On factor copula-based mixed regression models

In this article, a copula-based method for mixed regression models is proposed, where the conditional distribution of the response variable, given covariates, is modelled by a parametric family of continuous or discrete distributions, and the effect of a common latent variable pertaining to a cluster is modelled with a factor copula. We show how to estimate the parameters of the copula and the parameters of the margins, and we find the asymptotic behaviour of the estimation errors. Numerical experiments are performed to assess the precision of the estimators for finite samples. An example of an application is given using COVID-19 vaccination hesitancy from several countries. Computations are based on R package CopulaGAMM

Nitrogen Contamination in Elastic Neutron Scattering

Nitrogen gas accidentally sealed in a sample container produces various spurious effects in elastic neutron scattering measurements. These effects are systematically investigated and the details of the spurious scattering are presented

Structure characteristics of methane-doped solid normal hydrogen

Structure studies of the quantum crystal of solid normal hydrogen doped with methane and deuteromethane are carried out by powder x-ray diffraction within the temperature range 5 to 12 K. The concentration of the dopants in the gas mixtures used for sample preparation by quench condensing is varied from 0.5% to 5%. It is established that the equilibrium solubility of both methanes is substantially below the lower fraction indicated. The abnormally high apparent extra volumes per impurity may be ascribed to van der Waals complexes formed around isolated dopant particles

Properties of solid hydrogen doped by heavy atomic and molecular impurities

Using powder x-ray diffraction we studied the structural characteristics of normal and para hydrogen crystals doped with Ar, Kr, N₂, and O₂ impurities over the range from 5 K to the melting point of the hydrogen matrix. It has been established that in spite of very low solubility of the dopants in solid hydrogen, these impurities appreciably affect the structural characteristics. In particular, only nitrogen impurities do not change the molar volume of the matrix, the other three make the matrix expand. The Ar and Kr impurities also change the c/a ratio of the hcp matrix. The fact that both Ar and O₂ have smaller molar volumes than hydrogen may be treated as evidence that these impurities form van der Waals complexes with the hydrogen lattice environment

Modeling Polymorphic Molecular Crystals with Electronic Structure Theory

Interest in molecular crystals has grown thanks to their relevance to pharmaceuticals, organic semiconductor materials, foods, and many other applications. Electronic structure methods have become an increasingly important tool for modeling molecular crystals and polymorphism. This article reviews electronic structure techniques used to model molecular crystals, including periodic density functional theory, periodic second-order Møller-Plesset perturbation theory, fragment-based electronic structure methods, and diffusion Monte Carlo. It also discusses the use of these models for predicting a variety of crystal properties that are relevant to the study of polymorphism, including lattice energies, structures, crystal structure prediction, polymorphism, phase diagrams, vibrational spectroscopies, and nuclear magnetic resonance spectroscopy. Finally, tools for analyzing crystal structures and intermolecular interactions are briefly discussed