Characterization of supercommuting matrices

For a given n-by-n matrix A, we consider the set of matrices which commute with A and all of whose principal submatrices commute with the corresponding principal submatrices of A. The properties of this set are examined, with particular attention to its dimension.     

The influence of the liquid crystalline core geometry on the mesogenicity of novel chiral 2-(4-substituted-phenoxy)propanonitriles

The synthesis and characterization of seven novel (R)-2-(4-substituted-phenoxy)propanonitriles are described. The propanonitriles were prepared to evaluate their potential use as thermochromics and ferroelectric dopants, as well as to determine their twist sense properties. The materials exhibit smectic and chiral nematic phases of high thermal stability; the mesogenic behaviour of the nitriles is directly related to the type of two-ring core unit employed. The effects of the different molecular geometries and polarizabilities of the liquid crystalline cores on mesophase stability are discussed, particularly in relation to other members of this series. The chiral nematic phase of the propanonitriles is assigned as having a left-handed twist sense from contact preparation studies, and this is in agreement with rules relating absolute configuration and molecular structure to helical twist sense.     

Influence of Particle Morphology and Flow Conditions on the Dispersion Behavior of Fumed Silica in Silicone Polymers

The dispersion behavior of agglomerates of several grades of fumed silica in poly(dimethyl siloxane) liquids has been studied as a function of particle morphology and applied flow conditions. The effects of primary particle size and aggregate density and structure on cohesivity were probed through tensile and shear strength tests on particle compacts. These cohesivity tests indicated that the shear strength of particle compacts was two orders of magnitude higher than the tensile strength at the same overall packing density. Experiments carried out in both steady and time‐varying simple‐shear flows indicate that dispersion occurs through tensile failure. In the steady‐shear experiments,enhanced dispersion was obtained at higher levels of applied stress and, at comparable levels of applied stress, dispersion was found to proceed faster at higher shear rates. Experiments conducted in time‐varying flows further corroborated the results obtained in tensile cohesivity tests. Experiments in which the mean and maximum stresses in the time‐varying flows were matched to the stresses produced in steady shear flows highlight the influence of flow dynamics on dispersion behavior.     

Influence of concentration on the activation energy for diffusion in polymer-solvent systems

The self-diffusion of benzene, toluene, and ethylbenzene in polystyrene have been analyzed using the Vrentas/Duda free-volume diffusion model. Diffusion coefficient predictions suggest an exponential concentration dependence of the activation energy required to overcome attractive forces, E. Without the use of any diffusion data approximating E as zero over the entire concentration range yields self-diffusion coefficient predictions which are in good agreement with experimental data. © 1992 John Wiley & Sons, Inc.     

Synchronization Analysis of Coupled Noncoherent Oscillators

We present two different approaches to detect and quantify phase synchronization in the case of coupled non-phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the R?ssler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators.     

Numerical simulation on an interaction of a vortex street with an elliptical leading edge using an unstructured grid

An algorithm for a time accurate incompressible Navier–Stokes solver on an unstructured grid is presented. The algorithm uses a second order, three‐point, backward difference formula for the physical time marching. For each time step, a divergence free flow field is obtained based on an artificial compressibility method. An implicit method with a local time step is used to accelerate the convergence for the pseudotime iteration. To validate the code, an unsteady laminar flow over a circular cylinder at a Reynolds number of 200 is calculated. The results are compared with available experimental and numerical data and good agreements are achieved. Using the developed unsteady code, an interaction of a Karman vortex street with an elliptical leading edge is simulated. The incident Karman vortex street is generated by a circular cylinder located upstream. A clustering to the path of the vortices is achieved easily due to flexibility of an unstructured grid. Details of the interaction mechanism are analysed by investigating evolutions of vortices. Characteristics of the interactions are compared for large‐ and small‐scale vortex streets. Different patterns of the interaction are observed for those two vortex streets and the observation is in agreement with experiment. Copyright © 2004 John Wiley & Sons, Ltd.     

3,4‐[2,2‐Bis(methoxyethoxymethoxymethyl)propylenedithio]‐3′,4′‐(ethylenedithio)tetrathiafulvalene: a spiro‐substituted BEDT–TTF analogue

The crystal structure of the title compound [systematic name: 2‐(1,3‐dithiolo[4,5‐b][1,4]dithiin‐2‐ylidene)‐6,6‐bis(methoxyethoxymethoxymethyl)‐1,3‐dithiolo[4,5‐b][1,4]dithiepine], C₂₁H₃₀O₆S₈, a spiro‐substituted BEDT–TTF analogue [BEDT–TTF is bis(ethylenedithio)tetrathiafulvalene], has a strongly bent heterocyclic framework. The seven‐membered ring adopts a pseudo‐chair conformation with notably widened ring bond angles, especially at the methylene C atoms [119.49 (11) and 117.60 (11)°]. The axial side chain adopts an extended conformation, but the equatorial side chain curls back on itself and the O atom nearest the ring system is involved in three short contacts to H atoms (2.45–2.53 Å). The molecules pack in centrosymmetrically related pairs, which are isolated from each other by columns of the polyether side chains. This study emphasizes the ease of distortion of the neutral bis(propylenedithio)tetrathiafulvalene ring structure, and how the need to accommodate side chains can easily override the tendency of these donor systems to form stacks in the crystalline state.     

Synthesis and characterization of novel polyimides with 2,2‐bis[4(4‐aminophenoxy)phenyl]phthalein‐3′,5′‐bis(trifluoromethyl)anilide

2,2‐Bis[4(4‐aminophenoxy)phenyl]phthalein‐3′,5′‐bis(trifluoromethyl)anilide (6FADAP), containing fluorine and phthalimide moieties, was synthesized via the Williamson ether condensation reaction from 1‐chloro‐4‐nitrobenzene and phenolphthalein‐3′,5′‐bis(trifluoromethyl)anilide, which was followed by hydrogenation. Monomers such as 2,2‐bis[4(4‐aminophenoxy)phenyl]phthalein‐anilide containing phthalimide groups and 2,2‐bis[4(4‐aminophenoxy)phenyl]phthalein containing only phthalein moieties were also synthesized for comparison. The monomers were first characterized by Fourier transform infrared (FTIR), ¹H NMR, ¹⁹F NMR, elemental analysis, and titration and were then used to prepare polyimides with 2,2‐bis(3,4‐dicarboxyphenyl)hexafluoropropane dianhydride. The polyimides were designed to have molecular weights of 20,000 g/mol via off‐stoichiometry and were characterized by FTIR, NMR, gel permeation chromatography (GPC), differential scanning calorimetry, and thermogravimetric analysis. Their solubility, water absorption, dielectric constant, and refractive index were also evaluated. The polyimides prepared with 6FADAP, containing fluorine and phthalimide moieties, had excellent solubility in N‐methylpyrrolidinone, N,N‐dimethylacetamide, tetrahydrofuran, CHCl₃, tetrachloroethane, and acetone, and GPC analysis showed a molecular weight of 18,700 g/mol. The polyimides also exhibited a high glass‐transition temperature (290 °C), good thermal stability (～500 °C in air), low water absorption (1.9 wt %), a low dielectric constant (2.81), a low refractive index, and low birefringence (0.0041). © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3361–3374, 2003     

The comparison of detailed chemical kinetic mechanisms: Application to the combustion of methane

Detailed chemical kinetic mechanisms of complex chemical phenomena may be composed of hundreds of species and thousands of individual elementary reactions. It can be an extremely laborious and error‐prone procedure to compare two of these mechanisms, particularly if they come from different sources. We have created software tools which help to highlight the differences between mechanisms written in a Chemkin format and demonstrate their applicability to five literature mechanisms describing the high temperature oxidation of methane. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36:467–471, 2004