Korn inequality for a thin rod with rounded ends

We consider an elastic rod with rounded ends and diameter proportional to a small parameter h > 0. The roundness of the ends is described by an exponent m ∈ (0,1). We derive for the rod an asymptotically sharp Korn inequality with a special weighted anisotropic norm. Weight factors with m‐dependent powers of h appear both in the anisotropic norm and the Korn inequality itself, and we discover three critical values m = 1 ∕ 4, m = 1 ∕ 2 and m = 3 ∕ 4 at which these exponents are crucially changed. Copyright © 2014 John Wiley & Sons, Ltd.     

Hierarchical structure of SERS substrates possessing the silver ring morphology

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Molecular dynamics simulation of poly(3‐hexylthiophene) helical structure In Vacuo and in amorphous polymer surrounding

The stability of poly(3‐hexylthiophene) (P3HT) helical structure has been investigated in vacuo and in amorphous polymer surrounding via molecular dynamics‐based simulations at temperatures below and above the P3HT melting point. The results show that the helical chain remains stable at room temperature both in vacuo and in amorphous surrounding, and promptly loses its structure at elevated temperatures. However, the amorphous surrounding inhibits the destruction of the helix at higher temperatures. In addition, it is shown that the electrostatic interactions do not significantly affect the stability of the helical structure. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2448–2456     

Controlled ring‐opening homo‐ and copolymerization of ɛ‐caprolactone and d,l‐lactide by iminophenolate aluminum complexes: An efficient approach toward well‐defined macromonomers

The aluminum complexes containing two iminophenolate ligands of the type (p‐XC₆H₄NCHC₆H₄O‐o)₂AlR' (R′=Me ( 3, 4 ) or R′=O(CH₂)₄OCH=CH₂ ( 5, 6 ), X=H ( 3, 5 ), F( 4, 6 )) were synthesized and characterized by ¹H, ¹³C NMR spectroscopy, and X‐ray crystallography. The reaction of AlMe₃ with two equivalents of substituted iminophenols gave five‐coordinated {ONR}₂AlMe ( 3, 4 ) complexes. Subsequent reaction of these methyl complexes with unsaturated alcohol, HO(CH₂)₄OCH=CH₂, resulted in target compounds 5 and 6 in a good yield. It was shown that the complexes ( 3 ‐ 6 ) are monomeric in solution (NMR) and in solid state (X‐ray analysis). The catalytic activity of the complexes 5 and 6 towards ring‐opening polymerization (ROP) of ?‐caprolactone and d,l ‐lactide was assessed. Complex 5 showed higher activity as compared with 6 , while both of these catalysts induced controlled homo‐ and copolymerization to afford the macromonomers with high content of vinyl ether end groups (F_n > 80%) in a broad range of molecular weights (M_n = 4000–30,000 g mol^?1) with relatively narrow MWD (M_w/M_n = 1.1–1.5). © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1237–1250     

Optical Resonant Saturation of Dipole–Dipole Broadened Transitions in High-Density Atomic Vapor

Journal of Russian Laser Research - We discuss the experimental research of an optical resonant saturation of a dipole–dipole-broadened atomic transition in the high-density rubidium vapor....     

Enhanced spin capturing polymerization: Numerical investigation of mechanism

Simulation on the kinetic scheme of enhanced spin capturing polymerizations (ESCP) were performed to reveal the influence of different parameters, e.g., initiation rate, spin capturing and side reactions on the properties (the monomer conversion, degree of polymerization, polydispersity index, and the fraction of “living” chains) of polymer obtained. The kinetic scheme of ESCP was solved numerically as well as the method of statistical moments of molecular weight distribution was applied to get some numerical expressions for analysis. The simulations showed that fast initiation rate can lead to decrease of living fraction and broadening of molecular weight distribution. Whereas high rate of spin capturing makes the polymer chains shorter but increases living character. And side reactions always decrease livingness of the polymer obtained. Finally in the case of absence of side reaction we were able to formulate criteria for formation of polymer with target molecular weight and quota of living chains via ESCP process. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2546–2556