Related papers: On Metropolis Growth
Urban scaling theory explains the increasing returns to scale of urban wealth indicators by the per capita increase of human interactions within cities. This explanation implicitly assumes urban areas as isolated entities and ignores their…
The focus of the present research is on the analysis of local energy stability of high-order (including split-form) summation-by-parts methods, with e.g. two-point entropy-conserving fluxes, approximating non-linear conservation laws. Our…
Establishing a quantitative connection between the population growth rate and the generation times of single cells is a prerequisite for understanding evolutionary dynamics of microbes. However, existing theories fail to account for the…
Urban development is shaped by historical, geographical, and economic factors, presenting challenges for planners in understanding urban form. This study models commute flows across multiple U.S. cities, uncovering consistent patterns in…
A city (or an urban cluster) is not an isolated spatial unit, but a combination of areas with closely linked socio-economic activities. However, so far, we lack a consistent and quantitative approach to define multi-level urban clusters…
Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a…
Agglomeration economies drive urban growth at different spatial scales by enabling productivity gains, knowledge spillovers, and shared inputs among proximate firms and amenities. To develop a unified science of cities it is thus important…
Given that a group of cities follows a scaling law connecting urban population with socio-economic or infrastructural metrics (transversal scaling), should we expect that each city would follow the same behavior over time (longitudinal…
Probability distributions of money, income, and energy consumption per capita are studied for ensembles of economic agents. The principle of entropy maximization for partitioning of a limited resource gives exponential distributions for the…
The share of the world population living in cities with more than one million people rose from 11% in 1975 to 24% in 2025 (our estimates). Will this trend towards greater concentration in large cities continue or level off? We introduce two…
Cellular phones are now offering an ubiquitous means for scientists to observe life: how people act, move and respond to external influences. They can be utilized as measurement devices of individual persons and for groups of people of the…
Understanding scaling relations of social and environmental attributes of urban systems is necessary for effectively managing cities. Urban scaling theory (UST) has assumed that population density scales positively with city size. We…
Representation of cities as organisms with metabolic processes is a useful analogy for urban design, development and sustainability. Urban metabolism can be modeled by representing urban systems as networks. The various networks included in…
Urban land growth presents a major sustainability challenge, yet its growth patterns and dynamics remain unclear. We quantified urban land evolution by analyzing its statistical distribution in 14 regions and countries over 29 years. The…
We study the Metropolis dynamics of the simplest mean-field spin glass model, the Random Energy Model. We show that this dynamics exhibits aging by showing that the properly rescaled time change process between the Metropolis dynamics and a…
Cities are centers for the integration of capital and incubators of invention, and attracting venture capital (VC) is of great importance for cities to advance in innovative technology and business models towards a sustainable and…
Using a geographical scale-free network to describe relations between people in a city, we explain both superlinear and sublinear allometric scaling of urban indicators that quantify activities or performances of the city. The urban…
The growth of a population divided among spatial sites, with migration between the sites, is sometimes modelled by a product of random matrices, with each diagonal elements representing the growth rate in a given time period, and…
This paper examines the spatial agglomeration of workers and income in a continuous space-time framework. Local markets feature spatial spillovers and both exogenous and endogenous amenities. Workers relocate to maximise their instantaneous…
This study presents a computational simulation exploring the complex interactions between population density and economic factors over a 100-year period. Inspired by the Keller-Segel model, traditionally applied in biological contexts, my…