Carbonates in space - The challenge of low temperature data

Carbonates have repeatedly been discussed as possible carriers of stardust emission bands. However, the band assignments proposed so far were mainly based on room temperature powder transmission spectra of the respective minerals. Since very cold calcite grains have been claimed to be present in protostars and in Planetary Nebulae such as NGC 6302, the changes of their dielectric functions at low temperatures are relevant from an astronomical point of view. We have derived the IR optical constants of calcite and dolomite from reflectance spectra - measured at 300, 200, 100 and 10K - and calculated small particle spectra for different grain shapes, with the following results: i) The absorption efficiency factors both of calcite and dolomite are extremely dependent on the particle shapes. This is due to the high peak values of the optical constants of CaCO3 and CaMg[CO3]2. ii) The far infrared properties of calcite and dolomite depend also very significantly on the temperature. Below 200K, a pronounced sharpening and increase in the band strengths of the FIR resonances occurs. iii) In view of the intrinsic strength and sharpening of the 44 mum band of calcite at 200-100K, the absence of this band -- inferred from Infrared Space Observatory data -- in PNe requires dust temperatures below 45K. iv) Calcite grains at such low temperatures can account for the '92' mum band, while our data rule out dolomite as the carrier of the 60-65 mum band. The optical constants here presented are publicly available in the electronic database http://www.astro.uni-jena.de/Laboratory/OCDBComment: 20 pages, 10 figures, accepted by ApJ, corrected typo

Remarks on NonHamiltonian Statistical Mechanics: Lyapunov Exponents and Phase-Space Dimensionality Loss

The dissipation associated with nonequilibrium flow processes is reflected by the formation of strange attractor distributions in phase space. The information dimension of these attractors is less than that of the equilibrium phase space, corresponding to the extreme rarity of nonequilibrium states. Here we take advantage of a simple model for heat conduction to demonstrate that the nonequilibrium dimensionality loss can definitely exceed the number of phase-space dimensions required to thermostat an otherwise Hamiltonian system.Comment: 5 pages, 2 figures, minor typos correcte

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.

Time-reversal focusing of an expanding soliton gas in disordered replicas

We investigate the properties of time reversibility of a soliton gas, originating from a dispersive regularization of a shock wave, as it propagates in a strongly disordered environment. An original approach combining information measures and spin glass theory shows that time reversal focusing occurs for different replicas of the disorder in forward and backward propagation, provided the disorder varies on a length scale much shorter than the width of the soliton constituents. The analysis is performed by starting from a new class of reflectionless potentials, which describe the most general form of an expanding soliton gas of the defocusing nonlinear Schroedinger equation.Comment: 7 Pages, 6 Figure

Time-reversed symmetry and covariant Lyapunov vectors for simple particle models in and out of thermal equilibrium

Recently, a new algorithm for the computation of covariant Lyapunov vectors and of corresponding local Lyapunov exponents has become available. Here we study the properties of these still unfamiliar quantities for a number of simple models, including an harmonic oscillator coupled to a thermal gradient with a two-stage thermostat, which leaves the system ergodic and fully time reversible. We explicitly demonstrate how time-reversal invariance affects the perturbation vectors in tangent space and the associated local Lyapunov exponents. We also find that the local covariant exponents vary discontinuously along directions transverse to the phase flow.Comment: 13 pages, 11 figures submitted to Physical Review E, 201

Covariant hydrodynamic Lyapunov modes and strong stochasticity threshold in Hamiltonian lattices

We scrutinize the reliability of covariant and Gram-Schmidt Lyapunov vectors for capturing hydrodynamic Lyapunov modes (HLMs) in one-dimensional Hamiltonian lattices. We show that,in contrast with previous claims, HLMs do exist for any energy density, so that strong chaos is not essential for the appearance of genuine (covariant) HLMs. In contrast, Gram-Schmidt Lyapunov vectors lead to misleading results concerning the existence of HLMs in the case of weak chaos.Comment: 4 pages, 4 figures. Accepted for publication in Physical Review

Time-oscillating Lyapunov modes and auto-correlation functions for quasi-one-dimensional systems

The time-dependent structure of the Lyapunov vectors corresponding to the steps of Lyapunov spectra and their basis set representation are discussed for a quasi-one-dimensional many-hard-disk systems. Time-oscillating behavior is observed in two types of Lyapunov modes, one associated with the time translational invariance and another with the spatial translational invariance, and their phase relation is specified. It is shown that the longest period of the Lyapunov modes is twice as long as the period of the longitudinal momentum auto-correlation function. A simple explanation for this relation is proposed. This result gives the first quantitative connection between the Lyapunov modes and an experimentally accessible quantity.Comment: 4 pages, 3 figure

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

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