Non-Filippov dynamics arising from the smoothing of nonsmooth systems, and its robustness to noise

Switch-like behaviour in dynamical systems may be modelled by highly nonlinear functions, such as Hill functions or sigmoid functions, or alternatively by piecewise-smooth functions, such as step functions. Consistent modelling requires that piecewise-smooth and smooth dynamical systems have similar dynamics, but the conditions for such similarity are not well understood. Here we show that by smoothing out a piecewise-smooth system one may obtain dynamics that is inconsistent with the accepted wisdom --- so-called Filippov dynamics --- at a discontinuity, even in the piecewise-smooth limit. By subjecting the system to white noise, we show that these discrepancies can be understood in terms of potential wells that allow solutions to dwell at the discontinuity for long times. Moreover we show that spurious dynamics will revert to Filippov dynamics, with a small degree of stochasticity, when the noise magnitude is sufficiently large compared to the order of smoothing. We apply the results to a model of a dry-friction oscillator, where spurious dynamics (inconsistent with Filippov's convention or with Coulomb's model of friction) can account for different coefficients of static and kinetic friction, but under sufficient noise the system reverts to dynamics consistent with Filippov's convention (and with Coulomb-like friction).Comment: submitted to: Nonlinear Dynamic

Fast phase randomisation via two-folds

A two-fold is a singular point on the discontinuity surface of a piecewise-smooth vector field, at which the vector field is tangent to the discontinuity surface on both sides. If an orbit passes through an invisible two-fold (also known as a Teixeira singularity) before settling to regular periodic motion, then the phase of that motion cannot be determined from initial conditions, and, in the presence of small noise, the asymptotic phase of a large number of sample solutions is highly random. In this paper, we show how the probability distribution of the asymptotic phase depends on the global nonlinear dynamics. We also show how the phase of a smooth oscillator can be randomized by applying a simple discontinuous control law that generates an invisible two-fold. We propose that such a control law can be used to desynchronize a collection of oscillators, and that this manner of phase randomization is fast compared with existing methods (which use fixed points as phase singularities), because there is no slowing of the dynamics near a two-fold

Innovations in Light

CIBSE & SLL International Lighting Conferenc

A Platform for the Analysis of Qualitative and Quantitative Data about the Built Environment and its Users

There are many scenarios in which it is necessary to collect data from multiple sources in order to evaluate a system, including the collection of both quantitative data - from sensors and smart devices - and qualitative data - such as observations and interview results. However, there are currently very few systems that enable both of these data types to be combined in such a way that they can be analysed side-by-side. This paper describes an end-to-end system for the collection, analysis, storage and visualisation of qualitative and quantitative data, developed using the e-Science Central cloud analytics platform. We describe the experience of developing the system, based on a case study that involved collecting data about the built environment and its users. In this case study, data is collected from older adults living in residential care. Sensors were placed throughout the care home and smart devices were issued to the residents. This sensor data is uploaded to the analytics platform and the processed results are stored in a data warehouse, where it is integrated with qualitative data collected by healthcare and architecture researchers. Visualisations are also presented which were intended to allow the data to be explored and for potential correlations between the quantitative and qualitative data to be investigated

Thermal Properties of LiCl-KCl Molten Salt for Nuclear Waste Separation

This project addresses both practical and fundamental scientific issues of direct relevance to operational challenges of the molten LiCl-KCl salt pyrochemical process, while providing avenues for improvements in the process. In order to understand the effects of the continually changing composition of the molten salt bath during the process, the project team will systematically vary the concentrations of rare earth surrogate elements, lanthanum, cerium, praseodymium, and neodymium, which will be added to the molten LiCl-KCl salt. They will also perform a limited number of focused experiments by the dissolution of depleted uranium. All experiments will be performed at 500 deg C. The project consists of the following tasks. Researchers will measure density of the molten salts using an instrument specifically designed for this purpose, and will determine the melting points with a differential scanning calorimeter. Knowledge of these properties is essential for salt mass accounting and taking the necessary steps to prevent melt freezing. The team will use cyclic voltammetry studies to determine redox potentials of the rare earth cations, as well as their diffusion coefficients and activities in the molten LiCl-KCl salt. In addition, the team will perform anodic stripping voltammetry to determine the concentration of the rare earth elements and their solubilities, and to develop the scientific basis for an on-line diagnostic system for in situ monitoring of the cation species concentration (rare earths in this case). Solubility and activity of the cation species are critically important for the prediction of the salt's useful lifetime and disposal

Australian SMEs: Waste sent to landfill

Landfill waste has a negative impact on the environment and Small and Medium Enterprises (SMEs) are believed to be significant contributors. There is little government or scholarly research, however, quantifying the collective volume of waste SMEs send to landfill. The limited studies instead measure total volumes (landfill and recycling combined) and/or do not distinguish between specific waste streams (e.g. wood) and subcategories (e.g. dust). This paper contributes to knowledge by reconceptualising SME waste into subcategories and by measuring landfill volumes. It presents findings from 404 Australian SMEs which found that, in descending order, cardboard, paper, plastic wrap, wood dust and particleboard were the subcategories these SMEs sent to landfill in the greatest volumes. It also argues that this reconceptualisation and associated data collection protocols have the potential to enable scholars and policymakers to determine the waste subcategories to which SMEs contribute most, formulate targeted interventions and research/evaluate environmental outcomes

Climate, cartography, and the life and death of the ‘natural region’ in British geography

During the first fifteen years of the twentieth century, Oxford-based Scottish geographer Andrew Herbertson constructed a framework for comprehending and categorising climate and its interrelations: natural regions. Along with a large circle of students and collaborators, Herbertson promoted natural regions as the conceptual keystone for geographical teaching and research. This article shows how natural regions theory conceived of climate as an object that was differently defined in different academic disciplines. Geography’s climate, according to Herbertson and his supporters, was defined by its relations with other spatially distributed phenomena rather than being the quantifiable and isolable entity of modern climatology. Building on recent work in the history of cartography foregrounding map use and reception, the article also argues that natural regions were products of particular modes of map reading, comparison, and synthesis. Although maps were arguably the most influential medium for communicating natural regions, they also proved limited as bearers of the multiscalar version of climate that Herbertson and his successors sought to convey. Finally, the article explains how natural regions and associated conceptions of climate came to be sidelined in the mid-twentieth century as geographers foregrounded human agency in region formation and adopted climatology’s definitions and analytical tools. Revisiting the life and death of theories of natural regions illuminates the contested significance of climate in the discipline of geography, and contributes to ongoing efforts to pluralise the history of climate sciences

Poor choices: the limits of competitive markets in the provision of essential services to low-income consumers

A major study of the problems faced by the poor in the market for seven essential services in the UK - energy, food, housing, water, telecoms, transport, and financial services. Together these represent 60% of spending by the poorest 30% of households