Two-dimensional Optimal Velocity Model Research Articles

Flow instability originating from particle configurations using the two-dimensional optimal velocity model.

The two-dimensional optimal velocity model has potential applications to pedestrian dynamics and the collective motion of animals. In this paper, we extend the linear stability analysis presented in a previous paper [A Nakayama et al., Phys. Rev. E. 77, 016105 (2008)] and investigate the effects of particle configuration on the stability of several wave modes of collective oscillations of moving particles. We find that, when a particle moves without interacting with particles that are positioned in a diagonally forward or backward direction, the stable region of the particle flow is completely removed by the elliptically polarized mode.

A Two-Dimensional Optimal Velocity Model for Unidirectional Pedestrian Flow Based on Pedestrian's Visual Hindrance Field

Modeling and simulation of pedestrian movement is a feasible and effective way to evaluate evacuation facilities and risk. Inspired by the visual field and movement characteristic of pedestrians, we developed a 2-D continuous model that integrates a self-slowing, local direction-changing mechanism, and visual hindrance information. The model allows for the movement in continuous space and time, only controlled by simple kinematic equations and visual hindrance distribution. In order to get the parameters of the kinematic equations, we conducted controlled experiments, collected empirical data, and obtained velocity-changing and direction-changing relations. We then validate the model by simulating three experimental scenarios, i.e., passage, bottleneck, and classroom evacuation. It is found that some typical phenomena such as the stop-and-go waves in the passage and lane formation in the bottleneck can be reproduced. The obtained fundamental diagram and specific flow agree with classic conclusions and experimental measures very well. It is hoped that the idea of this study may be helpful in promoting the modeling and simulation study of pedestrian flow.

Effect of traffic information on the stability pedestrian flow*

Based on traffic information, an extended two-dimensional optimal velocity model is presented by incorporating velocity difference between two neighboring pedestrians. Linear stability conditions are obtained by theoretical analysis, and the results show that the traffic information can promote the stability of pedestrian flow. Furthermore, the model is applied to mixed pedestrian flow, where only part of pedestrians follows the information and others neglect it. It is found that the pedestrians complying with traffic guidance system (called TGS pedestrian) can make the mixed flow more stable, and some unstable regions can change to stable region when the proportion of TGS pedestrian is large enough. It is also found that the initial distribution of them has little effect on the flow.

Meandering instability in two-dimensional optimal velocity model for collective motion of self-propelled particles

We investigate the stability of a uniform flow of self-propelled particles in a two-dimensional optimal velocity model. As an initial condition, the particles are distributed uniformly in a narrow region of the space. This condition corresponds to a migration of organisms. It is found that the uniform flow is unstable and a meandering motion appears by numerical simulations. We also show the instability exists for any values of parameters by the linear analysis. It means that there is no stable uniform flow in this model.

Effect of attractive interaction on instability of pedestrian flow in a two-dimensional optimal velocity model

We incorporate an attractive interaction in a two-dimensional optimal velocity model and investigate the stability of homogeneous flow in the linear approximation. There exists a different type of instability in this model. We show the phase diagram and the behavior of the flow in each phase by numerical simulations. A new phase due to the new instability appears at low density, and the instability can be a candidate of the group formation mechanism of organisms.

Instability of pedestrian flow in 2D optimal velocity model with attractive interaction

We incorporate an attractive interaction in two-dimensional optimal velocity model and investigate the stability of homogeneous flow. There exists a new type of instability and a new phase appears. We also show the behavior of the flow in each phase by numerical simulations.

Instability of pedestrian flow and phase structure in a two-dimensional optimal velocity model

A two-dimensional optimal velocity model was proposed for the study of pedestrian and granular flow. We investigate the stability of homogeneous flow in the linear approximation and show the phase diagram of the model. We also investigate the property of the model by numerical simulation in the cases of unidirectional and counter flow. From these results, we present a unified understanding of the behavior of pedestrians and other related systems.