Crack kinking from an interface crack with initial contact between the crack lips

The authors recently theoretically studied crack kinking and opening from an initially closed crack (without friction) in some homogeneous medium. The same problem, but for an interface crack, is considered here. Comninou has shown that the asymptotic stress field prior to kinking is governed by a single, mode II stress intensity factor (SIF). Using this result, plus a homogeneity property of the problems of elastic fracture mechanics with unilateral contact envisaged, a change of scale, and two reasonable hypotheses, we establish the expression of the SIF at the tip of the small, open crack extension. It is shown that whatever the geometry of the external boundary and the crack and whatever the loading, these SIF depend solely upon the initial (mode II) SIF (in a linear way), the kink angle and Dundurs' parameters α and β. Using this result and Goldstein and Salganik's “principle of local symmetry” to predict the kink angle, one finds that it is independent of the loading but does depend upon Dundurs' parameters α and β. This contrasts with the case of an ordinary (initially closed) crack in some homogeneous medium, for which the kink angle was not only independent of the loading but an absolute constant. However, it is numerically found that the influence of the mismatch of elastic properties upon the kink angle is rather weak.     

Modèle électromagnétique d'objet dissimulé

We model propagation of electromagnetic waves in a medium, which is inhomogeneous with a rough layer, and which hides an object. We first get an effective medium, and then we solve the problem by integral equations.     

Size and sequence and the volume change of protein folding

The application of hydrostatic pressure generally leads to protein unfolding, implying, in accordance with Le Chatelier's principle, that the unfolded state has a smaller molar volume than the folded state. However, the origin of the volume change upon unfolding, ΔV(u), has yet to be determined. We have examined systematically the effects of protein size and sequence on the value of ΔV(u) using as a model system a series of deletion variants of the ankyrin repeat domain of the Notch receptor. The results provide strong evidence in support of the notion that the major contributing factor to pressure effects on proteins is their imperfect internal packing in the folded state. These packing defects appear to be specifically localized in the 3D structure, in contrast to the uniformly distributed effects of temperature and denaturants that depend upon hydration of exposed surface area upon unfolding. Given its local nature, the extent to which pressure globally affects protein structure can inform on the degree of cooperativity and long-range coupling intrinsic to the folded state. We also show that the energetics of the protein's conformations can significantly modulate their volumetric properties, providing further insight into protein stability.     

Connected functional working spaces: a framework for the teaching and learning of functions at upper secondary level

ZDM – Mathematics Education - This paper aims at contributing to remedy the narrow treatment of functions at upper secondary level. Assuming that students make sense of functions by working...     

N-Functionalised heterocyclic dicarbene complexes of silver: Synthesis and structural studies

A range of new diimidazolium salts, held together by an alkyl unit and bearing alcohol pendant arms on their nitrogen, was synthesized. A short modular reaction pathway leads to the N-heterocyclic carbene (NHC) precursors, differing by the flexibility of the bridge, the steric bulk of substituents in α-position of the OH groups and the anions. Treatment of diimidazolium salts with Ag₂O yields Ag^I(carbene)₂ complexes. The related trimethylene-bridged bis-NHC silver complexes 6 and 7 were crystallised with di-tosylate and di-hexafluorophosphate anions, respectively. Their X-ray structures revealed dimeric species, involving two ligands with different arrangements around the Ag cations, leading to crossed and parallel conformations.     

Intramolecular "hydroiminiumation and -amidiniumation" of alkenes: a convenient, flexible, and scalable route to cyclic iminium and imidazolinium salts

Addition of a stoichiometric amount of HCl to alkenylaldimines, -formamidines, and -amidines results in the protonation of the sp2-nitrogen atom. The resulting alkenylaldiminium, -formamidinium, and -amidinium salts can be isolated and fully characterized, including single-crystal X-ray diffraction studies. Heating solutions of these salts induces ring closure cleanly and regioselectively via formal "exo" addition of the nitrogen-hydrogen bond to the pendent carbon-carbon double bond, affording the corresponding cyclic aldiminium, dihydroisoquinolinium, and imidazolinium salts. Of special interest, novel 4,4-disubstituted imidazolinium salts are accessible via this synthetic route. Similarly, addition of phosgene to alkenyl ureas and alkenyl amides, followed by gentle heating, cleanly affords C-chloro imidazolinium, and cyclic C-chloro iminium salts, respectively. Treatment of the latter with tetrakis(triphenylphosphine)palladium allows for the preparation of the first transition-metal complex bearing a cyclic arylaminocarbene as ligand. Deuterium labeling experiments suggest that the mechanism of the hydroiminiumation and -amidiniumation reactions involves an intramolecular proton transfer to the double bond in the rate-determining step. This novel synthetic methodology gives access to a variety of N-heterocyclic carbene (NHC) and cyclic alkyl- and arylaminocarbene (CAAC) precursors.     

Design and synthesis of an array of selective androgen receptor modulators

We describe the design, using shape comparison and fast docking computer algorithms, and rapid parallel synthesis of a 1300 member array based on GSK7721, a 4-aminobenzonitrile androgen receptor (AR) antagonist identified by focused screening of the GSK compound collection. The array yielded 352 submicromolar and 17 subnanomolar AR agonists as measured by a cell-based reporter gene functional assay. The rapid synthesis of a large number of active compounds provided valuable information in the optimization of AR modulators, which may be useful in treating androgen deficiency in aging males.