Description of hard sphere crystals and crystal-fluid interfaces: a critical comparison between density functional approaches and a phase field crystal model

In materials science the phase field crystal approach has become popular to model crystallization processes. Phase field crystal models are in essence Landau-Ginzburg-type models, which should be derivable from the underlying microscopic description of the system in question. We present a study on classical density functional theory in three stages of approximation leading to a specific phase field crystal model, and we discuss the limits of applicability of the models that result from these approximations. As a test system we have chosen the three--dimensional suspension of monodisperse hard spheres. The levels of density functional theory that we discuss are fundamental measure theory, a second-order Taylor expansion thereof, and a minimal phase-field crystal model. We have computed coexistence densities, vacancy concentrations in the crystalline phase, interfacial tensions and interfacial order parameter profiles, and we compare these quantities to simulation results. We also suggest a procedure to fit the free parameters of the phase field crystal model.Comment: 21 page

Empirical Analyses on Federal Thrift Savings Plan Portfolio Optimization

There is ample historical data to suggest that log returns of stocks and indices are not independent and identically distributed Normally, as is commonly assumed. Instead, the returns of financial assets are skewed and have higher kurtosis. To account for skewness and excess kurtosis, it is necessary to have a distribution that is more flexible than the Gaussian distribution and uses additional information that may be present in higher moments. The federal government's Thrift Savings Plan (TSP) is the largest defined contribution retirement savings and investment plan, with nearly 3.6 million participants and over $173 billion in assets. The TSP offers five assets (government bond fund, fixed income fund, large-cap stock fund, small-cap stock fund, and international stock fund) to U.S. government civilian employees and uniformed service members. The limited choice of investments, in comparison to most 401(k) plans, may be disappointing from a participant's perspective; however, it provides an attractive framework for empirical study. In this study, we investigate how the optimal choice of TSP assets changes when traditional portfolio optimization methods are replaced with newer techniques. Specifically, the following research questions are posed and answered: (1) Does use of a non-Gaussian factor model for returns, generated with independent components analysis (ICA) and following the Variance Gamma (VG) process, provide any advantage in constructing optimal TSP portfolios? (2) Can excess TSP portfolio returns be generated through rebalancing to an optimal mix? If so, what frequency of rebalancing provides benefits that offset increased computationalal and administrative burden? (3) How does the use of coherent risk and portfolio performance measures, in place of variance as the traditional the measure for risk and Sharpe Ratio as the usual portfolio performance measure affect TSP portfolio selection? We show through simulation that some of the newer schemes should produce excess returns over conventional (mean-variance optimization with Normally-distributed returns) portfolio choice models. The use of some or all of these methods could benefit the nearly 4 million TSP participants in achieving their retirement savings and investment objectives. Furthermore, we propose two new portfolio performance measures based on recent developments in coherent measures of risk

Kinetic modelling of methanol synthesis over commercial catalysts: A critical assessment

Kinetic modelling of methanol synthesis over commercial catalysts is of high importance for reactor and process design. Literature kinetic models were implemented and systematically discussed against a newly developed kinetic model based on published kinetic data. Deviations in the sensitivities of the kinetic models were explained by means of the experimentally covered parameter range. The simulation results proved that an extrapolation of the working range of the kinetic models can lead towards significant simulation errors especially with regard to pressure, stoichiometric number and CO/CO$_{2}$-ratio considerably limiting the applicability of kinetic models frequently applied in scientific literature. Therefore, the validated data range for kinetic models should be considered when detailed reactor simulations are carried out. With regard to Power-to-Methanol processes special attention should be drawn towards the rate limiting effect of water at high CO$_{2}$ contents in the syngas. Moreover, it was shown that kinetic models based on data measured over outdated catalysts show significantly lower activity than those derived from state-of-the-art catalysts and should therefore be applied with caution for reactor and process simulations. The plausible behavior of the herein proposed kinetic model was demonstrated by a systematic comparison towards established kinetic approaches within both, an ideal kinetic reactor and an industrial steam cooled tubular reactor. Relative to the state-of-the-art kinetic models it was proven that the herein proposed kinetic model can be applied over the complete industrially relevant working range for methanol synthesis

Crystal structures and isometricity comparison of methylated bisphenol F derivatives

The syntheses and X-ray structures of three methylated bisphenol F derivatives and one respective analogue are reported. A special emphasis lies on the influence of methyl groups on the conformation of the common diphenylmethane scaffold. The introduction of four methyl groups to bisphenol F was found not to disturb its typical strong hydrogen bond network, and yet, to change the pattern of the aromatic interactions in the overall packing. According to the isometricity comparison, the addition of methyl groups to the diphenylmethane core has a greater influence on the conformation of the individual molecules, than the presence or absence of hydrogen bonding donors or acceptors. © 2013 Elsevier B.V. All rights reserved

Morphological stability of rod-shaped continuous phases

Morphological transition of a rod-shaped phase into a string of spherical particles is commonly observed in the microstructures of alloys during solidification (Ratke and Mueller, 2006). This transition phenomenon can be explained by the classic Plateau-Rayleigh theory which was derived for fluid jets based on the surface area minimization principle. The quintessential work of Plateau-Rayleigh considers tiny perturbations (amplitude much less than the radius) to the continuous phase and for large amplitude perturbations, the breakup condition for the rod-shaped phase is still a knotty issue. Here, we present a concise thermodynamic model based on the surface area minimization principle as well as a non-linear stability analysis to generalize Plateau-Rayleigh’s criterion for finite amplitude perturbations. Our results demonstrate a breakup transition from a continuous phase via dispersed particles towards a uniform-radius cylinder, which has not been found previously, but is observed in our phase-field simulations. This new observation is attributed to a geometric constraint, which was overlooked in former studies. We anticipate that our results can provide further insights on microstructures with spherical particles and cylinder-shaped phases