Influence of the surface morphology on the melting of polymer crystals. I. Loops of random length and adjacent reentry

A polymer crystal with a noncrystalline surface layer formed by chain loops of different lengths is considered. It is assumed that the length of each loop can be changed by longitudinal diffusion of the molecule through the crystal lattice. From the condition that the free energy of the system is minimum, the loop length distribution and the average loop length as function of temperature are calculated. In contrast to the results for loops of equal length, for the present model, a substantial thickness of the noncrystalline surface layer and a broad melting range is obtained also for the case of adjacent reentry. In order to get this result one has to take into account that even an “ideal fold” consists of at least four rigidly arranged CH2 groups in energetically unfavored conformation.     

The a posteriori error estimates of Chebyshev–Petrov–Galerkin methods for second-order equations

In this paper, the a posteriori error estimates of Chebyshev–Petrov–Galerkin approximations are investigated. For simplicity, we choose the Poisson equation with Dirichlet boundary conditions to discuss the a posteriori error estimators, and deduce their efficient and reliable properties. Some numerical experiments are performed to verify the theoretical analysis for the a posteriori error estimators.     

Site-selective C–H nitration of N-aryl-7-azaindoles under palladium(II) catalysis

The site-selective C–H nitration reaction of 7-azaindoles with t-butyl nitrite under palladium catalysis is described. This protocol provides an efficient method for the construction of ortho-nitrated N-aryl-7-azaindoles with excellent site-selectivity and functional group compatibility. The formed 7-azaindole derivatives can be readily transformed into 7-azaindoles containing an aniline functional group under palladium-catalyzed hydrogenation conditions.     

Phragmen–lindelöf principle for weak subsolutions and cooperative reaction–diffusion systems

One of the principal techniques for treating sustems of reaction–diffusion equations is based on a comparison method using sub and super–solutions. In practice this method is much more effective if non–smooth subsolutions are allowed. In this note we extend the analysis in [2,3] for cooperative systems and prove a comparison principle for a natural and rather general class of weak subsolutions satisfying a Phragmen–Lindelöf condition. An application is then given to a biological model in involving a pair of mutualists.     

Using symbolic computation software packages in production of multidimensional finite volume‐based large eddy simulation codes

The numerical simulation of turbulence is one of the most challenging tasks in the field of the modern computational science. At present, the most advanced approach is the large eddy simulation (LES) technique wherein a formal separation between resolved (large) and unresolved (small) scales of the motion is in effect by means of a filtering operation applied onto the governing equations. However, LES requires very sophisticated numerical discretizations in terms of both accuracy and efficiency. Often, the modelling of the unresolved subgrid scale terms adds further computational complexities. This paper illustrates the suitability in using software packages for symbolic computation (in the present case, Maple© for helping in the production of subroutines for a new multidimensional, high‐order accurate finite volume‐based LES code. Specifically, it will be detailed how producing, rapidly and efficiently, the routines for computing convective, diffusive as well as subgrid scale modelling fluxes. It is particularly detailed how exploiting the package for differential calculus and linear algebra for the analytical integration of the flux polynomials over the finite volume faces. The structure of the LES code is illustrated, and an accuracy analysis of the local truncation errors is performed comparing the third‐order accurate multidimensional upwind and the classical second‐order centred reconstruction in the wavenumbers space. Then, some numerical results for the turbulent plane channel and some brief points concerning the parallelization issue are addressed. Copyright © 2012 John Wiley & Sons, Ltd.     

Necessary and sufficient conditions for Hölder continuity of Gaussian processes

The continuity of Gaussian processes is an extensively studied topic and it culminates in Talagrand’s notion of majorizing measures that gives complicated necessary and sufficient conditions. In this note we study the Hölder continuity of Gaussian processes. It turns out that necessary and sufficient conditions can be stated in a simple form that is a variant of the celebrated Kolmogorov–Čentsov condition.     

Kibble–Slepian formula and generating functions for 2D polynomials

We prove a generalization of the Kibble–Slepian formula (for Hermite polynomials) and its unitary analogue involving the 2D Hermite polynomials recently proved in [16]. We derive integral representations for the 2D Hermite polynomials which are of independent interest. Several new generating functions for 2D q-Hermite polynomials will also be given.     

Calculation of the vibration–rotational transition intensities of water molecules trapped in an argon matrix: stretching O–H vibrations spectral region

The frequencies and intensities of vibration–rotational transitions of water molecules in an argon matrix were calculated for temperatures of 6 and 30 K. The rigid asymmetric top approximation was used with available literature values of the effective rotational constants in the ground and excited vibrational states. The calculations were carried out by taking into account the existence of a non-equilibrium population distribution between the rotational levels of ortho- and para-water isomers. It was assumed that the temperature relaxation of the population of rotational levels is independent of the ortho- and para-isomers. Comparison of the results of the theoretical calculations with experimental literature data shows good agreement for the majority of the rotational structure lines for symmetric and antisymmetric stretching vibrations both in the frequency values and in the values of the relative intensities.     

Liquid crystalline properties and photochromism of 4-alkyl-N-(4-alkloxysalicylidene)anilines

Eight new homologous series of 4-alkyl-N-(4-alkloxysalicylidene)anilines were synthesized. The phase transitions of these homologues were determined using differential scanning calorimetry and polarizing optical microscopy. The homologues began to exhibit liquid crystalline phases as the terminal alkyl or alkoxyl chains were lengthened. In addition, some members of these homologues series exhibited photochromism in the solid state.