Unsteady hydromagnetic flow of a reactive variable viscosity third‐grade fluid in a channel with convective cooling

This paper examines the combined effects of a transverse magnetic field and variable viscosity on unsteady flow of a reactive third‐grade electrically conducting fluid and heat transfer in a channel with convective cooling at the surface. It is assumed that the fluid has small electrical conductivity and the electromagnetic force produced is very small. The coupled nonlinear partial differential equations governing the problem are derived and solved numerically using a semi‐implicit finite‐difference scheme. Both numerical and graphical results are presented and physical aspects of the problem are discussed with respect to various parameters embedded in the system. It is in general noted that those parameters that increase/decrase one flow quantity (velocity or temperature) also lead to the increase/decrease respectively of the other quantity. Copyright © 2011 John Wiley & Sons, Ltd.     

Carbon Fibers: Precursor Systems,Processing, Structure,and Properties

This Review gives an overview of precursor systems, their processing, and the final precursor‐dependent structure of carbon fibers (CFs) including new developments in precursor systems for low‐cost CFs. The following CF precursor systems are discussed: poly(acrylonitrile)‐based copolymers, pitch, cellulose, lignin, poly(ethylene), and new synthetic polymeric precursors for high‐end CFs. In addition, structure–property relationships and the different models for describing both the structure and morphology of CFs will be presented.     

Wave body interaction in 2D using smoothed particle hydrodynamics (SPH) with variable particle mass

Wave interaction with bodies is an important practical application for smoothed particle hydrodynamics (SPH) which in principle applies to steep and breaking waves without special treatment. However, few detailed tests have been undertaken even with small amplitude waves. In order to reduce computer time a variable particle mass distribution is tested here with fine resolution near the body and coarse resolution further away, while maintaining a uniform kernel size. We consider two well‐defined test cases, in two dimensions, of waves generated by a heaving semi‐immersed cylinder and progressive waves interacting with a fixed cylinder. But first, still water with hydrostatic pressure is tested. The open‐source code SPHysics ( http://www.sphysics.org )^{§Update made here after initial online publication.} is used with a Riemann solver in an Arbitrary Lagrangian–Eulerian formulation. For the heaving cylinder, SPH results for far field wave amplitude and cylinder force show good agreement with the data of Yu and Ursell (J. Fluid Mech. 1961; 11 :529–551). For wave loading on a half‐submerged cylinder the agreement with the experimental data of Dixon et al. (J. Waterway Port Coastal Ocean Div. 1979; 105 :421–438) for the root mean square force is within 2%. For more submerged cases, the results show some discrepancy, but this was also found with other modelling approaches. The sensitivity of results to the value of the slope limiter used in the MUSCL‐based Riemann solver is demonstrated. The variable mass distribution leads to a computer run speedup of nearly 200% in these cases. Copyright © 2011 John Wiley & Sons, Ltd.     

Study on optical characterization of TGB and reentrant smectic-A phases in binary mixture of two liquid crystals

In this work, our investigation is to study the optical and thermal properties of the binary mixture of cholesteric and nematic compounds, namely, cholesteryl nonanoate and p-methoxybenzylidene-p-ethylaniline, which exhibits a very interesting liquid crystalline twisted grain boundary (TGB) phase and reentrant smectic-A phase. The chiral liquid crystalline TGB phases and reentrant smectic-A phases have been observed at different concentrations and at different temperatures. The existence of TGB and reentrant smectic-A phases is confirmed by differential scanning calorimetry and optical microscopic studies. The variation of optical anisotropy has been discussed. The helical pitch of the cholesteric phase has also been discussed.     

Effect of a lateral methyl group on azo-mesogens containing the naphthalene moiety

Two mesogenic homologous series, 2-[4-(4-n-alkoxybenzoyloxy)-2-methylphenylazo]-naphthalenes (I) and 2-[4-(4-n-alkoxybenzoyloxy)-3-methylphenylazo]naphthalenes (II) with a lateral methyl group have been synthesized. Both series are purely nematogenic. The mesomorphic properties of both series are compared with each other and also with the properties of other structurally related series to evaluate the effect of the lateral methyl group on mesomorphism. The chiral nematic (N*) mesophase was induced in the system by doping with a derivative of naturally occurring chiral menthol.     

New insights into the transitional behaviour of methyl-6-O-(n-dodecanoyl)-α-D-glucopyranoside using variable temperature FTIR spectroscopy and X-ray diffraction

The liquid crystalline behaviour of methyl-6-O-(n-dodecanoyl)-α-D-glucopyranoside, 1, has been characterised using X-ray diffraction and variable temperature Fourier transform infrared (FTIR spectroscopy). 1 exhibits a monotropic interdigitated smectic A phase consisting of bilayers in which the alkyl chains are overlapped. The crystal–isotropic transition is accompanied by a pronounced decrease in the strength of the hydrogen bonding network involving the sugar groups resulting in a marked change in the environment of the alkyl chains. The isotropic phase consists of disordered smectic-like domains stabilised via hydrogen bonding between the sugar groups. At the transition to the smectic A phase, a subtle change in hydrogen bonding is observed which is manifested by a change in the temperature dependence of the OH stretching peak position in the FTIR spectrum. On crystallisation, the strong hydrogen bonding network is re-established accompanied by a change in the conformational distribution of the alkyl chains. A model is proposed in which a combination of hydrogen bonding (enthalpic effects) and conformational arrangements (entropic effects) promotes initially the formation of smectic-like domains in the isotropic phase and subsequently stabilises the smectic A phase by inhibiting the microphase separation leading to the crystal phase.     

Uncommon suffix tries

Common assumptions on the source producing the words inserted in a suffix trie with n leaves lead to a height and saturation level. We provide an example of a suffix trie whose height increases faster than a power of n and another one whose saturation level is negligible with respect to . Both are built from VLMC (Variable Length Markov Chain) probabilistic sources and are easily extended to families of tries having the same properties. The first example corresponds to a “logarithmic infinite comb” and enjoys a non uniform polynomial mixing. The second one corresponds to a “factorial infinite comb” for which mixing is uniform and exponential. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 117–141, 2015