A modified two-dimensional triangular lattice model under honk environment

2020 ◽  
Vol 31 (06) ◽  
pp. 2050089
Author(s):  
Cong Zhai ◽  
Weitiao Wu
Keyword(s):  
Stability Analysis ◽  
Hydrodynamic Model ◽  
High Dimensional ◽  
Two Dimensional ◽  
Lattice Hydrodynamic Model ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The Stability ◽  
Honk Effect ◽  
Real Traffic

The honk effect is not uncommon in the real traffic and may exert great influence on the stability of traffic flow. As opposed to the linear description of the traditional one-dimensional lattice hydrodynamic model, the high-dimensional lattice hydrodynamic model is a gridded analysis of the real traffic environment, which is a generalized form of the one-dimensional lattice model. Meanwhile, the high-dimensional traffic flow exposed to the open-ended environment is more likely to be affected by the honk effect. In this paper, we propose an extension of two-dimensional triangular lattice hydrodynamic model under honk environment. The stability condition is obtained via the linear stability analysis, which shows that the stability region in the phase diagram can be effectively enlarged under the honk effect. Modified Korteweg–de Vries equations are derived through the nonlinear stability analysis method. The kink–antikink solitary wave solution is obtained by solving the equation, which can be used to describe the propagation characteristics of density waves near the critical point. Finally, the simulation example verifies the correctness of the above theoretical analysis.

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

2020 ◽  
Vol 31 (02) ◽  
pp. 2050031 ◽  
Author(s):  
Cong Zhai ◽  
Weitiao Wu
Keyword(s):  
Stability Analysis ◽  
Hydrodynamic Model ◽  
Mkdv Equation ◽  
Neutral Stability ◽  
Neutral Stability Curve ◽  
Lattice Hydrodynamic Model ◽  
Pedestrian Flow ◽  
Stability Curve ◽  
The Stability ◽  
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.

scholarly journals Analysis of a Novel Two-Dimensional Lattice Hydrodynamic Model Considering Predictive Effect

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2464
Author(s):  
Huimin Liu ◽  
Rongjun Cheng ◽  
Tingliu Xu
Keyword(s):  
Traffic Flow ◽  
Hydrodynamic Model ◽  
Traffic Information ◽  
Traffic Density ◽  
Two Dimensional ◽  
Lattice Hydrodynamic Model ◽  
Traffic Condition ◽  
Dimensional Lattice ◽  
The Stability ◽  
Predictive Effect

In actual driving, the driver can estimate the traffic condition ahead at the next moment in terms of the current traffic information, which describes the driver’s predictive effect. Due to this factor, a novel two-dimensional lattice hydrodynamic model considering a driver’s predictive effect is proposed in this paper. The stability condition of the novel model is obtained by performing the linear stability analysis method, and the phase diagram between the driver’s sensitivity coefficient and traffic density is drawn. The nonlinear analysis of the model is conducted and the kink-antikink of modified Korteweg-de Vries (mKdV) equation is derived, which describes the propagation characteristics of the traffic density flow waves near the critical point. The numerical simulation is executed to explore how the driver’s predictive effect affects the traffic flow stability. Numerical results coincide well with theoretical analysis results, which indicates that the predictive effect of drivers can effectively avoid traffic congestion and the fraction of eastbound cars can also improve the stability of traffic flow to a certain extent.

Lattice hydrodynamic model for bidirectional pedestrian flow with the consideration of pedestrian density difference

2015 ◽  
Vol 26 (08) ◽  
pp. 1550092 ◽  
Author(s):  
Jie Zhou ◽  
Zhong-Ke Shi
Keyword(s):  
Stability Analysis ◽  
Hydrodynamic Model ◽  
Density Difference ◽  
Subway Station ◽  
Lattice Hydrodynamic Model ◽  
Analysis Method ◽  
Pedestrian Flow ◽  
Reaction Coefficient ◽  
De Vries ◽  
The Stability

Considering the effect of density difference, an extended lattice hydrodynamic model for bidirectional pedestrian flow is proposed in this paper. The stability condition is obtained by the use of linear stability analysis. It is shown that the stability of pedestrian flow varies with the reaction coefficient of density difference. Based on nonlinear analysis method, the Burgers, Korteweg–de Vries (KdV) and modified Korteweg–de Vries (MKdV) equations are derived to describe the triangular shock waves, soliton waves and kink–antikink waves in the stable, metastable and unstable regions, respectively. The results show that jams may be alleviated by considering the effect of density difference. The findings also indicate that in the process of building and subway station design, a series of auxiliary facilities should be considered in order to alleviate the possible pedestrian jams.

von Neumann Stability Analysis of a Segregated Pressure-Based Solution Scheme for One-Dimensional and Two-Dimensional Flow Equations

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
Santosh Konangi ◽  
Nikhil K. Palakurthi ◽  
Urmila Ghia
Keyword(s):  
Stability Analysis ◽  
Euler Equations ◽  
Two Dimensional ◽  
Von Neumann ◽  
One Dimensional ◽  
Flow Equations ◽  
Solution Scheme ◽  
Von Neumann Stability ◽  
The Stability ◽  
Stability Limits

The goal of this paper is to derive the von Neumann stability conditions for the pressure-based solution scheme, semi-implicit method for pressure-linked equations (SIMPLE). The SIMPLE scheme lies at the heart of a class of computational fluid dynamics (CFD) algorithms built into several commercial and open-source CFD software packages. To the best of the authors' knowledge, no readily usable stability guidelines appear to be available for this popularly employed scheme. The Euler equations are examined, as the inclusion of viscosity in the Navier–Stokes (NS) equation serves to only soften the stability limits. First, the one-dimensional (1D) Euler equations are studied, and their stability properties are delineated. Next, a rigorous stability analysis is carried out for the two-dimensional (2D) Euler equations; the analysis of the 2D equations is considerably more challenging as compared to analysis of the 1D form of equations. The Euler equations are discretized using finite differences on a staggered grid, which is used to achieve equivalence to finite-volume discretization. Error amplification matrices are determined from the stability analysis, stable and unstable regimes are identified, and practical stability limits are predicted in terms of the maximum allowable Courant–Friedrichs–Lewy (CFL) number as a function of Mach number. The predictions are verified using the Riemann problem, and very good agreement is obtained between the analytically predicted and the “experimentally” observed CFL values. The successfully tested stability limits are presented in graphical form, as compared to complicated mathematical expressions often reported in published literature. Since our analysis accounts for the solution scheme along with the full system of flow equations, the conditions reported in this paper offer practical value over the conditions that arise from analysis of simplified 1D model equations.

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

scholarly journals Comparison of West Balkan adult trout habitat predictions using a Pseudo-2D and a 2D hydrodynamic model

2016 ◽  
Vol 48 (6) ◽  
pp. 1697-1709 ◽  
Author(s):  
Christina Papadaki ◽  
Vasilis Bellos ◽  
Lazaros Ntoanidis ◽  
Elias Dimitriou
Keyword(s):  
Hydrodynamic Model ◽  
River Discharge ◽  
Environmental Flow ◽  
Two Dimensional ◽  
Habitat Models ◽  
One Dimensional ◽  
2D Flow ◽  
A Cell ◽  
The One ◽  
Water Depths

Abstract Hydraulic-habitat models combine the dynamic behavior of river discharge with geomorphological and ecological responses. In this study, they are used for estimating environmental flow requirements. We applied a Pseudo-two-dimensional (2D) model based on the one-dimensional (1D) HEC-RAS model and an in-house 2D (FLOW-R2D) hydrodynamic model to a section of river for several flows in respect of summer conditions of the study reach, and compared the results derived from the models in terms of water depths and velocities as well as habitat predictions in terms of weighted usable area (WUA). In general, 2D models are more promising in habitat studies since they quantify spatial variations and combinations of flow patterns important to stream flora and fauna in a higher detail than the 1D models. Relationships between WUA and discharge for the two models were examined, to compare the similarity as well as the magnitude of predictions over the modelled discharge range. The models predicted differences in the location of maxima and changes in variation of velocity and water depth. Finally, differences in spatial distribution (in terms of suitability indices and WUA) between the Pseudo-2D and the fully 2D modelling results can be considerable on a cell-by-cell basis.

The flux difference memory integral effect on two-lane stability in the lattice hydrodynamic model

2018 ◽  
Vol 29 (09) ◽  
pp. 1850083 ◽  
Author(s):  
Guanghan Peng ◽  
Shuhong Yang ◽  
Hongzhuan Zhao ◽  
Li Qing
Keyword(s):  
Hydrodynamic Model ◽  
Historical Time ◽  
Lattice Hydrodynamic Model ◽  
Theoretic Analysis ◽  
Lane Changing ◽  
Reaction Coefficient ◽  
Integral Effect ◽  
The Stability ◽  
Flux Difference ◽  
Changing Rate

In this paper, the flux difference memory integral (FDMI) effect is introduced into the lattice hydrodynamic model for a two-lane freeway. The FDMI effect plays an important role on the linear stability condition, from theoretic analysis, in a two-lane system. The FDMI effect including the intensity reaction coefficient and the integral historical time are investigated on two lanes via simulation. From numerical simulation, both lane changing rate and FDMI effect strengthening the stability of traffic flow on two lanes is determined.

Chaos in the Rulkov Neuron Model Based on Marotto’s Theorem

2021 ◽  
Vol 31 (15) ◽  
Author(s):  
Penghe Ge ◽  
Hongjun Cao
Keyword(s):  
Neuron Model ◽  
Initial Conditions ◽  
Stability Conditions ◽  
Two Dimensional ◽  
Bifurcation Diagrams ◽  
Fast Subsystem ◽  
One Dimensional ◽  
Sensitive Dependence ◽  
The Stability ◽  
Slow Subsystem

The existence of chaos in the Rulkov neuron model is proved based on Marotto’s theorem. Firstly, the stability conditions of the model are briefly renewed through analyzing the eigenvalues of the model, which are very important preconditions for the existence of a snap-back repeller. Secondly, the Rulkov neuron model is decomposed to a one-dimensional fast subsystem and a one-dimensional slow subsystem by the fast–slow dynamics technique, in which the fast subsystem has sensitive dependence on the initial conditions and its snap-back repeller and chaos can be verified by numerical methods, such as waveforms, Lyapunov exponents, and bifurcation diagrams. Thirdly, for the two-dimensional Rulkov neuron model, it is proved that there exists a snap-back repeller under two iterations by illustrating the existence of an intersection of three surfaces, which pave a new way to identify the existence of a snap-back repeller.

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