Adaptive local grid refinement algorithms for finite-element collocation

An adaptive grid refinement procedure allows accurate solutions to advection-dominated, time-dependent flows using finite-element collocation. The technique relies on a data structure that is readily amenable to parallel computing. The paper discusses computational aspects of the method.     

The effect of nanoparticle shape on polymer‐nanocomposite rheology and tensile strength

Nanoparticles can influence the properties of polymer materials by a variety of mechanisms. With fullerene, carbon nanotube, and clay or graphene sheet nanocomposites in mind, we investigate how particle shape influences the melt shear viscosity η and the tensile strength τ, which we determine via molecular dynamics simulations. Our simulations of compact (icosahedral), tube or rod‐like, and sheet‐like model nanoparticles, all at a volume fraction ? ≈ 0.05, indicate an order of magnitude increase in the viscosity η relative to the pure melt. This finding evidently can not be explained by continuum hydrodynamics and we provide evidence that the η increase in our model nanocomposites has its origin in chain bridging between the nanoparticles. We find that this increase is the largest for the rod‐like nanoparticles and least for the sheet‐like nanoparticles. Curiously, the enhancements of η and τ exhibit opposite trends with increasing chain length N and with particle shape anisotropy. Evidently, the concept of bridging chains alone cannot account for the increase in τ and we suggest that the deformability or flexibility of the sheet nanoparticles contributes to nanocomposite strength and toughness by reducing the relative value of the Poisson ratio of the composite. The molecular dynamics simulations in the present work focus on the reference case where the modification of the melt structure associated with glass‐formation and entanglement interactions should not be an issue. Since many applications require good particle dispersion, we also focus on the case where the polymer‐particle interactions favor nanoparticle dispersion. Our simulations point to a substantial contribution of nanoparticle shape to both mechanical and processing properties of polymer nanocomposites. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1882–1897, 2007     

Optimal control of unsteady compressible viscous flows

The control of complex, unsteady flows is a pacing technology for advances in fluid mechanics. Recently, optimal control theory has become popular as a means of predicting best case controls that can guide the design of practical flow control systems. However, most of the prior work in this area has focused on incompressible flow which precludes many of the important physical flow phenomena that must be controlled in practice including the coupling of fluid dynamics, acoustics, and heat transfer. This paper presents the formulation and numerical solution of a class of optimal boundary control problems governed by the unsteady two‐dimensional compressible Navier–Stokes equations. Fundamental issues including the choice of the control space and the associated regularization term in the objective function, as well as issues in the gradient computation via the adjoint equation method are discussed. Numerical results are presented for a model problem consisting of two counter‐rotating viscous vortices above an infinite wall which, due to the self‐induced velocity field, propagate downward and interact with the wall. The wall boundary control is the temporal and spatial distribution of wall‐normal velocity. Optimal controls for objective functions that target kinetic energy, heat transfer, and wall shear stress are presented along with the influence of control regularization for each case. Copyright © 2002 John Wiley & Sons, Ltd.     

Methodology for the preparation of C1-monoalkylated 1,2-dihydro[C70)] derivatives: formation of the "other" regioisomer

Deprotonation of 1,2-C(70)H(2) with TBAOH, followed by alkylation with methyl bromoacetate, results in formation of a C1-monoalkylated 1,2-dihydro-C(70) derivative. The position of the alkyl group (C1) was established by NMR spectroscopy and comparison with literature spectra of C2-monoalkylated analogs. Presumably, C1-alkylation is the major process due to selective deprotonation of 1,2-C(70)H(2) at C1. Substitution of benzyl bromide for methyl bromoacetate results in rapid dialkylation, unless the amount of base is carefully controlled, in which case C1-monobenzylation is the major process. This methodology for alkylation at C1 is complimentary to methods for the C2-monoalkylation of C(70) with Zn and methyl bromoacetate.     

The effect of thermal processing on PVC—VI. The role of hydrogen chloride

The reaction between cumene hydroperoxide (CHP) and anhydrous hydrogen chloride under various conditions of temperature and concentration has been studied in an inert solvent (chlorobenzene) and in an oxidisable medium (cumene). The kinetics were first order with respect to each reactant; the energy of activation of the overall second-order reaction was 53.4 kJ mol^?1 K^?1. Competing ionic and free radical mechanisms were found to operate, the latter predominating at relatively high HCl concentrations, leading to rapid pro-oxidation in cumene. The effect of typical organo-tin PVC stabilizers on the pro-oxidant process were examined. It was found that dibutyltin maleate neutralized the HCl thus eliminating the pro-oxidant effect when used in stoichiometric proportions, but had little other effect. Dioctyltin bis(isol-octylthioglycollate) on the other hand not only neutralized the HCl stoichiometrically but gave additional oxidative stabilization over a wide concentration range.     

Mechanisms of antioxidant action: The effect of thermal processing on the antioxidant activity of sulphur compounds

The nickel dithiophosphates and their corresponding disulphides are shown to be more effective uv stabilisers for LDPE than the closely related nickel xanthates and disulphides (dixanthogens). In general, the nickel complexes in both series are more effective uv stabilisers than the disulphides.Evidence is presented to show that the better performance of the dithiophosphates than the xanthates is associated with their higher solubility in the polymer. For the same reason, nickel dithiolates containing long alkyl substituents are more effective uv stabilisers than those containing shorter alkyl substituents.Thermal processing adversely affects the photo-stabilising performance of nickel dithiolates whereas the performance of the less efficient disulphides is enhanced under the same conditions. In the former case, the uv stability of the polymer is shown to be directly proportional to the amount of the nickel complex left after processing. In the case of the disulphides, on the other hand, the evidence suggests that increasing the severity of their processing increases the extent of oxidation to products which are more effective uv stabilisers than the parent disulphides.