The resonance spectrum of the cusp map in the space of analytic functions

We prove that the Frobenius-Perron operator $U$ of the cusp map $F:[-1,1]\to [-1,1]$, $F(x)=1-2 x^{1/2}$ (which is an approximation of the Poincare section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for any $q\in (0,1)$ the spectrum of $U$ in the Hardy space in the disk $\{z\in C:|z-q|

The spectrum of the Liouville-von Neumann operator in the Hilbert-Schmidt space

The singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian.

On the spectrum of frequently hypercyclic operators

A bounded linear operator $T$ on a Banach space $X$ is called frequently hypercyclic if there exists $x\in X$ such that the lower density of the set $\{n\in\N:T^nx\in U\}$ is positive for any non-empty open subset $U$ of $X$. Bayart and Grivaux have raised a question whether there is a frequently hypercyclic operator on any separable infinite dimensional Banach space. We prove that the spectrum of a frequently hypercyclic operator has no isolated points. It follows that there are no frequently hypercyclic operators on all complex and on some real hereditarily indecomposable Banach spaces, which provides a negative answer to the above question.

Interhemispheric gradient of atmospheric radiocarbon reveals natural variability of Southern Ocean winds

Tree ring Delta C-14 data (Reimer et al., 2004; McCormac et al., 2004) indicate that atmospheric Delta C-14 varied on multi-decadal to centennial timescales, in both hemispheres, over the period between AD 950 and 1830. The Northern and Southern Hemispheric Delta C-14 records display similar variability, but from the data alone is it not clear whether these variations are driven by the production of C-14 in the stratosphere (Stuiver and Quay, 1980) or by perturbations to exchanges between carbon reservoirs (Siegenthaler et al., 1980). As the sea-air flux of (CO2)-C-14 has a clear maximum in the open ocean regions of the Southern Ocean, relatively modest perturbations to the winds over this region drive significant perturbations to the interhemispheric gradient. In this study, model simulations are used to show that Southern Ocean winds are likely a main driver of the observed variability in the interhemispheric gradient over AD 950-1830, and further, that this variability may be larger than the Southern Ocean wind trends that have been reported for recent decades (notably 1980-2004). This interpretation also implies that there may have been a significant weakening of the winds over the Southern Ocean within a few decades of AD 1375, associated with the transition between the Medieval Climate Anomaly and the Little Ice Age. The driving forces that could have produced such a shift in the winds at the Medieval Climate Anomaly to Little Ice Age transition remain unknown. Our process-focused suite of perturbation experiments with models raises the possibility that the current generation of coupled climate and earth system models may underestimate the natural background multi-decadal- to centennial-timescale variations in the winds over the Southern Ocean.

Infrared spectrum of an extremely cool white-dwarf star

White dwarfs are the remnant cores of stars that initially had masses of less than 8 solar masses. They cool gradually over billions of years, and have been suggested(1,2) to make up much of the 'dark matter' in the halo of the Milky way. But extremely cool white dwarfs have proved difficult to detect, owing to both their faintness and their anticipated similarity in colour to other classes of dwarf stars. Recent improved models(3-5) indicate that white dwarfs are much more blue than previously supposed, suggesting that the earlier searches may have been looking for the wrong kinds of objects. Here we report an infrared spectrum of an extremely cool white dwarf that is consistent with the new models. We determine the star's temperature to be 3,500 +/- 200 K, making it the coolest known white dwarf. The kinematics of this star indicate that it is in the halo of the Milky Way, and the density of such objects implied by the serendipitous discovery of this star is consistent with white dwarfs dominating the dark matter in the halo.

Application of atmospheric pressure nonthermal plasma for the in vitro eradication of bacterial biofilms

The use of atmospheric pressure nonthermal plasma represents an interesting and novel approach for the decontamination of surfaces colonized with microbial biofilms that exhibit enhanced tolerance to antimicrobial challenge. In this study, the influence of an atmospheric pressure nonthermal plasma jet, operated in a helium and oxygen gas mixture under ambient pressure, was evaluated against biofilms of Bacillus cereus,Staphylococcus aureus,Escherichia coli and Pseudomonas aeruginosa. Within <4 min of plasma exposure, complete eradication of the two Gram-positive bacterial biofilms was achieved. Although Gram-negative biofilms required longer treatment time, their complete eradication was still possible with 10 min of exposure. Whilst this study provides useful proof of concept data on the use of atmospheric pressure plasmas for the eradication of bacterial biofilms in vitro, it also demonstrates the critical need for improved understanding of the mechanisms and kinetics related to such a potentially significant approach. © 2012 Federation of European Microbiological Societies.