Escaping from nonhyperbolic chaotic attractors

We study the noise-induced escape process from chaotic attractors in nonhyperbolic systems. We provide a general mechanism of escape in the low noise limit, employing the theory of large fluctuations. Specifically, this is achieved by solving the variational equations of the auxiliary Hamiltonian system and by incorporating the initial conditions on the chaotic attractor unambiguously. Our results are exemplified with the H{\'e}non and the Ikeda map and can be implemented straightforwardly to experimental data.Comment: replaced with published versio

Stability Properties of Nonhyperbolic Chaotic Attractors under Noise

We study local and global stability of nonhyperbolic chaotic attractors contaminated by noise. The former is given by the maximum distance of a noisy trajectory from the noisefree attractor, while the latter is provided by the minimal escape energy necessary to leave the basin of attraction, calculated with the Hamiltonian theory of large fluctuations. We establish the important and counterintuitive result that both concepts may be opposed to each other. Even when one attractor is globally more stable than another one, it can be locally less stable. Our results are exemplified with the Holmes map, for two different sets of parameter, and with a juxtaposition of the Holmes and the Ikeda maps. Finally, the experimental relevance of these findings is pointed out.Comment: Phys.Rev. Lett., to be publishe

Almost Block Diagonal Linear Systems: Sequential and Parallel Solution Techniques, and Applications

Almost block diagonal (ABD) linear systems arise in a variety of contexts, specifically in numerical methods for two-point boundary value problems for ordinary differential equations and in related partial differential equation problems. The stable, efficient sequential solution of ABDs has received much attention over the last fifteen years and the parallel solution more recently. We survey the fields of application with emphasis on how ABDs and bordered ABDs (BABDs) arise. We outline most known direct solution techniques, both sequential and parallel, and discuss the comparative efficiency of the parallel methods. Finally, we examine parallel iterative methods for solving BABD systems. Copyright (C) 2000 John Wiley & Sons, Ltd

The importance of plume rise on the concentrations and atmospheric impacts of biomass burning aerosol

We quantified the effects of the plume rise of biomass burning aerosol and gases for the forest fires that occurred in Saskatchewan, Canada, in July 2010. For this purpose, simulations with different assumptions regarding the plume rise and the vertical distribution of the emissions were conducted. Based on comparisons with observations, applying a one-dimensional plume rise model to predict the injection layer in combination with a parametrization of the vertical distribution of the emissions outperforms approaches in which the plume heights are initially predefined. Approximately 30 % of the fires exceed the height of 2 km with a maximum height of 8.6 km. Using this plume rise model, comparisons with satellite images in the visible spectral range show a very good agreement between the simulated and observed spatial distributions of the biomass burning plume. The simulated aerosol optical depth (AOD) with data of an AERONET station is in good agreement with respect to the absolute values and the timing of the maximum. Comparison of the vertical distribution of the biomass burning aerosol with CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation) retrievals also showed the best agreement when the plume rise model was applied. We found that downwelling surface short-wave radiation below the forest fire plume is reduced by up to 50 % and that the 2 m temperature is decreased by up to 6 K. In addition, we simulated a strong change in atmospheric stability within the biomass burning plume

What determines the spreading of a wave packet?

The multifractal dimensions D2^mu and D2^psi of the energy spectrum and eigenfunctions, resp., are shown to determine the asymptotic scaling of the width of a spreading wave packet. For systems where the shape of the wave packet is preserved the k-th moment increases as t^(k*beta) with beta=D2^mu/D2^psi, while in general t^(k*beta) is an optimal lower bound. Furthermore, we show that in d dimensions asymptotically in time the center of any wave packet decreases spatially as a power law with exponent D_2^psi - d and present numerical support for these results.Comment: Physical Review Letters to appear, 4 pages postscript with figure

Enhancement of Noise-induced Escape through the Existence of a Chaotic Saddle

We study the noise-induced escape process in a prototype dissipative nonequilibrium system, the Ikeda map. In the presence of a chaotic saddle embedded in the basin of attraction of the metastable state, we find the novel phenomenon of a strong enhancement of noise-induced escape. This result is established by employing the theory of quasipotentials. Our finding is of general validity and should be experimentally observable.Comment: 4 page

The unacknowledged legacy

This paper presents a critical discussion of the treatment of mimetic art, and particularly poetry and the theatre, in the work of the Athenian philosopher Plato (427-347 BC). It centres on Plato's discussion of the corrupting powers of the arts in the Republic, and the implications that his fierce attack on poetry and theatre have for his construction of the ideal polity. The legacy of Platonic ideas in later elaborations of the corrupting power of the arts is discussed. Furthermore, the paper investigates the relationship between current debates on cultural policy and the Platonic idea that the transformative powers of the arts ought to be harnessed by the state to promote a just society. The conclusion thus reached is that “instrumental cultural policy”, rather then being a modern invention, was in fact first theorized precisely in Plato's Republic

Does oral sodium bicarbonate therapy improve function and quality of life in older patients with chronic kidney disease and low-grade acidosis (the BiCARB trial)? Study protocol for a randomized controlled trial

Date of acceptance: 01/07/2015 © 2015 Witham et al. 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. Acknowledgements UK NIHR HTA grant 10/71/01. We acknowledge the financial support of NHS Research Scotland in conducting this trial.Peer reviewedPublisher PD