The wall theorem for elastic moduli

New expressions for the elastic moduli of a classical system are derived. They involve only the two-point correlation function and the derivative of the onepoint correlation function, both only on the boundary of the system. These expressions, valid for any interaction derivable from a potential, are proved from a mechanical point of view by generalizing the virial theorem of Clausius, and from a statistical point of view by a direct method that constitutes an alternative to Green's dilatation method.     

Compression elastic modulus of neutral,ionic, and amphoteric hydrogels based on N‐vinylimidazole

Several hydrogels of N‐vinylimidazole and sodium styrenesulfonate have been prepared by radical cross‐linking copolymerization in aqueous solution, using N,N′‐methylene‐bisacrylamide as crosslinker. Depending on composition, these hydrogels were neutral, amphoteric, cationic or anionic. Compression‐strain measurements were performed on samples as‐synthesized and swollen in deionized water or in acid aqueous solutions, with and without salt. It was thus found that the cross‐linking densities determined by compression measurements on as‐synthesized samples are in good accordance with those calculated by means of the model of polymer networks with pendant vinyl groups. A non‐Gaussian parameter (β) was introduced to explain that the elastic moduli (G) of samples swollen at equilibrium are larger than predicted by the Gaussian model. The β values of the neutral or ionized systems increase with swelling and fall into a single curve, which denotes a common behavior. Swelling has two opposite effects on G; on the one hand G decreases because the polymer volume fraction diminish and the system shifts from the affine limit to the phantom one; on the other, β increases and contributes to increasing G. The balance of those two opposite effects determines the variation of G with swelling. The possible contribution of ionic crosslinks to ν_e for the polyampholyte and for the polycation wearing divalent counteranions was discussed. A peculiar system is poly(sodium styrenesulfonate), whose cross‐linking density is much lower than expected. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1078–1087, 2009     

Variable Selection and Regularization in Quantile Regression via Minimum Covariance Determinant Based Weights

The importance of variable selection and regularization procedures in multiple regression analysis cannot be overemphasized. These procedures are adversely affected by predictor space data aberrations as well as outliers in the response space. To counter the latter, robust statistical procedures such as quantile regression which generalizes the well-known least absolute deviation procedure to all quantile levels have been proposed in the literature. Quantile regression is robust to response variable outliers but very susceptible to outliers in the predictor space (high leverage points) which may alter the eigen-structure of the predictor matrix. High leverage points that alter the eigen-structure of the predictor matrix by creating or hiding collinearity are referred to as collinearity influential points. In this paper, we suggest generalizing the penalized weighted least absolute deviation to all quantile levels, i.e., to penalized weighted quantile regression using the RIDGE, LASSO, and elastic net penalties as a remedy against collinearity influential points and high leverage points in general. To maintain robustness, we make use of very robust weights based on the computationally intensive high breakdown minimum covariance determinant. Simulations and applications to well-known data sets from the literature show an improvement in variable selection and regularization due to the robust weighting formulation.     

P213 BN: a novel large-cell boron nitride polymorph

A new boron nitride polymorph, P2₁3 BN (space group: P2₁3), is investigated by first-principles calculations, including its structural properties, stability, elastic properties, anisotropy and electronic properties. It is found that the new boron nitride polymorph P2₁3 BN is mechanically, dynamically and thermodynamically stable. The bulk modulus (B), shear modulus (G) and Young's modulus of P2₁3 BN are 91 GPa, 41 GPa and 107 GPa, respectively, all of which are larger than that of Y carbon and TY carbon. By comparing with c-BN, the Young's modulus, shear modulus and Poisson's ratio of P2₁3 BN show tiny anisotropy in the (001), (010), (100) and (111) planes. At the same time, in contrast with most boron nitride polymorphs, P2₁3 BN is a semiconductor material with a smaller band gap of 1.826 eV. The Debye temperature and the anisotropic sound velocities of P2₁3 BN are also investigated in this work.     

The D'Alembert type waves and the soliton molecules in a (2+1)-dimensional Kadomtsev-Petviashvili with its hierarchy equation

For a one (2+1)-dimensional combined Kadomtsev-Petviashvili with its hierarchy equation, the missing D'Alembert type solution is derived first through the traveling wave transformation which contains several special kink molecule structures. Further, after introducing the Bäcklund transformation and an auxiliary variable, the N-soliton solution which contains some soliton molecules for this equation, is presented through its Hirota bilinear form. The concrete molecules including line solitons, breathers and a lump as well as several interactions of their hybrid are shown with the aid of special conditions and parameters. All these dynamical features are demonstrated through the different figures.     

Elastic electron scattering with formamide-(H2O)n complexes (n=1, 2): Influence of microsolvation on the π* and σ* resonances

We report elastic cross sections for low-energy electron scattering with formamide-(H₂O)_n complexes (n=1, 2) in the energy region of 0.01-8 eV. The scattering calculations are performed using the R-matrix method in the static-exchange (SE) approximation. We consider three structures of formamide-H₂O and six structures of formamide-(H₂O)₂ in the present work. Our purpose is to investigate effects of water molecules hydrogen-bonding to formamide. We focus on the influence of microsolvation on the π^* and σ^* resonances of formamide. The scattering result for complexes shows that the position of π^* resonance appears at lower or higher energies in the cluster than in the isolated formamide depending on the complex structure and the water role in the hydrogen bonding. We explain this behavior according to the net charge of the solute. It is found that the microsolvation environment has a substantial effect on the width of π^* resonance. Our results indicate that surrounding water molecules may affect the lifetime of the resonances, and hence the process is driven by the anion state, such as the dissociative electron attachment.