Mesoscopic Strain Fields Measurement During the Allotropic α − γ Transformation in High Purity Iron

The allotropic phase change from ferrite to austenite represents a moment of massive interplay between the microstructural and mechanical states of iron. The difference of compacity between the two phases induces a microplastic accommodation in the material at grain scale. However, mechanical heterogeneities resulting from the transformation process remain challenging to characterise due to the high temperature conditions it is associated with. We developed experimental equipment for in situ observation of α ? γ and γ ? α transformations. Images of the surface of an iron sample taken by an optical camera were used as input for a Digital Image Correlation (DIC) routine. Special care was taken to maximize image resolution to capture sub-grain phenomena. Observations show that, at the mesoscopic scale, shear strain fields exhibit strong localisations that are evidence of transformations that are occurring.

     

Thermodynamic study of transthyretin association (wild‐type and senile forms) with heparan sulfate proteoglycan: pH effect and implication of the reactive histidine residue

The tetramer destabilization of transthyretin into monomers and its fibrillation are phenomena leading to amyloid deposition. Heparan sulfate proteoglycan (HSPG) has been found in all amyloid deposits. A chromatographic approach was developed to compare binding parameters between wild‐type transthyretin (wtTTR) and an amyloidogenic transthyretin (sTTR). Results showed a greater affinity of sTTR for HSPG at pH 7.4 compared with wtTTR owing to the monomeric form of sTTR. Analysis of the thermodynamic parameters showed that van der Waals interactions were involved at the complex interface for both transthyretin forms. For sTTR, results from the plot representing the number of protons exchanged vs pH showed that the binding mechanism was pH‐dependent with a critical value at a pH 6.5. This observation was due to the protonation of a histidine residue as an imidazolium cation, which was not accessible when TTR was in its tetrameric structure. At pH >6.5, dehydration at the binding interface and several contacts between nonpolar groups of sTTR and HSPG were also coupled to binding for an optimal hydrogen‐bond network. At pH <6.5, the protonation of the His residue from sTTR monomer when pH decreased broke the hydrogen‐bond network, leading to its destabilization and thus producing slight conformational changes in the sTTR monomer structure. Copyright © 2014 John Wiley & Sons, Ltd.     

The cardinality of manifold atlases

It is shown that any finite dimensionalC ⁰ manifold (connected and Hausdorff but otherwise unrestricted) has an atlas of cardinality not greater than that of the continuum; while if it has a Hölder continuous pseudo-Riemannian metric then there is a countable atlas.     

Structure of solid monolayers and multilayers of n -hexane on graphite

We present all-atom molecular dynamics simulations ofn-hexane on the basal plane of graphite at monolayer and multilayer coverages. In keeping with experimental data, we find the presence of ordered adsorbed layers both at single monolayer coverage and when the adsorbed layer coexists with excess liquid adsorbate. Using a simulation method that does not impose any particular periodicity on the adsorbed layer, we quantitatively compare our results to the results of neutron diffraction experiments and find a structural transition from a uniaxially incommensurate lattice to a fully commensurate structure on increasing the coverage from a monolayer to a multilayer. The zig-zag backbone planes of all the alkane molecules lie parallel to the graphite surface at the multilayer coverage, while a few molecules are observed to attain the perpendicular orientation at monolayer coverage. Dedicated to Professor C N R Rao on his 70th birthday     

Optical Diffractive Memories: Angular Selectivity and Diffraction Efficiency in Dichromated Gelatin

Two thousand images of resolution 512×512 pixels as a regular matrix pattern of 10×10 elements are stored, where each element is angularly multiplexed 20 times in a 25 μm thickness of dichromated gelatin emulsion without cross-talk effect. The surface area of the matrix is 1 cm². We show good concordance of the angular selectivity between the experimental result and theory. The diffraction efficiency of each 20 multiplexed images is measured and has nearly the same value. Examples of reconstructed images for multiple applications are given, for example, storage of 160,000 images on a 3′1/2 floppy disc format, which is about 100 min of black and white film. Application can be made to automobile cartography and storage of X-ray images as well as weather forecast images. Colored diffractive images are also possible and are illustrated.     

Dynamic programming in cricket: optimizing batting order for a sticky wicket

In cricket, a rain-affected pitch can make batting more difficult than normal. Several other conditions such as poor light or an initially lively pitch, may also result in difficulties for the batsmen. In this note, we refer to all of them as ‘sticky wickets’. On sticky wickets, lower order batsmen are often sent into ‘hold the fort’ until conditions improve. In this paper, a stochastic dynamic programming model is used to examine the appropriateness of this policy. The model suggests that the tactic is often optimal when the sticky wicket persists until the end of the day's play, but not often when the sticky wicket is transitory. In some circumstances, it is worthwhile, on a normal wicket near the end of the day, to send in a lower order batsman to hold the fort (a night watchman): when the wicket is sticky, this tactic is even more worthwhile.     

On the convergence of Newton's method when estimating higher dimensional parameters

In this paper, we consider the estimation of a parameter of interest where the estimator is one of the possibly several solutions of a set of nonlinear empirical equations. Since Newton's method is often used in such a setting to obtain a solution, it is important to know whether the so obtained iteration converges to the locally unique consistent root to the aforementioned parameter of interest. Under some conditions, we show that this is eventually the case when starting the iteration from within a ball about the true parameter whose size does not depend on n. Any preliminary almost surely consistent estimate will eventually lie in such a ball and therefore provides a suitable starting point for large enough n. As examples, we will apply our results in the context of M-estimates, kernel density estimates, as well as minimum distance estimates.     

Toward phenanthridin-2-ylidene: electrophilicity versus acidity in planar-constrained C-aryl iminium salts

A phenanthridinium salt was prepared in four steps, including an intramolecular CH-arylation and a hydride abstraction reaction. Treatment with sterically demanding bases does not lead to the corresponding carbene, but rather to addition products: the planar-constrained geometry significantly enhances the electrophilicity over the acidity of C-aryl iminium salts.