Thermodynamic potentials and phase change for transport systems

“Thermodynamics of the City” (Wilson 2008) poses the question, in relation to the doubly constrained trip distribution model –What is Z?- where Z is the partition function. To answer this question the entropy maximising procedure of Jaynes(1957) is employed, the partition function derived and expressions given for Helmholtz free energy, for more general free energies and for specific heat. Phase changes are identified using these measures. The implications of these results are discussed and the possibility of a spatially based exergy analysis is suggested

Spatial Interaction, Imperfect Competition and the Evaluation of User Benefit

The spatial interaction model as represented by the entropy maximising trip distribution model is located in economic theory as a model that represents imperfect competition. In doing so it minimises the consumer deadweight loss associated with imperfect competition although it never eliminates it. The evaluation of benefits under imperfect competition is shown to require the inclusion of changes in land rent but is otherwise similar to the standard cost benefit analysis. A worked example suggests that the inclusion of rents and a correction for double counting results in lower estimates of benefit than obtain when only trip costs are measured

Entropy, complexity, and spatial information

We pose the central problem of defining a measure of complexity, specifically for spatial systems in general, city systems in particular. The measures we adopt are based on Shannon's (in Bell Syst Tech J 27:379-423, 623-656, 1948) definition of information. We introduce this measure and argue that increasing information is equivalent to increasing complexity, and we show that for spatial distributions, this involves a trade-off between the density of the distribution and the number of events that characterize it; as cities get bigger and are characterized by more events-more places or locations, information increases, all other things being equal. But sometimes the distribution changes at a faster rate than the number of events and thus information can decrease even if a city grows. We develop these ideas using various information measures. We first demonstrate their applicability to various distributions of population in London over the last 100 years, then to a wider region of London which is divided into bands of zones at increasing distances from the core, and finally to the evolution of the street system that characterizes the built-up area of London from 1786 to the present day. We conclude by arguing that we need to relate these measures to other measures of complexity, to choose a wider array of examples, and to extend the analysis to two-dimensional spatial systems

Gravity Model Calibration by Rent

The maximum entropy spatial interaction model is derived and shown to incorporate both trip cost and von Thünen (Puu 1997) rent per trip, a pure location rent. The similarity in result between calibrating against mean trip cost and calibrating against rent is then demonstrated. This is shown by generating a sequence of models using given values of and then calibrating these by rent to give a comparison of values. An example of the use of location rent as a measure of accessibility is outlined

Decentralising the United Kingdom: the Northern Powerhouse strategy and urban ownership links between firms since 2010

This paper explores a decentralisation initiative in the United Kingdom - the Northern Powerhouse strategy (NPS) - in terms of its main goal: strengthening connectivity between Northern cities of England. It focuses on economic interactions of these cities, defined by ownership linkages between firms, since the NPS's launch in 2010. The analysis reveals a relatively weak increase in the intensity of economic regional patterns in the North, in spite of a shift away from NPS cities' traditional manufacturing base. These results suggest potential directions for policy-makers in terms of the future implementation of the NPS

Urban Transfer Entropy across Scales

The morphology of urban agglomeration is studied here in the context of information exchange between different spatio-temporal scales. Urban migration to and from cities is characterised as non-random and following non-random pathways. Cities are multidimensional non-linear phenomena, so understanding the relationships and connectivity between scales is important in determining how the interplay of local/regional urban policies may affect the distribution of urban settlements. In order to quantify these relationships, we follow an information theoretic approach using the concept of Transfer Entropy. Our analysis is based on a stochastic urban fractal model, which mimics urban growing settlements and migration waves. The results indicate how different policies could affect urban morphology in terms of the information generated across geographical scales

Delineating the spatio-temporal pattern of local authority house prices variation in England between 2009 and 2016

Most spatio-temporal studies of house price in the UK are carried out at national or regional scale, but house prices differences could be better understood at finer spatial scales. Since England’s house prices, standardised by the size of the property (£/m2), have been shown to be somewhat clustered at local authority level and highly clustered at Middle Layer Super Output (MSOA) level, in the period 2009 to 2016, this research aims to further explore the nature of spatial and temporal variation in house prices at local authority level in England. Growth curve modelling offers a model-based description of the spatio-temporal patterns of local authority house price variation. This research explores local authority effects and three different time effects (quarter, half-year and year) on house price spatio-temporal variation. Results show that these three time effects are essentially identical and are extremely small, in comparison with local authority effects. Since annual effects provide the best fit, local authority annual house price trajectories between 2009 and 2016 are further explored. Local authorities with higher house prices in 2009 are found to have faster growing prices over the eight-year period than local authorities with lower house prices. Moreover, two clear geographic hubs of house price change over the period are observed, one centred on London, the other on Brist

Understanding housing affordability to determine the best property search areas for homeowners moving out of London

In this paper we created a novel framework for understanding housing affordability in England using a linked house price dataset. Regional house price studies revealed that after the global economic crisis, there was an unprecedented regional house price divergence driven by faster price increases in London from 2009 onwards. To ease England’s resulting housing affordability issues, we consider the scenario of a typical London homeowner to offer a new insight into local housing affordability by different property type in England and explore the best property search areas for homeowners moving out of London

Exploring local authority travel time to London effects on spatio-temporal pattern of local authority house prices variation in England

The spatial and temporal diffusion of house prices has been investigated at regional level in England, with London and the South East playing a leading role in terms of spillovers to other regions. High house prices in London not only increase neighbouring house prices but also force workers to live outside London and commuting in. To better understand this London effect, this research aims to explore the effect of travel time to London on house price variation across England. We conducted this research at local authority level rather than region level to offer a clearer insight into the relationship between house price variation and travel time to London, concentrating especially on the period post the 2008 financial crisis. Results show that local authorities with shorter travel tomes to London generally have greater house prices increases, but with some exceptions. The majority of local authorities within 75 minutes travel time to London had a high house price increase between 2009 and 2016. This underlies the London ripple effect and is reinforced by the high proportion of workers commuting to London