Practical techniques for a three‐dimensional FEM analysis of incompressible fluid flow contained with slip walls and a downstream tube bundle

Two practical techniques are proposed in this paper to simulate a flow contained in a plenum with a downstream tube bundle under a PC environment. First, a technique to impose slip wall conditions on smooth‐faced planes and sharp edges is proposed to compensate for the mesh coarseness relative to boundary layer thickness. In particular, a new type of Poisson equation is formulated to simultaneously satisfy both such velocity boundary conditions on walls and the incompressibility constraint. Second, a numerical model for a downstream tube bundle is proposed, where hydraulic resistance in a tube is imposed as a traction boundary condition on a fluid surface contacting the tube bundle end. The effectiveness of the techniques is numerically demonstrated in the application to a flow in a condenser water box. Copyright © 2001 John Wiley & Sons, Ltd.     

A new positive‐definite regularization of incompressible Navier–Stokes equations discretized with Q1/P0 finite element

A new regularization method is proposed for the Galerkin approximation of the incompressible Navier–Stokes equations with Q1/P0 element, by newly introducing a square‐type linear form into the variational divergence‐free constraint regularized with the global pressure jump (GPJ) method. The addition of the square‐type linear form is intended to eliminate the hydrostatic pressure mode appearing in confined flows, and to make the discretized matrix positive definite and then non‐singular without the pressure pegging trick. Effects of the free parameters for the regularization on the solutions are numerically examined with a 2‐D driven cavity flow problem. Furthermore, the convergences in the conjugate gradient iteration for the solution of the pressure Poisson equation are compared among the mixed method, the GPJ method and the present method for both leaky and non‐leaky 3‐D driven cavity flows. Finally, the non‐leaky 3‐D cavity flows at different Re numbers are solved to compare with the literature data and to demonstrate the accuracy of the proposed method. Copyright © 2003 John Wiley & Sons, Ltd.     

On streamline diffusion arising in Galerkin FEM with predictor/multi‐corrector time integration

In the present paper, the author shows that the predictor/multi‐corrector (PMC) time integration for the advection–diffusion equations induces numerical diffusivity acting only in the streamline direction, even though the equations are spatially discretized by the conventional Galerkin finite element method (GFEM). The transient 2‐D and 3‐D advection problems are solved with the PMC scheme using both the GFEM and the streamline upwind/Petrov Galerkin (SUPG) as the spatial discretization methods for comparison. The solutions of the SUPG‐PMC turned out to be overly diffusive due to the additional PMC streamline diffusion, while the solutions of the GFEM‐PMC were comparatively accurate without significant damping and phase error. A similar tendency was seen also in the quasi‐steady solutions to the incompressible viscous flow problems: 2‐D driven cavity flow and natural convection in a square cavity. Copyright © 2002 John Wiley & Sons, Ltd.     

Baseline noise and measurement uncertainty in liquid chromatography.

The stochastic properties of baseline noise in HPLC systems with a UV photo-diode array, photo-multiplier and gamma-ray detector were examined by dividing the noise into auto-correlated random process (Markov process) and an independent process (white noise). The present work focused on the effect of the stochastic noise properties on a theoretical estimation of the standard deviation (SD) of area measurements in instrumental analyses. An estimation theory, called FUMI theory (Function of Mutual Information), was taken as an example. A computer simulation of noise was also used. It was shown that the reliability (confidence intervals) of theoretical SD estimates mainly depends on the following factors: the ratio of the white noise and Markov process occurring in the baselines; the number of data points used for the estimation; the width of a target peak for which the SD is estimated.     

Labelless impedance immunosensor based on polypyrrole-pyrolecarboxylic acid copolymer for hCG detection

In this work, a sensitive label-free impedimetric hCG-immunosensor was constructed by using a commercial screen-printing carbon ink electrode (namely disposable electrochemical printed chip) as the basis. The carbon ink electrode of DEP chip is modified first by deposition of polypyrrole-pyrole-2-carboxylic acid copolymer and thence hCG antibody immobilization via the COOH groups of pyrrole-2-carboxylic acid, which can serve as a linker for covalent biomolecular immobilization. The experimental results exposed that the designed immunosensor is more sensitive than other previously reported immunosensors, in the case of detection limit and linear range for antigen detection. With optimal fabrication parameters, the detection limit for α-hCG was 2.3 pg/mL in 10 mM phosphate buffer saline (PBS) solution containing 1% bovine serum albumine (BSA). Moreover, the use of inexpensive DEP chip as a basis for these immunosensors will allow for simple instrumentation, disposable and portable at low cost. This work also demonstrates a new approach to develop a sensitive and label-free impedimetric immunosensor based on screen-printed electrode for applications in clinical diagnosis.     

Proton transport properties of poly(aspartic acid) with different average molecular weights

We synthesized seven partially protonated poly(aspartic acids)/sodium polyaspartates (P-Asp) with different average molecular weights to study their proton transport properties. The number-average degree of polymerization (DP) for each P-Asp was 30 (P-Asp30), 115 (P-Asp115), 140 (P-Asp140), 160 (P-Asp160), 185 (P-Asp185), 205 (P-Asp205), and 250 (P-Asp250). The proton conductivity depended on the number-average DP. The maximum and minimum proton conductivities under a relative humidity of 70% and 298 K were 1.7 · 10^?3 S cm^?1 (P-Asp140) and 4.6 · 10^?4 S cm^?1 (P-Asp250), respectively. Differential thermogravimetric analysis (TG-DTA) was carried out for each P-Asp. The results were classified into two categories. One exhibited two endothermic peaks between t = (270 and 300) °C, the other exhibited only one peak. The P-Asp group with two endothermic peaks exhibited high proton conductivity. The high proton conductivity is related to the stability of the polymer. The number-average molecular weight also contributed to the stability of the polymer.     

Laplace's method for the laws of heat processes on loop spaces

In this paper, we will consider Laplace's method for a class of heat processes on loop spaces. We will obtain the first term of the asymptotics under assumptions that the function under consideration attains its minimum at a unique point and that the Hessian at the point is non-degenerate. This kind of process was first introduced by P. Malliavin in 1990 for the loop group case and then gradually generalized by various authors. Our tool is the rough path theory of T. Lyons. This technique was pioneered by S. Aida for finite-dimensional processes in his unpublished paper.     

Detection limit estimated from slope of calibration curve: an application to competitive ELISA.

This paper theoretically derives a general rule that while the slope of the semi-logarithmic plot (Y vs. log X) of a calibration curve varies depending on analyte concentration, X, the slope takes a specific value at the detection limit (L(D)). This rule holds good irrespective of the shape of the calibration curve (linear or non-linear) and in this paper, is applied to competitive ELISA (enzyme linked immunosorbent assay). The following relationship is deduced: slope of log-dose B/B0 at L(D) = [relative standard deviation (RSD) of blank responses] / 0.13. The L(D) obtained from the above-mentioned slope corresponds to the dose at which the RSD of dose estimates is 0.3 (= 30%). A commercial kit for 17alpha-hydroxyprogesterone is taken as an example.     

A novel synthesis of alkyl phenylsulfinates

Alkyl phenylsulfinates (Ph-SO-OR) were prepared from thiophenol (or diphenyldisulfide) by electrolysis in acetic acid with alcohols and sodium acetate in satisfactory yields.