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

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

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

Volume of a vortex and the Bradlow bound

We demonstrate that the geometric volume of a soliton coincides with the thermodynamical volume also for field theories with higher-dimensional vacuum manifolds (e.g., for gauged scalar field theories supporting vortices or monopoles), generalizing the recent results of Ref. [C. Adam, M. Haberichter, and A. Wereszczynski, Phys. Lett. B 754, 18 (2016).]. We apply this observation to understand Bradlow-type bounds for general Abelian gauge theories supporting vortices, as well as some thermodynamical aspects of said theories. In the case of SDiff Bogomolny-Prasad-Sommerfield (BPS) models (being examples of perfect fluid models) we show that the base-space independent geometric volume (area) of the vortex is exactly equal to the Bradlow volume (a minimal volume for which BPS soliton solutions exist). This volume can be finite for compactons or infinite for infinitely extended solitons (in flat Minkowski space-time)

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

Single vortex structure in two models of iron pnictide s±s^\pm superconductivity

The structure of a single vortex in a FeAs superconductor is studied in the framework of two formulations of superconductivity for the recently proposed sign-reversed $s$ wave ($s^\pm$) scenario: {\it (i)} a continuum model taking into account the existence of an electron and a hole band with a repulsive local interaction between the two; {\it (ii)} a lattice tight-binding model with two orbitals per unit cell and a next-nearest-neighbour attractive interaction. In the first model, the local density of states (LDOS) at the vortex centre, as a function of energy, exhibits a peak at the Fermi level, while in the second model such LDOS peak is deviated from the Fermi level and its energy depends on band filling. An impurity located outside the vortex core has little effect on the LDOS peak, but an impurity close to the vortex core can almost suppress it and modify its position.Comment: 17 pages, 15 figures. Accepted for publication in New Journal of Physic

Developing European conservation and mitigation tools for pollination services: approaches of the STEP (Status and Trends of European Pollinators) project

Pollinating insects form a key component of European biodiversity, and provide a vital ecosystem service to crops and wild plants. There is growing evidence of declines in both wild and domesticated pollinators, and parallel declines in plants relying upon them. The STEP project (Status and Trends of European Pollinators, 2010-2015, www.stepproject.net) is documenting critical elements in the nature and extent of these declines, examining key functional traits associated with pollination deficits, and developing a Red List for some European pollinator groups. Together these activities are laying the groundwork for future pollinator monitoring programmes. STEP is also assessing the relative importance of potential drivers of pollinator declines, including climate change, habitat loss and fragmentation, agrochemicals, pathogens, alien species, light pollution, and their interactions. We are measuring the ecological and economic impacts of declining pollinator services and floral resources, including effects on wild plant populations, crop production and human nutrition. STEP is reviewing existing and potential mitigation options, and providing novel tests of their effectiveness across Europe. Our work is building upon existing and newly developed datasets and models, complemented by spatially-replicated campaigns of field research to fill gaps in current knowledge. Findings are being integrated into a policy-relevant framework to create evidence-based decision support tools. STEP is establishing communication links to a wide range of stakeholders across Europe and beyond, including policy makers, beekeepers, farmers, academics and the general public. Taken together, the STEP research programme aims to improve our understanding of the nature, causes, consequences and potential mitigation of declines in pollination services at local, national, continental and global scales