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A Kuramoto-type approach to address flocking phenomena is presented. First, we analyze a simple generalization of the Kuramoto model for interacting active particles, which is able to show the flocking transition (the emergence of coordinated movements in a group of interacting self-propelled agents). In the case of all-to-all interaction, the proposed model reduces to the Kuramoto model for phase synchronization of identical motionless noisy oscillators. In general, the nature of this non-equilibrium phase transition depends on the range of interaction between the particles. Namely, for a small range of interaction, the transition is first order, while for a larger range of interaction, it is a second order transition. Moreover, for larger interaction ranges, the system exhibits the same features as in the case of all-to-all interaction, showing a spatially homogeneous flux when flocking phenomenon has emerged, while for lower interaction ranges, the flocking transition is characterized by cluster formation. We compute the phase diagram of the model, where we distinguish three phases as a function of the range of interaction and the effective coupling strength: a disordered phase, a spatially homogeneous flocking phase, and a cluster-flocking phase. Then, we present a general discussion about the applicability of this way of modeling to more realistic and general situations, ending with a brief presentation of a second example (a second model with a conservative interaction) where the flocking transition may be studied within the framework that we are proposing.

There is growing interest in understanding the lateral dimension of traffic. This trend has been motivated by the detection of phenomena unexplained by traditional models and the emergence of new technologies. Previous attempts to address this dimension have focused on lane-changing and non-lane-based traffic. The literature on vehicles keeping their lanes has generally been limited to simple statistics on vehicle position while models assume vehicles stay perfectly centered. Previously the author developed a two-dimensional traffic model aiming to capture such behavior qualitatively. Still pending is a deeper, more accurate comprehension and modeling of the relationships between variables in both axes. The present paper is based on the Next Generation SIMulation (NGSIM) datasets. It was found that lateral position is highly dependent on the longitudinal position, a phenomenon consistent with data capture from multiple cameras. A methodology is proposed to alleviate this problem. It was also discovered that the standard deviation of lateral velocity grows with longitudinal velocity and that the average lateral position varies with longitudinal velocity by up to 8 cm, possibly reflecting greater caution in overtaking. Random walk models were proposed and calibrated to reproduce some of the characteristics measured. It was determined that drivers’ response is much more sensitive to the lateral velocity than to position. These results provide a basis for further advances in understanding the lateral dimension. It is hoped that such comprehension will facilitate the design of autonomous vehicle algorithms that are friendlier to both passengers and the occupants of surrounding vehicles.

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