Non-equilibrium interfaces in colloidal fluids

The time-dependent structure, interfacial tension, and evaporation of an oversaturated colloid-rich (liquid) phase in contact with an undersaturated colloid-poor (vapor) phase of a colloidal dispersion is investigated theoretically during the early-stage relaxation, where the interface is relaxing towards a local equilibrium state while the bulk phases are still out of equilibrium. Since systems of this type exhibit a clear separation of colloidal and solvent relaxation time scales with typical times of interfacial tension measurements in between, they can be expected to be suitable for analogous experimental studies, too. The major finding is that, irrespective of how much the bulk phases differ from two-phase coexistence, the interfacial structure and the interfacial tension approach those at two-phase coexistence during the early-stage relaxation process. This is a surprising observation since it implies that the relaxation towards global equilibrium of the interface is not following but preceding that of the bulk phases. Scaling forms for the local chemical potential, the flux, and the dissipation rate exhibit qualitatively different leading order contributions depending on whether an equilibrium or a non-equilibrium system is considered. The degree of non-equilibrium between the bulk phases is found to not influence the qualitative relaxation behavior (i.e., the values of power-law exponents), but to determine the quantitative deviation of the observed quantities from their values at two-phase coexistence. Whereas the underlying dynamics differs between colloidal and molecular fluids, the behavior of quantities such as the interfacial tension approaching the equilibrium values during the early-stage relaxation process, during which non-equilibrium conditions of the bulk phases are not changed, can be expected to occur for both types of systems.Comment: Submitte

Stock options as incentive contracts and dividend policy

Executive Stock Option Programs (SOPs) have become the dominant compensation instrument for top-management in recent years. The incentive effects of an SOP both with respect to corporate investment and financing decisions critically depend on the design of the SOP. A specific problem in designing SOPs concerns dividend protection. Usually, SOPs are not dividend protected, i.e. any dividend payout decreases the value of a manager’s options. Empirical evidence shows that this results in a significant decrease in the level of corporate dividends and, at the same time, into an increase in share repurchases. Yet, few suggestions have been made on how to account for dividends in SOPs. This paper applies arguments from principal-agent-theory and from the theory of finance to analyze different forms of dividend protection, and to address the relevance of dividend protection in SOPs. Finally, the paper relates the theoretical analysis to empirical work on the link between share repurchases and SOPs

Attraction and ionic correlations between charged stiff polyelectrolytes

We use Molecular Dynamics simulations to study attractive interactions and the underlying ionic correlations between parallel like-charged rods in the absence of additional salt. For a generic bulk system of rods we identify a reduction of short range repulsions as the origin of a negative osmotic coefficient. The counterions show signs of a weak three-dimensional order in the attractive regime only once the rod-imposed charge-inhomogeneities are divided out. We also treat the case of attraction between a single pair of rods for a few selected line charge densities and rod radii. Measurements of the individual contributions to the force between close rods are studied as a function of Bjerrum length. We find that even though the total force is always attractive at sufficiently high Bjerrum length, the electrostatic contribution can ultimately become repulsive. We also measure azimuthal and longitudinal correlation functions to answer the question how condensed ions are distributed with respect to each other and to the neighboring rod. For instance, we show that the prevalent image of mutually interlocked ions is qualitatively correct, even though modifications due to thermal fluctuations are usually strong.Comment: 14 pages, 14 figures, REVTeX4 styl

VLA, PHOENIX, and BATSE observations of an X1 flare

We present observations of an X1 flare (18 Jul. 1991) detected simultaneously with the Very Large Array (VLA), the PHOENIX Digital Radio Spectrometer and the Burst and Transient Source Experiment (BATSE) aboard the Gamma Ray Observatory (GRO). The VLA was used to produce snapshot maps of the impulsive acceleration in the higher corona several minutes before the onset of the hard x ray burst detected by BATSE. Comparisons with high spectral and temporal observations by PHOENIX reveal a variety of radio bursts at 20 cm, such as type 3 bursts, intermediate drift bursts, and quasi-periodic pulsations during different stages of the X1 flare. From the drift rates of these radio bursts we derive information on local density scale heights, the speed of radio exciters, and the local magnetic field. Radio emission at 90 cm shows a type 4 burst moving outward with a constant velocity of 240 km/s. The described X1 flare is unique in the sense that it appeared at the east limb (N06/E88), providing the most accurate information on the vertical structure of different flare tracers visible in radio wavelengths

Machine Learning for Observables: Reactant to Product State Distributions for Atom-Diatom Collisions

Machine learning-based models to predict product state distributions from a distribution of reactant conditions for atom-diatom collisions are presented and quantitatively tested. The models are based on function-, kernel- and grid-based representations of the reactant and product state distributions. While all three methods predict final state distributions from explicit quasi-classical trajectory simulations with R$^2$ > 0.998, the grid-based approach performs best. Although a function-based approach is found to be more than two times better in computational performance, the kernel- and grid-based approaches are preferred in terms of prediction accuracy, practicability and generality. The function-based approach also suffers from lacking a general set of model functions. Applications of the grid-based approach to nonequilibrium, multi-temperature initial state distributions are presented, a situation common to energy distributions in hypersonic flows. The role of such models in Direct Simulation Monte Carlo and computational fluid dynamics simulations is also discussed

Optimized Periodic Coulomb Potential in Two Dimension

The 1/r Coulomb potential is calculated for a two dimensional system with periodic boundary conditions. Using polynomial splines in real space and a summation in reciprocal space we obtain numerically optimized potentials which allow us efficient calculations of any periodic (long-ranged) potential up to high precision. We discuss the parameter space of the optimized potential for the periodic Coulomb potential. Compared to the analytic Ewald potential, the optimized potentials can reach higher precisions by up to several orders of magnitude. We explicitly give simple expressions for fast calculations of the periodic Coulomb potential where the summation in reciprocal space is reduced to a few terms