A variety of nonlinear follow-the-leader models of traffic flow are discussed in the light of available observational and experimental data. Emphasis is placed on steady-state flow equations. Some trends regarding the advantages of certain follow-the-leader functionals over others are established. However, it is found from extensive correlation studies that more data are needed before one can establish the unequivocal superiority of one particular model. A discussion is given of some ideas concerning the possible reasons for the existence of a bimodal flow versus concentration curve especially for multilane highways.

The propagation of free harmonic waves along a hollow circular cylinder of infinite extent is discussed within the framework of the linear theory of elasticity. A characteristic equation appropriate to the circular hollow cylinder is obtained by use of the Helmholtz potentials for arbitrary values of the physical parameters involved. Axially symmetric waves, the limiting modes of infinite wavelength, and a special family of equivoluminal modes are derived and discussed as degenerate cases of the general equations.

The steady-state flow is examined for a car-following model in which the acceleration at time t of a car attempting to follow a lead car is proportional to the relative velocity at a time t − Δ and in which the sensitivity λ is no longer taken constant as in previous work but is inversely proportional to the car spacing. The characteristics of the steady-state flow for this model are described and compared with experimental data.

A theoretical analysis and observations of the behavior of motorists confronted by an amber signal light are presented. A discussion is given of the following problem: when confronted with an improperly timed amber light phase a motorist may find himself, at the moment the amber phase commences, in the predicament of being too close to the intersection to stop safely or comfortably and yet too far from it to pass completely through the intersection before the red signal commences. The influence on this problem of the speed of approach to the intersection is analyzed. Criteria are presented for the design of amber signal light phases through whose use such 'dilemma zones' can be avoided, in the interest of overall safety at intersections. W 7, tE LIVE in a difficult and increasingly complex world where manmade systems, man-made laws and human behavior are not always compatible. This paper deals with a problem peculiar to our present civilization, for which a satisfactory solution based on existing information and analysis is not available. The problem in question is that of the amber signal light in traffic flow. Undoubtedly everyone has observed at some time or other the occurrence of a driver crossing an intersection partly during the red phase of the signal cycle. There are few of us who have not frequently been faced with such a decision-making situation when the amber signal light first appears, namely, whether to stop too quickly (and perhaps come to rest partly within the intersection) or to chance going through the intersection, possibly during the red light phase. In view of this situation we were led to consider the following problem: can criteria presently employed in setting the duration of the amber signal light at intersections lead to a situation wherein a motorist driving along a road within the legal speed limit finds himself, when the green signal turns to amber, in the predicament of being too close to the intersection to stop safely and comfortably and yet too far from it to pass through, before the signal changes to red, without exceeding the speed limit? From experience we feel that a problem exists, and we ask if it is feasible to construct a signal light system such that the characteristics of a driver and his car, the geometry

Given an arbitrary tensor in an n-dimensional Euclidean space, it is required to find its 'nearest' tensor of some preassigned symmetry, i.e. the tensor of this symmetry which has the minimum invariant 'distance' from the given tensor. General theorems are given concerning the construction and properties of these nearest tensors. The theorems are applied, in the case of elastic tensors, for the construction of the nearest isotropic and cubic tehsors to a given anisotropic elastic tensor, and the nearest hexagonal polar tensor to a cubic elastic tensor.