Related papers: A comparison of simple models for urban morphogene…
Although the average population density of a city is an extremely simple indicator, it is often used as a determinant factor for describing various aspects of urban phenomena. On the other hand, a plethora of different measures that aim at…
The dynamical relaxation and scaling properties of three different variants of the contact process in two spatial dimensions are analysed. Dynamical contact processes capture a variety of contagious processes such as the spreading of…
Several approaches and corresponding definitions of complexity have been developed in different fields. Urban systems are the archetype of complex socio-technical systems concerned with these different viewpoints. We suggest in this chapter…
Many growing phenomena in both nature and society can be predicted with sigmoid function. The growth curve of the level of urbanization is a typical S-shaped one, and can be described by using logistic function. The logistic model implies a…
Understanding cities is central to addressing major global challenges from climate and health to economic resilience. Although increasingly perceived as fundamental socio-economic units, the detailed fabric of urban economic activities is…
The application of the network approach to the urban case poses several questions in terms of how to deal with metric distances, what kind of graph representation to use, what kind of measures to investigate, how to deepen the correlation…
Traffic congestion is a major problem in megacities which increases vehicle emissions and degrades ambient air quality. Various models have been developed to address the universal features of traffic jams. These models range from micro…
Urban form has been empirically demonstrated to be of scaling invariance and can be described with fractal geometry. However, the rational range of fractal dimension value and the relationships between various fractal indicators of cities…
The fundamental processes of biological development are governed by multiple signaling molecules that create non-uniform concentration profiles known as morphogen gradients. It is widely believed that the establishment of morphogen…
The continuous evolution of cities poses significant challenges in terms of managing and understanding their complex dynamics. With the increasing demand for transparency and the growing availability of open urban data, it has become…
A model of the urban agglomeration and segregation is formulated, in which two types of agents move around on the square-lattice aligned cells. The model is shown to exhibit, when the density of agents are varied as the control parameter,…
A distinguishing feature of a multicellular living system is that it operates at various scales, from the intracellular to organismal. Very little is known at present on how tissue level properties are related to cell and subcellular…
The relationships between diversity, productivity and scale determine much of the structure and robustness of complex biological and social systems. While arguments for the link between specialization and productivity are common, diversity…
This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in literature and the derivation of the respective macroscopic partial differential…
The processes of interplant competition within a field are still poorly understood. However, they explain a large part of the heterogeneity in a field and may have longer-term consequences, especially in mixed stands. Modeling can help to…
Understanding and modeling human mobility is central to challenges in transport planning, sustainable urban design, and public health. Despite decades of effort, simulating individual mobility remains challenging because of its complex,…
The interactions between diffusing molecules and membrane-bound receptors drive numerous cellular processes. In this work, we develop a spatial model of molecular interactions with membrane receptors by homogenizing the cell membrane and…
This paper develops a general force-based pedestrian model named CosForce, in which cosine functions are employed to describe asymmetric interactions. These functions implicitly capture the mechanisms of anticipation and reaction. By…
Urban growth sometimes leads to rigid infrastructure that struggles to adapt to changing demand. This paper introduces a novel approach, aiming to enable cities to evolve and respond more effectively to such dynamic demand. It identifies…
Many approaches have dealt with the hypothesis that the environment contain information, mostly focusing on how humans decode information from the environment in visual perception, navigation, and spatial decision-making. A question yet to…