Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time. The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

Mean flow and turbulence statistics over groups of urban-like cubical obstacles

Direct numerical simulations of turbulent flow over regular arrays of urban-like, cubical obstacles are reported. Results are analysed in terms of a formal spatial averaging procedure to enable interpretation of the flow within the arrays as a canopy flow, and of the flow above as a rough wall boundary layer. Spatial averages of the mean velocity, turbulent stresses and pressure drag are computed. The statistics compare very well with data from wind-tunnel experiments. Within the arrays the time-averaged flow structure gives rise to significant 'dispersive stress' whereas above the Reynolds stress dominates. The mean flow structure and turbulence statistics depend significantly on the layout of the cubes. Unsteady effects are important, especially in the lower canopy layer where turbulent fluctuations dominate over the mean flow.

The role of protecting groups in the formation of organogels through a nano-fibrillar network formed by self-assembling terminally protected tripeptides

A series of eight synthetic self-assembling terminally blocked tripeptides have been studied for gelation. Some of them form gels in various aromatic solvents including benzene, toluene, xylene, and chlorobenzene. It has been found that the protecting groups play an important role in the formation of organogels. It has been observed that, if the C-terminal has been changed from methyl ester to ethyl ester the gelation property does not change significantly (keeping the N-terminal protecting group same), while the change of the protecting group from ethyl ester to isopropyl ester completely abolishes the gelation property. Similarly, keeping the identical C-terminal protecting group (methyl ester) the results of the gelation study indicate that the substitution of N-terminal protection Boc-(tert-butyloxycarbonyl) to Cbz-(benzyloxycarbonyl) does change the gelation property insignificantly, while the change from Boc- to pivaloyl (Piv-) or acetyl (Ac-) group completely eliminates the gelation property. Morphological studies of the dried gels of two of the peptides indicate the presence of an entangled nano-fibrillar network that might be responsible for gelation. FTIR studies of the gels demonstrate that an intermolecular hydrogen bonding network is formed during gelation. Results of X-ray powder diffraction studies for these gelator peptides in different states (dried gels, gel, and bulk solids) reflected that the structure in the wet gel is distinctly different from the dried gel and solid state structures. Single crystal X-ray diffraction studies of a non-gelator peptide, which is structurally similar to the gelator molecules reveal that the peptide forms an antiparallel beta-sheet structure in crystals. (c) 2007 Elsevier Ltd. All rights reserved.

Thermally responsive elastomeric supramolecular polymers featuring flexible aliphatic hydrogen-bonding end-groups

The present paper details the synthesis, characterization, and preliminary physical analyses of a series of polyisobutylene derivatives featuring urethane and urea end-groups that enable supramolecular network formation to occur via hydrogen bonding. These polymers are readily accessible from relatively inexpensive and commercially available starting materials using a simple two-step synthetic approach. In the bulk, these supramolecular networks were found to possess thermoreversible and elastomeric characteristics as determined by temperature-dependent rheological analysis. These thermoreversible and elastomeric properties make these supramolecular materials potentially very useful in applications such as adhesives and healable surface coatings.

One-pot synthesis and characterization of soluble poly(aryl ether-ketone)s having pendant carboxyl groups

Aromatic poly(ether-ketone)s having pendant carboxyl groups have been obtained by direct, one-pot, Friedel-Crafts copolycondensation of 4,4'-diphenoxybenzophenone with a mixture of terephthaloyl chloride (TC) and trimellitic anhydride acid chloride (TAAC), over a wide range of TAAC/TC molar ratios, in the presence of anhydrous aluminum chloride. The syntheses were performed as precipitation-polycondensations, and the polymers were obtained in particulate form. Besides globular particles of polymer, small quantities of elongated, needlelike particles were observed when the mole ratio TAAC/TC was less than 1. Use of X-ray microdiffraction with synchrotron radiation has revealed that the needlelike material consists of a cyclic compound containing 10 phenylene units, i.e., the crystals are of a [2 + 2] macrocyclic dimer. The polymers obtained are soluble in strong acids and in mixtures of methanesulfonic acid or trifluoroacetic acid with chlorinated hydrocarbons. The molecular structures of the polymers were confirmed by H-1 and C-13 NMR spectroscopy. Reaction of TAAC with 4,4'-diphenoxybenzophenone produced mainly meta-orientation of the resulting ketone linkages. The size of the polymer particles, their molecular weights, and the melting behavior of the products obtained depend on the TAAC/TC ratio used. Ortho-keto acid residues, formed during reaction of anhydride groups of TAAC with 4,4'-diphenoxybenzophenone, exhibit ring-chain tautomerism. A carboxyl-containing aromatic polyketone derived from p-terphenyl, and thus having with no ether linkages in the main chain, was prepared by analogous chemistry, and functional derivatives of carboxy-substituted polyketones were also obtained and characterized.

Finite element aided design evolution of composite leaf spring

This paper shows the process of the virtual production development of the mechanical connection between the top leaf of a dual composite leaf spring system to a shackle using finite element methods. The commercial FEA package MSC/MARC has been used for the analysis. In the original design the joint was based on a closed eye-end. Full scale testing results showed that this configuration achieved the vertical proof load of 150 kN and 1 million cycles of fatigue load. However, a problem with delamination occurred at the interface between the fibres going around the eye and the main leaf body. To overcome this problem, a second design was tried using transverse bandages of woven glass fibre reinforced tape to wrap the section that is prone to delaminate. In this case, the maximum interlaminar shear stress was reduced by a certain amount but it was still higher than the material’s shear strength. Based on the fact that, even with delamination, the top leaf spring still sustained the maximum static and fatigue loads required, the third design was proposed with an open eye-end, eliminating altogether the interface where the maximum shear stress occurs. The maximum shear stress predicted by FEA is reduced significantly and a safety factor of around 2 has been obtained. Thus, a successful and safe design has been achieved.

Antitumour activity of [1,2-di(cyclopentadienyl)-1,2-di(p-N,N-dimethylaminophenyl)-ethanediyl] titanium dichloride in xenografted Ehrlich's ascites tumour

The effects of a new titanocene compound with an ansa ligand in the cyclopentadienyl rings, the 1,2-di(cyclopentadienyl)-1,2-di(p-NNdimethylaminophenyl)-ethanediyl] titanium dichloride (TITANOCENE X), on the growth and differentiation of granulocyte-macrophage progenitor cells [colony-forming unit-granulocyte-macrophage (CFU-GM)] and Natural killer (NK) cell activity in Ehrlich's ascites tumour (EAT)-bearing mice were studied. Myelosuppression concomitant with increased numbers of spleen CFU-GM was observed in tumour-bearing mice. Treatment of these animals with TITANOCENE X (2.5-50mg/kg/day) produced an increase in myelopoicsis, in a dose-dependent manner, and reduced spleen colony formation. In addition, the treatment of EAT-bearing mice with 3 doses of 20 or 50 mg/kg TITANOCENE X restored to normal values the reduced Natural killer cell function observed during tumour growth. In parallel, TITANOCENE X prolonged, in a dose-dependent manner, the survival of mice inoculated with Ehrlich's ascites tumour. The highest dose of 50 mg/kg prolonged in 50% the survival time of EAT-bearing mice, compared to non-treated tumour-bearing controls. In comparison with previous results from our laboratory addressing the effects of titanocenes on haematopoiesis, we observed with TITANOCENE X a similar effective profile as for bis(cyclopentadienyl) dithiocyanate titanium(IV), being both less effective than di(cyclopentadienyl) dichloro titanium(IV), since the latter not only prolonged, but also increased the rate of survival. These differences in efficacy may be due to the nature of the ansa-cyclopentadienyl ligand used in TITANOCENE X, since the C, bridge between the two cyclopentadienyl groups will increase the hydrolytic stability by an organometallic chelate effect. Also, the introduction of two dimethylamino substituents increases the water solubility of TITANOCENE X when compared to titanocene dichloride itself (c) 2006 Elsevier B.V. All rights reserved.

A novel experimental method for measuring vergence and accommodation responses to the main near visual cues in typical and atypical groups

Binocular disparity, blur, and proximal cues drive convergence and accommodation. Disparity is considered to be the main vergence cue and blur the main accommodation cue. We have developed a remote haploscopic photorefractor to measure simultaneous vergence and accommodation objectively in a wide range of participants of all ages while fixating targets at between 0.3 and 2 m. By separating the three main near cues, we can explore their relative weighting in three-, two-, one-, and zero-cue conditions. Disparity can be manipulated by remote occlusion; blur cues manipulated by using either a Gabor patch or a detailed picture target; looming cues by either scaling or not scaling target size with distance. In normal orthophoric, emmetropic, symptom-free, naive visually mature participants, disparity was by far the most significant cue to both vergence and accommodation. Accommodation responses dropped dramatically if disparity was not available. Blur only had a clinically significant effect when disparity was absent. Proximity had very little effect. There was considerable interparticipant variation. We predict that relative weighting of near cue use is likely to vary between clinical groups and present some individual cases as examples. We are using this naturalistic tool to research strabismus, vergence and accommodation development, and emmetropization.