IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v392y2013i1p252-270.html
   My bibliography  Save this article

Territorial developments based on graffiti: A statistical mechanics approach

Author

Listed:
  • Barbaro, Alethea B.T.
  • Chayes, Lincoln
  • D’Orsogna, Maria R.

Abstract

We study the well-known sociological phenomenon of gang aggregation and territory formation through an interacting agent system defined on a lattice. We introduce a two-gang Hamiltonian model where agents have red or blue affiliation but are otherwise indistinguishable. In this model, all interactions are indirect and occur only via graffiti markings, on-site as well as on nearest neighbor locations. We also allow for gang proliferation and graffiti suppression. Within the context of this model, we show that gang clustering and territory formation may arise under specific parameter choices and that a phase transition may occur between well-mixed, possibly dilute configurations and well separated, clustered ones. Using methods from statistical mechanics, we study the phase transition between these two qualitatively different scenarios. In the mean-fields rendition of this model, we identify parameter regimes where the transition is first or second order. In all cases, we have found that the transitions are a consequence solely of the gang to graffiti couplings, implying that direct gang to gang interactions are not strictly necessary for gang territory formation; in particular, graffiti may be the sole driving force behind gang clustering. We further discuss possible sociological—as well as ecological—ramifications of our results.

Suggested Citation

  • Barbaro, Alethea B.T. & Chayes, Lincoln & D’Orsogna, Maria R., 2013. "Territorial developments based on graffiti: A statistical mechanics approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 252-270.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:1:p:252-270
    DOI: 10.1016/j.physa.2012.08.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843711200787X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2012.08.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Stauffer, Dietrich, 2004. "Introduction to statistical physics outside physics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 1-5.
    2. Chayes, L. & Machta, J., 1997. "Graphical representations and cluster algorithms I. Discrete spin systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 239(4), pages 542-601.
    3. Luca Giuggioli & Jonathan R Potts & Stephen Harris, 2011. "Animal Interactions and the Emergence of Territoriality," PLOS Computational Biology, Public Library of Science, vol. 7(3), pages 1-9, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Abdulaziz Alsenafi & Alethea B. T. Barbaro, 2021. "A Multispecies Cross-Diffusion Model for Territorial Development," Mathematics, MDPI, vol. 9(12), pages 1-39, June.
    2. Alsenafi, Abdulaziz & Barbaro, Alethea B.T., 2018. "A convection–diffusion model for gang territoriality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 765-786.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guzmán-Vargas, L. & Hernández-Pérez, R., 2006. "Small-world topology and memory effects on decision time in opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 372(2), pages 326-332.
    2. Chayes, L. & Machta, J., 1998. "Graphical representations and cluster algorithms II11Work supported in part by the NSF under the grant DMR-96-32898 (J.M.)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 254(3), pages 477-516.
    3. Ausloos, M. & Petroni, F., 2009. "Statistical dynamics of religion evolutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(20), pages 4438-4444.
    4. Marcel Ausloos & Roy Cerqueti, 2016. "A Universal Rank-Size Law," PLOS ONE, Public Library of Science, vol. 11(11), pages 1-15, November.
    5. Lux, Thomas & Alfarano, Simone, 2016. "Financial power laws: Empirical evidence, models, and mechanisms," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 3-18.
    6. Galam, Serge, 2004. "Sociophysics: a personal testimony," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 49-55.
    7. Clippe, Paulette & Ausloos, Marcel, 2012. "Benford’s law and Theil transform of financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6556-6567.
    8. Ruggieri, Giovanni & Iannolino, Salvatore & Baggio, Rodolfo, 2022. "Tourism destination brokers: A network analytic approach," Annals of Tourism Research, Elsevier, vol. 97(C).
    9. Sells, Sarah N. & Mitchell, Michael S., 2020. "The economics of territory selection," Ecological Modelling, Elsevier, vol. 438(C).
    10. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034, Decembrie.
    11. Baggio, Rodolfo, 2020. "Tourism destinations: A universality conjecture based on network science," Annals of Tourism Research, Elsevier, vol. 82(C).
    12. Thomas O. Richardson & Nathalie Stroeymeyt & Alessandro Crespi & Laurent Keller, 2022. "Two simple movement mechanisms for spatial division of labour in social insects," Nature Communications, Nature, vol. 13(1), pages 1-15, December.
    13. Barreira da Silva Rocha, André, 2013. "Evolutionary dynamics of nationalism and migration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(15), pages 3183-3197.
    14. Nicolas Perony & Claudio J Tessone & Barbara König & Frank Schweitzer, 2012. "How Random Is Social Behaviour? Disentangling Social Complexity through the Study of a Wild House Mouse Population," PLOS Computational Biology, Public Library of Science, vol. 8(11), pages 1-11, November.
    15. Ausloos, Marcel, 2012. "Econophysics of a religious cult: The Antoinists in Belgium [1920–2000]," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3190-3197.
    16. María Cecilia Gimenez & Luis Reinaudi & Ana Pamela Paz-García & Paulo Marcelo Centres & Antonio José Ramirez-Pastor, 2021. "Opinion evolution in the presence of constant propaganda: homogeneous and localized cases," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(1), pages 1-11, January.
    17. Frank Marten & Krasimira Tsaneva-Atanasova & Luca Giuggioli, 2012. "Bacterial Secretion and the Role of Diffusive and Subdiffusive First Passage Processes," PLOS ONE, Public Library of Science, vol. 7(8), pages 1-12, August.
    18. Lutnesky, Marvin M.F. & Brown, Thomas R., 2015. "Simulation of movement that potentially maximizes assessment, presence, and defense in territorial animals with varying movement strategies," Ecological Modelling, Elsevier, vol. 313(C), pages 50-58.
    19. Jovanovic, Franck & Mantegna, Rosario N. & Schinckus, Christophe, 2019. "When financial economics influences physics: The role of Econophysics," International Review of Financial Analysis, Elsevier, vol. 65(C).
    20. Oliveira dos Santos Soares, Ricardo & Martinez, Alexandre Souto, 2006. "The geometrical patterns of cooperation evolution in the spatial prisoner's dilemma: An intra-group model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 823-829.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:392:y:2013:i:1:p:252-270. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.