Magnesium perchlorate anhydrate,Mg(ClO4)2, from laboratory X‐ray powder data

The previously unknown crystal structure of magnesium perchlorate anhydrate, determined and refined from laboratory X‐ray powder diffraction data, represents a new structure type. The title compound was obtained by heating magnesium perchlorate hexahydrate at 523 K for 2 h under vacuum and it crystallizes in the monoclinic space group P2₁/c. The asymmetric unit contains one Mg (site symmetry on special position 2a), one Cl and four O sites (on general positions 4e). The structure consists of a three‐dimensional network resulting from the corner‐sharing of MgO₆ octahedra and ClO₄ tetrahedra. Each MgO₆ octahedron share corners with six ClO₄ tetrahedra. Each ClO₄ tetrahedron shares corners with three MgO₆ octahedra, with one O‐atom corner dangling. The ClO₄ tetrahedra are oriented in such a way that one‐dimensional channels parallel to [100] are formed between the dangling O atoms.     

A time-domain nonlinear system identification method based on multiscale dynamic partitions

Based on a theoretical foundation for empirical mode decomposition, which dictates the correspondence between the analytical and empirical slow-flow analyses, we develop a time-domain nonlinear system identification (NSI) technique. This NSI method is based on multiscale dynamic partitions and direct analysis of measured time series, and makes no presumptions regarding the type and strength of the system nonlinearity. Hence, the method is expected to be applicable to broad classes of applications involving time-variant/time-invariant, linear/nonlinear, and smooth/non-smooth dynamical systems. The method leads to nonparametric reduced order models of simple form; i.e., in the form of coupled or uncoupled oscillators with time-varying or time-invariant coefficients forced by nonhomogeneous terms representing nonlinear modal interactions. Key to our method is a slow/fast partition of transient dynamics which leads to the identification of the basic fast frequencies of the dynamics, and the subsequent development of slow-flow models governing the essential dynamics of the system. We provide examples of application of the NSI method by analyzing strongly nonlinear modal interactions in two dynamical systems with essentially nonlinear attachments.     

The influence of boundary layers on supersonic inlet flow unstart induced by mass injection

A transverse jet is injected into a supersonic model inlet flow to induce unstart. Planar laser Rayleigh scattering from condensed CO₂ particles is used to visualize flow dynamics during the unstart process, while in some cases, wall pressure traces are simultaneously recorded. Studies conducted over a range of inlet configurations reveal that the presence of turbulent wall boundary layers strongly affect the unstart dynamics. It is found that relatively thick turbulent boundary layers in asymmetric wall boundary layer conditions prompt the formation of unstart shocks; in symmetric boundary conditions lead to the propagation of pseudo-shocks; and in both cases facilitate fast inlet unstart, when compared with thin, laminar boundary layers. Incident shockwaves and associated reflections are found to affect the speed of pressure disturbances. These disturbances, which induce boundary layer separation, are found to precede the formation of unstart shocks. The results confirm the importance of and need to better understand shock-boundary layer interactions in inlet unstart dynamics.     

Quenching phenomena for a non-local diffusion equation with a singular absorption

In this paper we study the quenching problem for the non-local diffusion equation

Finite mixture-of-gamma distributions: estimation,inference, and model-based clustering

Advances in Data Analysis and Classification - Finite mixtures of (multivariate) Gaussian distributions have broad utility, including their usage for model-based clustering. There is increasing...     

Long Distance Electronic Effects on the Rotational Potential Barriers Around the Caromatic-Cethylenic Bond

A systematic study of the rotational activation free energy around the C_aromatic-C_ethylenic bond of para-substituted styrene systems is carried out in the present work from a quantum chemistry point of view.

Calculations of the rotational potential barriers in the AM1 approach are developed as function of the electron-donor groups localized on the aromatic ring. Based on these calculations and thermodynamical data, we predict changes in the activation free energy barriers due to the long distance electronic effects of the substituents in acetophenones, cinnamaldehydes and benzalketones according to the following equation:

Our results agree the experimental measurements registered up to date and the standard deviations are similar to experimental determinations.     

Soft X‐ray absorption spectroscopy and resonant inelastic X‐ray scattering spectroscopy below 100 eV: probing first‐row transition‐metal M‐edges in chemical complexes

X‐ray absorption and scattering spectroscopies involving the 3d transition‐metal K‐ and L‐edges have a long history in studying inorganic and bioinorganic molecules. However, there have been very few studies using the M‐edges, which are below 100 eV. Synchrotron‐based X‐ray sources can have higher energy resolution at M‐edges. M‐edge X‐ray absorption spectroscopy (XAS) and resonant inelastic X‐ray scattering (RIXS) could therefore provide complementary information to K‐ and L‐edge spectroscopies. In this study, M_2,3‐edge XAS on several Co, Ni and Cu complexes are measured and their spectral information, such as chemical shifts and covalency effects, are analyzed and discussed. In addition, M_2,3‐edge RIXS on NiO, NiF₂ and two other covalent complexes have been performed and different d–d transition patterns have been observed. Although still preliminary, this work on 3d metal complexes demonstrates the potential to use M‐edge XAS and RIXS on more complicated 3d metal complexes in the future. The potential for using high‐sensitivity and high‐resolution superconducting tunnel junction X‐ray detectors below 100 eV is also illustrated and discussed.