Constructal Pattern Formation in Nature, Pedestrian Motion, and Epidemics Propagation

  • Antonio F. Miguel
Conference paper


Constructal Theory Infective Population Walking Velocity Stony Coral Crowd Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Anderson, R. M. and May, R. M. (1992) Infectious Diseases of Humans. Oxford University Press, London.Google Scholar
  2. Ando, T., Ota, H. and Oki, T. (1988) Forecasting the flow of people. Railw. Res. Rev. 45, 8–14.Google Scholar
  3. Anthony, K. R. N. (1999) Coral suspension feeding on fine particulate matter. J. Exp. Mar. Biol. Ecol. 232, 85–106.CrossRefGoogle Scholar
  4. Barreto, A., Aragon, M. and Epstein, R. (1994) Bubonic plague in Mozambique. Lancet 345, 983–984.CrossRefGoogle Scholar
  5. Bégué, P. and Lorente, S. (2006) Migration vs. diffusion through porous media: time dependent scale analysis. J. Porous Media 7, 637–650.Google Scholar
  6. Bejan, A. (1997) Advanced Engineering Thermodynamics, 2nd edn, Wiley, New York.Google Scholar
  7. Bejan, A. (1999) How nature takes shape: extensions of constructal theory to ducts, rivers, turbulence, cracks, dendritic crystals and spatial economics. Int. J. Therm. Sci. 38, 653–663.CrossRefGoogle Scholar
  8. Bejan, A. (2000) Shape and Structure, from Engineering to Nature. Cambridge University Press, Cambridge, UK.zbMATHGoogle Scholar
  9. Bejan, A. (2002) Fundamentals of exergy analysis, entropy generation minimiza-tion, and the generation of flow architecture. Int. J. Energy Res. 26, 545–565.Google Scholar
  10. Bejan, A. (2005) The constructal law of organization in nature: tree-shaped flows and body size. J. Exp. Biol. 208, 1677–1686.CrossRefGoogle Scholar
  11. Bejan, A. and Ledezma, G. A. (1998) Streets tree networks and urban growth: optimal geometry for quickest access between a finite-size volume and one point. Physica A 255, 211–217.CrossRefGoogle Scholar
  12. Bejan, A. and Lorente, S. (2005) La Loi Constructale. L’Harmattan, Paris.Google Scholar
  13. Bejan, A., Dincer, I., Lorente, S., Miguel, A. F. and Reis, A. H. (2004) Porous and Complex Flow Structures in Modern Technologies. Springer, New York.Google Scholar
  14. Bejan, A., Lorente, S., Miguel, A. F. and Reis, A. H. (2006) Along with Constructal Theory, University of Lausanne, Faculty of Geosciences.Google Scholar
  15. Ben-Jacob, E., Cohen, I., Shochet, O., Aronson, I., Levine, H. and Tsimering, L. (1995) Complex bacterial patterns. Nature 373, 566–567.CrossRefGoogle Scholar
  16. Blue, V. and Adler, J. (1999) Bi-directional emergent fundamental pedestrian flows from cellular automata microsimulation. In A. Ceder (ed.), Proc. Int. Symp. Traffic and Transportation Theory (ISTTT’99). Pergamon, Amsterdam, pp. 235–254.Google Scholar
  17. Brauer, F. and Castillo-Chavez, C. (2001) Mathematical Models in Population Biology and Epidemiology. Springer, New York.zbMATHGoogle Scholar
  18. Caraco, T., Glavanakov, S., Chen, G., Flaherty, J. E., Ohsumi, T. K. and Szymanski, B. K. (2002) Stage-structured infection transmission and a spatial epidemic: A model for Lyme disease. Am. Nat. 160, 348–359.CrossRefGoogle Scholar
  19. Cohn, S. K. (2002) The Black Death: end of a paradigm. Am. Hist. Rev. 107, 703–738.Google Scholar
  20. Diekmann, O. and Heesterbeek, J. A. P. (2000) Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation. Wiley, New York.Google Scholar
  21. Donald, I. and Canter, D. (1990) Behavioural aspects of the King’s Cross disaster. In D. Canter (ed.), Fires and Human Behaviour. David Fulton, London, pp. 15–30.Google Scholar
  22. Fang, Z., Lo, S. M. and Lu, J. A. (2003) On the relationship between crowd density and movement velocity. Fire Saf. J. 38, 271–283.CrossRefGoogle Scholar
  23. Fruin, J. (1971) Pedestrian and planning design. Metropolitan Association of Urban Designers and Environmental Planners. Library of Congress catalogue number 70–159312.Google Scholar
  24. Fukui, M. and Ishibashi, Y. (1999) Self-organized phase transitions in CA-models for pedestrians. J. Phys. Soc. Japan 8, 2861–2863.Google Scholar
  25. Gettling, A. V. (1998) Rayleigh-Benard Convection: Structures and Dynamics. World Scientific, Singapore.Google Scholar
  26. Graat, E., Midden, C. and Bockholts, P. (1999) Complex evacuation: effects of motivation level and slope of stairs on emergency egress time in a sports stadium. Saf. Sci. 31, 127–141.CrossRefGoogle Scholar
  27. Hankin, B. D. and Wright, R. A. (1958) Passenger flow in subways. Oper. Res. 9, 81–88.CrossRefGoogle Scholar
  28. Heidemann, D. (1996) A queueing theory approach to speed–flow–density relationships, transportation and traffic theory. Proc. 13th Int. Symp. Transport. Traffic Theory, Lyon, pp. 14–26.Google Scholar
  29. Helbing, D. (1992) A fluid-dynamic model for the movement of pedestrians. Complex Syst. 6, 391–415.zbMATHMathSciNetGoogle Scholar
  30. Helbing, D. and Molnár, P. (1995) Social force model for pedestrian dynamics. Phys. Rev. E 51, 4282–4286.CrossRefGoogle Scholar
  31. Helbing, D., Keltsch, J. and Molnár, P. (1997) Modeling the evolution of human trail systems. Nature 388, 47–50.CrossRefGoogle Scholar
  32. Helbing, D., Schweitzer, F., Keltsch, J. and Molnár, P. (1997) Active walker model for the formation of human and animal trail systems. Phys. Rev. E 56, 2527–2539.CrossRefGoogle Scholar
  33. Helbing, D. Molnár, P. Farkas, I. J. and Bolay, K. (2001) Self-organizing pedestrian movement. Environ. Plan. Plan. Des. 28, 361–383.CrossRefGoogle Scholar
  34. Henderson, L. F. (1971) The statistics of crowd fluids. Nature 229, 381–383.CrossRefGoogle Scholar
  35. Hodge, A., Robinson, D., Griffiths, B. S. and Fitter, A. H. (1999) Why plants bother: root proliferation results in increased nitrogen capture from an organic patch when two grasses compete. Plant Cell Environ. 22, 811–820.CrossRefGoogle Scholar
  36. Hoogendoorn, S. and Bovy, P. H. L. (2000) Gas-kinetic modeling and simulation of pedestrian flows. Transp. Res. Rec. 1710, 28–36.CrossRefGoogle Scholar
  37. Hoogendoorn, S., Bovy, P. and Daamen, W. (2002). Microscopic pedestrian way finding and dynamics modelling. In M. Schreckenberg and S. Sharma (eds.), Pedestrian and Evacuation Dynamics. Springer, New York, pp. 123–155.Google Scholar
  38. Hsu, C. C., Chen, T., Chang, M. and Chang, Y. K. (2006) Confidence in controlling a SARS outbreak: Experiences of public health nurses in managing home quarantine measures in Taiwan. Am. J. Infect. Control 34, 176–181.CrossRefGoogle Scholar
  39. Hughes, R. L. (2002) A continuum theory for the flow of pedestrians. Transp. Res. B 36, 507–535.CrossRefGoogle Scholar
  40. Hughes, R. L. (2003) The flow of human crowds. Annu. Rev. Fluid. Mech. 35, 169–182.CrossRefGoogle Scholar
  41. Hunter, K., Petty, M. D. and McKenzie, F. D. (2005) Experimental evaluation of the effect of varying levels of crowd behavior fidelity on the outcome of certain military scenarios. In Spring 2005 Simulation Interoperability Workshop, San Diego, CA.Google Scholar
  42. Kaandorp, J. A. and Sloot, P. M. A. (2001) Morphological models of radiate accretive growth and the influence of hydrodynamics. J. Theor. Biol. 209, 257–274.CrossRefGoogle Scholar
  43. Kallen, A., Arcuri, P. and Murray, J. D. (1985) A simple model for the spatial spread and control of rabies. J. Theor. Biol. 116, 377–394.CrossRefMathSciNetGoogle Scholar
  44. Kermack, W. O. and McKendrick, A. G. (1927) A contribution to the mathematical theory of epidemics. Proc. R. Soc. London A 115, 700–721.CrossRefGoogle Scholar
  45. Koopmans, M., Wilbrink, B., Conyn, M., Natrop, G., van der Nat. H., Vennema, H., Meijer, A., van Steenbergen, J., Fouchier, R., Osterhaus, A. and Bosman, A. (2004) Transmission of H7N7 avian influenza A virus to human beings during a large outbreak in commercial poultry farms in the Netherlands. Lancet 363, 587–593.CrossRefGoogle Scholar
  46. Langer, W. L. (1964) The black death. Scient. Am. 210, 114–121.CrossRefGoogle Scholar
  47. Langston, P. A., Masling, R. and Asmar, B. N. (2006) Crowd dynamics discrete element multi-circle model, Saf. Sci. 44, 395–417CrossRefGoogle Scholar
  48. Mena-Lorca, J. and Hethcote, H. (1992) Dynamic models of infection diseases as regulator of population sizes. J. Math. Biol. 30, 693–716.zbMATHCrossRefMathSciNetGoogle Scholar
  49. Merks, R., Hoekstra, A., Kaandorp, J. and Sloot, P. (2003) Models of coral growth: spontaneous branching, compactification and the Laplacian growth assumption. J. Theor. Biol. 224, 153–166.CrossRefMathSciNetGoogle Scholar
  50. Miguel, A. F. (2004) Dendritic growth: classical models and constructal analysis. In R. Rosa, A.H. Reis, A.F. Miguel (eds.) Bejan’s Constructal Theory of Shape and Structure. CGE-UE, Evora, pp. 75–93Google Scholar
  51. Miguel, A. F. (2006) Constructal pattern formation in stony corals, bacterial colonies and plant roots under different hydrodynamics conditions. J. Theor. Biol. 242, 954–961CrossRefMathSciNetGoogle Scholar
  52. Muramatsu, M., Irie, T. and Nagatani, T. (1999) Jamming transition in pedestrian counter flow. Physica A 267, 487–498.CrossRefGoogle Scholar
  53. Navin, P. D. and Wheeler, R. J. (1969) Pedestrian flow characteristics. Traffic Eng. 39, 31–36.Google Scholar
  54. Nelson, H. E. and Maclennan, H. A. (1995) Emergency movement. The SFPE Handbook of Fire Protection Engineering, 2nd edn, NFPA, Quincy, MA.Google Scholar
  55. Noble, J. V. (1974) Geographic and temporal development of plagues. Nature 250, 276–279.CrossRefGoogle Scholar
  56. Older, S. J. (1968) Movement of pedestrians on footways in shopping streets. Traffic Eng. Control 10, 160–163.Google Scholar
  57. Oxford, J. S., Lambkin. R., Sefton, A., Daniels, R., Elliot, A., Brown, R. and Gill, D. (2005) A hypothesis: the conjunction of soldiers, gas, pigs, ducks, geese and horses in Northern France during the Great War provided the conditions for the emergence of the “Spanish” influenza pandemic of 1918–1919. Vaccine 23, 940–945.CrossRefGoogle Scholar
  58. Predtechenskii, V.M. and Milinski, A. I. (1969) Planning for Foot Traffic Flow in Buildings. Stroiizdat Publishers, Moscow.Google Scholar
  59. Reis, A. H., Miguel. A. F. and Aydin, M. (2004) Constructal theory of flow architecture of the lungs. Med. Phys. 31, 1135–1140.CrossRefGoogle Scholar
  60. Reis, A. H. (2006a) Constructal view of scaling laws of river basins. Geomorphology 78, 201–206.CrossRefGoogle Scholar
  61. Reis, A. H. (2006b) Constructal theory: from engineering to physics, and how flow systems develop shape and structure. Appl. Mech. Rev. 59, 269–282.CrossRefGoogle Scholar
  62. Reis, A. H. and Miguel, A. F. (2006) Constructal theory and flow architectures in living systems. J. Thermal Sci. 10, 57–64.CrossRefGoogle Scholar
  63. Reynolds, C. W. (1987) Flocks, herds, and schools: a distributed behavioral model. Comput. Graphics 21, 25–34.CrossRefGoogle Scholar
  64. Robinson, D. (1994) The responses of plants to non-uniform supplies of nutrients. New Phytol. 127, 635–674.CrossRefGoogle Scholar
  65. Rosa, R., Reis, A. H. and Miguel, A. F. (2004) Bejan’s Constructal Theory of Shape and Structure. Geophysics Center of Evora, University of Evora, Portugal.Google Scholar
  66. Sandahl, J. and Percivall, M. (1972) A pedestrian traffic model for town centers. Traffic Q. 26, 359–372.Google Scholar
  67. Schweitzer, F. (1997) Self-organization of Complex Structures: From Individual to Collective Dynamics. Gordon and Breach, London.zbMATHGoogle Scholar
  68. Sebens, K. P., Witting, J. and Helmuth, B. (1997) Effects of water flow and branch spacing on particle capture by the reef coral Madracis mirabilis (Duchassaing and Michelotti). J. Exp. Mar. Biol. col. 211, 1–28.CrossRefGoogle Scholar
  69. Smith, R. A. and Dickie, J. F. (1993) Engineering for Crowd Safety. Elsevier, Amsterdam.Google Scholar
  70. Suwandono, A., Kosasih, H., Nurhayati, H., Kusriastuti, R., Harun, S., Maroef, C., Wuryadi, S., Herianto, B., Yuwono, D., Porter, K. R., Beckett, C. G. and Blair, P. J. (2006) Four dengue virus serotypes found circulating during an outbreak of dengue fever and dengue haemorrhagic fever in Jakarta, Indonesia, during 2004. Trans. R. Soc. Trop. Med. Hyg. 100, 855–862.CrossRefGoogle Scholar
  71. Thaler, P. and Pages L. (1998) Modeling the influence of assimilate availability on root growth and architecture. Plant Soil 201, 307–320.CrossRefGoogle Scholar
  72. Thar, R. and Kühl, M. (2005) Complex pattern formation of marine gradient bacteria explained by a simple computer model. FEMS Microbiol. Lett. 246, 75–79.CrossRefGoogle Scholar
  73. The Green Guide (1997) Guide to Safety at Sports Grounds, 4th edn, HMSO, London.Google Scholar
  74. Thompson, P. A. and Marchant, E. W. (1995) A computer model for the evacuation of large building populations. Fire Saf. J. 24, 131–148.CrossRefGoogle Scholar
  75. Timmermans, H., van der Hagen, X. and Borgers, A. (1992) Transportation systems, retail environments and pedestrian trip chaining behaviour: modelling issues and applications. Transport. Res. B: Methodological 26, 45–59.CrossRefGoogle Scholar
  76. Togawa, K. (1955) Study on fire escape based on the observations of multitude currents. Report No. 4. Building Research Institute, Ministry of Construction, Japan.Google Scholar
  77. TRB (1985) Pedestrians. In Highway Capacity Manual, special report 209, Transportation Research Board, Washington, DC, Chapter 13.Google Scholar
  78. Vandaele, N., Woensel, T. V. and Verbruggen, A. (2000) A queueing based traffic flow model. Transport. Res. D 5, 121–135.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC. 2007

Authors and Affiliations

  • Antonio F. Miguel

There are no affiliations available

Personalised recommendations