On critical parameters in homogenization of perforated domains by thin tubes with nonlinear flux and related spectral problems

Let u_? be the solution of the Poisson equation in a domain perforated by thin tubes with a nonlinear Robin‐type boundary condition on the boundary of the tubes (the flux here being β(?)σ(x,u_?)), and with a Dirichlet condition on the rest of the boundary of Ω. ? is a small parameter that we shall make to go to zero; it denotes the period of a grid on a plane where the tubes/cylinders have their bases; the size of the transversal section of the tubes is O(a_?) with a_???. A certain nonperiodicity is allowed for the distribution of the thin tubes, although the perimeter is a fixed number a. Here, is a strictly monotonic function of the second argument, and the adsorption parameter β(?) > 0 can converge toward infinity. Depending on the relations between the three parameters ?, a_?, and β(?), the effective equations in volume are obtained. Among the multiple possible relations, we provide critical relations, which imply different averages of the process ranging from linear to nonlinear. All this allows us to derive spectral convergence as ?→0 for the associated spectral problems in the case of σ a linear function of u_?. Copyright © 2014 John Wiley & Sons, Ltd.     

Simulation of melting in crystalline polyethylene

We carry out a molecular dynamics simulation of the first stages of constrained melting in crystalline polyethylene (PE). When heated, the crystal undergoes two structural phase transitions: from the orthorhombic (O) phase to the monoclinic (M) phase, and then to the columnar (C), quasi-hexagonal, phase. The M phase represents the tendency to the parallel packing of planes of PE zigzags, and the C phase proves to be some kind of oriented melt. We follow both the transitions O→M and M→C in real time and establish that, at their beginning, the crystal tries (and fails) to pass into the partially ordered phases similar to the RI and RII phases of linear alkanes, correspondingly. We discuss the molecular mechanisms and driving forces of the observed transitions, as well as the reasons why the M and C phases in PE crystals substitute for the rotator phases in linear alkanes.     

On the applicability of the Frenkel-Kontorova model to describing the dynamics of vacancies in a polymeric crystal chain

The necessary conditions of the applicability of the Frenkel-Kontorova one-dimensional model [the approximation of immobile neighboring chains plus sine-Gordon (continual) equation for nonlinear dynamics of the chain under consideration] to describing the dynamics of vacancies in a polymeric crystal chain are determined. It is shown that these conditions are satisfied for polyethylene crystals. The physical mechanism of model applicability limitations is established.     

Effects of Hydrogen Peroxide on In Vitro Cultures of Tea (Camellia sinensis L.) Grown in the Dark and in the Light: Morphology,Content of Malondialdehyde,and Accumulation of Various Polyphenols

Tea plants (Camellia sinensis L.) are phenol-accumulating crops that are widely used for public health. The healing effect of tea leaf products is due to the biosynthesis of such phenolic compounds (PCs) as flavans, which have P-vitamin capillary-strengthening activity. Due to their limited habitat and the value of their specialized metabolites of a phenolic nature, a promising approach is to establish in vitro cultures from them that retain the ability to form PCs, which is characteristic of ex vivo tea plants. The aim of this study was to investigate the effect of exogenic H₂O₂ (0.01 mM; 0.1 mM; 1 mM) on the growth, morphology, degree of stress response, and accumulation of various phenolic compounds in tea plant callus cultures of different ages (24 or 36 days) grown under different cultivation conditions (darkness or light). According to the results obtained, the H₂O₂ effect on tea callus cultures of different ages did not cause changes in their morphophysiological characteristics, both after 2 h of exposure (rapid response of callus culture, RRCC) and after 48 h (delayed response of callus culture, DRCC). The determination of the malondialdehyde (MDA) content, which serves as an indicator of changes in the level of lipid peroxidation (LPO) and the presence of stress responses in plant cells, indicated either its maintenance at the control level, a decrease, or an increase. All these effects depended on the growth conditions of the tea callus cultures (darkness or light), their age, the duration of exposure (rapid or delayed response), and the H₂O₂ concentration. Similar trends were noted for the total content of PCs as well as the amount of flavans, proanthocyanidins (soluble and insoluble forms), and lignin. The plant cell responses reflected changes in its adaptation programs, when specialized metabolites act as a target for the action of H₂O₂, thereby contributing to an increase in their resistance.