Cities, complexity and sustainability

Supervisors: Yong Mao (Physics), Peer-Olaf Siebers (Computer Science) and Darren Robinson (Engineering)

In order to understand the behaviour of complex systems we must understand not only the behaviour of the parts but how they act together to form the behaviour of the whole [1]. Cities can be defined as such complex systems [2]. Mathematical models as well as simulation help us to better understand and gain insight into the behaviour of such systems.

The mathematical application of non-linear dynamics and self-organisation was pioneered by Allen [3] to study the spatial dynamics of urban land usage. Within this approach, key parameters are identified (e.g. type of usage, population, employment, transport), and Differential Equations (DE) are formulated to relate those key parameters, thus describing the dynamics of the system. The DEs are solved either analytically or numerically, to reveal the consequences of the interactions between different actors, and offer an understanding of the spatio-temporal evolution of urban land usage. The strengths of the DE approach are: it can offer a clear overall picture without being overwhelmed by detail; there are established techniques in non-linear dynamics that can help us to understand regimes such as chaos and criticality [4]; finally it allows useful thermodynamic analysis involving physical quantities such as energy use and entropy change [5]. However, the DE approach is limited by the number of parameters that can be reasonably dealt with, and therefore necessarily represents a coarse-grained description. Indeed, at such aggregation levels instabilities that arise due to local interactions may be neglected, requiring additional parameters to capture such effects.

In contrast, simulation approaches using cellular automata or more general agent based models start with individual cells or agents, whose behaviours (including local interactions), are formulated as rules and collectively simulated to study the properties that emerge. The results can deepen our insights into the evolution of systems, and they have been successfully applied to analyse a broad range of natural and social phenomena; urban land usage being one [6, 7]. These models allow for the testing of different hypotheses and theories for urban change, thus leading to a greater understanding of how cities work [8].

In this project, we propose a multi-method modelling approach which will bridge the gap between the ’macro’ DE and the ’micro’ multi-agent approaches. Beginning with experiments of hypothetical city forms and verifying our predictions using benchmark datasets, we will develop and calibrate our modelling methodology to facilitate large scale simulations, across different levels of specification, using data of land usage from 2 cities: a small city (Nottingham) and a megacity (Shanghai). In this we will also consider the energy implications of building uses and the transport of goods and people between them, to better understand and positively influence relationships between urban form and cities’ environmental sustainability.