CNDO/2 study of systems modelling the nitration of polybutadienes

It has been shown that the linear trimer of butadiene can be used as a convenient model for describing the chemical behaviour of polybutadienes. The reactivity of these systems was found to be considerably determined by the π-electron charge which is partially delocalized. The most probable positions of electrophilic substitution are on the carbons linking the monomer units. These positions are not influenced by the presence of N-containing substituents indicating thus the statistical nature of the nitration of polybutadienes. CC bridged bonds are also the preferred sites for main chain degradations. On nitration, these bonds become more stable and formation of nitrogen oxides prevails over chain degradation.     

Cooperative behavior between oscillatory and excitable units: the peculiar role of positive coupling-frequency correlations

We study the collective dynamics of noise-driven excitable elements, so-called active rotators. Crucially here, the natural frequencies and the individual coupling strengths are drawn from some joint probability distribution. Combining a mean-field treatment with a Gaussian approximation allows us to find examples where the infinite-dimensional system is reduced to a few ordinary differential equations. Our focus lies in the cooperative behavior in a population consisting of two parts, where one is composed of excitable elements, while the other one contains only self-oscillatory units. Surprisingly, excitable behavior in the whole system sets in only if the excitable elements have a smaller coupling strength than the self-oscillating units. In this way positive local correlations between natural frequencies and couplings shape the global behavior of mixed populations of excitable and oscillatory elements.     

An approach for decomposition of finite rotations

Based on Lie groups theory, this work considers the problem of decomposition of a given rotation into three successive finite rotations with prescribed in advance axes. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)