Dynamic behavior classification of a model for a continuous bio-reactor subject to product inhibition

The dynamic behavior of the continuous biological reactor subject to product inhibition is analysed and classified in terms of multiplicity and stability of steady states and existence and stability character of limit cycles. Various boundary conditions are derived which delineate the parameter space into regions of dynamically different behavior. The predicted types of behavior are then illustrated by numerical computation of cells and product concentration trajectories.     

Morphology of Nylon-6 blends with styrenic polymers

The morphology of blends of styrenic polymers in a matrix of 75% Nylon-6 prepared in a Brabender Plasti-Corder was examined by scanning electron microscopy. Styrene/acrylonitrile copolymers (SAN) form smaller particles as the AN level increases owing to the corresponding decrease in the SAN–polyamide interfacial tension. Various styrenic polymers containing functional groups, maleic anhydride or oxazoline type, that can react with Nylon-6 during melt processing were added to the SAN phase which also led to a decrease in the particle size owing to the graft copolymer formed in situ. The effects of functional group type, amount of functional groups per chain, amount of functional polymer added, and the miscibility of the styrene/maleic anhydride (SMA) and SAN copolymers on the morphology of the styrenic phase in the Nylon-6 matrix are described. © 1992 John Wiley & Sons, Inc.     

Analysis of transient wave scattering from an inclusion with an unilateral smoothly contact interface by BEM

Summary A 2D time-domain Boundary Element Method (BEM) is applied to solve the problem of transient scattering of plane waves by an inclusion with a unilateral smooth contact interface. The incident wave is assumed strong enough so that localized separations take place along the interface. The present problem is indeed a nonlinear boundary value problem since the mixed boundary conditions involve unknown intervals (separation and contact regions). In order to determine the unknown intervals, an iterative technique is developed. As an example, we consider the scattering of plane waves by the cross section of a circular cylinder embedded in an infinite solid. Numerical results for the near field solutions are presented. The distortion of the response waves and the variation of the interface states are discussed. The financial support by the China National Natural Science Foundation under Grant No. 19872001 and No. 59878004 is gratefully acknowledged. The second author is also grateful to the support of the National Science Fund for Distinguished Young Scholars under Grant No. 10025211.     

Theoretical study of hydrolysis mechanism of khellin

This paper describes khellin hydrolysis mechanism using semiemperical PM3 implemented in Gaussian 03 package. The calculations show that in the presence of an acidic media, an enolate molecular ion leads directly to ω-acetokhellinone while in the basic media it leads to khellinone.     

Grid‐free surface vorticity method applied to flow induced vibration of flexible cylinders

In order to study cross flow induced vibration of heat exchanger tube bundles, a new fluid–structure interaction model based on surface vorticity method is proposed. With this model, the vibration of a flexible cylinder is simulated at Re=2.67 × 10⁴, the computational results of the cylinder response, the fluid force, the vibration frequency, and the vorticity map are presented. The numerical results reproduce the amplitude‐limiting and non‐linear (lock‐in) characteristics of flow‐induced vibration. The maximum vibration amplitude as well as its corresponding lock‐in frequency is in good agreement with experimental results. The amplitude of vibration can be as high as 0.88D for the case investigated. As vibration amplitude increases, the amplitude of the lift force also increases. With enhancement of vibration amplitude, the vortex pattern in the near wake changes significantly. This fluid–structure interaction model is further applied to simulate flow‐induced vibration of two tandem cylinders and two side‐by‐side cylinders at similar Reynolds number. Promising and reasonable results and predictions are obtained. It is hopeful that with this relatively simple and computer time saving method, flow induced vibration of a large number of flexible tube bundles can be successfully simulated. Copyright © 2004 John Wiley & Sons, Ltd.     

Thickness decrease of a grafted polyelectrolyte membrane exposed to shear flow

The effect of the shear flow on the thickness change of a polyelectrolyte membrane grafted onto a glass substrate was directly investigated with a flow cell combined with a confocal laser scanning microscope. The membrane thickness decreased proportionally to an increase in the shear stress of the flow when the shear rate exceeded a critical value of 1 s^?1. The higher the ionic strength was of the fluid, the greater the thinning effect was. The correlation between the critical shear rate and the relaxation of the polymer in the gel membrane was examined. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2808–2815, 2003     

Isospectral theory of Euler equations

Isospectral problem of both 2D and 3D Euler equations of inviscid fluids, is investigated. Connections with the Clay problem are described. Spectral theorem of the Lax pair is studied.     

The Spectrum of a Linearized 2D Euler Operator

We study the spectral properties of the linearized Euler operator obtained by linearizing the equations of incompressible two-dimensional fluid at a steady state with the vorticity that contains only two nonzero complex conjugate Fourier modes. We prove that the essential spectrum coincides with the imaginary axis, and give an estimate from above for the number of isolated nonimaginary eigenvalues. In addition, we prove that the spectral mapping theorem holds for the group generated by the linearized 2D Euler operator.     

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