Application of nonlinear continuum dislocation theory to antiplane shear

We apply the nonlinear dislocation theory to the problem of antiplane constrained shear in a single crystal with one slip system. By taking dissipation into account, the relaxed energy functional has to be minimized. We show that, up to a threshold strain, no dislocations are nucleated and therefore the plastic slip is zero. Since this threshold value depends on the width of the specimen, a size effect takes place. The stress strain curve turns out to be a hysteresis loop exhibiting the work hardening due to the dislocation pile-up. It is shown that the Bauschinger effect holds true. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Forbidden Configurations and Product Constructions

A simple matrix is a (0,1)-matrix with no repeated columns. For a (0,1)-matrix F, we say that a (0,1)-matrix A has F as a configuration if there is a submatrix of A which is a row and column permutation of F (trace is the set system version of a configuration). Let \({\|A\|}\) denote the number of columns of A. We define \({{\rm forb}(m, F) = {\rm max}\{\|A\| \,:\, A}\) is m-rowed simple matrix and has no configuration F. We extend this to a family \({\mathcal{F} = \{F_1, F_2, \ldots , F_t\}}\) and define \({{\rm forb}(m, \mathcal{F}) = {\rm max}\{\|A\| \,:\, A}\) is m-rowed simple matrix and has no configuration \({F \in \mathcal{F}\}}\) . We consider products of matrices. Given an m ₁ × n ₁ matrix A and an m ₂ × n ₂ matrix B, we define the product A × B as the (m ₁ + m ₂) × n ₁ n ₂ matrix whose columns consist of all possible combinations obtained from placing a column of A on top of a column of B. Let I _k denote the k × k identity matrix, let \({I_k^{c}}\) denote the (0,1)-complement of I _k and let T _k denote the k × k upper triangular (0,1)-matrix with a 1 in position i, j if and only if i ≤ j. We show forb(m, {I ₂ × I ₂, T ₂ × T ₂}) is \({\Theta(m^{3/2})}\) while obtaining a linear bound when forbidding all 2-fold products of all 2 × 2 (0,1)-simple matrices. For two matrices F, P, where P is m-rowed, let \({f(F, P) = {\rm max}_{A} \{\|A\| \,:\,A}\) is m-rowed submatrix of P with no configuration F}. We establish f(I ₂ × I ₂, I _m/2 × I _m/2) is \({\Theta(m^{3/2})}\) whereas f(I ₂ × T ₂, I _m/2 × T _m/2) and f(T ₂ × T ₂, T _m/2 × T _m/2) are both \({\Theta(m)}\) . Additional results are obtained. One of the results requires extensive use of a computer program. We use the results on patterns due to Marcus and Tardos and generalizations due to Klazar and Marcus, Balogh, Bollobás and Morris.     

A comparison of quantitative nuclear magnetic resonance methods: internal,external, and electronic referencing

The performance of three quantitative NMR methods was compared in terms of short‐term and long‐term precision and accuracy, robustness, linear range, and general applicability. The Internal Reference method employs a reference material co‐dissolved with sample; the External Reference method employs a reference material contained in a separate solution; and the third method, known as Electronic REference To access In vivo Concentrations (ERETIC), employs an externally calibrated digital reference peak. The Internal Reference method results were the most precise and remained stable within 0.1% for at least 4 weeks. The results from the External Reference and ERETIC methods were practically equivalent to each other during this time. These methods exhibited small differences relative to the standard set by the Internal Reference method and slightly lower precision, establishing them as practical alternatives to the Internal Reference method. In contrast to the Internal Reference method, the External Reference and ERETIC methods possess several advantages that address peak overlap, flexibility of calibration, and duration of applicability. The study was designed such that each spectrum contained the information needed to compare the three methods while all other variables were kept constant. Applicability of pulse width compensation is addressed. ERETIC software compensation and minor adjustments to 90° pulse width were concluded to be unnecessary for this system. Although each of the methods was applied here to specifically calculate and compare chemical purity values, this evaluation applies generally to absolute quantitation by NMR. Copyright © 2013 John Wiley & Sons, Ltd.     

Short communication: Stille coupling reactions of functionalized triorganotin halides

Convenient conditions for the Stille coupling of halide‐bearing triorganotin compounds, which do not normally react under typical Stille reaction conditions, are presented. The coupling of vinylstannanes with allyl bromide using palladium(II) catalysis is accomplished under fluoride assistance to give the substituted 2,5‐hexadien‐1‐ols in Z‐configuration. Copyright © 2004 John Wiley & Sons, Ltd.     

Book review

Ernest R. Alexander Published by Gordon and Breach Publishers, Amsterdam, Holland 1995. 355 pages. ISBN 2-88449-173-2     

Structure of Artificial Grain Boundaries in Sapphire Bicrystals with Intermediate Layers

The structure of the artificial grain boundaries in Al₂O₃ bicrystals withY₃Al₅O₁₂ and Y-stabilizedZrO₂ (Y-ZrO₂) intermediate layers was studiedwith high resolution electron microscopy, electron diffraction and energydispersive X-ray analysis. TheY₃Al₅O₁₂ intermediate layer wasfound to be polycrystalline with three different orientation relationshipsbetween the ₂O₃ and theY₃Al₅O₁₂. The structure of theY₃Al₅O₁₂/₂O₃ interfaces is described.Also₂O₃ bicrystals with an Y-ZrO₂/₂O₃/Y-ZrO₂/₂O₃/Y-ZrO₂intermediate layer, prepared at two different temperatures, werestudied.Recry stallization of the intermediate layers occurred during thesolid phase intergrowth of the ₂O₃ bicrystalsparts and only an Y-ZrO₂ layer was found as intermediatelayer. The misorientation between the consecutive Y-ZrO₂grains was less than 1.5°. Misfit dislocations and atomic height stepsdecorate the Y-ZrO₂/₂O₃interface.     

Interacting neural networks and the emergence of social structure

The article describes a computational model for the simulation of the emergence of social structure or social order, respectively. The model is theoretically based on the theory of social typifying by Berger and Luckmann. It consists of interacting artificial actors (agents), which are represented by two neural networks, an action net, and a perception net. By mutually adjusting of their actions, the agents are able to constitute a self‐organized social order in dependency of their personal characteristics and certain features of their environment. A fictitious example demonstrates the applicability of the model to problems of extra‐terrestrial robotics. © 2007 Wiley Periodicals, Inc. Complexity 12: 41–52, 2007     

Linear systems on projective spaces

In the paper the propertiesÑ _p (a generalization of the propertiesN _p for projectively normal embeddings of projective varieties) are investigated for noncomplete Veronese embeddings. It is shown that the linear projection of a complete Veronese embedding ? _n →? _N from a general linear subspace of ? _N of low dimension satisfies propertyÑ ₀. Moreover, Theorem 3.1 yields an upper bound forp for a noncomplete Veronese embedding of the projective plane ?₂ to satisfy propertyÑ _p .