18,027 research outputs found
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
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