Dynamical Systems on Networks: A Tutorial

We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more complicated scenarios. We briefly motivate why examining dynamical systems on networks is interesting and important, and we then give several fascinating examples and discuss some theoretical results. We also briefly discuss dynamical systems on dynamical (i.e., time-dependent) networks, overview software implementations, and give an outlook on the field.Comment: 39 pages, 1 figure, submitted, more examples and discussion than original version, some reorganization and also more pointers to interesting direction

Control of Ship capsize in stern quartering seas.

A non-linear mathematical model for the roll-yaw behaviour of a ship is used to predict capsize of a small tanker which sank in the North Sea some years ago. This capsize problem was initially simulated on an analogue computer by the Danish Maritime Authorities as well as being tank tested. The problem was simulated using the digital package SIMULINK, which produced comparable results indicating instability in waves of just less than 3 m in height. Validation of the results is attempted and a discussion of possible improvements to the model is given. Simulated responses of the tanker with simple hydrodynamic fin stabilisers show that capsize could have been prevented by this means in waves up to 7 m in height. Active PID control using a simple full span elevon is used to show a factor of ten reduction in roll angle to much greater waves. This work is of use to ship designers illustrating that stability can be enhanced for a fraction of the cost of major redesign of the ship hull and can be tailored to load conditions

An analytical approach to sorting in periodic potentials

There has been a recent revolution in the ability to manipulate micrometer-sized objects on surfaces patterned by traps or obstacles of controllable configurations and shapes. One application of this technology is to separate particles driven across such a surface by an external force according to some particle characteristic such as size or index of refraction. The surface features cause the trajectories of particles driven across the surface to deviate from the direction of the force by an amount that depends on the particular characteristic, thus leading to sorting. While models of this behavior have provided a good understanding of these observations, the solutions have so far been primarily numerical. In this paper we provide analytic predictions for the dependence of the angle between the direction of motion and the external force on a number of model parameters for periodic as well as random surfaces. We test these predictions against exact numerical simulations

A Simple Generative Model of Collective Online Behaviour

Human activities increasingly take place in online environments, providing novel opportunities for relating individual behaviours to population-level outcomes. In this paper, we introduce a simple generative model for the collective behaviour of millions of social networking site users who are deciding between different software applications. Our model incorporates two distinct components: one is associated with recent decisions of users, and the other reflects the cumulative popularity of each application. Importantly, although various combinations of the two mechanisms yield long-time behaviour that is consistent with data, the only models that reproduce the observed temporal dynamics are those that strongly emphasize the recent popularity of applications over their cumulative popularity. This demonstrates---even when using purely observational data without experimental design---that temporal data-driven modelling can effectively distinguish between competing microscopic mechanisms, allowing us to uncover new aspects of collective online behaviour.Comment: Updated, with new figures and Supplementary Informatio

Multilayer Networks

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure

Detailed analysis of data from heat pumps installed via the Renewable Heat Premium Payment Scheme

The RHPP policy provided subsidies for private householders, Registered social landlords and communities to install renewable heat measures in residential properties. Eligible measures included air and ground-source heat pumps, biomass boilers and solar thermal. Around 18,000 heat pumps were installed via this scheme. DECC funded a detailed monitoring campaign, which covered 700 heat pumps (around 4% of the total). The aim of this monitoring campaign was to assess the efficiencies of the heat pumps and to estimate the carbon and bill savings and amount of renewable heat generated. Data was collected from 31/10/2013 to 31/03/2015. This report represents the analysis of this data and represents the most complete and reliable data in-situ residential heat pump performance in the UK to date

Development of a collagen calcium-phosphate scaffold as a novel bone graft substitute.

Previous investigations have shown that collagen shows excellent biological performance as a scaffold for tissue engineering. As a primary constituent of bone and cartilage, it demonstrates excellent cell adhesion and proliferation. However, in bone tissue engineering, it has insufficient mechanical properties for implantation in a load-bearing defect. The objective of this preliminary study was to investigate the possibility of developing a collagen/calcium-phosphate composite scaffold which would combine the biological performance and the high porosity of a collagen scaffold with the high mechanical stiffness of a calcium-phosphate scaffold. Collagen scaffolds were produced by a lyophilisation process from a collagen slurry. The scaffolds were soaked for different exposure times in solutions of 0.1 M, 0.5 M or 1.0 M NaNH4HPO4 followed by 0.1 M, 0.5 M or 1.0 M CaCl2. Mechanical tests of each scaffold were performed on a uniaxial testing system. Young\u27s moduli were determined from stress-strain curves. The pore structure and porosity of the scaffolds were investigated using micro-computed tomography. A pure collagen scaffold served as a control. All scaffolds showed a significantly increased compressive stiffness relative to the pure collagen scaffolds. The exposure to the 0.5 M solutions showed significantly superior results compared to the other groups. Analysis of the pore structure indicated a decrease in the overall porosity of the composite scaffolds relative to the controls. Regarding mechanical stiffness and porosity, scaffolds after 1 hour exposure to the 0.5 M solutions showed the best properties for bone tissue engineering. Further work will involve producing a scaffold with a more homogeneous calcium phosphate distribution

On the making and taking of professionalism in the further education workplace

This paper examines the changing nature of professional practice in English further education. At a time when neo-liberal reform has significantly impacted on this under-researched and over-market-tested sector, little is known about who its practitioners are and how they construct meaning in their work. Sociological interest in the field has tended to focus on further education practitioners as either the subjects of market and managerial reform or as creative agents operating within the contradictions of audit and inspection cultures. In challenging such dualism, which is reflective of wider sociological thinking, the paper examines the ways in which agency and structure combine to produce a more transformative conception of the further education professional. The approach contrasts with a prevailing policy discourse that seeks to re-professionalise and modernise further education practice without interrogating either the terms of its professionalism or the neo-liberal practices in which it resides