Similarity solutions for immiscible phase migration in porous media: an analysis of free boundaries

A fuel pollutant migrating in a water flow throughout a porous medium is distributed between the moving (continuous) and residual (discontinuous) phases. Usually, there is an equilibrium condition between these phases. In this study, the migration of a fuel slug confied within free boundaries moving in the porous medium is considered. This type of fuel migration pertains to circumstances in which convective fuel transport dominates fuel dispersion when fuel saturation approaches zero. A one-dimensional self-similar model is developed, describing the movement of fuel saturation fronts in a porous medium against and with the water flow direction. Several analytical solutions are found revealing the effects of the pore size, fuel viscosity, fuel mass, and the capillary number on the fuel migration in the porous medium.     

Polymerization of vinyl fluoride initiated by the system silver nitrate–tetraethyl lead

The initiator system AgNO₃–tetraethyl lead was used for the polymerization of vinyl fluoride. Dimethyl sulfoxide was found to have a specific effect on the half-life of the initiating system, which leads to long reaction times and high conversions at ambient temperatures. This effect was explained by the complexing power of DMSO on silver ions, which slows down the rate of formation of AgEt and permits the polymerization to proceed for longer periods than in other solvents. The kinetics of the polymerization agreed with the scheme developed earlier. Tetraethyl lead acts as a powerful chain transfer agent and determines to a large extent the resulting polymers.     

Use of 18O water and ESI-MS detection in subsite characterisation and investigation of the hydrolytic action of an endoglucanase

We present a novel method for investigating subsite-substrate interactions of glycoside hydrolases and the determination of the oligosaccharide cleavage point based on the analysis of the hydrolysis products produced in the presence of ¹⁸O-labelled water. Conventional techniques for such determination of the hydrolysis pattern call for the chemical modification of the substrate, whereas the method presented makes it possible to use natural substrates, utilising the selectivity and sensitivity of mass spectrometry. This method is very useful for the detection and analysis of enzyme-catalysed hydrolysis, provided that the conditions are chosen where ¹⁸O incorporation without the presence of the enzyme is absent or undetectable. Such conditions were found and used in incubations of cellopentaose with the well-characterised endoglucanase Cel5A from Bacillus agaradhaerens. We were able to confirm that the preferred glycoside bond to be hydrolysed is the third one counting from the non-reducing end of the cellopentaose. Thus, cellopentaose prefers to bind from the –3 to the +2 subsites, which is in accordance with published crystallographic data. The main advantage of the method presented is that there is no need for a priori chemical modification/labelling of oligosaccharide substrates, which are processes that can disturb the enzyme–substrate interaction. From ¹⁸O incorporation we could demonstrate that the enzyme also has an oxygen-exchange activity on cellotriose and cellobiose. This is in agreement with the mechanism for transglycosylation and indicates that it is possible for the enzyme to perform such reactions.     

On an Isospectral Lie–Poisson System and Its Lie Algebra

In this paper we analyze the matrix differential system X' = [N,X²], where N is skew-symmetric and X(0) is symmetric. We prove that it is isospectral and that it is endowed with a Poisson structure, and we discuss its invariants and Casimirs. Formulation of the Poisson problem in a Lie-Poisson setting, as a flow on a dual of a Lie algebra, requires a computation of its faithful representation. Although the existence of a faithful representation, assured by the Ado theorem and a symbolic algorithm, due to de Graaf, exists for the general computation of faithful representations of Lie algebras, the practical problem of forming a "tight" representation, convenient for subsequent analytic and numerical work, belongs to numerical algebra. We solve it for the Poisson structure corresponding to the equation X' = [N,X²].     

Liquid chromatography-mass spectrometry analysis of enzyme-hydrolysed carboxymethylcellulose for investigation of enzyme selectivity and substituent pattern

A series of celloendoglucanases: Bacillus agaradhaerens Cel 5a, Humicola insolens Cel 5a, H. insolens Cel 7b, H. insolens Cel 45a, Trichoderma reesei Cel 7b, and T. reesei Cel 45a were used to hydrolyse carboxymethylcellulose (CMC) and the hydrolysis products were investigated with a novel liquid chromatography-mass spectrometry (LC-MS) method. Separation was achieved using a graphitised carbon chromatographic column which allowed the use of electrospay compatible eluents. Analysis of the compounds produced during enzyme hydrolysis of CMC is used to understand enzyme selectivities and substitution pattern of CMC. Conventional high-performance anion-exchange chromatography (HPAEC)-pulsed amperometric detection (PAD), size-exclusion chromatography (SEC)-refractive index (RI) detection, and reducing end analysis are also used to analyse enzyme-hydrolysed CMC. The LC-MS method presented allows for a more detailed investigation of hydrolysis products, which facilitates characterisation of both enzymes and substrates.     

On the numerical quadrature of highly-oscillating integrals I: Fourier transforms

Highly-oscillatory integrals are allegedly difficult to calculate.The main assertion of this paper is that that impression isincorrect. As long as appropriate quadrature methods are used,their accuracy increases when oscillation becomes faster andsuitable choice of quadrature points renders this welcome phenomenonmore pronounced. We focus our analysis on Filon-type quadratureand analyse its behaviour in a range of frequency regimes forintegrals of the form ₀^h f(x)e^{i x} w(x)d x, where h>0 issmall and | | large. Our analysis is applied to modified Magnus methods for highly-oscillatoryordinary differential equations. Received 6 June 2003. Revised 14 October 2003.     

The forbidden (J → J + 1) spectrum of CH4 in the ground vibronic state

The pure rotational R-branch spectrum of CH₄ arising from the centrifugal distortion moment has been studied using a simple 12.10-m light-pipe cell and a conventional interferometer. Ten forbidden (J → J + 1) transitions for J = 7 to J = 16 have been observed in the spectral region 80–200 cm^?1 with a theoretical resolution of 0.5 cm^?1. The integrated intensity of the six strongest lines has been measured and was found to be of the order of twice that calculated from the distortion moment obtained earlier from a molecular beam study of the (J = 2) rotational level. In the approximation that frequency shifts due to this excess intensity are neglible, it has been determined that the rotational constant B₀ = (5.245 ± 0.004) cm^?1 and the scalar distortion constant D_S = (1.19 ± 0.09) × 10^?4 cm^?1. It is argued that the excess intensity is due to higher-order terms in the dipole moment operator and the validity of the frequency analysis is considered in this context.