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Related papers: The growth equation of cities

200 papers

Many outputs of cities scale in universal ways, including infrastructure, crime, and economic activity. Through a mathematical model, this study investigates the interplay between such scaling laws in human organization and governmental…

Physics and Society · Physics 2025-06-05 Bryce Morsky

Entropy relates the fast, microscopic behaviour of the elements in a system to its slow, macroscopic state. We propose to use it to explain how, as complexity theory suggests, small scale decisions of individuals form cities. For this, we…

Physics and Society · Physics 2017-11-28 Martin Barner , Clémentine Cottineau , Carlos Molinero , Hadrien Salat , Kiril Stanilov , Elsa Arcaute

The emerging field of the Science of Cities has unveiled previously undiscovered facets of urban life. Contrary to the expectation of chaotic behaviour influenced solely by cultural and geographic factors, cities globally exhibit universal…

Physics and Society · Physics 2025-10-20 Airton Deppman

Evidences are presented concerning tantalizing regularities in cities' population-flows in what regards to space and time correlations. The former exhibit a distance-behavior (for large distances) compatible with the inverse square law,…

Applications · Statistics 2012-07-30 A. Hernando , A. Plastino

Analyzing and modeling the mobility process with tour behavior is fundamental to understanding a wide range of complex systems, including animal foraging, human mobility and freight transportation. However, despite their importance, the…

Physics and Society · Physics 2026-03-09 Xu-Jie Lin , Yitao Yang , Wei-Peng Nie , Xiao-Yong Yan

Understanding the statistical dynamics of growth and inequality is a fundamental challenge to ecology and society. Recent analyses of wealth and income dynamics in contemporary societies show that economic inequality is very dynamic and…

Physics and Society · Physics 2022-10-19 Jordan T. Kemp , Luis M. A. Bettencourt

We study rank-size distribution of cities in Japan on the basis of data analysis. From the census data after World War II, we find that the rank-size distribution of cities is composed of two parts, each of which has independent power…

Data Analysis, Statistics and Probability · Physics 2009-11-13 Hiroto Kuninaka , Mitsugu Matsushita

We present a broad, phenomenological picture of the distribution of the length of open space linear segments, $l$, derived from maps of 36 cities in 14 different countries. By scaling the Zipf plot of $l$, we obtain two master curves for a…

Statistical Mechanics · Physics 2007-05-23 Rui Carvalho , Alan Penn

Uncovering the mechanism leading to the scaling law in human trajectories is of fundamental importance in understanding many spatiotemporal phenomena. We propose a hierarchical geographical model to mimic the real traffic system, upon which…

Data Analysis, Statistics and Probability · Physics 2015-05-13 Xiaopu Han , Qiang Hao , Binghong Wang , Tao Zhou

The concept of city or urban resilience has emerged as one of the key challenges for the next decades. As a consequence, institutions like the United Nations or Rockefeller Foundation have embraced initiatives that increase or improve it.…

Social and Information Networks · Computer Science 2016-08-08 Sofiane Abbar , Tahar Zanouda , Javier Borge-Holthoefer

Zipf's law states that the frequency of an observation with a given value is inversely proportional to the square of that value; Taylor's law, instead, describes the scaling between fluctuations in the size of a population and its mean.…

Physics and Society · Physics 2018-09-26 Charlotte James , Sandro Azaele , Amos Maritan , Filippo Simini

Urban land cover doubled between 1985 and 2015, yet the spatial dynamics of urban form remain under-quantified, despite its importance for sustainability, infrastructure planning, and climate risk. Urban expansion is a non-equilibrium…

Physics and Society · Physics 2026-03-10 Marc Barthelemy , Ulysse Marquis

In this second part of our survey on the social and natural distributions, we investigate some models, which intend to explain the statistical regularity of the natural and social distributions. There is a large variety of models and in…

Physics and Society · Physics 2016-07-05 L. Benguigui , M. Marinov

Ecologists have long argued about the strength of density dependence and population regulation, respectively defined as the short-term and long-term rates of return to equilibrium. Here, I give three arguments for the intractability of…

Populations and Evolution · Quantitative Biology 2024-12-24 Evan C. Johnson

Growth is a multi-layered phenomenon in human societies, composed of socioeconomic and demographic change at many different scales. Yet, standard macroeconomic indicators average over most of these processes, blurring the spatial and…

Physics and Society · Physics 2025-11-11 Jordan T Kemp , Laura Fürsich , Luís M A Bettencourt

Urban sprawl reshapes cities, yet its quantitative laws remain elusive. Analyzing built-up expansion in 19 cities (1985-2015) with tools from surface growth physics in radial geometry, we reveal anisotropic, branch-like growth and a…

Physics and Society · Physics 2025-11-04 Ulysse Marquis , Oriol Artime , Riccardo Gallotti , Marc Barthelemy

Cities are characterized by the coexistence of general aggregate patterns, along with many local variations. This poses challenges for analyses of urban phenomena, which tend to be either too aggregated or too local, depending on the…

Physics and Society · Physics 2025-09-30 Luís M. A. Bettencourt , Ivanna Rodriguez , Jordan T. Kemp , José Lobo

Entropy is arguably one of the most powerful concepts to understand the world, from the behavior of molecules to the expansion of the universe, from how life emerges to how hybrid complex systems like cities come into being and continue…

Physics and Society · Physics 2024-04-03 Vinicius M. Netto , Otavio Peres , Caio Cacholas

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

The scaling relations between city attributes and population are emergent and ubiquitous aspects of urban growth. Quantifying these relations and understanding their theoretical foundation, however, is difficult due to the challenge of…

Physics and Society · Physics 2023-01-31 Keith Burghardt , Johannes H. Uhl , Kristina Lerman , Stefan Leyk