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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 A., Reggiani, L. A., Schintler, D. A., Czamanski, & R., Patuelli (Eds.), Handbook on Entropy, Complexity and Spatial Dynamics (pp. 474-485). Cheltenham: Edward Elgar.

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アイテムのパーマリンク: https://publications.pik-potsdam.de/pubman/item/item_26802 版のパーマリンク: https://publications.pik-potsdam.de/pubman/item/item_26802_1
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 作成者:
Rybski, Diego1, 著者              
Li, Yunfei1, 著者              
所属:
1Potsdam Institute for Climate Impact Research, ou_persistent13              

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 要旨: 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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 日付: 2021-12-14
 出版の状態: Finally published
 ページ: -
 出版情報: -
 目次: -
 査読: 査読あり
 識別子（DOI, ISBNなど）: DOI: 10.4337/9781839100598.00037
PIKDOMAIN: RD2 - Climate Resilience
Organisational keyword: RD2 - Climate Resilience
MDB-ID: yes - 3283
 学位: -

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出版物 1

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出版物名: Handbook on Entropy, Complexity and Spatial Dynamics
種別: 書籍
 著者・編者:
Reggiani, Aura, 編集者
Schintler, Laurie A., 編集者
Czamanski, Danny A., 編集者
Patuelli, Roberto, 編集者
所属:
-
出版社, 出版地: Cheltenham : Edward Elgar
ページ: - 巻号: - 通巻号: - 開始・終了ページ: 474 - 485 識別子（ISBN, ISSN, DOIなど）: -