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arXiv 1102.1261cs.MA
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复杂社会系统行为中的对称性--与对称性条件相一致的人群疏散模型的讨论

Symmetry in behavior of complex social systems - discussion of models of crowd evacuation organized in agreement with symmetry conditions

W. Sikora, J. Malinowski

摘要:

足球场场景的疏散作为实现有序状态的模型进行了讨论,描述为根据位移场的个人运动,相应地计算给定的情况。在位移场的计算中考虑了疏散空间的对称性,将疏散空间中每一点的位移在坐标系中以最适合于给定对称空间群的方式表示出来,该对称空间群的不可约表示的基向量集为。在所提出的模型中,每个点处的个人速度具有相同的量。作为结果,给出了疏散时间和疏散过程中作用在个人身上的平均力。这两个参数相比,相同的参数没有对称性的考虑。它们是在模拟程序中计算的。新的程序(使用修改后的Helbing模型)已详细阐述,并提出了在这项工作中实现的模拟任务。

英文摘要:

The evacuation of football stadium scenarios are discussed as model realizing ordered states, described as movements of individuals according to fields of displacements, calculated correspondingly to given scenario. The symmetry of the evacuation space is taken into account in calculation of displacements field - the displacements related to every point of this space are presented in the coordinate frame in the best way adapted to given symmetry space group, which the set of basic vectors of irreducible representation of given group is. The speeds of individuals at every point in the presented model have the same quantity. As the results the times of evacuation and average forces acting on individuals during the evacuation are given. Both parameters are compared with the same parameters got without symmetry considerations. They are calculated in the simulation procedure. The new program (using modified Helbing model) has been elaborated and presented in this work for realization the simulation tasks the.

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