1,211 research outputs found
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
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