Arvind Kumar Gupta

Bio: Arvind Kumar Gupta is an academic researcher from Indian Institute of Technology Ropar. The author has contributed to research in topics: Asymmetric simple exclusion process & Medicine. The author has an hindex of 24, co-authored 78 publications receiving 2558 citations. Previous affiliations of Arvind Kumar Gupta include Indian Institute of Technology Roorkee.

Analyses of driver’s anticipation effect in sensing relative flux in a new lattice model for two-lane traffic system

Abstract: In this paper, a new lattice hydrodynamic traffic flow model is proposed by considering the driver’s anticipation effect in sensing relative flux (DAESRF) for two-lane system. The effect of anticipation parameter on the stability of traffic flow is examined through linear stability analysis and shown that the anticipation term can significantly enlarge the stability region on the phase diagram. To describe the phase transition of traffic flow, mKdV equation near the critical point is derived through nonlinear analysis. The theoretical findings have been verified using numerical simulation which confirms that traffic jam can be suppressed efficiently by considering the anticipation effect in the new lattice model for two-lane traffic.

Analyses of shock waves and jams in traffic flow

Abstract: In this paper, we study the certain qualitative properties of a new anisotropic continuum traffic flow model in which the dimensionless parameter or anisotropic factor controls the non-isotropic character and diffusive influence. We discussed the travelling wave solution for our model and find out the condition for the shock wave. Shock and rarefaction waves are obtained from the new model and are consistent with the diverse nonlinear dynamical phenomena observed in a real traffic flow. However, our model for large values of anisotropic parameter removes the discontinuity as pointed out by Berg et al (2000 Phys. Rev. E 61 1056). The nonlinear theory of the cluster effect in a traffic flow i.e., the effect of appearance of a region of high density and low average velocity of vehicles in an initially homogeneous flow, is also discussed. It is shown that an appearance of a localized perturbation of finite amplitude in the stable homogeneous flow can lead to a self-formation of a local cluster of vehicles. It is also been observed that the cluster effect from our model shows a good agreement with the results of Kerner and Konhauser (1994 Phys. Rev. E 50 54) and Jiang et al (2002 Trans. Res. B 36 405).

A new anisotropic continuum model for traffic flow

Abstract: This paper develops a new continuum model based upon an improved car-following model by using a series expansion of the headway in terms of the density. The new model contains an additional speed gradient term (Anisotropic term) in comparison to the Berg's model [Berg et al., Phys. Rev. E 61(2) (2000) 1056]. This anisotropic term guarantees the property that the characteristic speeds are always less than or equal to the macroscopic flow speed. This new model also overcomes the problem of negative flows and negative speeds (i.e. wrong way travel) that exists in almost every higher order continuum models. It is known that diffusive wave could lead to a “wrong way travel” under certain circumstances [C. F. Daganzo, Trans. Res. B 29 (1995) 277]. In our general model, a traffic dependent anisotropic factor controls the non-isotropic character and diffusive influence in these special circumstances. The stability of traffic flow is analyzed and found out that this new continuum model obeys the same stability criterion as Berg's model for zero anisotropic parameter.

Stochastic Processes in Physics and Chemistry

Abstract: N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.