Tracing the development of dust around evolved stars: The case of 47 Tuc

We observed mid-infrared (7.5-22 mum) spectra of AGB stars in the globular cluster 47 Tuc with the Spitzer telescope and find significant dust features of various types. Comparison of the characteristics of the dust spectra with the location of the stars in a logP-K-diagram shows that dust mineralogy and position on the AGB are related. A 13 mum feature is seen in spectra of low luminosity AGB stars. More luminous AGB stars show a broad feature at 11.5 mum. The spectra of the most luminous stars are dominated by the amorphous silicate bending vibration centered at 9.7 mum. For 47 Tuc AGB stars, we conclude that early on the AGB dust consisting primarily of Mg-, Al- and Fe oxides is formed. With further AGB evolution amorphous silicates become the dominant species.Comment: 2 figures, accepted for publication in ApJ Letter

Lyapunov instability of fluids composed of rigid diatomic molecules

We study the Lyapunov instability of a two-dimensional fluid composed of rigid diatomic molecules, with two interaction sites each, and interacting with a WCA site-site potential. We compute full spectra of Lyapunov exponents for such a molecular system. These exponents characterize the rate at which neighboring trajectories diverge or converge exponentially in phase space. Quam. These exponents characterize the rate at which neighboring trajectories diverge or converge exponentially in phase space. Qualitative different degrees of freedom -- such as rotation and translation -- affect the Lyapunov spectrum differently. We study this phenomenon by systematically varying the molecular shape and the density. We define and evaluate ``rotation numbers'' measuring the time averaged modulus of the angular velocities for vectors connecting perturbed satellite trajectories with an unperturbed reference trajectory in phase space. For reasons of comparison, various time correlation functions for translation and rotation are computed. The relative dynamics of perturbed trajectories is also studied in certain subspaces of the phase space associated with center-of-mass and orientational molecular motion.Comment: RevTeX 14 pages, 7 PostScript figures. Accepted for publication in Phys. Rev.

Plant functioning in a changing global atmosphere

Editorial, Plant Biology, Volume 22, Issue S1, Special Issue: Plant Functioning in a Changing Global Atmoshphere

Long-term development of acid deposition (1880-2030) in sensitive freshwater regions in Europe

Time series of the deposition of acidifying substances are a pre-requisite for the study of the acidification and recovery of ecosystems such as surface waters. This paper reports the derivation and calculation of deposition trends of the potentially acidifying compounds SO2, NOx and NH3 in sensitive freshwater regions in Europe studied in the EU-funded RECOVER: 2010 project. The time interval covered is 151 years: from 1880, which can be considered as the pre-industrial era in most countries, to 2030, taking into account the consequences of current emission reduction agreements in Europe. The historic and predicted emissions for European countries are used to calculate the deposition development in the study areas, using meteorologically averaged atmospheric source-receptor transfer coefficients derived from the EMEP Lagrangian acid deposition model. These time series were used as driving forces for the application of the dynamic acidification model MAGIC to study the acidification and recovery of sensitive freshwater ecosystems in Europe

Goldstone modes in Lyapunov spectra of hard sphere systems

In this paper, we demonstrate how the Lyapunov exponents close to zero of a system of many hard spheres can be described as Goldstone modes, by using a Boltzmann type of approach. At low densities, the correct form is found for the wave number dependence of the exponents as well as for the corresponding eigenvectors in tangent-space. The predicted values for the Lyapunov exponents belonging to the transverse mode are within a few percent of the values found in recent simulations, the propagation velocity for the longitudinal mode is within 1%, but the value for the Lyapunov exponent belonging to the longitudinal mode deviates from the simulations by 30%. For higher densities, the predicted values deviate more from the values calculated in the simulations. These deviations may be due to contributions from ring collisions and similar terms, which, even at low densities, can contribute to the leading order.Comment: 12 pages revtex, 5 figures, accepted by Physical Review

Lyapunov spectra of billiards with cylindrical scatterers: comparison with many-particle systems

The dynamics of a system consisting of many spherical hard particles can be described as a single point particle moving in a high-dimensional space with fixed hypercylindrical scatterers with specific orientations and positions. In this paper, the similarities in the Lyapunov exponents are investigated between systems of many particles and high-dimensional billiards with cylindrical scatterers which have isotropically distributed orientations and homogeneously distributed positions. The dynamics of the isotropic billiard are calculated using a Monte-Carlo simulation, and a reorthogonalization process is used to find the Lyapunov exponents. The results are compared to numerical results for systems of many hard particles as well as the analytical results for the high-dimensional Lorentz gas. The smallest three-quarters of the positive exponents behave more like the exponents of hard-disk systems than the exponents of the Lorentz gas. This similarity shows that the hard-disk systems may be approximated by a spatially homogeneous and isotropic system of scatterers for a calculation of the smaller Lyapunov exponents, apart from the exponent associated with localization. The method of the partial stretching factor is used to calculate these exponents analytically, with results that compare well with simulation results of hard disks and hard spheres.Comment: Submitted to PR

Modelling the impacts of European emission and climate change scenarios on acid-sensitive catchments in Finland

The dynamic hydro-chemical Model of Acidification of Groundwater in Catchments (MAGIC) was used to predict the response of 163 Finnish lake catchments to future acidic deposition and climatic change scenarios. Future deposition was assumed to follow current European emission reduction policies and a scenario based on maximum (technologically) feasible reductions (MFR). Future climate (temperature and precipitation) was derived from the HadAM3 and ECHAM4/OPYC3 general circulation models under two global scenarios of the Intergovernmental Panel on Climate Change (IPCC: A2 and B2). The combinations resulting in the widest range of future changes were used for simulations, i.e., the A2 scenario results from ECHAM4/OPYC3 (highest predicted change) and B2 results from HadAM3 (lowest predicted change). Future scenarios for catchment runoff were obtained from the Finnish watershed simulation and forecasting system. The potential influence of future changes in surface water organic carbon concentrations was also explored using simple empirical relationships based on temperature and sulphate deposition. Surprisingly, current emission reduction policies hardly show any future recovery; however, significant chemical recovery of soil and surface water from acidification was predicted under the MFR emission scenario. The direct influence of climate change (temperate and precipitation) on recovery was negligible, as runoff hardly changed; greater precipitation is offset by increased evapotranspiration due to higher temperatures. However, two exploratory empirical DOC models indicated that changes in sulphur deposition or temperature could have a confounding influence on the recovery of surface waters from acidification, and that the corresponding increases in DOC concentrations may offset the recovery in pH due to reductions in acidifying depositions

The Lyapunov spectrum of the many-dimensional dilute random Lorentz gas

For a better understanding of the chaotic behavior of systems of many moving particles it is useful to look at other systems with many degrees of freedom. An interesting example is the high-dimensional Lorentz gas, which, just like a system of moving hard spheres, may be interpreted as a dynamical system consisting of a point particle in a high-dimensional phase space, moving among fixed scatterers. In this paper, we calculate the full spectrum of Lyapunov exponents for the dilute random Lorentz gas in an arbitrary number of dimensions. We find that the spectrum becomes flatter with increasing dimensionality. Furthermore, for fixed collision frequency the separation between the largest Lyapunov exponent and the second largest one increases logarithmically with dimensionality, whereas the separations between Lyapunov exponents of given indices not involving the largest one, go to fixed limits.Comment: 8 pages, revtex, 6 figures, submitted to Physical Review

Comment on ``Lyapunov Exponent of a Many Body System and Its Transport Coefficients''

In a recent Letter, Barnett, Tajima, Nishihara, Ueshima and Furukawa obtained a theoretical expression for the maximum Lyapunov exponent $\lambda_1$ of a dilute gas. They conclude that $\lambda_1$ is proportional to the cube root of the self-diffusion coefficient $D$, independent of the range of the interaction potential. They validate their conjecture with numerical data for a dense one-component plasma, a system with long-range forces. We claim that their result is highly non-generic. We show in the following that it does not apply to a gas of hard spheres, neither in the dilute nor in the dense phase.Comment: 1 page, Revtex - 1 PS Figs - Submitted to Physical Review Letter