Nicholas McCullen

The origin of power-law emergent scaling in large binary networks

We study the macroscopic conduction properties of large but finite binary networks with conducting bonds. By taking a combination of a spectral and an averaging based approach we derive asymptotic formulae for the conduction in terms of the component proportions p and the total number of components N. These formulae correctly identify both the percolation limits and also the emergent power-law behaviour between the percolation limits and show the interplay between the size of the network and the deviation of the proportion from the critical value of p=1/2. The results compare excellently with a large number of numerical simulations.

Pattern Formation on Networks: from Localised Activity to Turing Patterns

Networks of interactions between competing species are used to model many complex systems, such as in genetics, evolutionary biology or sociology and knowledge of the patterns of activity they can exhibit is important for understanding their behaviour. The emergence of patterns on complex networks with reaction-diffusion dynamics is studied here, where node dynamics interact via diffusion via the network edges. Through the application of a generalisation of dynamical systems analysis this work reveals a fundamental connection between small-scale modes of activity on networks and localised pattern formation seen throughout science, such as solitons, breathers and localised buckling. The connection between solutions with a single and small numbers of activated nodes and the fully developed system-scale patterns are investigated computationally using numerical continuation methods. These techniques are also used to help reveal a much larger portion of of the full number of solutions that exist in the system at different parameter values. The importance of network structure is also highlighted, with a key role being played by nodes with a certain so-called optimal degree, on which the interaction between the reaction kinetics and the network structure organise the behaviour of the system.

Emergent behaviour in large electrical networks

Many complex systems have emergent behaviour which results from 6 the way in that the components of the system interact, rather than their individual 7 properties. However, it is often unclear as to what this emergent behaviour can be, 8 or inded how large the system should be for such behaviour to arise. In this paper we 9 will address these problems for the specific case of an electrical network comprising 10 a mixture of resistive and reactive elements. Using this model we will show, using 11 some spectral theory, the types of emergent behaviour that we expect and also how 12 large a system we need for this to be observed.

Urban Transport: Analysis Of Commute Energy Use

Worldwide energy consumption is generally related with fossil fuels that increase CO₂ and other greenhouse gases (GHG) emissions. The transport sector represents a significant part of energy demand. As its share comes mostly from petroleum products, known for their highly polluting effects, there is the need to quantify energy use by transport. This assessment supports the planning and implementation of energy consumption mitigation policies that reduce negative environmental outcomes of transport systems. The research introduces an approach to estimate transport energy consumption obtained from available data and scaling factors. As the emphasis is put on urban transport, only commute road and rail transport are considered in the analysis. Data is stored and managed in a Geographical Information Systems (GIS) framework environment that also supports mapping the results. These maps allow identifying higher energy consumption areas by mode of transport and type of vehicle. Plotting the results also enables understanding the geographic distribution of energy demand from urban to rural regions, providing tools to perceive the relationship between urban form and energy consumption of the transport sector. Taking into account that the analysis is produced at a large scale, the obtained results offer support to planners and policy makers that seek solving transport-related problems, as pollution and high energy demand. Large scale analysis allows and enhances better planning, primarily when designing strategies for such detailed areas as urban spaces. Assessing and analysing energy consumption of the transport sector, enables deriving alternative energy layouts that present better energy efficiency, aiming for the final goal of mitigate the negative effects of urban transport systems.