Symmetry Approach to Evacuation Scenarios

  • Wieslawa Sikora
  • Janusz Malinowski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6071)


The symmetry analysis method based on the theory of group representations is used for description of complex systems and their behavior in this work. The first trial of using the symmetry analysis in modeling of behavior of complex social system is presented. The evacuation of large building scenarios are discussed as transition from chaotic to 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 is the set of basic vectors of irreducible representation of given symmetry group.. The results obtained with using the symmetry consideration are compared with corresponding results calculated under assumption of shortest way to exits (Voronoi assumption).


social systems evacuation scenario symmetry analysis method 


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  1. 1.
    Izyumov, Y.A., Syromyatnikov, V.N.: Phase Transitions and Crystal Symmetry, ch. 2. Kluwer Academic Publishers, Dordrecht (1990)Google Scholar
  2. 2.
    Sikora, W., et al.: J. Appl. Cryst. 37, 1015–1019 (2004)CrossRefGoogle Scholar
  3. 3.
    Kovalev, O.V.: Representations of the Crystallographic Space Groups. In: Stokes, H.T., Hatch, D.M. (eds.). Gordon & Breach, London (1993)Google Scholar
  4. 4.
    Sikora, W., Malinowski, J.: Symmetry analysis in parametrization of complex systems. In: The Tenth International School on Theoretical Physics, SSPCM 2009, Myczkowce, Poland (2009)Google Scholar
  5. 5.
    Helbing, D., et al.: Simulating dynamical features of escape panic. Nature 407, 487 (2000)CrossRefGoogle Scholar
  6. 6.
  7. 7.
    Sikora, W., Malinowski, J., Figiel, H.: J. Alloys Compd., 446–447, 423-428 (2007), doi:10.1016/j.jallcom.2006.12.092Google Scholar
  8. 8.
    Sikora, W., Kuna, A.: Acta Physica Polonica A 113, 1211–1224 (2008)Google Scholar
  9. 9.
    Fischer, P., Pomjakushin, V., Keller, L., Daoud-Aladine, A., Sikora, W., Domman, A., Hulliger, F.: Phys. Rev. B 72, 134–413 (2005)Google Scholar
  10. 10.
    Sikora, W., Pytlik, L., Bialas, F., Malinowski, J.: J. Alloys Compd. 442, 61–69 (2007), doi:10.1016/j.jallcom.2006.08.34Google Scholar
  11. 11.
    Sikora, W., Malinowski, J., Kuna, A., Pytlik, L.: Journal of Physics: Conference Series 1004 012023 (2008), doi:10.1088/1742-6596/104/012023Google Scholar
  12. 12.
    Wigner, E.P.: Group Theory and its Application to the Quantum Mechanics of Atomic Spectra. Academic Press, New York (1959)zbMATHGoogle Scholar
  13. 13.
    Lubarski, G.J.: Teoria grup i jej zastosowania w fizyce. PWN, Warszawa (1961)Google Scholar
  14. 14.
    Cracknell, A.P.: Applied Group Theory. Pergamon Press, Oxford (1968)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Wieslawa Sikora
    • 1
  • Janusz Malinowski
    • 1
  1. 1.Faculty of Physics and Applied Computer ScienceAGH - University of Science and TechnologyKrakowPoland

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