Stable embedded solitons

Stable embedded solitons are discovered in the generalized third-order nonlinear Schroedinger equation. When this equation can be reduced to a perturbed complex modified KdV equation, we developed a soliton perturbation theory which shows that a continuous family of sech-shaped embedded solitons exist and are nonlinearly stable. These analytical results are confirmed by our numerical simulations. These results establish that, contrary to previous beliefs, embedded solitons can be robust despite being in resonance with the linear spectrum.Comment: 2 figures. To appear in Phys. Rev. Let

Using the theory of planned behaviour as a process evaluation tool in randomised trials of knowledge translation strategies : A case study from UK primary care

Peer reviewedPublisher PD

Transcritical flow of a stratified fluid: The forced extended Korteweg-de Vries model

Transcritical, or resonant, flow of a stratified fluid over an obstacle is studied using a forced extended Korteweg-de Vries model. This model is particularly relevant for a two-layer fluid when the layer depths are near critical, but can also be useful in other similar circumstances. Both quadratic and cubic nonlinearities are present and they are balanced by third-order dispersion. We consider both possible signs for the cubic nonlinear term but emphasize the less-studied case when the cubic nonlinear term and the dispersion term have the same-signed coefficients. In this case, our numerical computations show that two kinds of solitary waves are found in certain parameter regimes. One kind is similar to those of the well-known forced Korteweg-de Vries model and occurs when the cubic nonlinear term is rather small, while the other kind is irregularly generated waves of variable amplitude, which may continually interact. To explain this phenomenon, we develop a hydraulic theory in which the dispersion term in the model is omitted. This theory can predict the occurence of upstream and downstream undular bores, and these predictions are found to agree quite well with the numerical computations. © 2002 American Institute of Physics.published_or_final_versio

Heating up the cold bounce

Self-dual string cosmological models provide an effective example of bouncing solutions where a phase of accelerated contraction smoothly evolves into an epoch of decelerated Friedmann--Robertson--Walker expansion dominated by the dilaton. While the transition to the expanding regime occurs at sub-Planckian curvature scales, the Universe emerging after the bounce is cold, with sharply growing gauge coupling. However, since massless gauge bosons (as well as other massless fields) are super-adiabatically amplified, the energy density of the maximally amplified modes re-entering the horizon after the bounce can efficiently heat the Universe. As a consequence the gauge coupling reaches a constant value, which can still be perturbative.Comment: 28 pages, 13 figure

The impact of Cochrane Systematic Reviews : a mixed method evaluation of outputs from Cochrane Review Groups supported by the UK National Institute for Health Research

© 2014 Bunn et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.Background: There has been a growing emphasis on evidence-informed decision making in health care. Systematic reviews, such as those produced by the Cochrane Collaboration, have been a key component of this movement. The UK National Institute for Health Research (NIHR) Systematic Review Programme currently supports 20 Cochrane Review Groups (CRGs). The aim of this study was to identify the impacts of Cochrane reviews published by NIHR funded CRGs during the years 2007-11. Methods: We sent questionnaires to CRGs and review authors, interviewed guideline developers and used bibliometrics and documentary review to get an overview of CRG impact and to evaluate the impact of a sample of 60 Cochrane reviews. We used a framework with four categories (knowledge production, research targeting, informing policy development, and impact on practice/services). Results: A total of 1502 new and updated reviews were produced by the 20 NIHR funded CRGs between 2007-11. The clearest impacts were on policy with a total of 483 systematic reviews cited in 247 sets of guidance; 62 were international, 175 national (87 from the UK) and 10 local. Review authors and CRGs provided some examples of impact on practice or services, for example safer use of medication, the identification of new effective drugs or treatments and potential economic benefits through the reduction in the use of unproven or unnecessary procedures. However, such impacts are difficult to objectively document and the majority of reviewers were unsure if their review had produced specific impacts. Qualitative data suggested that Cochrane reviews often play an instrumental role in informing guidance although a poor fit with guideline scope or methods, reviews being out of date and a lack of communication between CRGs and guideline developers were barriers to their use. Conclusions: Health and economic impacts of research are generally difficult to measure. We found that to be the case with this evaluation. Impacts on knowledge production and clinical guidance were easier to identify and substantiate than those on clinical practice. Questions remain about how we define and measure impact and more work is needed to develop suitable methods for impact analysis.Peer reviewe

Nonlinear interfacial waves in a constant-vorticity planar flow over variable depth

Exact Lagrangian in compact form is derived for planar internal waves in a two-fluid system with a relatively small density jump (the Boussinesq limit taking place in real oceanic conditions), in the presence of a background shear current of constant vorticity, and over arbitrary bottom profile. Long-wave asymptotic approximations of higher orders are derived from the exact Hamiltonian functional in a remarkably simple way, for two different parametrizations of the interface shape.Comment: revtex, 4.5 pages, minor corrections, summary added, accepted to JETP Letter

Thermal diffusion of supersonic solitons in an anharmonic chain of atoms

We study the non-equilibrium diffusion dynamics of supersonic lattice solitons in a classical chain of atoms with nearest-neighbor interactions coupled to a heat bath. As a specific example we choose an interaction with cubic anharmonicity. The coupling between the system and a thermal bath with a given temperature is made by adding noise, delta-correlated in time and space, and damping to the set of discrete equations of motion. Working in the continuum limit and changing to the sound velocity frame we derive a Korteweg-de Vries equation with noise and damping. We apply a collective coordinate approach which yields two stochastic ODEs which are solved approximately by a perturbation analysis. This finally yields analytical expressions for the variances of the soliton position and velocity. We perform Langevin dynamics simulations for the original discrete system which fully confirm the predictions of our analytical calculations, namely noise-induced superdiffusive behavior which scales with the temperature and depends strongly on the initial soliton velocity. A normal diffusion behavior is observed for very low-energy solitons where the noise-induced phonons also make a significant contribution to the soliton diffusion.Comment: Submitted to PRE. Changes made: New simulations with a different method of soliton detection. The results and conclusions are not different from previous version. New appendixes containing information about the system energy and soliton profile

Looking inside the black box: results of a theory-based process evaluation exploring the results of a randomized controlled trial of printed educational messages to increase primary care physicians' diabetic retinopathy referrals [Trial registration number ISRCTN72772651]

Background: Theory-based process evaluations conducted alongside randomized controlled trials provide the opportunity to investigate hypothesized mechanisms of action of interventions, helping to build a cumulative knowledge base and to inform the interpretation of individual trial outcomes. Our objective was to identify the underlying causal mechanisms in a cluster randomized trial of the effectiveness of printed educational materials (PEMs) to increase referral for diabetic retinopathy screening. We hypothesized that the PEMs would increase physicians’ intention to refer patients for retinal screening by strengthening their attitude and subjective norm, but not their perceived behavioral control. Methods: Design: A theory based process evaluation alongside the Ontario Printed Educational Material (OPEM) cluster randomized trial. Postal surveys based on the Theory of Planned Behavior were sent to a random sample of trial participants two months before and six months after they received the intervention. Setting: Family physicians in Ontario, Canada. Participants: 1,512 family physicians (252 per intervention group) from the OPEM trial were invited to participate, and 31.3% (473/1512) responded at time one and time two. The final sample comprised 437 family physicians fully completing questionnaires at both time points. Main outcome measures: Primary: behavioral intention related to referring patient for retinopathy screening; secondary: attitude, subjective norm, perceived behavioral control. Results: At baseline, family physicians reported positive intention, attitude, subjective norm, and perceived behavioral control to advise patients about retinopathy screening suggesting limited opportunities for improvement in these constructs. There were no significant differences on intention, attitude, subjective norm, and perceived behavioral control following the intervention. Respondents also reported additional physician- and patient-related factors perceived to influence whether patients received retinopathy screening. Conclusions: Lack of change in the primary and secondary theory-based outcomes provides an explanation for the lack of observed effect of the main OPEM trial. High baseline levels of intention to advise patients to attend retinopathy screening suggest that post-intentional and other factors may explain gaps in care. Process evaluations based on behavioral theory can provide replicable and generalizable insights to aid interpretation of randomized controlled trials of complex interventions to change health professional behavior

Unsteady undular bores in fully nonlinear shallow-water theory

We consider unsteady undular bores for a pair of coupled equations of Boussinesq-type which contain the familiar fully nonlinear dissipationless shallow-water dynamics and the leading-order fully nonlinear dispersive terms. This system contains one horizontal space dimension and time and can be systematically derived from the full Euler equations for irrotational flows with a free surface using a standard long-wave asymptotic expansion. In this context the system was first derived by Su and Gardner. It coincides with the one-dimensional flat-bottom reduction of the Green-Naghdi system and, additionally, has recently found a number of fluid dynamics applications other than the present context of shallow-water gravity waves. We then use the Whitham modulation theory for a one-phase periodic travelling wave to obtain an asymptotic analytical description of an undular bore in the Su-Gardner system for a full range of "depth" ratios across the bore. The positions of the leading and trailing edges of the undular bore and the amplitude of the leading solitary wave of the bore are found as functions of this "depth ratio". The formation of a partial undular bore with a rapidly-varying finite-amplitude trailing wave front is predicted for ``depth ratios'' across the bore exceeding 1.43. The analytical results from the modulation theory are shown to be in excellent agreement with full numerical solutions for the development of an undular bore in the Su-Gardner system.Comment: Revised version accepted for publication in Phys. Fluids, 51 pages, 9 figure

Analytic model for a frictional shallow-water undular bore

We use the integrable Kaup-Boussinesq shallow water system, modified by a small viscous term, to model the formation of an undular bore with a steady profile. The description is made in terms of the corresponding integrable Whitham system, also appropriately modified by friction. This is derived in Riemann variables using a modified finite-gap integration technique for the AKNS scheme. The Whitham system is then reduced to a simple first-order differential equation which is integrated numerically to obtain an asymptotic profile of the undular bore, with the local oscillatory structure described by the periodic solution of the unperturbed Kaup-Boussinesq system. This solution of the Whitham equations is shown to be consistent with certain jump conditions following directly from conservation laws for the original system. A comparison is made with the recently studied dissipationless case for the same system, where the undular bore is unsteady.Comment: 24 page