A fractal design is shown to be highly efficient both as a load bearing structure and as a general metamaterial. Through changing the hierarchical order of the structure, the scaling of material required for stability against loading can be manipulated. We show that the transition from solid to hollow beams changes the scaling in a manner analogous to increasing the hierarchical order by one. An example second order solid beam frame is constructed using rapid prototyping techniques. The optimal hierarchical order of the structure is found for different values of loading. Possible fabrication methods and applications are then discussed.

Since its conception over 150 years ago, entropy has enlightened and confused scholars and students alike, from its origins in physics and beyond. More recently, it has been considered within the urban context in a rather eclectic range of applications. The entropy maximization approach, as applied by Alan Wilson and others from the 1960s, contrasts with considerations from the 1990s of the city as a thermodynamic dissipative system, in the tradition of Ilya Prigogine. By reviewing the relevant mathematical theory, we draw the distinction among three interrelated definitions of entropy, the thermodynamic, the figurative, and the information statistical. The applications of these definitions to urban systems within the literature are explored, and the conflation of the thermodynamic and figurative interpretations are disentangled. We close this paper with an outlook on future uses of entropy in urban systems analysis.

We introduce an adaptive network for public transport route optimisation by scaling down the available street network to a level where optimisation methods such as genetic algorithms can be applied. Our scaling is adapted to preserve the characteristics of the street network. The methodology is applied to the urban area of Nottingham, UK, to generate a new benchmark dataset for bus route optimisation studies. All travel time and demand data as well as information of permitted start and end points of routes, are derived from openly available data. The scaled network is tested with the application of a genetic algorithm adapted for restricted route start and end points. The results are compared with the real-world bus routes.

Despite the progress in the field of automatic public transport route optimisation in recent years, there exists a clear gap between the development of optimisation algorithms and their applications in real-world planning processes. In this study, we bridge this gap by developing an interface between the urban transit routing problem (UTRP) and the professional transport modelling software PTV Visum. The interface manages the differences in data requirements between the two worlds of research and allows the optimisation of public transport lines in Visum network models. This is demonstrated with the application of selection hyper-heuristics on two network models representing real-world urban areas. The optimisation objectives include the passengers’ average travel time and operators’ costs. Furthermore, we show how our approach can be combined with a mode choice model to optimise the use of public transport in relation to other modes. This feature is applied in a special optimisation experiment to reduce the number of private vehicles on a selected set of links in the network. The results demonstrate the successful implementation of our interface and the applied optimisation methods for a multi-modal public transport network.

Understanding the energy demand of a city’s housing stock is an important focus for local and national administrations to identify strategies for reducing carbon emissions. Building energy simulation offers a promising approach to understand energy use and test plans to improve the efficiency of residential properties. As part of this, models of the urban stock must be created that accurately reflect its size, shape and composition. However, substantial effort is required in order to generate detailed urban scenes with the appropriate level of attribution suitable for spatially explicit simulation of large areas. Furthermore, the computational complexity of microsimulation of building energy necessitates consideration of approaches that reduce this processing overhead. We present a workflow to automatically generate 2.5D urban scenes for residential building energy simulation from UK mapping datasets. We describe modelling the geometry, the assignment of energy characteristics based upon a statistical model and adopt the CityGML EnergyADE schema which forms an important new and open standard for defining energy model information at the city-scale. We then demonstrate use of the resulting urban scenes for estimating heating demand using a spatially explicit building energy microsimulation tool, called CitySim+, and evaluate the effects of an off-the-shelf geometric simplification routine to reduce simulation computational complexity.