-based lattice model is proposed by incorporating the lateral separation effects of the lane width in traffic flow. The stability condition of the extended model is obtained by using the linear stability theory. The modified KdV equation near the critical point is derived to describe the phase transition of traffic flow and to estimate the evolution of traffic congestion through nonlinear analysis. Numerical simulation also shows that the incorporation of the lane width effects in lattice model can stabilize traffic flow and suppress the traffic jam, which implies that the lateral separation effects have important impacts in lattice models.
MSC:
90B20Traffic problems
76M28Particle methods and lattice-gas methods (fluid mechanics)
35Q53KdV-like (Korteweg-de Vries) equations
37K45Stability problems (infinite-dimensional systems)
References:
[1]Case, H. W.; Hulbert, S. F.; Mount, G. E.; Brenner, R.: Highway research board, Highway research board 32, 364 (1953)
[2]Khan, S. I.; Maini, P.: Transportation research record, Transportation research record 1678, 234 (1999)
[3]Michales, R. M.; Cozan, L. W.: Public roads, Public roads 32, 233 (1963)
[4]Gunay, B.: Transportation research part B, Transportation research part B 41, 722 (2007)
[5]Jin, S.; Wang, D. H.; Tao, P. F.; Li, P. F.: Physica A, Physica A 389, 4654 (2010)
[6]Nagatani, T.: Physica A, Physica A 261, 599 (1998)
[7]Nagatani, T.: Physica A, Physica A 264, 581 (1999)
[8]Xue, Y.: Acta phys. Sin., Acta phys. Sin. 53, 25 (2004)
[9]Ge, H. X.; Dai, S. Q.; Xue, Y.; Dong, L. Y.: Phys. rev. E, Phys. rev. E 71, 066119 (2005)
[10]Ge, H. X.; Cheng, R. J.: Physica A, Physica A 387, 6952 (2008)
[11]Zhu, H. B.: Chinese physics B, Chinese physics B 18, 1322 (2009)
[12]Li, X. L.; Li, Z. P.; Han, X. L.; Dai, S. Q.: Commun. nonlinear sci. Numer. simulat., Commun. nonlinear sci. Numer. simulat. 14, 2171 (2009)
[13]Ge, H. X.: Physica A, Physica A 388, 1682 (2009)
[14]Ge, H. X.; Cheng, R. J.; Lei, L.: Physica A, Physica A 389, 2825 (2010)
[15]Nagatani, T.: Physica A, Physica A 271, 200 (1999)
[16]Nagatani, T.: Phys. rev. E, Phys. rev. E 59, 4857 (1999)
[17]Nagatani, T.: Physica A, Physica A 272, 592 (1999)
[18]Nagatani, T.: Physica A, Physica A 265, 297 (1999)
[19]Tang, T. Q.; Huang, H. J.; Xue, Y.: Acta phys. Sin., Acta phys. Sin. 55, 4026 (2006)
[20]Peng, G. H.: Acta phys. Sin., Acta phys. Sin. 59, 108 (2010)
[21]Peng, G. H.; Cai, X. H.; Liu, C. Q.; Cao, B. F.: Phys. lett. A, Phys. lett. A 375, 2153 (2011)
[22]Tian, J. F.; Jia, B.; Li, X. G.; Gao, Z. Y.: Chin. phys. B, Chin. phys. B 19, 040303 (2010)
[23]Sun, D. H.; Tian, C.; Liu, W. N.: Chin. phys. B, Chin. phys. B 19, 080514 (2010)
[24]Sun, D. H.; Tian, C.: Acta phys. Sin., Acta phys. Sin. 60, 068901 (2011)
[25]Li, Z. P.; Li, X. L.; Liu, F. Q.: International journal of modern physics C, International journal of modern physics C 19, 1163 (2008)
[26]Ge, H. X.; Cheng, R. J.; Dai, S. Q.: Physica A, Physica A 357, 466 (2005)