Abstract

The optimal velocity model of traffic is extended to take the relative velocity into account. The traffic behavior is investigated numerically and analytically with this model. It is shown that the car interaction with the relative velocity can effect the stability of the traffic flow and raise critical density. The jamming transition between the freely moving and jamming phases is investigated with the linear stability analysis and nonlinear perturbation methods. The traffic jam is described by the kink solution of the modified Korteweg–de Vries equation. The theoretical result is in good agreement with the simulation.

In res [I], V. E. Najenov studied the conditions that when the viscosity of the liquid is an exponential function of temperature, the pipe flow, having stead)' heat transfer, is onedimensional and with nonun!(orm temperature. For plane canal and circular pipe he still studied the velocitv and the temperture fields.In this paper, the author presents two new method.~ for solving the .same problem. The metht, d as in ref [1] may be regarded as the natural branch of the methods of this paper. One of our new methods onl)' can solve the same problem as in ref [I] and the complex degree of its computing process is nearly the same as that in ref [I]. But the other can gobeyond the studying scope of ref.[1], namely, for the case that the curvatures of circumference of the cross section of the pipe are not equivalent everywhere, the problem rm~y also, be solved.

The solution of the cylindrical detonation wave generated by the linear explosion was obtained by numerical method in ref [ 1 ].In this paper, when the ratio of specific heat ~ >> I by using the enlargement coordinate method, the first-order analytical solutions are obtained. The Perturbation parameter is e= I/l~z . The correction of these solutions is checked at the end of this paper.

In [ 1 ]