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  Comparing power laws and exponentials in simulations of gravitational growth

Rybski, D., Li, Y. (2021): Comparing power laws and exponentials in simulations of gravitational growth. - In: Reggiani, A., Schintler, L. A., Czamanski, D. A., Patuelli, R. (Eds.), Handbook on Entropy, Complexity and Spatial Dynamics, Cheltenham : Edward Elgar, 474-485.
https://doi.org/10.4337/9781839100598.00037

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Datensatz-Permalink: https://publications.pik-potsdam.de/pubman/item/item_26802 Versions-Permalink: https://publications.pik-potsdam.de/pubman/item/item_26802_1
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 Urheber:
Rybski, Diego1, Autor              
Li, Yunfei1, Autor              
Affiliations:
1Potsdam Institute for Climate Impact Research, ou_persistent13              

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 Zusammenfassung: Urban gravitation represents an established process of city morphology, based on two "axioms", i.e. the attraction force of a center (agglomeration externalities) and the friction of space due to geographical separation. However, there is no consensus about the actual form of the attraction function. Here we compare power-law and exponential attraction in the stochastic gravitation model. Therefore, we run numerical simulations with both forms and analyze the generated structures. Specifically, we compare the area-perimeter relation, the perimeter width, the cluster size distribution, and the probability as a function of the distance to the closest urban cell. The area-perimeter relation indicates that the perimeter of the central cluster generated by the exponential attraction approximately corresponds to a circle. The width of the perimeters generated by the power-law attraction is larger than the one of those generated by the exponential attraction. According to the simulations, exponential attraction leads to somewhat large Zipf-exponents -- this means a rather uneven number of small and large cities emerges. For exponential attraction, the likelihood of urban development vanishes at short distances from the largest cluster, which inhibits the emergence of satellite clusters. In summary, power-law attraction generates more realistic patterns than exponential attraction. We also observe that the model-parameter _ of the power-law attraction mostly influences the properties of the smaller surrounding clusters while the characteristics of the main cluster are rather constant.

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 Datum: 2021-12-14
 Publikationsstatus: Final veröffentlicht
 Seiten: -
 Ort, Verlag, Ausgabe: -
 Inhaltsverzeichnis: -
 Art der Begutachtung: Expertenbegutachtung
 Identifikatoren: DOI: 10.4337/9781839100598.00037
PIKDOMAIN: RD2 - Climate Resilience
Organisational keyword: RD2 - Climate Resilience
MDB-ID: yes - 3283
 Art des Abschluß: -

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Titel: Handbook on Entropy, Complexity and Spatial Dynamics
Genre der Quelle: Buch
 Urheber:
Reggiani, Aura, Herausgeber
Schintler, Laurie A., Herausgeber
Czamanski, Danny A., Herausgeber
Patuelli, Roberto, Herausgeber
Affiliations:
-
Ort, Verlag, Ausgabe: Cheltenham : Edward Elgar
Seiten: - Band / Heft: - Artikelnummer: - Start- / Endseite: 474 - 485 Identifikator: -