Coupled symplectic maps as models for subdiffusive processes in disordered Hamiltonian lattices

© 2015 IMACS We investigate dynamically and statistically diffusive motion in a chain of linearly coupled 2-dimensional symplectic McMillan maps and find evidence of subdiffusion in weakly and strongly chaotic regimes when all maps of the chain possess a saddle point at the origin and the central map is initially excited. In the case of weak coupling, there is either absence of diffusion or subdiffusion with q > 1-Gaussian probability distributions, characterizing weak chaos. However, for large enough coupling and already moderate number of maps, the system exhibits strongly chaotic (q≈1) subdiffusive behavior, reminiscent of the subdiffusive energy spreading observed in a disordered Klein–Gordon Hamiltonian. Our results provide evidence that coupled symplectic maps can exhibit physical properties similar to those of disordered Hamiltonian systems, even though the local dynamics in the two cases is significantly different

Complex statistics and diffusion in nonlinear disordered particle chains.

We investigate dynamically and statistically diffusive motion in a Klein-Gordon particle chain in the presence of disorder. In particular, we examine a low energy (subdiffusive) and a higher energy (self-trapping) case and verify that subdiffusive spreading is always observed. We then carry out a statistical analysis of the motion, in both cases, in the sense of the Central Limit Theorem and present evidence of different chaos behaviors, for various groups of particles. Integrating the equations of motion for times as long as 10(9), our probability distribution functions always tend to Gaussians and show that the dynamics does not relax onto a quasi-periodic Kolmogorov-Arnold-Moser torus and that diffusion continues to spread chaotically for arbitrarily long times

Clinical Focus on Lung Cancer: A snapshot of lung cancer for Ontario health care providers and managers

This monograph on lung cancer has been prepared to provide information on patterns of practice to those directly involved in the provision of care to lung cancer patients. As well, it should be helpful to those who are responsible for managing aspects of the cancer system that impact on the care that lung cancer patients receive across the province of Ontario. The practice patterns are shown against the backdrop of the evidence-based guidelines developed by the Lung Disease Site Group of Cancer Care Ontario’s Program in Evidence based Care. In addition to information on patterns of practice, this monograph provides information on the timeliness of access to care, as well as a brief overview of the incidence and mortality of lung cancer, and the trends in the main risk factor for developing lung cancer, namely smoking. In brief, it provides a snapshot of the quality of care for lung cancer patients in the province of Ontario. It is hoped that this monograph will assist those responsible for care delivery to achieve the best possible results for patients with a diagnosis of lung cancer

Erratum to: 36th International Symposium on Intensive Care and Emergency Medicine

[This corrects the article DOI: 10.1186/s13054-016-1208-6.]

The effect of long-range interactions on the dynamics and statistics of 1D Hamiltonian lattices with on-site potential

We examine the role of long-range interactions on the dynamical and statistical properties of two 1D lattices with on-site potentials that are known to support discrete breathers: the Klein–Gordon (KG) lattice which includes linear dispersion and the Gorbach–Flach (GF) lattice, which shares the same on-site potential but its dispersion is purely nonlinear. In both models under the implementation of long-range interactions (LRI), we find that single-site excitations lead to special low-dimensional solutions, which are well described by the undamped Duffing oscillator. For random initial conditions, we observe that the maximal Lyapunov exponent λ scales as N^(−0.12) in the KG model and as N^(−0.27) in the GF with LRI, suggesting in that case an approach to integrable behavior towards the thermodynamic limit. Furthermore, under LRI, their non-Gaussian momentum distributions are distinctly different from those of the FPU model

The effect of long–range interactions on the dynamics and statistics of 1D Hamiltonian lattices with on–site potential

We examine the role of long–range interactions on the dynamical and statistical properties of two 1D lattices with on–site potentials that are known to support discrete breathers: the Klein–Gordon (KG) lattice which includes linear dispersion and the Gorbach–Flach (GF) lattice, which shares the same on–site potential but its dispersion is purely nonlinear. In both models under the implementation of long–range interactions (LRI) we find that single–site excitations lead to special low–dimensional solutions, which are well described by the undamped Duffing oscillator. For random initial conditions we observe that the maximal Lyapunov exponent scales as N−0.12 in the KG model and as N−0.27 in the GF with LRI, suggesting in that case an approach to integrable behavior towards the thermodynamic limit. Furthermore, under LRI, their non-Gaussian momentum distributions are distinctly different from those of the FPU model

On the non-integrability of a family of Duffing-van der Pol oscillators

We investigate the non-integrability of a family of Duffing-van der Pol oscillators x+ alpha x(x2-1)+x+ beta x3= gamma cos omega t by studying the analytic properties of the dynamics in complex time. We find that the solutions of (∗) have no worse than algebraic singularities at t, with only (t-t∗)½ terms present in their series expansions, unlike, for example, the alpha =0 Duffing case, where, typically, log(t-t∗) terms arise. Still, when integrating (∗) around long enough contours, a remarkably intricate pattern of square root singularities emerges, on different sheets, which appears to prevent solutions from ever returning to the original sheet. Such evidence of infinitely-sheeted solutions, termed the ISS property, has also been observed in a number of Hamiltonian systems and is illustrated here on a simple example of a single, first-order differential equation. We suggest that the ISS property is a necessary condition for non-integrability, i.e. non-existence of a complete set of analytic, single-valued constants of the motion, which would permit the complete integration of a dynamical system in terms of quadratures

On the adsorption-desorption relaxation time of carbon in very narrow ducts

Loudspeakers generally have boxes to prevent rear wave cancellation at low frequencies. However, the stiffness of the air in a small box reduces the diaphragm's excursion at low frequencies. Hence the box size is generally a compromise between low frequency performance and practicality. Activated carbon has been found to increase the apparent size of a given box through adsorption of the air molecules when the pressure increases and likewise desorption when it decreases. However, the exact viscous effects in the granular structure are difficult to model. Thus it is impossible determine the high frequency limit due to the natural adsorption/desorption relaxation time in the absence of viscous losses. In this study, a tube model is presented which takes into account viscous and thermal losses with boundary slip together with adsorption. Impedance measurements are performed on an array of 12 million holes, each 2 micrometers in diameter, etched in a 0.25 mm thick silicon wafer so that the viscous and thermal losses can be verified against the model without adsorption. Impedance measurements are then performed on an array of holes coated with graphite in order to create an activated carbonlike structure, thus enabling the adsorption/desorption relaxation time to be evaluated