Rational matrix approximation with a priori error bounds for non-symmetric matrix Riccati equations with analytic coefficients

In this paper the exact solution of the non-symmetric matrixRiccati equation with analytic coefficients is approximatedby a rational matrix function with a prefixed accuracy. Thisrational matrix function is locally defined as the exact solutionof a Riccati problem with matrix polynomial coefficients obtainedby truncation of the Taylor expansions of the matrix coefficientsof the original problem.     

High-temperature organic reactions at room temperature using plasmon excitation: decomposition of dicumyl peroxide

Photoexcitation of gold nanoparticles in their plasmon transition around 530 nm provides the means to carry high-energy reactions at room temperature. In the case of dicumyl peroxide (with activation energy of 34.3 kcal/mol) the reaction occurs in less than 1 min under 532 nm laser excitation. The results suggest that the peroxide is exposed to temperatures of ~500 °C for submicrosecond times, and provides a guide as to which type of organic reactions may benefit from plasmon-mediated energy delivery.     

On the determination of the force distribution in overconstrained cable-driven parallel mechanisms

This paper addresses the determination of the force distribution in the cables of a redundantly actuated cable-driven parallel mechanism. First, the static model of cable-driven parallel mechanisms is derived based on the wrench matrix. Then, four performance indices are considered in order to solve the underdetermined problem associated with the distribution of the forces. A simple numerical example is then developed in order to provide insight into the problem, which leads to a geometric interpretation of the results. Based on the presented results, it is proposed to use a p-norm (e.g. a 4-norm) to optimize the distribution of the forces in a cable-driven parallel mechanism in order to minimize the largest deviations from the median forces (or other target values) while maintaining continuity in the solution. A non-iterative polynomial formulation is then proposed for the 4-norm. It is also pointed out that this formulation leads to a unique real solution.     

Combined compact difference method for solving the incompressible Navier–Stokes equations

This paper presents a numerical method for solving the two‐dimensional unsteady incompressible Navier–Stokes equations in a vorticity–velocity formulation. The method is applicable for simulating the nonlinear wave interaction in a two‐dimensional boundary layer flow. It is based on combined compact difference schemes of up to 12th order for discretization of the spatial derivatives on equidistant grids and a fourth‐order five‐ to six‐alternating‐stage Runge–Kutta method for temporal integration. The spatial and temporal schemes are optimized together for the first derivative in a downstream direction to achieve a better spectral resolution. In this method, the dispersion and dissipation errors have been minimized to simulate physical waves accurately. At the same time, the schemes can efficiently suppress numerical grid‐mesh oscillations. The results of test calculations on coarse grids are in good agreement with the linear stability theory and comparable with other works. The accuracy and the efficiency of the current code indicate its potential to be extended to three‐dimensional cases in which full boundary layer transition happens. Copyright © 2011 John Wiley & Sons, Ltd.     

Anisotropic surface melting in lyotropic cubic crystals

From experiments with metal crystals, in the vicinity of their crystal/liquid/vapor triple points, it is known that melting of crystals starts on their surfaces and is anisotropic. Recently, we have shown that anisotropic surface melting occurs also in lyotropic systems. In our previous paper (Eur. Phys. J. E 19, 223 (2006)), we have focused on the case of poor faceting at the Pn3m/L1 interface in C12EO2/water binary mixtures. There anisotropic melting occurs in the vicinity of a Pn3m/L3/L1 triple point. In the present paper, we focus on the opposite case of a rich devil's-staircase-type faceting at Ia3d/vapor interfaces in monoolein/water and phytantriol/water mixtures. We show that anisotropic surface melting takes place in these systems in a narrow humidity range close to the Ia3d-L2 transition. As whole (hkl) sets of facets disappear one after another when the transition is approached, surface melting occurs in a facet-by-facet type.     

Anisotropic surface melting in lyotropic cubic crystals

From experiments with ice or metal crystals, in the vicinity of their crystal/liquid/vapor triple points, it is known that melting of crystals starts on their surfaces and is anisotropic. It is shown here by direct observations under an optical microscope that this anisotropic surface melting phenomenon occurs also in lyotropic systems. In the case of C12EO2/water mixture, it takes place in the vicinity of the peritectic Pn3m/L3/L1 triple point. Above the peritectic triple point, where the Pn3m and L1 phases coexist in the bulk, the surface of a Pn3m-in-L1 crystal is composed of (111)-type facets surrounded by rough surfaces. The angular junction suggests that rough surfaces are wet by a L3-like layer while facets stay “dry”. This is analogous to the pre-melting at rough surfaces in solid crystals. Upon cooling below the peritectic triple point, where L3 and L1 phases coexist in the bulk, a thick layer of the L3 phase grows from the pre-melted, rough Pn3m/L1 interface. Simultaneously, facets stay dry and their radius decreases. In this tri-phasic configuration, stable in a narrow temperature range, the L3/L1 and L3/Pn3m interfaces have shapes of constant mean curvature surfaces having common borders: edges of facets.     

T2 relaxation time histograms in multiple sclerosis

An accurate measurement of the transverse relaxation time T₂, and the histogram of T₂ in the brain parenchyma can be accomplished in vivo using a multi-echo magnetic resonance imaging sequence. An estimate of the error in the T₂ measurement is derived using copper sulfate doped water phantoms. Correction factors are calculated and applied to the signal intensity of each voxel prior to the in vivo T₂ evaluation. These corrected T₂ are in good agreement with the theoretical values calculated from copper sulfate concentrations. This technique is then applied to calculate T₂ histograms of the brain. The population studied was composed of normal volunteers and multiple sclerosis patients. The corrected T₂ histogram method discriminates the normal control population from the MS population, and also discriminates between relapsing-remitting patients and primary progressive or secondary progressive patients. Moreover using this approach we are able to detect in MS patients a global shift of the T₂ of the white mater toward higher values. The results of this study showed that the method is easy to implement and may be used to characterize MS pathology.     

Reaction epoxy-amine: Suivi du mecanisme reactionnel et de la cinetique par RMN 13C, 15N et HPLC

The curing reaction of diglycidyl ether of bisphenol A (DGEBA) with metaphenylene diamine (mPDA) was investigated with high performance liquid chromatography (HPLC) and Fourier transform nuclear magnetic resonance spectroscopy (FT NMR ¹³C and ¹⁵N). With the results obtained from a series of models a mechanism was proposed and the cure kinetics were obtained at 100°C. The major conclusion is that the cure proceeded mainly by chain extension, whereas crosslinking occurred in the reaction of hydroxyl groups with epoxides and resulted in the formation of ether linkages.     

Cooperative ordering of gapped and gapless spin networks in Cu2Fe2Ge4O13

The unusual magnetic properties of a novel low-dimensional quantum ferrimagnet Cu2Fe2Ge4O13 are studied using bulk methods, neutron diffraction, and inelastic neutron scattering. It is shown that this material can be described in terms of two low-dimensional quantum spin subsystems, one gapped and the other gapless, characterized by two distinct energy scales. Long-range magnetic ordering observed at low temperatures is a cooperative phenomenon caused by weak coupling of these two spin networks.     

Enantiomeric Distribution Studies of Linalool and Linalyl Acetate. A Powerful Tool for Authenticity Control of Essential Oils

The enantiomeric distributions of linalool and linalyl acetate in various natural products are measured by enantioselective gas chromatography on alkyl-substituted cyclodextrins. Different plant cultivars were investigated by four extraction processes: steam distillation, solvent extraction, supercritical fluid extraction, and headspace analysis. Careful attention must be paid to linalool which undergoes partial racemization under certain processing conditions. In most cases, enantiomeric distribution is a powerful tool for authenticity testing.