Related papers: Mathematical modeling of urban sprawl
Study of urban form is an important area of research in urban planning/design that contributes to our understanding of how cities function and evolve. However, classical approaches are based on very limited observations and inconsistent…
Quantifying the improvement in human living standard, as well as the city growth in developing countries, is a challenging problem due to the lack of reliable economic data. Therefore, there is a fundamental need for alternate, largely…
Urban forecasting has increasingly benefited from high-dimensional spatial data through two primary approaches: graph-based methods that rely on predefined spatial structures, and region-based methods that focus on learning expressive urban…
In this paper, we use a stochastic partial differential equation (SPDE) as a model for the density of a population under the influence of random external forces/stimuli given by the environment. We study statistical properties for two…
The spatial pattern of urban-rural regional system is associated with the dynamic process of urbanization. How to characterize the urban-rural terrain using quantitative measurement is a difficult problem remaining to be solved. This paper…
Urban mobility plays a crucial role in the functioning of cities, influencing economic activity, accessibility, and quality of life. However, the effectiveness of analytical models in understanding urban mobility patterns can be…
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…
For the modelling of pedestrian dynamics we treat persons as self-driven objects moving in a continuous space. On the basis of a modified social force model we qualitatively analyze the influence of various approaches for the interaction…
The \b{eta} index is one of important measurements reflecting development level of traffic networks. However, how to explain and predict the \b{eta} index growth for a geographical region is a pending problem. With the help of mathematical…
The Transformer architecture has revolutionized artificial intelligence, yet a principled theoretical understanding of its internal mechanisms remains elusive. This paper introduces a novel analytical framework that reconceptualizes the…
Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…
Complex systems have been widely studied by social and natural scientists in terms of their dynamics and their structure. Scholars of cities and urban planning have incorporated complexity theories from qualitative and quantitative…
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…
We analyze a scaling law for the consumption of agricultural soil by cities. The nonlinear dependence of the size of the city on the number of inhabitants gives rise to an equation for population dynamics. We found the asymptotic limit of…
The future of the human race is urban. The world's population is projected to grow an additional 2.5 billion by 2050, with all expected to live in urban areas. This will increase the percentage of urban population from 55% today to 70%…
Environmental and climate processes are often distributed over large space-time domains. Their complexity and the amount of available data make modelling and analysis a challenging task. Statistical modelling of environment and climate data…
Urban expansion fronts display a robust local roughness exponent together with strongly dispersed growth and nonuniversal dynamic exponents. We show that this coexistence can arise from a disorder-controlled crossover in projected-front…
This paper presents a mathematical framework for modeling the dynamics of heterogeneous populations. Models describing local and non-local growth and transport processes, dependent on dynamically changing population structures, appear in a…
Sustainability and resilience of urban systems are multifaceted concepts, requiring information about multiple system attributes to adequately evaluate and characterize. However, despite the scientific consensus on the multivariate nature…
Understanding urban growth is one with understanding how society evolves to satisfy the needs of its individuals in sharing a common space and adapting to the territory. We propose here a quantitative analysis of the historical development…