Efficient stochastic FEM for flow in heterogeneous porous media. Part 1: random Gaussian conductivity coefficients

This paper is concerned with the development of efficient iterative methods for solving the linear system of equations arising from stochastic FEMs for single‐phase fluid flow in porous media. It is assumed that the conductivity coefficient varies randomly in space according to some given correlation function and is approximated using a truncated Karhunen–Loève expansion. Distinct discretizations of the deterministic and stochastic spaces are required for implementations of the stochastic FEM. In this paper, the deterministic space is discretized using classical finite elements and the stochastic space using a polynomial chaos expansion. The highly structured linear systems which result from this discretization mean that Krylov subspace iterative solvers are extremely effective. The performance of a range of preconditioned iterative methods is investigated and evaluated in terms of robustness with respect to mesh size and variability of the conductivity coefficient. An efficient symmetric block Gauss–Seidel preconditioner is proposed for problems in which the conductivity coefficient has a large standard deviation.The companion paper, herein, referred to as Part 2, considers the situation in which Gaussian random fields are transformed into lognormal ones by projecting the truncated Karhunen–Loève expansion onto a polynomial chaos basis. This results in a stochastic nonlinear problem because the random fields are represented using polynomial chaos containing terms that are generally nonlinear in the random variables. Copyright © 2013 John Wiley & Sons, Ltd.     

Modal and characteristics-based approaches for modeling elastic waves induced by time-dependent boundary conditions

In this paper, we present a characteristics-based approach for solving elastic wave problems with time-dependent traction boundary conditions. A generalized mathematical model for this important class of problems is expressed as a set of first-order, linear, hyperbolic partial differential equations. We analyze the mathematical structure of this first-order linear system, verify its hyperbolicity, derive its characteristic form, and deduce its eigenvalues, eigenvectors, and Riemann invariants. The eigenvalues correspond to the wave speeds, while the Riemann invariants are used to construct a solution by the method of characteristics.     

Nucleophilic imidoesterification of dicarbonyl compounds with cyanatobenzenes through C-C bond formation

Under neat conditions,an efficient method for synthesis of imidoesters has been developed using cyanatobenzenes and dicarbonyl compounds.Nucleophilic addition spontaneously occurred between the two kinds of materials at room temperature with yields of up to 90%.A mechanism directed towards to the imidoester formation has been proposed.     

Synthesis and mesomorphic properties of some fluorinated phenyl 4-[(4-n-alkoxyphenyl)ethynyl]benzoates

Eight homologous series of fluorinated phenyl 4-[(4-n-alkoxyphenyl)ethynyl]benzoates have been synthesized. Textural observations by polarizing microscopy and DSC measurements of the phase transitions show that most of these compounds are thermotropic liquid crystals with nematic and smectic A phases; furthermore, several show monotropic high order smectic phases. The results showed that the SmA phase is enhanced with increasing degree of fluorosubstitution on the para- and meta-positions of the terminal phenyl groups. The mesomorphic properties of these compounds are also affected by the direction of ester bonds. The effect of triple bonds is also discussed.     

Determination of chikusetsusaponin V and chikusetsusaponin IV in rat plasma by liquid chromatography–mass spectrometry and its application to a preliminary pharmacokinetic study

A sensitive liquid chromatography–electrospray ionization–mass spectrometry method has been developed and validated for determination of two major bioactive saponins in rat plasma after oral administration of saponins extracted from Rhizoma Panacis Japonici, including chikusetsusaponin V and chikusetsusaponin IV for the first time. Akebia saponin D was used as the internal standard (IS). Plasma samples were prepared by protein precipitation with methanol. A Phenomenex C₁₈ column (150 × 4.6 mm, 4 µm) was used as the analytical column with a mobile phase of acetonitrile and 0.05% aqueous formic acid. Mass spectrometric detection was achieved by single quadrupole mass spectrometer equipped with an electrospray ionization interface operating in negative ionization mode. Calibration curves showed good linearity over the concentration range of 5–500 ng/mL for the two analytes in rat plasma. The lower limit of quantification was 5 ng/mL. The intra‐ and inter‐batch precisions were within 10.3% and accuracy ranged from ?3.9 to 5.4%. The method was validated and successfully applied to the preliminary pharmacokinetic study of chikusetsusaponin V and chikusetsusaponin IV in rat plasma after oral administration of saponins extracted from Rhizoma Panacis Japonici. Copyright © 2013 John Wiley & Sons, Ltd.