Kinks in dipole chains

It is shown that the topological discrete sine-Gordon system introduced by Speight and Ward models the dynamics of an infinite uniform chain of electric dipoles constrained to rotate in a plane containing the chain. Such a chain admits a novel type of static kink solution which may occupy any position relative to the spatial lattice and experiences no Peierls-Nabarro barrier. Consequently the dynamics of a single kink is highly continuum like, despite the strongly discrete nature of the model. Static multikinks and kink-antikink pairs are constructed, and it is shown that all such static solutions are unstable. Exact propagating kinks are sought numerically using the pseudo-spectral method, but it is found that none exist, except, perhaps, at very low speed.Comment: Published version. 21 pages, 5 figures. Section 3 completely re-written. Conclusions unchange

Discrete Klein-Gordon models with static kinks free of the Peierls-Nabarro potential

For the nonlinear Klein-Gordon type models, we describe a general method of discretization in which the static kink can be placed anywhere with respect to the lattice. These discrete models are therefore free of the {\it static} Peierls-Nabarro potential. Previously reported models of this type are shown to belong to a wider class of models derived by means of the proposed method. A relevant physical consequence of our findings is the existence of a wide class of discrete Klein-Gordon models where slow kinks {\it practically} do not experience the action of the Peierls-Nabarro potential. Such kinks are not trapped by the lattice and they can be accelerated by even weak external fields.Comment: 6 pages, 2 figure

Briefing: Disruptive socio-technical solutions to drive re-visualisation of water service provision

The UK Engineering and Physical Sciences Research Council has launched a £4 million, 5-year grand challenge multi-disciplinary research consortium (TWENTY65) to achieve sustainable clean water for all through the development and demonstration of disruptive socio-technical solutions. The aim of this transformative research is to drive re-visualisation of water service provision and revolutionise the way innovation is delivered in the water sector. This briefing introduces concepts of disruptive innovation that could lead to a new paradigm for water service provision

Sustainable water systems of the future: how to ensure public health protection?

With climate change and a rising global population, water utilities face significant challenges over the next 50 years. In this article, Vanessa Speight, of the University of Sheffield, discusses the need for greater collaboration between the water industry and public health professionals to raise awareness of potential water quality issues and plan for a safe and sustainable future of water service provision

Translationally invariant nonlinear Schrodinger lattices

Persistence of stationary and traveling single-humped localized solutions in the spatial discretizations of the nonlinear Schrodinger (NLS) equation is addressed. The discrete NLS equation with the most general cubic polynomial function is considered. Constraints on the nonlinear function are found from the condition that the second-order difference equation for stationary solutions can be reduced to the first-order difference map. The discrete NLS equation with such an exceptional nonlinear function is shown to have a conserved momentum but admits no standard Hamiltonian structure. It is proved that the reduction to the first-order difference map gives a sufficient condition for existence of translationally invariant single-humped stationary solutions and a necessary condition for existence of single-humped traveling solutions. Other constraints on the nonlinear function are found from the condition that the differential advance-delay equation for traveling solutions admits a reduction to an integrable normal form given by a third-order differential equation. This reduction also gives a necessary condition for existence of single-humped traveling solutions. The nonlinear function which admits both reductions defines a two-parameter family of discrete NLS equations which generalizes the integrable Ablowitz--Ladik lattice.Comment: 24 pages, 4 figure

Integrability of Differential-Difference Equations with Discrete Kinks

In this article we discuss a series of models introduced by Barashenkov, Oxtoby and Pelinovsky to describe some discrete approximations to the \phi^4 theory which preserve travelling kink solutions. We show, by applying the multiple scale test that they have some integrability properties as they pass the A_1 and A_2 conditions. However they are not integrable as they fail the A_3 conditions.Comment: submitted to the Proceedings of the workshop "Nonlinear Physics: Theory and Experiment.VI" in a special issue di Theoretical and Mathematical Physic

Effect of pipe size and location on water-main head loss in water distribution systems

This study discusses practical implications of considering unit head loss in different pipe sizes and in different locations of water distribution systems (WDSs) with regard to operation and maintenance. By visualizing unit head loss (using the Hazen-Williams relationship) in pipes obtained from 18 WDSs in North America, changes in unit head loss are put into perspective in different pipe sizes and different WDS locations. The results suggest that the importance of diameter is greater than that of the Hazen-Williams roughness factor, that flow rate plays a more important role than diameter in determination of head loss in pipes closer to water sources, and that diameter seems to be more important than flow rate in pipes at the periphery. Moreover, aging, tuberculation, and subsequently reduction in effective diameter can have a more critical effect on head loss in smaller pipes at the periphery of a system. Finally, effects of water conservation and pump scheduling in different locations of the network, as far as head loss is concerned, can potentially be more evident on larger pipes closer to the water source and in some cases on smaller pipes at the periphery. Therefore, it is suggested that network-level energy management decisions can have different effects on different pipe sizes in different locations

Slow Schroedinger dynamics of gauged vortices

Multivortex dynamics in Manton's Schroedinger--Chern--Simons variant of the Landau-Ginzburg model of thin superconductors is studied within a moduli space approximation. It is shown that the reduced flow on M_N, the N vortex moduli space, is hamiltonian with respect to \omega_{L^2}, the L^2 Kaehler form on \M_N. A purely hamiltonian discussion of the conserved momenta associated with the euclidean symmetry of the model is given, and it is shown that the euclidean action on (M_N,\omega_{L^2}) is not hamiltonian. It is argued that the N=3 flow is integrable in the sense of Liouville. Asymptotic formulae for \omega_{L^2} and the reduced Hamiltonian for large intervortex separation are conjectured. Using these, a qualitative analysis of internal 3-vortex dynamics is given and a spectral stability analysis of certain rotating vortex polygons is performed. Comparison is made with the dynamics of classical fluid point vortices and geostrophic vortices.Comment: 22 pages, 2 figure

Self-Organizing Maps For Knowledge Discovery From Corporate Databases To Develop Risk Based Prioritization For Stagnation 

Stagnation or low turnover of water within water distribution systems may result in water quality issues, even for relatively short durations of stagnation / low turnover if other factors such as deteriorated aging pipe infrastructure are present. As leakage management strategies, including the creation of smaller pressure management zones, are implemented increasingly more dead ends are being created within networks and hence potentially there is an increasing risk to water quality due to stagnation / low turnover. This paper presents results of applying data driven tools to the large corporate databases maintained by UK water companies. These databases include multiple information sources such as asset data, regulatory water quality sampling, customer complaints etc. A range of techniques exist for exploring the interrelationships between various types of variables, with a number of studies successfully using Artificial Neural Networks (ANNs) to probe complex data sets. Self Organising Maps (SOMs), are a class of unsupervised ANN that perform dimensionality reduction of the feature space to yield topologically ordered maps, have been used successfully for similar problems to that posed here. Notably for this application, SOM are trained without classes attached in an unsupervised fashion. Training combines competitive learning (learning the position of a data cloud) and co-operative learning (self-organising of neighbourhoods). Specifically, in this application SOMs performed multidimensional data analysis of a case study area (covering a town for an eight year period). The visual output of the SOM analysis provides a rapid and intuitive means of examining covariance between variables and exploring hypotheses for increased understanding. For example, water age (time from system entry, from hydraulic modelling) in combination with high pipe specific residence time and old cast iron pipe were found to be strong explanatory variables. This derived understanding could ultimately be captured in a tool providing risk based prioritisation scores

Diffusion of particles in an expanding sphere with an absorbing boundary

We study the problem of particles undergoing Brownian motion in an expanding sphere whose surface is an absorbing boundary for the particles. The problem is akin to that of the diffusion of impurities in a grain of polycrystalline material undergoing grain growth. We solve the time dependent diffusion equation for particles in a d-dimensional expanding sphere to obtain the particle density function (function of space and time). The survival rate or the total number of particles per unit volume as a function of time is evaluated. We have obtained particular solutions exactly for the case where d=3 and a parabolic growth of the sphere. Asymptotic solutions for the particle density when the sphere growth rate is small relative to particle diffusivity and vice versa are derived.Comment: 12 pages. To appear in J. Phys. A: Math. Theor. 41 (2008