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.     

A generalized Adadorov theory for anisotropic thin-walled beams

This paper presents a generalized Adadorov theory for anisotropic thin—walled beams. The theory takes account of the shear strain of the middle surface, which exerts a significant influence on the anisotropic thin-walled beams. A new approach is established to solve the governing equations, which have the same form for both open and closed section beams. The numerical examples show that the effects of the shear strain cannot be neglected for this class of beams.This work was part of research project supported by the National Natural Science Foundation of China     

A simple four-node quadrilateral finite element for plates

A simple and accurate four-node quadrilateral finite element based on the Mindlin plate theory and Kirchhoff constraints is presented for general thin plate bending applications. The derivation of the element stiffness properties is straightforward, starting with a specified eight-node interpolation; usual discrete Kirchhoff (DK) constraints are employed to constrain out the four midside nodes of the element. The present resulting DK element passes patch tests with elements of arbitrary and even highly distorted mesh types. Numerical studies of the element convergence behaviours are undertaken for various plate bending problems so far investigated. It is indicated from comparative examples that fairly good convergence characteristics have been achieved.     

Synthesis and studies of antibacterial activity of pongaglabol

Pongaglabol [8-hydroxy-5-phenyl-furo[2,3-h]benzo(b)pyran-7-one] was synthesized and tested for antibacterial effects againstShigella dysenteriae, Salmonella typhi, Streptococcus β-haemolyticus andStaphylococcus aureus. The synthesized compounds were characterized using UV, IR and¹H NMR spectral data     

Kinetics and mechanism of polymerization of methyl methacrylate initiated by stibonium ylide

Homopolymerization of methyl methacrylate (MMA) was carried out in the presence of triphenylstibonium 1,2,3,4-tetraphenyl-cyclopentadienylide as an initiator in dioxane at 65°C±0·l°C. The system follows non-ideal radical kinetics (R _p ∝ [M]^1·4 [I]^0·44 @#@) due to primary radical termination as well as degradative chain-transfer reaction. The overall activation energy and average value ofk ₂ ^p /k _t were 64 kJmol⁻¹ and 0.173 × 10⁻³ 1 mol⁻¹ s⁻¹ respectively     

Kinetics and mechanism of the reactions of hexaaqua rhodium (III) with sulphur (IV) in aqueous medium

An O-bonded sulphito complex, Rh(OH₂)₅(OSO₂H)²⁺, is reversibly formed in the stoppedflow time scale when Rh(OH₂) ₆ ³⁺ and SO₂/HSO ₃ ⁻ buffer (1 <pH< 3) are allowed to react. For Rh(OH₂)₅OH₂₊+ SO₂ □ Rh(OH₂)₅(OSO₂H)²⁺ (k₁/k_-1), k₁ = (2.2 ±0.2) × 10³ dm³ mol⁻¹ s⁻¹, k₋1 = 0.58 ±0.16 s⁻¹ (25°C,I = 0.5 mol dm⁻³). The protonated O-sulphito complex is a moderate acid (K _d = 3 × 10⁻⁴ mol dm⁻³, 25°C, I= 0.5 mol dm⁻³). This complex undergoes (O, O) chelation by the bound bisulphite withk= 1.4 × 10⁻³ s⁻¹ (31°C) to Rh(OH₂)₄(O₂SO)⁺ and the chelated sulphito complex takes up another HSO ₃ ⁻ in a fast equilibrium step to yield Rh(OH₂)₃(O₂SO)(OSO₂H) which further undergoes intramolecular ligand isomerisation to the S-bonded sulphito complex: Rh(OH₂)₃(O₂SO)(OSO₂)^- → Rh(OH₂)₃(O₂SO)(SO₃)⁻ (k _iso = 3 × 10⁻⁴ s⁻¹, 31°C). A dinuclear (μ-O, O) sulphite-bridged complex, Na₄[Rh₂(μ-OH)₂(OH)₂(μ-OS(O)O)(O₂SO)(SO₃) (OH₂)]5H₂O with (O, O) chelated and S-bonded sulphites has been isolated and characterized. This complex is sparingly soluble in water and most organic solvents and very stable to acid-catalysed decomposition     

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.