Thermodynamics of liquids: standard molar entropies and heat capacities of common solvents from 2PT molecular dynamics

We validate here the Two-Phase Thermodynamics (2PT) method for calculating the standard molar entropies and heat capacities of common liquids. In 2PT, the thermodynamics of the system is related to the total density of states (DoS), obtained from the Fourier Transform of the velocity autocorrelation function. For liquids this DoS is partitioned into a diffusional component modeled as diffusion of a hard sphere gas plus a solid component for which the DoS(υ) → 0 as υ → 0 as for a Debye solid. Thermodynamic observables are obtained by integrating the DoS with the appropriate weighting functions. In the 2PT method, two parameters are extracted from the DoS self-consistently to describe diffusional contributions: the fraction of diffusional modes, f, and DoS(0). This allows 2PT to be applied consistently and without re-parameterization to simulations of arbitrary liquids. We find that the absolute entropy of the liquid can be determined accurately from a single short MD trajectory (20 ps) after the system is equilibrated, making it orders of magnitude more efficient than commonly used perturbation and umbrella sampling methods. Here, we present the predicted standard molar entropies for fifteen common solvents evaluated from molecular dynamics simulations using the AMBER, GAFF, OPLS AA/L and Dreiding II forcefields. Overall, we find that all forcefields lead to good agreement with experimental and previous theoretical values for the entropy and very good agreement in the heat capacities. These results validate 2PT as a robust and efficient method for evaluating the thermodynamics of liquid phase systems. Indeed 2PT might provide a practical scheme to improve the intermolecular terms in forcefields by comparing directly to thermodynamic properties

Taxes and Growth in a Financially Underdeveloped Country: Evidence from the Chilean Investment Boom

This paper argues that taxation of retained profits is particularly distortionary in an economy with good growth prospects and poorly developed financial markets because it primarily reduces the investment of financially constrained firms, investment that has marginal product greater than the after-tax market real interest rate. Contrarily, taxes on distributed profits or capital gains primarily reduce the investment of financially unconstrained firms. Chile experienced a banking crisis over the period from 1982 to 1986 and in 1984 reduced its tax rate on retained profits from 50 percent to 10 percent. We show that, consistent with our theory, there was a large increase in aggregate investment after the reform which was entirely funded by an increase in retained profits. Further, we show that investment grew by more in industries that depend more on external financing, according to the Rajan and Zingales (1998) measure. Finally, we present some weak evidence from comparisons of investment rates across firms for several different measures of their likelihood of being financially constrained.

A MEMS electrostatic particle transportation system

We demonstrate here an electrostatic MEMS system capable of transporting particles 5-10μm in diameter in air. This system consists of 3-phase electrode arrays covered by insulators (Figs. 1, 2). Extensive testing of this system has been done using a variety of insulation materials (silicon nitride, photoresist, and Teflon), thickness (0- 12μm), particle sizes (1-10μm), particle materials (metal, glass, polystyrene, spores, etc), waveforms, frequencies, and voltages. Although previous literature [1-2] claimed it impractical to electrostatically transport particles with sizes 5-10μm due to complex surface forces, this effort actually shows it feasible (as high as 90% efficiency) with the optimal combination of insulation thickness, electrode geometry, and insulation material. Moreover, we suggest a qualitative theory for our particle transportation system which is consistent with our data and finite-element electrostatic simulations

A Study of Longitudinal Oscillations of Propellant Tanks and Wave Propagations in Feed Lines. Part III - Wave Propagation in an Elastic Pipe Filled with Incompressible Viscous Streaming Fluid

Longitudinal wave propagation in elastic pipe filled with incompressible viscous streaming flui

Splittings of monomial ideals

We provide some new conditions under which the graded Betti numbers of a monomial ideal can be computed in terms of the graded Betti numbers of smaller ideals, thus complementing Eliahou and Kervaire's splitting approach. As applications, we show that edge ideals of graphs are splittable, and we provide an iterative method for computing the Betti numbers of the cover ideals of Cohen-Macaulay bipartite graphs. Finally, we consider the frequency with which one can find particular splittings of monomial ideals and raise questions about ideals whose resolutions are characteristic-dependent.Comment: minor changes: added Cor. 3.10 and some references. To appear in Proc. Amer. Math. So