The quasi-periodic doubling cascade in the transition to weak turbulence

The quasi-periodic doubling cascade is shown to occur in the transition from regular to weakly turbulent behaviour in simulations of incompressible Navier-Stokes flow on a three-periodic domain. Special symmetries are imposed on the flow field in order to reduce the computational effort. Thus we can apply tools from dynamical systems theory such as continuation of periodic orbits and computation of Lyapunov exponents. We propose a model ODE for the quasi-period doubling cascade which, in a limit of a perturbation parameter to zero, avoids resonance related problems. The cascade we observe in the simulations is then compared to the perturbed case, in which resonances complicate the bifurcation scenario. In particular, we compare the frequency spectrum and the Lyapunov exponents. The perturbed model ODE is shown to be in good agreement with the simulations of weak turbulence. The scaling of the observed cascade is shown to resemble the unperturbed case, which is directly related to the well known doubling cascade of periodic orbits

Circular dichroism of cholesteric polymers and the orbital angular momentum of light

We explore experimentally if the light's orbital angular momentum (OAM) interacts with chiral nematic polymer films. Specifically, we measure the circular dichroism of such a material using light beams with different OAM. We investigate the case of strongly focussed, non-paraxial light beams, where the spatial and polarization degrees of freedom are coupled. Within the experimental accuracy, we cannot find any influence of the OAM on the circular dichroism of the cholesteric polymer.Comment: 3 pages, 4 figure

The Gastropods of Lake West Okoboji, Iowa, Twenty Years Later

The snails of Lake West Okoboji were collected at the same 53 stations, using the same techniques and with equivalent effort as in a study 20 years earlier. The total number of snails collected was very similar. The same 12 species are present. The relative densities of the 8 major species have shifted strikingly, with a decrease in the more pollution tolerant pulmonates and concomitant increase in the less tolerant gilled species. The number of species per station has increased throughout the lake. The decline in the gastropod fauna appears to have been halted, probably due to the completion of a sanitary system around the lake

A Cantor set of tori with monodromy near a focus-focus singularity

We write down an asymptotic expression for action coordinates in an integrable Hamiltonian system with a focus-focus equilibrium. From the singularity in the actions we deduce that the Arnol'd determinant grows infinitely large near the pinched torus. Moreover, we prove that it is possible to globally parametrise the Liouville tori by their frequencies. If one perturbs this integrable system, then the KAM tori form a Whitney smooth family: they can be smoothly interpolated by a torus bundle that is diffeomorphic to the bundle of Liouville tori of the unperturbed integrable system. As is well-known, this bundle of Liouville tori is not trivial. Our result implies that the KAM tori have monodromy. In semi-classical quantum mechanics, quantisation rules select sequences of KAM tori that correspond to quantum levels. Hence a global labeling of quantum levels by two quantum numbers is not possible.Comment: 11 pages, 2 figure

(Genetic) Epidemiology of Aging

Longevity is usually defined as age at death or survival to an exceptional age, such as 90 years or older or even 100 years or older. In the past century, most Western countries have experienced substantial increases in life expectancy. This has been mostly due to a marked reduction in early life mortality during the first half of the twentieth century, followed by an almost twofold reduction in mortality at ages above 70 years in the past 50 years (Figure 1; source: CBS). Longevity is a complex phenotype to which both environmental factors such as lifestyle and genetic factors are known to contribute. The genetic contribution to age at death has been estimated to range from 15 to 25%, and up to 40% for reaching longevity, suggesting a significant but relatively modest genetic contribution to the human lifespan. However, the clustering of extreme a

Differential constraints for the Kaup -- Broer system as a reduction of the 1D Toda lattice

It is shown that some special reduction of infinite 1D Toda lattice gives differential constraints compatible with the Kaup -- Broer system. A family of the travelling wave solutions of the Kaup -- Broer system and its higher version is constructed.Comment: LaTeX, uses IOP styl

Quenched growth of nanostructured lead thin films on insulating substrates

Lead island films were obtained via vacuum vapor deposition on glass and ceramic substrates at 80 K. Electrical conductance was measured during vapor condensation and further annealing of the film up to room temperature. The resistance behavior during film formation and atomic force microscopy of annealed films were used as information sources about their structure. A model for the quenched growth, based on ballistic aggregation theory, was proposed. The nanostructure, responsible for chemiresistive properties of thin lead films and the mechanism of sensor response are discussed.Comment: 2 figures; accepted to Thin Solid Film

Bifurcation curves of subharmonic solutions

We revisit a problem considered by Chow and Hale on the existence of subharmonic solutions for perturbed systems. In the analytic setting, under more general (weaker) conditions, we prove their results on the existence of bifurcation curves from the nonexistence to the existence of subharmonic solutions. In particular our results apply also when one has degeneracy to first order -- i.e. when the subharmonic Melnikov function vanishes identically. Moreover we can deal as well with the case in which degeneracy persists to arbitrarily high orders, in the sense that suitable generalisations to higher orders of the subharmonic Melnikov function are also identically zero. In general the bifurcation curves are not analytic, and even when they are smooth they can form cusps at the origin: we say in this case that the curves are degenerate as the corresponding tangent lines coincide. The technique we use is completely different from that of Chow and Hale, and it is essentially based on rigorous perturbation theory.Comment: 29 pages, 2 figure