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Urban population density always follows the exponential distribution and can be described with Clark's model. Because of this, the spatial distribution of urban population used to be regarded as non-fractal pattern. However, Clark's model…

Physics and Society · Physics 2016-06-15 Yanguang Chen , Jian Feng

Understanding urban form is crucial for sustainable urban planning and enhancing quality of life. This study presents a data-driven framework to systematically identify and compare urban typologies across geographically and culturally…

Computers and Society · Computer Science 2025-05-07 Arthur Carmès , Léo Catteau , Andrew Sonta , Arash Tavakoli

We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological…

Statistical Mechanics · Physics 2015-07-08 Ricardo Martínez-García , Clara Murgui , Emilio Hernández-García , Cristóbal López

Urban planning still lacks appropriate standards to define city boundaries across urban systems. This issue has historically been left to administrative criteria, which can vary significantly across countries and political systems,…

Physics and Society · Physics 2020-05-07 Boris Sotomayor-Gómez , Horacio Samaniego

This study employs percolation theory to investigate the hierarchical organisation of Australian urban centres through the connectivity of their road networks. The analysis demonstrates how discrete urban clusters have developed into…

Physics and Society · Physics 2024-08-20 M. K. M Ng , Z. Shabrina , S. Sarkar , H. Han , C. Pettit

Quantifying urban areas is crucial for addressing associated urban issues such as environmental and sustainable problems. Remote sensing data, especially the nighttime light images, have been widely used to delineate urbanized areas across…

Physics and Society · Physics 2021-01-26 Wenpu Cao , Lei Dong , Lun Wu , Yu Liu

Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of…

Dynamical Systems · Mathematics 2016-01-07 Martin Ritchie , Luc Berthouze , Istvan Z. Kiss

Predicting urban growth is important for practical reasons, and also for the challenge it presents to theoretical frameworks for cluster dynamics. Recently, the model of diffusion limited aggregation (DLA) has been applied to describe urban…

Condensed Matter · Physics 2007-05-23 Hernan A. Makse , Shlomo Havlin , H. Eugene Stanley

The appearance of large geolocated communication datasets has recently increased our understanding of how social networks relate to their physical space. However, many recurrently reported properties, such as the spatial clustering of…

The empirical studies of city-size distribution show that Zipf's law and the hierarchical scaling law are linked in many ways. The rank-size scaling and hierarchical scaling seem to be two different sides of the same coin, but their…

Physics and Society · Physics 2018-12-21 Yanguang Chen

Understanding the dynamics of traffic clusters is crucial for enhancing urban transportation systems, particularly in managing congestion and free-flow states. This study applies computational percolation theory to analyze the formation and…

Physics and Society · Physics 2025-07-30 Yongsung Kwon , Minjin Lee , Mi Jin Lee , Seung-Woo Son

Urban mobility increasingly relies on multimodality, combining the use of bicycle paths, streets, and rail networks. These different modes of transportation are well described by multiplex networks. Here we propose the overlap census method…

Physics and Society · Physics 2020-06-16 Luis Natera , Federico Battiston , Gerardo Iñiguez , Michael Szell

Cities are often compared through scaling laws, usually expressed as power-law relations between population size and aggregate urban quantities related to infrastructure, socioeconomic activity, or environmental impacts. These laws are…

Physics and Society · Physics 2026-05-19 Ulysse Marquis , Marc Barthelemy

Zipf's law of city-size distributions can be expressed by three types of mathematical models: one-parameter form, two-parameter form, and three-parameter form. The one-parameter and one of the two-parameter models are familiar to urban…

Physics and Society · Physics 2018-12-19 Yanguang Chen

Spatiotemporal distribution of urban population is crucial to understand the structure and dynamics of cities. Most studies, however, have focused on the microscopic structure of cities such as their few most crowded areas. In this work, we…

Physics and Society · Physics 2025-01-14 Yunwoo Nam , Young-Ho Eom

Urbanization has been the dominant demographic trend in the entire world, during the last half century. Rural to urban migration, international migration, and the re-classification or expansion of existing city boundaries have been among…

Physics and Society · Physics 2013-12-19 Philippe Blanchard , Dimitri Volchenkov

Using the APM cluster data we investigate whether the dynamical status of clusters is related to the large-scale structure of the Universe. We find that cluster substructure is strongly correlated with the tendency of clusters to be aligned…

Astrophysics · Physics 2009-11-06 Manolis Plionis

The clusters of a distribution are often defined by the connected components of a density level set. However, this definition depends on the user-specified level. We address this issue by proposing a simple, generic algorithm, which uses an…

Methodology · Statistics 2015-10-29 Ingo Steinwart

The phase diagram, ($T,\rho$), of a finite, constrained, and classical system is built from the analysis of cluster distributions in phase and configurational space. The obtained phase diagram can be split in three regions. One, low density…

Nuclear Theory · Physics 2007-05-23 A. Chernomoretz , P. Balenzuela , C. O. Dorso

Human settlements on Earth are scattered in a multitude of shapes, sizes and spatial arrangements. These patterns are often not random but a result of complex geographical, cultural, economic and historical processes that have profound…

Physics and Society · Physics 2021-06-03 Emanuele Strano , Filippo Simini , Marco De Nadai , Thomas Esch , Mattia Marconcini