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

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.

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

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

Emergence of order in selection-mutation dynamics

We characterize the time evolution of a d-dimensional probability distribution by the value of its final entropy. If it is near the maximally-possible value we call the evolution mixing, if it is near zero we say it is purifying. The evolution is determined by the simplest non-linear equation and contains a d times d matrix as input. Since we are not interested in a particular evolution but in the general features of evolutions of this type, we take the matrix elements as uniformly-distributed random numbers between zero and some specified upper bound. Computer simulations show how the final entropies are distributed over this field of random numbers. The result is that the distribution crowds at the maximum entropy, if the upper bound is unity. If we restrict the dynamical matrices to certain regions in matrix space, for instance to diagonal or triangular matrices, then the entropy distribution is maximal near zero, and the dynamics typically becomes purifying.Comment: 8 pages, 8 figure