Localized behavior in the Lyapunov vectors for quasi-one-dimensional many-hard-disk systems

We introduce a definition of a "localization width" whose logarithm is given by the entropy of the distribution of particle component amplitudes in the Lyapunov vector. Different types of localization widths are observed, for example, a minimum localization width where the components of only two particles are dominant. We can distinguish a delocalization associated with a random distribution of particle contributions, a delocalization associated with a uniform distribution and a delocalization associated with a wave-like structure in the Lyapunov vector. Using the localization width we show that in quasi-one-dimensional systems of many hard disks there are two kinds of dependence of the localization width on the Lyapunov exponent index for the larger exponents: one is exponential, and the other is linear. Differences, due to these kinds of localizations also appear in the shapes of the localized peaks of the Lyapunov vectors, the Lyapunov spectra and the angle between the spatial and momentum parts of the Lyapunov vectors. We show that the Krylov relation for the largest Lyapunov exponent $\lambda\sim-\rho\ln\rho$ as a function of the density $\rho$ is satisfied (apart from a factor) in the same density region as the linear dependence of the localization widths is observed. It is also shown that there are asymmetries in the spatial and momentum parts of the Lyapunov vectors, as well as in their $x$ and $y$-components.Comment: 41 pages, 21 figures, Manuscript including the figures of better quality is available from http://www.phys.unsw.edu.au/~gary/Research.htm

Role of chaos for the validity of statistical mechanics laws: diffusion and conduction

Several years after the pioneering work by Fermi Pasta and Ulam, fundamental questions about the link between dynamical and statistical properties remain still open in modern statistical mechanics. Particularly controversial is the role of deterministic chaos for the validity and consistency of statistical approaches. This contribution reexamines such a debated issue taking inspiration from the problem of diffusion and heat conduction in deterministic systems. Is microscopic chaos a necessary ingredient to observe such macroscopic phenomena?Comment: Latex, 27 pages, 10 eps-figures. Proceedings of the Conference "FPU 50 years since" Rome 7-8 May 200

Accelerated surgery versus standard care in hip fracture (HIP ATTACK) : an international, randomised, controlled trial

Background: Observational studies have suggested that accelerated surgery is associated with improved outcomes in patients with a hip fracture. The HIP ATTACK trial assessed whether accelerated surgery could reduce mortality and major complications. Methods: HIP ATTACK was an international, randomised, controlled trial done at 69 hospitals in 17 countries. Patients with a hip fracture that required surgery and were aged 45 years or older were eligible. Research personnel randomly assigned patients (1:1) through a central computerised randomisation system using randomly varying block sizes to either accelerated surgery (goal of surgery within 6 h of diagnosis) or standard care. The coprimary outcomes were mortality and a composite of major complications (ie, mortality and non-fatal myocardial infarction, stroke, venous thromboembolism, sepsis, pneumonia, life-threatening bleeding, and major bleeding) at 90 days after randomisation. Patients, health-care providers, and study staff were aware of treatment assignment, but outcome adjudicators were masked to treatment allocation. Patients were analysed according to the intention-to-treat principle. This study is registered at ClinicalTrials.gov (NCT02027896). Findings: Between March 14, 2014, and May 24, 2019, 27 701 patients were screened, of whom 7780 were eligible. 2970 of these were enrolled and randomly assigned to receive accelerated surgery (n=1487) or standard care (n=1483). The median time from hip fracture diagnosis to surgery was 6 h (IQR 4\u20139) in the accelerated-surgery group and 24 h (10\u201342) in the standard-care group (p<0\ub70001). 140 (9%) patients assigned to accelerated surgery and 154 (10%) assigned to standard care died, with a hazard ratio (HR) of 0\ub791 (95% CI 0\ub772 to 1\ub714) and absolute risk reduction (ARR) of 1% ( 121 to 3; p=0\ub740). Major complications occurred in 321 (22%) patients assigned to accelerated surgery and 331 (22%) assigned to standard care, with an HR of 0\ub797 (0\ub783 to 1\ub713) and an ARR of 1% ( 122 to 4; p=0\ub771). Interpretation: Among patients with a hip fracture, accelerated surgery did not significantly lower the risk of mortality or a composite of major complications compared with standard care. Funding: Canadian Institutes of Health Research