Generic Stability and Essential Components of Generalized KKM Points and Applications

We propose the definition of T-KKM points and consider generic stability of T-KKM mappings and essential components of sets of T-KKM points. As applications, using a unified approach, we derive from these results the existence of essential components of solution sets to various optimization-related problems. We do this in two steps. First, we deduce the corresponding results for variational inclusions, which are new. Then we obtain, as consequences, the existence of essential components of solutions to other problems, which are new or include recent ones in the literature.     

Temperature-responsive self-assembly of charged and uncharged hydroxyethylcellulose-<Emphasis Type="Italic">graft</Emphasis>-poly(<Emphasis Type="Italic">N</Emphasis>-isopropylacrylamide) copolymer in aqueous solution

Temperature-induced interchain association and contraction of species in aqueous solutions of charged (MHEC(−)-g-PNIPAAM) and uncharged (MHEC-g-PNIPAAM) modified hydroxyethylcellulose-graft-poly(N-isopropylacrylamide) copolymer have been studied with the aid of turbidimetry and dynamic light scattering (DLS). It was shown that by attaching PNIPAAM chains to the backbone of a hydrophilic cellulose derivative, a strongly temperature-responsive copolymer could be prepared. The results show an intriguing interplay between interchain association and contraction of the multichain species. The transition zone for compression is narrow, and the compaction effect is promoted by a low polymer concentration and charges on the polymer moieties. The findings from DLS revealed two populations of species, namely molecularly dispersed molecules or small clusters and interchain complexes, which exhibit temperature-induced collapse. The magnitude of the cluster contraction can be modulated by changing the polymer concentration and charge density of the copolymer.     

First and Second Order Optimality Conditions Using Approximations for Nonsmooth Vector Optimization in Banach Spaces

We use the first and second order approximations of mappings to establish both necessary and sufficient optimality conditions for unconstrained and constrained nonsmooth vector optimization problems. Ideal solutions, efficient solutions, and weakly efficient solutions are considered. The data of the problems need not even be continuous. Some often imposed compactness assumptions are also relaxed. Examples are provided to compare our results and some known recent results.This work was partially supported by the National Basic Research Program in Natural Sciences of Vietnam.     

Boundary contour analysis for surface stress recovery in 2-D elasticity and Stokes flow

Summary A variant of the boundary element method, called the boundary contour method, offers a further reduction in dimensionality. Consequently, boundary contour analysis of 2-D problems does not require any numerical integration at all. In a boundary contour analysis, boundary stresses can be accurately computed using the approach proposed in Ref. [1]. However, due to singularity, this approach can be used only to calculate boundary stresses at points that do not lie at an end of a boundary element. Herein, it is shown that a technique based on the displacement/velocity shape functions can overcome this drawback. Further, the approach is much simpler to apply, requires less computational effort, and provides competitive accuracy. Numerical solutions and convergence study for some well-known problems in linear elasticity and Stokes flow are presented to show the effectiveness of the proposed approach. This research was supported in part by the 2004 Ralph E. Powe Junior Faculty Enhancement Award from Oak Ridge Associated Universities and by the University of South Alabama Research Council.     

Boundary element simulations of spheres settling in circular,square and triangular conduits

Numerical simulations of a spherical particle sedimenting in circular, triangular and square conduits containing a viscous, inertialess, Newtonian fluid were investigated using the Boundary Element Method (BEM). Settling velocities and pressure drops for spheres falling along the centre-lines of the conduits were computed for a definitive range of sphere sizes. The numerical simulations for the settling velocities showed good agreement with existing experimental data. The most accurate analytic solution for a sphere settling along the axis of a circular conduit produced results which were almost indistinguishable from the present BEM calculations. For a sphere falling along the centre-line of a square conduit, the BEM calculations for small spheres agreed well with analytic results. No analytic results for a sphere falling along the axis of a triangular conduit were available for comparison. Extrapolation of the BEM predictions for the pressure drops, to infinitely small spheres, showed remarkable agreement with analytic results. For the circular conduit, the sphere's settling velocity and angular velocity were computed as a function of drop position for small, medium and large spheres. Excellent agreement with a reflection solution was achieved for the small sphere. In addition, end effects were investigated for centre-line drops and compared where possible with available experimental data and analytic results.Los Alamos National Laboratory, Los Alamos, New Mexico, USA.     

Instability and friction

A review on the stability analysis of solids in unilateral and frictional contact is given. The presentation is focussed on the stability of an equilibrium position of an elastic solid in frictional contact with a fixed or moving obstacle. The problem of divergence instability and the obtention of a criterion of static stability are discussed first for the case of a fixed obstacle. The possibility of flutter instability is then considered for a steady sliding equilibrium with a moving obstacle. The steady sliding solution is generically unstable by flutter and leads to a dynamic response which can be chaotic or periodic. This dynamic response leads to the generation of stick–slip–separation waves on the contact surface in a similar way as Schallamach waves in statics. Illustrating examples and principal results recently obtained in the literature are reported. Some problems of friction-induced vibration and noise emittence, such as brake squeal for example, can be interpreted in this spirit. To cite this article: Q.S. Nguyen, C. R. Mecanique 331 (2003).     

Influence of microgel architecture and oil polarity on stabilization of emulsions by stimuli-sensitive core-shell poly(N-isopropylacrylamide-co-methacrylic acid) microgels: Mickering versus Pickering behavior?

Charged poly(N-isopropylacrylamide-co-methacrylic acid) [P(NiPAM-co-MAA)] microgels can stabilize thermo- and pH-sensitive emulsions. By placing charged units at different locations in the microgels and comparing the emulsion properties, we demonstrate that their behaviors as emulsion stabilizers are very different from molecular surfactants and rigid Pickering stabilizers. The results show that the stabilization of the emulsions is independent of electrostatic repulsion although the presence and location of charges are relevant. Apparently, the charges facilitate emulsion stabilization via the extent of swelling and deformability of the microgels. The stabilization of these emulsions is linked to the swelling and structure of the microgels at the oil-water interface, which depends not only on the presence of charged moieties and on solvent polarity but also on the microgel (core-shell) morphology. Therefore, the internal soft and porous structure of microgels is important, and these features make microgel-stabilized emulsions characteristically different from classical, rigid-particle-stabilized Pickering emulsions, the stability of which depends on the surface properties of the particles.     

Droplet synthesis of well-defined block copolymers using solvent-resistant microfluidic device

Well-defined diblock copolymers were synthesized via an exothermic RAFT route by a droplet microfluidic process using a solvent-resistant and thermally stable fluoropolymer microreactor fabricated by a non-lithographic embedded template method. The resulting polymers were compared to products obtained from continuous flow capillary reactor and conventional bulk synthesis. The droplet based microreactor demonstrated superior molecular weight distribution control by synthesizing a higher molecular weight product with higher conversion and narrow polydispersity in a much shorter reaction time. The high quality of the as-synthesized block copolymer PMMA-b-PS led to a generation of micelles with a narrow size distribution that could be used as a template for well-ordered mesoporous silica with regular frameworks and high surface areas.     

Study of Tamiflu sensitivity to variants of A/H5N1 virus using different force fields

An accurate estimation of binding free energy of a ligand to receptor ΔG(bind) is one of the most important problems in drug design. The success of solution of this problem is expected to depend on force fields used for modeling a ligand-receptor complex. In this paper, we consider the impact of four main force fields, AMBER99SB, CHARMM27, GROMOS96 43a1, and OPLS-AA/L, on the binding affinity of Oseltamivir carboxylate to the wild-type and Y252H, N294S, and H274Y mutants of glycoprotein neuraminidase from the pandemic A/H5N1 virus. Having used the molecular mechanic-Poisson-Boltzmann surface area method, we have shown that ΔG(bind), obtained by AMBER99SB, OPLS-AA/L, and CHARMM27, shows the high correlation with the available experimental data. They correctly capture the binding ranking Y252H → WT → N294S → H274Y observed in experiments (Collins, P. J. et al. Nature 2008, 453, 1258). In terms of absolute values of binding scores, results obtained by AMBER99SB are in the nearest range with experiments, while OPLS-AA/L, which is applied to study binding of Oseltamivir to the influenza virus for the first time, gives rather big negative values for ΔG(bind). GROMOS96 43a1 provides a lower correlation as it supports Oseltamivir to be more resistant to N294S than H274Y. Our study suggests that force fields have pronounced influence on theoretical estimations of binding free energy of a ligand to receptor. The effect of all-atom models on dynamics of the binding pocket as well as on the hydrogen-bond network between Oseltamivir and receptors is studied in detail. The hydrogen network, obtained by GROMOS, is weakest among four studied force fields.