A new lattice hydrodynamic model for bidirectional pedestrian flow with consideration of pedestrians’ honk effect

Understanding the pedestrian behavior contributes to traffic simulation and facility design/redesign. In practice, the interactions between individual pedestrians can lead to virtual honk effect, such as urging surrounding pedestrians to walk faster in a crowded environment. To better reflect the reality, this paper proposes a new lattice hydrodynamic model for bidirectional pedestrian flow with consideration of pedestrians’ honk effect. To this end, the concept of critical density is introduced to define the occurrence of pedestrians’ honk event. In the linear stability analysis, the stability condition of the new bidirectional pedestrian flow model is given based on the perturbation method, and the neutral stability curve is also obtained. Based on this, it is found that the honk effect has a significant impact on the stability of pedestrian flow. In the nonlinear stability analysis, the modified Korteweg–de Vries (mKdV) equation of the model is obtained based on the reductive perturbation method. By solving the mKdV equation, the kink-antikink soliton wave is obtained to describe the propagation mechanism and rules of pedestrian congestion near the neutral stability curve. The simulation example shows that the pedestrians’ honk effect can mitigate the pedestrians crowding efficiently and improve the stability of the bidirectional pedestrian flow.

On the neutral stability curve for shallow conical shells subjected to lateral pressure

This work presents a detailed asymptotic description of the neutral stability envelope for the linear bifurcations of a shallow conical shell subjected to lateral pressure. The eighth-order boundary-eigenvalue problem investigated originates in the Donnell shallow-shell theory coupled with a linear membrane pre-bifurcation state, and leads to a neutral stability curve that exhibits two distinct growth rates. By using singular perturbation methods we propose accurate approximations for both regimes and explore a number of other novel features of this problem. Our theoretical results are compared with several direct numerical simulations that shed further light on the problem.

The Korteweg-De Vries Equation of a New Lattice Model with a Consideration of the Next-Nearest-Neighbor Site and its Numerical Simulation

Based on Nagatanis model, a new lattice hydrodynamic model of traffic flow with a consideration of the next-nearest-neighbor site is proposed. Using nonlinear analysis, we derive the Korteweg-de Vries (KdV, for short) equation near the neutral stability curve to describe the density waves. Numerical simulations are consonant with the analytical results and shows that the consideration of the next-nearest-neighbor interaction helps suppress traffic jam.

Analytical Solution of Congested Traffic Pattern Formation for a Viscous High-Order Model

In this paper, a new viscous vehicular flow model proposed by Song et al is discussed from the perspective of the capability to reproduce nonlinear traffic behavors observed in real traffic. The linear stability condition for stationary and equilibrium flow is derived. Near the neutral stability curve, the Korteweg–de Vries (KdV) equation describing congested traffic pattern is derived with use of the reduction perturbation method. And the corresponding analytical soliton solution is obtained.

Instability of a gravity-modulated fluid layer with surface tension variation

Gravity modulation of an unbounded fluid layer with surface tension variations along its free surface is investigated. The stability of such systems is often characterized in terms of the wavenumber, α and the Marangoni number, Ma. In (α, Ma) parameter space, modulation has a destabilizing effect on the unmodulated neutral stability curve for large Prandtl number, Pr, and small modulation frequency, Ω, while a stabilizing effect is observed for small Pr and large Ω. As Ω → ∞ the modulated neutral stability curves approach the unmodulated neutral stability curve. At certain values of Pr and Ω, multiple minima are observed and the neutral stability curves become highly distorted. Closed regions of subharmonic instability are also observed. In (1/Ω, g1Ra)-space, where g1 is the relative modulation amplitude, and Ra is the Rayleigh number, alternating regions of synchronous and subharmonic instability separated by thin stable regions are observed. However, fundamental differences between the stability boundaries occur when comparing the modulated Marangoni–Bénard and Rayleigh–Bénard problems. Modulation amplitudes at which instability tongues occur are strongly influenced by Pr, while the fundamental instability region is weakly affected by Pr. For large modulation frequency and small amplitude, empirical relations are derived to determine modulation effects. A one-term Galerkin approximation was also used to reduce the modulated Marangoni–Bénard problem to a Mathieu equation, allowing qualitative stability behaviour to be deduced from existing tables or charts, such as Strutt diagrams. In addition, this reduces the parameter dependence of the problem from seven transport parameters to three Mathieu parameters, analogous to parameter reductions of previous modulated Rayleigh–Bénard studies. Simple stability criteria, valid for small parameter values (amplitude and damping coefficients), were obtained from the one-term equations using classical method of averaging results.