Fully-developed pipe and planar flows of multimode viscoelastic fluids

Two solutions are presented for fully-developed pipe and planar flows of multimode viscoelastic models. The fluids have a Newtonian solvent contribution and the polymer modes are described by the Phan-Thien—Tanner (PTT), the FENE-P or the Giesekus equation. The first solution is exact and can handle any number of modes, but is only semi-analytical. The second solution, which is presented only for the PTT model with a linear stress coefficient and the FENE-P model, can also handle any number of modes. It is based on a truncated series expansion and is completely analytical, but provides only an approximated solution. The complexity of the multimode solutions is investigated first with the exact semi-analytical method and it is shown that at high Deborah number flows the high-order stresses can become as important as the stress of the first mode. It is also under these conditions that the approximated analytical solution deviates from the exact semi-analytical solution. A criterion for the accurate use of the approximated solution is presented. Fortran codes are provided to obtain these solutions at the internet address at the end.     

Global exponential stability for nonautonomous cellular neural networks with delays

In this Letter, by utilizing Lyapunov functional method and Halanay inequalities, we analyze global exponential stability of nonautonomous cellular neural networks with delay. Several new sufficient conditions ensuring global exponential stability of the network are obtained. The results given here extend and improve the earlier publications. An example is given to demonstrate the effectiveness of the obtained results.     

A new generalized algebra method and its application in the (2 + 1) dimensional Boiti–Leon–Pempinelli equation

In the present paper, some types of general solutions of a first-order nonlinear ordinary differential equation with six degree are given and a new generalized algebra method is presented to find more exact solutions of nonlinear differential equations. As an application of the method and the solutions of this equation, we choose the (2 + 1) dimensional Boiti Leon Pempinelli equation to illustrate the validity and advantages of the method. As a consequence, more new types and general solutions are found which include rational solutions and irrational solutions and so on. The new method can also be applied to other nonlinear differential equations in mathematical physics.     

The quadratic trace identity for constructing Hamiltonian structures of the multicomponent equation hierarchies

The quadratic trace identity is presented, which is devoted to constructing the Hamiltonian structures of some multicomponent equation hierarchies.     

Control of mesoporous structure of aerogels derived from cresol-formaldehyde

Polycondensation of a cresol mixture (C(m)) with formaldehyde (F) in basic aqueous solutions leads to formation of highly cross-linked C(m)F aquagels that can be supercritically dried with carbon dioxide to form organic C(m)F aerogels. Aerogels synthesized with different catalyst contents and reactant concentrations are characterized by low-temperature nitrogen adsorption. The present experimental results suggest that the C(m)F aerogels are typical mesoporous materials and have almost no micropores in bulk. The microstructure of the organic C(m)F aerogels can be controlled and tailored effectively by varying synthesis conditions during the initial sol-gel process. C(m)F organic aerogels with specific surface area as high as 627 m(2)/g and corresponding pore volume 2.06 ml/g have been obtained with a dominant pore size of 30 nm. C(m)F organic aerogels with peaky pore size distributions concentrated at 11 nm have also been prepared.     

Characteristic sequences for DNA primary sequence

A DNA sequence can be identified with a word over an alphabet N = [A, C, G, T]. Characteristic sequences of a DNA sequence are given in term of classifications of bases of nucleic acids. Using the characteristic sequences, we construct a set of 2 x 2 matrices to represent DNA primary sequences, which are based on counting of the frequency of occurrence of all (0,1) triplets of characteristic sequences. Furthermore, the leading eigenvalues of these matrices are computed and considered as invariants for the DNA primary sequences. Similarity and dissimilarity analysis based on the characteristic sequences are given for eight exon-1 genes of beta-globin about eight species.     

Lyotropic liquid crystalline poly(aryl ether ketone) copolymer containing phthalazinone moiety and biphenyl mesogen

A novel lyotropic liquid crystalline material poly(aryl ether ketone) copolymer containing phthalazinone moiety and biphenyl mesogen named P-8515 was developed by a mild solution polycondensation method. The molecular weight (M_n) was 53,000 and the value of molecular weight distribution index (MDI) was 2.49 detected by GPC. The critical concentration (C^∗) of P-8515 was 36 wt% and P-8515 exhibited characteristic nematic lyotropic liquid crystalline phases in NMP solution at different concentrations and the phase morphology changed to a typical threaded texture when shear forces were induced from PLM observations. The T_g value was 238 °C and the value for 5% weight loss temperature was 515 °C in nitrogen from DSC and TGA determinations, respectively.     

A simple and efficient method for the allylation of heteroarenes catalyzed by PdCl2

The PdCl₂-catalyzed allylation of heteroarenes is presented. Various heteroarenes including O-, N-, and S-based ones were allylated efficiently with a rich range of allylic acetates in the presence of only 2 mol % of PdCl₂, without the need of bases/acids, additives, and external supporting ligands. In addition, the reactions were carried out under mild and simple conditions just by stirring the two reactants and catalyst in CH₂Cl₂ at 60 °C. Moreover, the by-product produced was non-toxic acetic acid. Thus, the method presented in this work provides a general, clean, and operationally simple approach for the functionalization of heteroarenes. Finally, a preliminary mechanistic study suggested that the Pd(II) may be reduced in situ by the heteroarenes to Pd(0), which serves as the active metal center to catalyze the following allylations of heteroarenes via a Tsuji–Trost pathway.