Pit your wits against young minds!

This column is a place for those bits of contagious mathematics that travel from person to person in the community, because they are so elegant, suprising, or appealing that one has an urge to pass them on. Contributions are most welcome.     

Use of X-ray diffraction data in stereochemical studies of (−)-menthone reactions with aromatic aldehydes

X-ray diffraction analysis proved that the stereochemical configuration of interaction products of (−)-menthone with aromatic aldehydes (α,β-unsaturated ketones or β-hydroxyketones) depends on the generation conditions of intermediate enolate carbanions. In irreversible deprotonation of (−)-menthone with strong sterically hindered organometallic bases, products of interaction with aldehydes preserve the 1R,4S-configuration; in equilibrium conditions, 1R,4R-diastereomers of the corresponding α,β-unsaturated ketones are formed with high stereoselectivity. Institute of Single Crystals, Academy of Sciences of Ukrainian Republic. Translated fromZhurnal Strukturnoi Khimii, Vol. 35, No. 5, pp. 133–142, September–October, 1994. Translated by T. Yudanova     

N. Charton,A. Feldermann,A. Theis,M. H. Stenzel,T. P. Davis,C. Barner‐Kowollik,Initiator efficiency of 2,2′‐azobis(isobutyronitrile) in bulk dodecyl acrylate free‐radical polymerizations over a wide conversion and molecular weight range (2004) 42(20) 5170–5179

The original article to which this Erratum refers was published in J Polym Sci Part A: Polym Chem (2004) 42(20) 5170–5179. No abstract.     

Atomistic phenomena in dense fluid shock waves

The shock structure problem is one of the classical problems of fluid mechanics and at least for non-reacting dilute gases it has been considered essentially solved. Here we present a few recent findings, to show that this is not the case. There are still new physical effects to be discovered provided that the numerical technique is general enough to not rule them out a priori. While the results have been obtained for dense fluids, some of the effects might also be observable for shocks in dilute gases.     

Approximation of transient temperatures in complex geometries using fractional derivatives

It is shown that time-dependent temperatures in a transient, conductive system can be approximately modeled by a fractional-order differential equation, the order of which depends on the Biot number. This approximation is particularly suitable for complex shapes for which a first-principles approach is too difficult or computationally time-consuming. Analytical solutions of these equations can be written in terms of the Mittag-Leffler function. The approximation is especially useful if a suitable fractional-order controller is to be designed for the system.     

Damage and fracture evaluation of granular composite materials by digital image correlation method

This paper presents the applications of digital image correlation technique to the mesoscopic damage and fracture study of some granular based composite materials including steelfiber reinforced concrete, sandstone and crystal-polymer composite. The deformation fields of the composite materials resulted from stress localization were obtained by the correlation computation of the surface images with loading steps and thus the related damage prediction and fracture parameters were evaluated. The correlation searching could be performed either directly based on the gray levels of the digital images or from the wavelet transform (WT) coefficients of the transform spectrum. The latter was developed by the authors and showed higher resolution and sensitivity to the singularity detection. Because the displacement components came from the rough surfaces of the composite materials without any coats of gratings or fringes of optical interferometry, both surface profiles and the deformation fields of the composites were visualized which was helpful to compare each other to analyze the damage of those heterogeneous materials. The project supported by the National Natural Science Foundation of China (10125211 and 10072002), the Scientific Committee of Yunnan Province for the Program of Steel Fiber Reinforced Concrete, and the Institute of Chemical Materials, CAEP at Mianyang     

Hysteretic galvano-mechanical effect on charging and discharging ionistor structures

The size of an ionistor capacitor structure is found to change during its charging and discharging. The specific feature of this effect that distinguishes it from other known effects of changing sizes under electric and magnetic fields (the piezoelectric effect and striction) is the complete hysteresis; i.e., the size reached under the exposure remains unchanged after the field is turned off.