Numerical approximation of generalized Newtonian fluids using Powell–Sabin–Heindl elements: I. theoretical estimates

In this paper we consider the numerical approximation of steady and unsteady generalized Newtonian fluid flows using divergence free finite elements generated by the Powell–Sabin–Heindl elements. We derive a priori and a posteriori finite element error estimates and prove convergence of the method of successive approximations for the steady flow case. A priori error estimates of unsteady flows are also considered. These results provide a theoretical foundation and supporting numerical studies are to be provided in Part II. Copyright © 2003 John Wiley & Sons, Ltd.     

The reaction pattern of norbornene with excited state carbonyl compounds: Photochemical preparations of norbornene derivatives

We established that acetylacetone and acetone photolytically sensitize norbornene to undergo an efficient radical addition of solvent (ranging from hexane, cyclic ethers, haloalkanes, acetone, alcohols and acetonitrile) across the double bond. In view of its synthetic applicability, sensitized photoreactions of norbornene were reviewed and their mechanisms were compared. Photolysis of acetylacetone in the presence of norbornene in hexane induced i) acetylacetone to cycloadd to norbornene giving the expected 1,5-diketone, and ii) sensitization by triplet excited acetylacetone to generate reactive norbornene, which underwent dimerization as well as the addition of a solvent molecule by radical chain processes. In other solvents, the radical chain addition of solvent dominated the photoreaction, and superseded the cycloaddition, to give excellent to good yields of adducts to norbornene. While the excited species of acetylacetone for the sensitization was deduced to be its spectroscopic triplet excited state, that for the cycloaddition should involve a different one which may be a twisted triplet acetylacetone; sensitization experiments showed that the cycloaddition did not occur from the spectroscopic triplet state. Triplet excited acetone sensitized norbornene to undergo the same solvent addition more efficiently and cleanly than acetylacetone did. In view of various conflicts existing in the proposed energy transfer mechanism, the sensitized norbornene reactions were rationalized with electron transfer and a cation radical chain mechanism.     

Finite element error estimates for non-linear elliptic equations of monotone type

Summary In this paper we shall consider the application of the finite element method to a class of second order elliptic boundary value problems of divergence form and with gradient nonlinearity in the principal coefficient, and the derivation of error estimates for the finite element approximations. Such problems arise in many practical situations — for example, in shock-free airfoil design, seepage through coarse grained porous media, and in some glaciological problems. By making use of certain properties of the nonlinear coefficients, we shall demonstrate that the variational formulations associated with these boundary value problems are well-posed. We shall also prove that the abstract operators accompanying such problems satisfy certain continuity and monotonicity inequalities. With the aid of these inequalities and some standard results from approximation theory, we show how one may derive error estimates for the finite element approximations in the energy norm.     

Temperature anomaly of the Cd hyperfine field in a trivacancy complex in Ni

The temperature dependence of the Cd hyperfine field in a trivacancy complex in Ni between 25 and300 K is reported. It was found that, unlike the Cd substitutional field in Ni which follows the temperature dependence of the magnetization, the Cd hyperfine field in a trivacancy complex is essentially temperature independent. This temperature anomaly is compared with other temperature anomaly of impurity hyperfine fields in ferromagnetic hosts.     

Extraction mechanism of monovalent ion-pairs by polyurethane foams

The extractability sequence of K(+) approximately Rb(+) > Cs(+) > Na(+) > Li(+) for the extraction with polyether foam suggests that the cation chelation mechanism might be operative. However, the same order was obtained for the extraction with 100% polypropylene oxide polyether foam which does not normally adopt a helical structure to form oxygen-rich cavities as easily or as effectively as polyethylene oxide to accommodate alkali metal ions. This result indicates that a hole-size/cation-diameter relationship may not be required for the high extraction of K(+). The extraction of alkali metal DPAs and hydroxides from methanol demonstrates the importance of the solvent effect. It indicates that the water-structure enforced ion-pairing (WSEIP) is the driving force for extraction of the ion-pairs. The extraction mechanism for ionic species can be described as an ion-pair extraction process. The overall effect of ion-pair formation in water and interaction of the extracted ions with foam appears to determine the extractability of the ions of the extractable ion-pair.     

Photoinduced electron transfer across linearly fused oligo-norbornyl structures

The rates of photoinduced electron transfer (ET) reactions across two oligo-norbornyl spacer groups (S), that is, structure 1 fused by two norbornadiene (NBD) units and structure 2 fused by three NBD units, are examined. Substituted naphthalene acted as an electron donor (D), whilst ethylene-1,2-dicarboxylate as an electron acceptor (A). ET rates were measured by fluorescence quenching experiments on these D-S-A dyads, and the results were correlated with reaction free energies according to the Marcus relationship. It was found that naphthalene with phenyl substituents showed relatively slower ET rates. The conformational flexibility of phenyl substituents may cause a hindrance on the electronic coupling between D and A. Another salient feature was the abnormally high quenching rates observed in nonpolar solvents such as cyclohexane, the results of which may be ascribed to a competing energy transfer process.     

Dielectrophoretic force on a sphere near a planar boundary

The small gap distance separating a spherical colloidal particle in electrophoretic motion from a planar nonconducting surface is a required parameter for calculating its electrophoretic mobility. In the presence of an externally applied electric field, this gap distance is determined by balancing the van der Waals, electrical double layer interaction, and gravitational forces with a dielectrophoretic (DEP) force. Here, the DEP force was determined analytically by integration of the Maxwell stress over the surface of the particle. The account of this force showed that its previous omission from the analysis always resulted in underpredicted gap distances. Furthermore, the DEP force dominated under conditions of low particle density or high electric field strength and led to much higher gap distances on the order of a few microns. In one particular case, a combination of low particle density and small particle size produced two possible equilibrium gap distances for the particle. However, the particle was unstable in the second equilibrium position when subjected to small perturbations. In general, larger particles had smaller gap sizes. The effects of four other parameters on gap distance were studied, and gap distances were found to increase with lower particle density, higher electric field strength, higher particle and wall zeta potentials, and lower Hamaker constants. Retardation effects on van der Waals attraction were considered.     

Electrophotographic and microwave photodielectric studies on titanium dioxide pigments in the solid state

In this paper, we report some novel preliminary findings on the photoactivity of titanium dioxide pigments using photoconductive and microwave dielectric techniques. A variety of pigment types were investigated by both methods, including the two crystalline forms of titanium dioxide, anatase and rutile, and a variety of coated pigments. Analysis of the data obtained indicates that there are possible relationships between the photoconductive and photodielectric results, and that these may be used to characterize the pigment types rapidly. Photoconductive measurements were carried out on pigmented films of poly(N-vinylcarbazole) (PVK). Uncoated pigments were found to be more photoconductive than coated pigments with the anatase modification being the more active. It is believed that the pigments act as “trapping” sites to the holes produced by PVK, and that the more photoactive the pigment, the easier it is to regenerate the holes. Various factors influence the band gap of the pigment and these have a significant effect on the photoactivity and photoconductivity of the pigment samples. These include the presence of traps and recombination centres (present as coatings on the surface of the pigment particle) and impurities which can act as acceptors or donors.

Microwave dielectric measurements were carried out on the different anatase and rutile pigments, each exhibiting a different microwave resonant frequency loss depending on the nature of the crystalline modification and the coating. However, on illumination on the pigments with polychromatic light in the microwave cavity, the resonant frequency losses exhibit shifts, the nature of which depend on the pigment type and the coating. Thus the anatase pigments exhibit greater responses than the rutile pigments, particularly with regard to the shift in the resonant frequency values and the change in the Q factor of the resonant peak. The resonant frequency values of the anatase samples are also higher than those obtained for the rutile samples. Furthermore, the frequency shifts are in opposite directions, with the anatase modification exhibiting a more rapid shift to lower frequencies and rutile a slower shift to higher frequencies. It appears that, when the anatase samples are irradiated, their dielectric properties change from those characteristic of a conductor-like material to those of an insulator-like material. However, these changes are reversible once the illumination is terminated. With the rutile samples, irradiation increases the resonant frequency values and hence their dielectric constants. Thus the pigments appear to become more like conductors.     

Impact of prefractionation using Gradiflow on two-dimensional gel electrophoresis and protein identification by matrix assisted laser desorption/ionization-time of flight-mass spectrometry

Prefractionation of protein samples prior to two-dimensional electrophoresis (2-DE) has the potential to increase the dynamic detection range for proteomic analysis. We evaluated a membrane-based electrophoretic separation technique (Gradiflow) for its ability to fractionate an exoproteome sample from the filamentous fungus Trichoderma reesei. The sample was separated on the basis of size and charge. Buffer optimization was found to be necessary for successful size fractionation. Fractionation by charge was used to resolve the sample into four fractions that were subjected to analysis by two-dimensional electrophoresis (2-DE). Enhanced detection of low-abundance proteins with selective removal of high-abundance species was achieved. Fractionated and unfractionated samples were examined for differences in the ability to identify proteins following 2-DE using trypsin in-gel digestion followed by peptide mass fingerprinting using matrix assisted laser desorption/ionization-time of flight-mass spectrometry (MALDI-TOF-MS). Fractionated samples showed marked improvement in protein identification ability and sequence coverage. This study demonstrates the utility of the Gradiflow for fractionation, resulting in an enhancement of resolution and characterization of a moderately complex proteome.