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

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

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

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

Travelling kinks in discrete phi^4 models

In recent years, three exceptional discretizations of the phi^4 theory have been discovered [J.M. Speight and R.S. Ward, Nonlinearity 7, 475 (1994); C.M. Bender and A. Tovbis, J. Math. Phys. 38, 3700 (1997); P.G. Kevrekidis, Physica D 183, 68 (2003)] which support translationally invariant kinks, i.e. families of stationary kinks centred at arbitrary points between the lattice sites. It has been suggested that the translationally invariant stationary kinks may persist as 'sliding kinks', i.e. discrete kinks travelling at nonzero velocities without experiencing any radiation damping. The purpose of this study is to check whether this is indeed the case. By computing the Stokes constants in beyond-all-order asymptotic expansions, we prove that the three exceptional discretizations do not support sliding kinks for most values of the velocity - just like the standard, one-site, discretization. There are, however, isolated values of velocity for which radiationless kink propagation becomes possible. There is one such value for the discretization of Speight and Ward and three 'sliding velocities' for the model of Kevrekedis.Comment: To be published in Nonlinearity. 22 pages, 5 figures. Extensive clarifications to the text have been mad

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

The role of primary healthcare professionals in oral cancer prevention and detection

AIM: To investigate current knowledge, examination habits and preventive practices of primary healthcare professionals in Scotland, with respect to oral cancer, and to determine any relevant training needs. SETTING: Primary care. METHOD: Questionnaires were sent to a random sample of 357 general medical practitioners (GMPs) and 331 dental practitioners throughout Scotland. Additionally, focus group research and interviews were conducted amongst primary healthcare team members. RESULTS: Whilst 58% of dental respondents reported examining regularly for signs of oral cancer, GMPs examined patients' mouths usually in response to a complaint of soreness. The majority of GMPs (85%) and dentists (63%) indicated that they felt less than confident in detecting oral cancer, with over 70% of GMPs identifying lack of training as an important barrier. Many practitioners were unclear concerning the relative importance of the presence of potentially malignant lesions in the oral cavity. A high proportion of the GMPs indicated that they should have a major role to play in oral cancer detection (66%) but many felt strongly that this should be primarily the remit of the dental team. CONCLUSION: The study revealed a need for continuing education programmes for primary care practitioners in oral cancer-related activities. This should aim to improve diagnostic skills and seek to increase practitioners' participation in preventive activities

Evaluation of data-driven and process-based real-time flow forecasting techniques for informing operation of surface water abstraction

This paper presents an approach to managing surface water abstraction utilizing real-time flow forecasting and control techniques. To evaluate the effectiveness of alternative data-driven and process-based methods, flow forecasts at a case study site (River Dove, UK) using (1) a probability-distributed rainfall-runoff model (PDM), (2) PDM coupled with an autoregressive integrated moving average (ARIMA) error predictor, and (3) a long short-term memory (LSTM) neural network are integrated into a water resources management model coupled with genetic algorithm optimization to simulate and compare water abstractions, reservoir storage, downstream river flows, and pumping energy costs. When compared to historical data, results show that both PDM plus ARIMA and LSTM forecasts led to improved water abstraction operations, i.e., increased water abstraction volumes during dry periods while maintaining river environmental flows, as well as reduced pumping costs. Cost savings were found to be sensitive to the accuracy of the forecasting technique only within specific flow ranges. This study demonstrates the water resource benefits of real-time flow forecasting in supporting flexible water pumping schedules and further discusses the benefits of alternative modeling approaches in the specific context of controlling water abstraction

Discrete kink dynamics in hydrogen-bonded chains I: The one-component model

We study topological solitary waves (kinks and antikinks) in a nonlinear one-dimensional Klein-Gordon chain with the on-site potential of a double-Morse type. This chain is used to describe the collective proton dynamics in quasi-one-dimensional networks of hydrogen bonds, where the on-site potential plays role of the proton potential in the hydrogen bond. The system supports a rich variety of stationary kink solutions with different symmetry properties. We study the stability and bifurcation structure of all these stationary kink states. An exactly solvable model with a piecewise ``parabola-constant'' approximation of the double-Morse potential is suggested and studied analytically. The dependence of the Peierls-Nabarro potential on the system parameters is studied. Discrete travelling-wave solutions of a narrow permanent profile are shown to exist, depending on the anharmonicity of the Morse potential and the cooperativity of the hydrogen bond (the coupling constant of the interaction between nearest-neighbor protons).Comment: 12 pages, 20 figure