Related papers: Mathematical modeling of urban sprawl
Urban form plays a crucial role in shaping transportation patterns, accessibility, energy consumption, and more. Our study examines the relationship between urban form and transportation energy use by developing a parametric model that…
Urban morphology has long been recognized as a factor shaping human mobility, yet comparative and formal classifications of urban form across metropolitan areas remain limited. Building on theoretical principles of urban structure and…
Cities emerged independently across different world regions and historical periods, raising fundamental questions: How did the first urban settlements develop? What social and spatial conditions enabled their emergence? Are these processes…
Measures of wealth and production have been found to scale superlinearly with the population of a city. Therefore, it makes economic sense for humans to congregate together in dense settlements. A recent model of population dynamics showed…
The urban spatial structure represents the distribution of public and private spaces in cities and how people move within them. While it usually evolves slowly, it can change fast during large-scale emergency events, as well as due to urban…
Analyzing 9,000 urban areas' street networks, we identify properties, including extreme betweenness centrality heterogeneity, that typical spatial network models fail to explain. Accordingly we propose a universal, parsimonious, generative…
The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional…
Recent years have witnessed an explosion of extensive geolocated datasets related to human movement, enabling scientists to quantitatively study individual and collective mobility patterns, and to generate models that can capture and…
In this work we propose a novel space-dependent multiscale model for the spread of infectious diseases in a two-dimensional spatial context on realistic geographical scenarios. The model couples a system of kinetic transport equations…
Spatial road networks have been widely employed to model the structure and connectivity of cities. In such representation, the question of spatial scale of the entities in the network, i.e. what its nodes and edges actually embody in…
From tumour invasion to cell sorting and animal territoriality, many biological systems rely on nonlocal interactions that drive complex spatial organisation. Partial differential equations (PDEs) with nonlocal advection are increasingly…
Essential to each other, growth and exploration are jointly observed in populations, be it alive such as animals and cells or inanimate such as goods and money. But their ability to move, crucial to cope with uncertainty and optimize…
Recent years have seen an increased interest in using mean-field density based modelling and control strategy for deploying robotic swarms. In this paper, we study how to dynamically deploy the robots subject to their physical constraints…
Diverse sociocultural influences in rapidly growing dense urban areas may induce strain on civil services and reduce the resilience of those areas to exogenous and endogenous shocks. We present a novel approach with foundations in computer…
The accurate modeling of individual movement in cities has significant implications for policy decisions across various sectors. Existing research emphasizes the universality of human mobility, positing that simple models can capture…
Urban mobility models are essential tools for understanding and forecasting how people and goods move within cities, which is vital for transportation planning. The spatial scale at which urban mobility is analysed is a crucial determinant…
Given multiple images that describe chaotic reaction-diffusion dynamics, parameters of a PDE model are estimated using autosynchronization, where parameters are controlled by synchronization of the model to the observed data. A…
Because of increasing global urbanization and its immediate consequences, including changes in patterns of food demand, circulation and land use, the next century will witness a major increase in the extent of paved roads built worldwide.…
Stochastic partial differential equations (SPDEs) represent a very active research field with numerous recent developments and breakthrough results. There are several well-established approaches and methods used to construct solutions for…
Having good knowledge of terrain information is essential for improving the performance of various downstream tasks on complex terrains, especially for the locomotion and navigation of legged robots. We present a novel framework for neural…