Thermophysical properties of liquid carbon dioxide under shock compressions: Quantum molecular dynamic simulations

Quantum molecular dynamic simulations are introduced to study the dynamical, electrical, and optical properties of carbon dioxide under dynamic compressions. The principal Hugoniot derived from the calculated equation of states is demonstrated to be well accordant with experimental results. Molecular dissociation and recombination are investigated through pair correlation functions, and decomposition of carbon dioxide is found to be between 40 and 50 GPa along the Hugoniot, where nonmetal-metal transition is observed. In addition, the optical properties of shock compressed carbon dioxide are also theoretically predicted along the Hugoniot

The equation of state and nonmetal-metal transition of benzene under shock compression

We employ quantum molecular dynamic simulations to investigate the behavior of benzene under shock conditions. The principal Hugoniot derived from the equation of state is determined. We compare our firs-principles results with available experimental data and provide predictions of chemical reactions for shocked benzene. The decomposition of benzene is found under the pressure of 11 GPa. The nonmetal-metal transition, which is associated with the rapid C-H bond breaking and the formation of atomic and molecular hydrogen, occurs under the pressure around 50 GPa. Additionally, optical properties are also studied.Comment: 12 pages, 5 figure

Power of Observational Hubble Parameter Data: a Figure of Merit Exploration

We use simulated Hubble parameter data in the redshift range 0 \leq z \leq 2 to explore the role and power of observational H(z) data in constraining cosmological parameters of the {\Lambda}CDM model. The error model of the simulated data is empirically constructed from available measurements and scales linearly as z increases. By comparing the median figures of merit calculated from simulated datasets with that of current type Ia supernova data, we find that as many as 64 further independent measurements of H(z) are needed to match the parameter constraining power of SNIa. If the error of H(z) could be lowered to 3%, the same number of future measurements would be needed, but then the redshift coverage would only be required to reach z = 1. We also show that accurate measurements of the Hubble constant H_0 can be used as priors to increase the H(z) data's figure of merit.Comment: 8 pages, 1 table, 8 figures. v2: version accepted by Ap

Generalized rational first integrals of analytic differential systems

In this paper we mainly study the necessary conditions for the existence of functionally independent generalized rational first integrals of ordinary differential systems via the resonances. The main results extend some of the previous related ones, for instance the classical Poincar\'e's one \cite{Po}, the Furta's one, part of Chen's ones, and the Shi's one. The key point in the proof of our main results is that functionally independence of generalized rational functions implies the functionally independence of their lowest order rational homogeneous terms.Comment: 22. Journal of Differential Equations, 201

A Scalable and Extensible Framework for Superposition-Structured Models

In many learning tasks, structural models usually lead to better interpretability and higher generalization performance. In recent years, however, the simple structural models such as lasso are frequently proved to be insufficient. Accordingly, there has been a lot of work on "superposition-structured" models where multiple structural constraints are imposed. To efficiently solve these "superposition-structured" statistical models, we develop a framework based on a proximal Newton-type method. Employing the smoothed conic dual approach with the LBFGS updating formula, we propose a scalable and extensible proximal quasi-Newton (SEP-QN) framework. Empirical analysis on various datasets shows that our framework is potentially powerful, and achieves super-linear convergence rate for optimizing some popular "superposition-structured" statistical models such as the fused sparse group lasso