The Aza‐Morita–Baylis–Hillman Reaction: A Mechanistic and Kinetic Study

The aza‐Morita‐Baylis–Hillman (aza‐MBH) reaction has been studied in a variety of solvents, a selection of imine substrates and with various combinations of PPh₃ and para‐nitrophenol as the catalyst system. The measured kinetic data indicates that the effects of solvent and protic co‐catalyst are strongly interdependent. These results are most easily reconciled with a mechanistic model involving the reversible protonation of zwitterionic intermediates in the catalytic cycle, which is also supported by ³¹P NMR spectroscopy and quantum chemical studies.     

In situ variable temperature X-ray diffraction studies on the transformations of nano-precursors to La-Ni-O phases

In situ variable temperature XRD (VT-XRD) measurements on the transformation of nano-precursors to LaNiO phases are presented. Experimental results showed that LaNiO₃ and La₂NiO₄ phases were formed at ca. 700 °C via the reaction of La₂O₃ and NiO (from the initial nano-precursors), where a relatively low temperature of 700 °C was found for the synthesis of La₂NiO₄. The formation of La₃Ni₂O₇ at higher temperature (up to 1150 °C) appeared to proceed through a further reaction of La₂NiO₄ with unreacted NiO, whilst the formation of La₄Ni₃O₁₀ (at 1075 °C) proceeded via a further decomposition of LaNiO₃. Although phase pure La₃Ni₂O₇ and La₄Ni₃O₁₀ were not directly obtained under the processing conditions herein, the results of this study allow for a better understanding of formation pathways, particularly for the higher order La-Ni-O phases.     

Cavitation in elastomeric solids: I—A defect-growth theory

It is by now well established that loading conditions with sufficiently large triaxialities can induce the sudden appearance of internal cavities within elastomeric (and other soft) solids. The occurrence of such instabilities, commonly referred to as cavitation, can be attributed to the growth of pre-existing defects into finite sizes. This paper introduces a new theory to study the phenomenon of cavitation in soft solids that: (i) allows to consider general 3D loading conditions with arbitrary triaxiality, (ii) applies to large (including compressible and anisotropic) classes of nonlinear elastic solids, and (iii) incorporates direct information on the initial shape, spatial distribution, and mechanical properties of the underlying defects at which cavitation can initiate. The basic idea is to first cast cavitation in elastomeric solids as a homogenization problem of nonlinear elastic materials containing random distributions of zero-volume cavities, or defects. This problem is then addressed by means of a novel iterated homogenization procedure, which allows to construct solutions for a specific, yet fairly general, class of defects. These include solutions for the change in size of the defects as a function of the applied loading conditions, from which the onset of cavitation — corresponding to the event when the initially infinitesimal defects suddenly grown into finite sizes — can be readily determined. In spite of the generality of the proposed approach, the relevant calculations amount to solving tractable Hamilton-Jacobi equations, in which the initial size of the defects plays the role of “time” and the applied load plays the role of “space”. When specialized to the case of hydrostatic loading conditions, isotropic solids, and defects that are vacuous and isotropically distributed, the proposed theory recovers the classical result of Ball (1982) for radially symmetric cavitation. The nature and implications of this remarkable connection are discussed in detail.     

Mobile and immobile fluid transport: Coupling framework

We introduce a solver method for mobile and immobile transport regions. The motivation is driven by transport processes in porous media (e.g. waste disposal, chemical deposition processes). We analyze the coupled transport‐reaction equation with mobile and immobile areas. We apply analytical methods, such as Laplace‐transformation, and for the numerical methods we apply Godunov's scheme, see (Mat. Sb. 1959; 47 :271–306; Finite Volume Methods for Hyperbolic Problems. Cambridge University Press: Cambridge, 2002). The method is based numerically on flux‐based characteristic methods and is an attractive alternative to the classical higher‐order TVD methods, see (J. Comput. Phys. 1993; 49 :357–393). In this paper, we will focus on the derivation of analytical solutions for general and special solutions of the characteristic methods that are embedded in a finite‐volume method. At the end of the paper, we illustrate the higher‐order method for different benchmark problems. Copyright © 2010 John Wiley & Sons, Ltd.     

Bayesian Multiscale Smoothing for Making Inferences About Features in Scatterplots

A rather common problem of data analysis is to find interesting features, such as local minima, maxima, and trends in a scatterplot. Variance in the data can then be a problem and inferences about features must be made at some selected level of significance. The recently introduced SiZer technique uses a family of nonparametric smooths of the data to uncover features in a whole range of scales. To aid the analysis, a color map is generated that visualizes the inferences made about the significance of the features. The purpose of this article is to present Bayesian versions of SiZer methodology. Both an analytically solvable regression model and a fully Bayesian approach that uses Gibbs sampling are presented. The prior distributions of the smooths are based on a roughness penalty. Simulation based algorithms are proposed for making simultaneous inferences about the features in the data.     

Energetic Silver Salts with 5-Aminotetrazole Ligands

Methylation of 5-amino-1H-tetrazole ( 1 ) gives 1-methyl-5-amino-1H-tetrazole ( 2 ) and 2-methyl-5-amino-1H-tetrazole ( 3 ). A new family of energetic silver complexes based on ligands 1 , 2 and 3 with perchlorate and nitrate anions ( 10 – 15 ) were synthesized and characterized by using IR, Raman, and NMR (¹H, ¹³C, ¹⁴N, and ³⁵Cl NMR) spectroscopy, elemental analysis, and mass spectrometry. The crystal structures of the compounds were determined where possible and reveal interesting structural details that are discussed herein. Additionally, differential scanning calorimetry was used to assess the thermal stability of the new salts, which showed excellent thermal stabilities at temperatures up to and above 225 °C. Standard tests were also used to assess the sensitivity of the materials towards impact and friction. All the silver complexes showed increased sensitivity values in comparison with analogous protonated 5-amino-1H-tetrazolium perchlorate and nitrate salts. Some of these materials have sensitivity values that are comparable to commonly used primary explosives and all of them either deflagrate ( 12 – 14 ) or detonate loudly ( 10 and 11 ) on contact with an open flame. Lastly, nitrate salt 11 is easily initiated by thermal shock. It shows reasonably low sensitivity in comparison with other silver salts (e.g., silver azide or silver fulminate), which makes handling it much less hazardous. Compound 11 also has good thermal stability, decomposing at ≈300 °C, and shows interesting properties as a more environmentally benign alternative to lead(II) diazide in initiation devices for civil and military applications.     

Markovian trees: properties and algorithms

In this paper we introduce a structure called the Markovian tree (MT). We define the MT and explore its alternative representation as a continuous-time Markovian Multitype Branching Process. We then develop two algorithms, the Depth and Order algorithms to determine the probability of eventual extinction of the MT process. We show that both of these algorithms have very natural physically intuitive interpretations and are analogues of the Neuts and U algorithms in Matrix-analytic Methods. Furthermore, we show that a special case of the Depth algorithm sheds new light on the interpretation of the sample paths of the Neuts algorithm.     

Combined finite difference and spectral methods for the numerical solution of hyperbolic equation with an integral condition

In this work the combined finite difference and spectral methods have been proposed for the numerical solution of the one‐dimensional wave equation with an integral condition. The time variable is approximated using a finite difference scheme. But the spectral method is employed for discretizing the space variable. The main idea behind this approach is that we can get high‐order results. The new method is used for two test problems and the numerical results are obtained to support our theoretical expectations. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007