Stickiness in Chaos

We distinguish two types of stickiness in systems of two degrees of freedom (a) stickiness around an island of stability and (b) stickiness in chaos, along the unstable asymptotic curves of unstable periodic orbits. We studied these effects in the standard map with a rather large nonlinearity K=5, and we emphasized the role of the asymptotic curves U, S from the central orbit O and the asymptotic curves U+U-S+S- from the simplest unstable orbit around the island O1. We calculated the escape times (initial stickiness times) for many initial points outside but close to the island O1. The lines that separate the regions of the fast from the slow escape time follow the shape of the asymptotic curves S+,S-. We explained this phenomenon by noting that lines close to S+ on its inner side (closer to O1) approach a point of the orbit 4/9, say P1, and then follow the oscillations of the asymptotic curve U+, and escape after a rather long time, while the curves outside S+ after their approach to P1 follow the shape of the asymptotic curves U- and escape fast into the chaotic sea. All these curves return near the original arcs of U+,U- and contribute to the overall stickiness close to U+,U-. The isodensity curves follow the shape of the curves U+,U- and the maxima of density are along U+,U-. For a rather long time the stickiness effects along U+,U- are very pronounced. However after much longer times (about 1000 iterations) the overall stickiness effects are reduced and the distribution of points in the chaotic sea outside the islands tends to be uniform.Comment: 28 pages, 12 figure

Highest weight Macdonald and Jack Polynomials

Fractional quantum Hall states of particles in the lowest Landau levels are described by multivariate polynomials. The incompressible liquid states when described on a sphere are fully invariant under the rotation group. Excited quasiparticle/quasihole states are member of multiplets under the rotation group and generically there is a nontrivial highest weight member of the multiplet from which all states can be constructed. Some of the trial states proposed in the literature belong to classical families of symmetric polynomials. In this paper we study Macdonald and Jack polynomials that are highest weight states. For Macdonald polynomials it is a (q,t)-deformation of the raising angular momentum operator that defines the highest weight condition. By specialization of the parameters we obtain a classification of the highest weight Jack polynomials. Our results are valid in the case of staircase and rectangular partition indexing the polynomials.Comment: 17 pages, published versio

Advance telephone calls ahead of reminder questionnaires increase response rate in non-responders compared to questionnaire reminders only : The RECORD phone trial

Peer reviewedPublisher PD

The study of metaphor as part of Critical Discourse Analysis

This article discusses how the study of metaphoric and more generally, figurative language use contributes to critical discourse analysis (CDA). It shows how cognitive linguists’ recognition of metaphor as a fundamental means of concept- and argument-building can add to CDA's account of meaning constitution in the social context. It then discusses discrepancies between the early model of conceptual metaphor theory and empirical data and argues that discursive-pragmatic factors as well as sociolinguistic variation have to be taken into account in order to make cognitive analyses more empirically and socially relevant. In conclusion, we sketch a modified cognitive approach informed by Relevance Theory within CDA

Chaos and Noise in a Truncated Toda Potential

Results are reported from a numerical investigation of orbits in a truncated Toda potential which is perturbed by weak friction and noise. Two significant conclusions are shown to emerge: (1) Despite other nontrivial behaviour, configuration, velocity, and energy space moments associated with these perturbations exhibit a simple scaling in the amplitude of the friction and noise. (2) Even very weak friction and noise can induce an extrinsic diffusion through cantori on a time scale much shorter than that associated with intrinsic diffusion in the unperturbed system.Comment: 10 pages uuencoded PostScript (figures included), (A trivial mathematical error leading to an erroneous conclusion is corrected

Chaotic mixing in noisy Hamiltonian systems

This paper summarises an investigation of the effects of low amplitude noise and periodic driving on phase space transport in 3-D Hamiltonian systems, a problem directly applicable to systems like galaxies, where such perturbations reflect internal irregularities and.or a surrounding environment. A new diagnsotic tool is exploited to quantify how, over long times, different segments of the same chaotic orbit can exhibit very different amounts of chaos. First passage time experiments are used to study how small perturbations of an individual orbit can dramatically accelerate phase space transport, allowing `sticky' chaotic orbits trapped near regular islands to become unstuck on suprisingly short time scales. Small perturbations are also studied in the context of orbit ensembles with the aim of understanding how such irregularities can increase the efficacy of chaotic mixing. For both noise and periodic driving, the effect of the perturbation scales roughly in amplitude. For white noise, the details are unimportant: additive and multiplicative noise tend to have similar effects and the presence or absence of a friction related to the noise by a Fluctuation- Dissipation Theorem is largely irrelevant. Allowing for coloured noise can significantly decrease the efficacy of the perturbation, but only when the autocorrelation time, which vanishes for white noise, becomes so large that t here is little power at frequencies comparable to the natural frequencies of the unperturbed orbit. This suggests strongly that noise-induced extrinsic diffusion, like modulational diffusion associated with periodic driving, is a resonance phenomenon. Potential implications for galaxies are discussed.Comment: 15 pages including 18 figures, uses MNRAS LaTeX macro

Noise-Induced Phase Space Transport in Two-Dimensional Hamiltonian Systems

First passage time experiments were used to explore the effects of low amplitude noise as a source of accelerated phase space diffusion in two-dimensional Hamiltonian systems, and these effects were then compared with the effects of periodic driving. The objective was to quantify and understand the manner in which ``sticky'' chaotic orbits that, in the absence of perturbations, are confined near regular islands for very long times, can become ``unstuck'' much more quickly when subjected to even very weak perturbations. For both noise and periodic driving, the typical escape time scales logarithmically with the amplitude of the perturbation. For white noise, the details seem unimportant: Additive and multiplicative noise typically have very similar effects, and the presence or absence of a friction related to the noise by a Fluctuation-Dissipation Theorem is also largely irrelevant. Allowing for colored noise can significantly decrease the efficacy of the perturbation, but only when the autocorrelation time becomes so large that there is little power at frequencies comparable to the natural frequencies of the unperturbed orbit. Similarly, periodic driving is relatively inefficient when the driving frequency is not comparable to these natural frequencies. This suggests strongly that noise-induced extrinsic diffusion, like modulational diffusion associated with periodic driving, is a resonance phenomenon. The logarithmic dependence of the escape time on amplitude reflects the fact that the time required for perturbed and unperturbed orbits to diverge a given distance scales logarithmically in the amplitude of the perturbation.Comment: 15 pages, including 13 Figures and 1 Table, uses Phys. Rev. macro

Enabling recruitment success in bariatric surgical trials: pilot phase of the By-Band-Sleeve study

This is the final version. Available on open access from Springer Nature via the DOI in this recordData availability: The data (transcripts) that support the findings of this study are available on request from the corresponding author. The data are not publicly available because of them containing information that could compromise privacy/consent, but the authors will be able to consider specific requests on a case-by-case basis.BACKGROUND: Randomized controlled trials (RCTs) involving surgical procedures are challenging for recruitment and infrequent in the specialty of bariatrics. The pilot phase of the By-Band-Sleeve study (gastric bypass versus gastric band versus sleeve gastrectomy) provided the opportunity for an investigation of recruitment using a qualitative research integrated in trials (QuinteT) recruitment intervention (QRI). PATIENTS/METHODS: The QRI investigated recruitment in two centers in the pilot phase comparing bypass and banding, through the analysis of 12 in-depth staff interviews, 84 audio recordings of patient consultations, 19 non-participant observations of consultations and patient screening data. QRI findings were developed into a plan of action and fed back to centers to improve information provision and recruitment organization. RESULTS: Recruitment proved to be extremely difficult with only two patients recruited during the first 2 months. The pivotal issue in Center A was that an effective and established clinical service could not easily adapt to the needs of the RCT. There was little scope to present RCT details or ensure efficient eligibility assessment, and recruiters struggled to convey equipoise. Following presentation of QRI findings, recruitment in Center A increased from 9% in the first 2 months (2/22) to 40% (26/65) in the 4 months thereafter. Center B, commencing recruitment 3 months after Center A, learnt from the emerging issues in Center A and set up a special clinic for trial recruitment. The trial successfully completed pilot recruitment and progressed to the main phase across 11 centers. CONCLUSIONS: The QRI identified key issues that enabled the integration of the trial into the clinical setting. This contributed to successful recruitment in the By-Band-Sleeve trial-currently the largest in bariatric practice-and offers opportunities to optimize recruitment in other trials in bariatrics.National Institute for Health Research Health Technology Assessment ProgrammeMedical Research Council (MRC

Chaos and Noise in Galactic Potentials

ABBREVIATED ABSTRACT: This paper summarises an investigation of the effects of weak friction and noise in time-independent, nonintegrable potentials which admit both regular and stochastic orbits. The aim is to understand the qualitative effects of internal and external irregularities associated, e.g., with discreteness effects or couplings to an external environment, which stars in any real galaxy must experience. The two principal conclusions are: (1) These irregularities can be important on time scales much shorter than the natural relaxation time scale t_R associated with the friction and noise. For stochastic orbits friction and noise induce an average exponential divergence from the unperturbed Hamiltonian trajectory at a rate set by the value of the local Lyapunov exponent. Even weak noise can make a pointwise interpretation of orbits suspect already on time scales much shorter than t_R. (2) The friction and noise can also have significant effects on the statistical properties of ensembles of stochastic orbits, these also occurring on time scales much shorter than t_R. Potential implications for galactic dynamics are discussed, including the problem of shadowing.Comment: 45 pages, uuencoded PostScript (figures included), LA-UR-94-282