Finite element approximation of a sixth order nonlinear degenerate parabolic equation

We consider a finite element approximation of the sixth order nonlinear degenerate parabolic equation ut = ?.( b(u)? 2u), where generically b(u) := |u|? for any given ? ? (0,?). In addition to showing well-posedness of our approximation, we prove convergence in space dimensions d ? 3. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. Finally some numerical experiments in one and two space dimensions are presented.

Interactions of decay-accelerating factor (DAF) with haemagglutinating human enteroviruses: utilizing variation in primate DAF to map virus binding sites

A cellular receptor for the haemagglutinating enteroviruses (HEV), and the protein that mediates haemagglutination, is the membrane complement regulatory protein decay accelerating factor (DAF; CD55). Although primate DAF is highly conserved, significant differences exist to enable cell lines derived from primates to be utilized for the characterization of the DAF binding phenotype of human enteroviruses. Thus, several distinct DAF-binding phenotypes of a selection of HEVs (viz. coxsackievirus A21 and echoviruses 6, 7, 11-13, 29) were identified from binding and infection assays using a panel of primate cells derived from human, orang-utan, African Green monkey and baboon tissues. These studies complement our recent determination of the crystal structure of SCR(34) of human DAF [Williams, P., Chaudhry, Y., Goodfellow, I. G., Billington, J., Powell, R., Spiller, O. B., Evans, D. J. & Lea, S. (2003). J Biol Chem 278, 10691-10696] and have enabled us to better map the regions of DAF with which enteroviruses interact and, in certain cases, predict specific virus-receptor contacts.

The structure of echovirus type 12 bound to a two-domain fragment of its cellular attachment protein decay-accelerating factor (CD 55)

Echovirus type 12 (EV12), an enterovirus of the Picornaviridae family, uses the complement regulator, decay-accelerating factor (DAF, CD55) as a cellular receptor. We have calculated a three-dimensional reconstruction of EV12 bound to a fragment of DAF, consisting of short consensus repeat domains 3 and 4, from cryo-negative stain electron microscopy data (EMD #1057). This shows that, as for an earlier reconstruction of the related echovirus type 7 bound to DAF, attachment is not within the viral canyon but occurs close to the two-fold symmetry axes. Despite this general similarity, our reconstruction reveals a receptor interaction that is quite different from that observed for EV7. Fitting of the crystallographic co-ordinates for DAF34 and EV11 into the reconstruction shows a close agreement between the crystal structure of the receptor fragment and the density for the virus-bound receptor, allowing unambiguous positioning of the receptor with respect to the virion (PDB #1UPN). Our finding that the mode of virus-receptor interaction in EV12 is distinct from that seen for EV7 raises interesting questions regarding the evolution and biological significance of the DAF-binding phenotype in these viruses.

Mapping CD55 function: the structure of two pathogen-binding domains at 1.7 A

Decay-accelerating factor (CD55), a regulator of the alternative and classical pathways of complement activation, is expressed on all serum-exposed cells. It is used by pathogens, including many enteroviruses and uropathogenic Escherichia coli, as a receptor prior to infection. We describe the x-ray structure of a pathogen-binding fragment of human CD55 at 1.7 A resolution containing two of the three domains required for regulation of human complement. We have used mutagenesis to map biological functions onto the molecule; decay-accelerating activity maps to a single face of the molecule, whereas bacterial and viral pathogens recognize a variety of different sites on CD55.

Movement time for motion-impaired users assisted by force-feedback: effects of movement amplitude, target width and gravity well width

This paper presents a study investigating how the performance of motion-impaired computer users in point and click tasks varies with target distance (A), target width (W), and force-feedback gravity well width (GWW). Six motion-impaired users performed point and click tasks across a range of values for A, W, and GWW. Times were observed to increase with A, and to decrease with W. Times also improved with GWW, and, with the addition of a gravity well, a greater improvement was observed for smaller targets than for bigger ones. It was found that Fitts Law gave a good description of behaviour for each value of GWW, and that gravity wells reduced the effect of task difficulty on performance. A model based on Fitts Law is proposed, which incorporates the effect of GWW on movement time. The model accounts for 88.8% of the variance in the observed data.

Condensed tannins act against cattle nematodes

The use of natural plant anthelmintics was suggested as a possible alternative control of gastrointestinal nematodes (GIN) in ruminants. Direct anthelmintic effects of tannin-containing plants have already been shown in sheep and goat GIN. These anthelmintic properties are mainly associated with condensed tannins. In the present study, we evaluated possible in vitro effects of three tannin-containing plants against bovine GIN. Effects of Onobrychis viciifolia, Lotus pedunculatus and Lotus corniculatus condensed tannin (CT) extracts on Cooperia oncophora and Ostertagia ostertagi were determined by a larval feeding inhibition assay (LFIA) and a larval exsheathment assay (LEA). In the LFIA, all three plant extracts significantly inhibited larval feeding behaviour of both C. oncophora and O. ostertagi first stage larvae in a dose-dependent manner. The L. pedunculatus extract, based on EC50 (effective concentration for 50% inhibition), was the most effective against both nematodes, followed by O. viciifolia and L. corniculatus. The effect of CT extracts upon larval feeding behaviour correlates with CT content and procyanidin/prodelphidin ratio. Larval exsheathment of C. oncophora and O. ostertagi L3 larvae (third stage larvae) was also affected by CT extracts from all three plants. In both in vitro assays, extracts with added polyvinylpolypyrrolidone, an inhibitor of tannins, generated almost the same values as the negative control; this confirms the role of CT in the anthelmintic effect of these plant extracts. Our results, therefore, indicated that tannin-containing plants could act against cattle nematodes.

Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation

We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the $L^2$ condition numbers for these formulations, and also on the norms of the classical acoustic single- and double-layer potential operators. These bounds to some extent make explicit the dependence of condition numbers on the wave number $k$, the geometry of the scatterer, and the coupling parameter. For example, with the usual choice of coupling parameter they show that, while the condition number grows like $k^{1/3}$ as $k\to\infty$, when the scatterer is a circle or sphere, it can grow as fast as $k^{7/5}$ for a class of `trapping' obstacles. In this paper we prove further bounds, sharpening and extending our previous results. In particular we show that there exist trapping obstacles for which the condition numbers grow as fast as $\exp(\gamma k)$, for some $\gamma>0$, as $k\to\infty$ through some sequence. This result depends on exponential localisation bounds on Laplace eigenfunctions in an ellipse that we prove in the appendix. We also clarify the correct choice of coupling parameter in 2D for low $k$. In the second part of the paper we focus on the boundary element discretisation of these operators. We discuss the extent to which the bounds on the continuous operators are also satisfied by their discrete counterparts and, via numerical experiments, we provide supporting evidence for some of the theoretical results, both quantitative and asymptotic, indicating further which of the upper and lower bounds may be sharper.

A high frequency boundary element method for scattering by convex polygons with impedance boundary conditions

We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions. Standard finite or boundary element methods require the number of degrees of freedom to grow at least linearly with respect to the frequency of the incident wave in order to maintain accuracy. Extending earlier work by Chandler-Wilde and Langdon for the sound soft problem, we propose a novel Galerkin boundary element method, with the approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh with smaller elements closer to the corners of the polygon. Theoretical analysis and numerical results suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency of the incident wave.