Study on mechanics of crowd jam based on the cusp-catastrophe model

Zheng, Xiaoping; Sun, Jun; Zhong, Tingkuan

doi:10.1016/j.ssci.2010.07.003

Cited by 15 publications

(5 citation statements)

References 14 publications

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“…Here, Δ = 8 M 3 + 27 N 2 is the criterion for deciding whether or not the situations corresponding to various control intervals are stable. In order to confirm the boundary of the mutation area, we simply need to make Δ = 0, i.e., 8 M 3 = -27 N 2 ; in other words, any M and N that satisfy the equation lie on the edge of the mutation area of the cusp catastrophe model [ 19 , 20 ]. The distribution relationship between the situations of the navigational environment and the control variables is shown in Fig 2 .…”

Section: Cusp Catastrophe Model Of Navigational Environmentmentioning

confidence: 99%

Use of Cusp Catastrophe for Risk Analysis of Navigational Environment: A Case Study of Three Gorges Reservoir Area

et al. 2016

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A water traffic system is a huge, nonlinear, complex system, and its stability is affected by various factors. Water traffic accidents can be considered to be a kind of mutation of a water traffic system caused by the coupling of multiple navigational environment factors. In this study, the catastrophe theory, principal component analysis (PCA), and multivariate statistics are integrated to establish a situation recognition model for a navigational environment with the aim of performing a quantitative analysis of the situation of this environment via the extraction and classification of its key influencing factors; in this model, the natural environment and traffic environment are considered to be two control variables. The Three Gorges Reservoir area of the Yangtze River is considered as an example, and six critical factors, i.e., the visibility, wind, current velocity, route intersection, channel dimension, and traffic flow, are classified into two principal components: the natural environment and traffic environment. These two components are assumed to have the greatest influence on the navigation risk. Then, the cusp catastrophe model is employed to identify the safety situation of the regional navigational environment in the Three Gorges Reservoir area. The simulation results indicate that the situation of the navigational environment of this area is gradually worsening from downstream to upstream.

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Section: Cusp Catastrophe Model Of Navigational Environmentmentioning

confidence: 99%

Use of Cusp Catastrophe for Risk Analysis of Navigational Environment: A Case Study of Three Gorges Reservoir Area

et al. 2016

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“…The examination of catastrophic issues, such as equilibrium points, catastrophic manifold, capacitance, and phenomenon jump, has been of great interest for a long time because of its increasing applications in physical, biological, and social sciences. Some writers, such as [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], and the authors made important contributions to the examination of various topics, such as points of balance, catastrophic models, recurring patterns, stability and instability, and phenomena linked to forced vibrations. This study aims to determine periodic solutions in a non-linear differential equation and assess their stability and semi-stability.…”

Section: Introductionmentioning

confidence: 99%

The Stability and Catastrophic Behavior of Finite Periodic Solutions in Non-Linear Differential Equations

Faeq,

Abdalrahman

2023

Tikrit J. Pure Sci.

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This study focuses on the stability and catastrophic behavior of finite periodic solutions in non-linear differential equations. The occurrence of folding surfaces and their relationship with saddle-node bifurcations are explored, being classified as fold and butterfly types of catastrophes. Additionally, the application of catastrophe theory is discussed to analyze the qualitative changes in solutions with the change in system parameters.

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“…In the study of a structural system's stability, Liu et al (2008) established a mechanical model of the coal pillar roof structural system and the mechanical stability condition of the strip-shaped coal pillar. By combining the beam model in material mechanics and catastrophe theory, Zhang et al (2011) analysed the mechanical structure of strip-shaped pillars in an underground mine. He et al (2008) analysed the stability of the structural system of a multiple strip-shaped pillar-roof and its influencing factors.…”

Section: Introductionmentioning

confidence: 99%

Archives of Mining Sciences

Chen¹,

Wu²,

Zhao³

2020

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STUDY ON THE MECHANICS AND MICRO/MACROECONOMICS OF MULTIPLE STRIP-SHAPED PILLAR RECOVERYThe structural system of a multiple strip-shaped pillar-roof is common in underground mine exploitation, and research on its mechanics and micro/macroeconomics is meaningful for utilizing strip--shaped pillar resources. A general model of the structural system of a multiple strip-shaped pillar-roof was established, the deformation mechanism of the model was analysed by material mechanics, and the deflection curve equations of the model were obtained. Based on the stress strain constitutive relation of the strip pillar and cusp catastrophe theory, the nonlinear dynamic instability mechanism of the structural system of a multiple strip-shaped pillar-roof was analysed, and the expressions of the pillar width for maintaining the stability of different types of structural systems were derived. The benefits of different structural systems were calculated using micro/macroeconomic theory, the type of the structural system was determined, and different recovery schemes were obtained. Theoretical application research was applied to a large manganese mine, and the results demonstrate that no pillar recovery was needed in 2016, a 9-m wide artificial pillar could be built to replace a pillar in 2017, and the construction of 14-m wide artificial pillars can be conducted in 2018.

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Study on mechanics of crowd jam based on the cusp-catastrophe model

Cited by 15 publications

References 14 publications

Use of Cusp Catastrophe for Risk Analysis of Navigational Environment: A Case Study of Three Gorges Reservoir Area

Use of Cusp Catastrophe for Risk Analysis of Navigational Environment: A Case Study of Three Gorges Reservoir Area

The Stability and Catastrophic Behavior of Finite Periodic Solutions in Non-Linear Differential Equations

Archives of Mining Sciences

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