Global existence and decay estimate of solutions to magneto-micropolar fluid equations

We are concerned with magneto-micropolar fluid equations (1.3)–(1.4). The global existence of solutions to the Cauchy problem is investigated under certain conditions. Precisely, for the magneto-micropolar-Navier–Stokes (MMNS) system, we obtain global existence and large time behavior of solutions near a constant states in ${\mathbb{R}}^3$. Appealing to a refined pure energy method, we first obtain a global existence theorem by assuming that the $H^3$ norm of the initial data is small, but the higher order derivatives can be arbitrary large. If the initial data belongs to homogeneous Sobolev norms ${\dot{H}}^{?s}$ $(0\le s<\frac{3}{2})$ or homogeneous Besov norms ${\dot{B}}_{2,\infty }^{?s}$ $(0<s\le \frac{3}{2})$, we obtain the optimal decay rates of the solutions and its higher order derivatives. As an immediate byproduct, we also obtain the usual $L^p?L^2$ $(1\le p\le 2)$ type of the decay rates without requiring that the $L^p$ norm of initial data is small. At last, we derive a weak solution to (1.3)–(1.4) in ${\mathbb{R}}^2$ with large initial data.     

Hydrodynamic limit for the Ginzburg–Landau ∇ϕ interface model with non-convex potential

The hydrodynamic limit of the Ginzburg–Landau $??$ interface model was derived in Funaki and Spohn (1997) and Nishikawa (2003) for strictly convex potentials. This paper deals with non-convex potentials under suitable assumptions on the free energy and identification of the extremal Gibbs measures which have been recently established at sufficiently high temperature in Cotar and Deuschel (2012). Because of the non-convexity, many difficulties arise, especially, on the identification of equilibrium states. We show the equivalence between the stationarity and the Gibbs property under quite general settings, and we complete the identification of equilibrium states. We also establish some uniform estimates for variances of extremal Gibbs measures.     

Wetting-Induced Aggregation of Colloids

More than two decades ago, in a seminal paper John Cahn proposed scaling arguments for the possibility of a wetting transition in two coexisting fluid phases near the critical point. Since then, Cahn's model has been tested in many fluid systems and further refined by including the real interactions between the fluid and the solid wall. A fascinating consequence of the existence of a wetting transition is the possibility for a transition from weak to strong adsorption in the homogeneous phase. The situation is further enriched in nonstandard geometries having special geometrical constraints. The subject of this review concerns one such situation, where charge-stabilized colloidal particles are suspended in the homogeneous region of a binary liquid mixture. In this case, the preferential adsorption of one of the liquid components on to the colloid surface completely modifies the stability of the particles leading to an aggregation process. Although the exact mechanism underlying the adsorption phenomenon is still debated, it is closely related to the wetting transition. Recent experimental developments concerning the static and dynamic aspects of this phenomenon are reviewed. In addition, the main findings of a theoretical model based on the adsorption-modified electrostatic interactions between the colloidal particles are discussed.     

Anchoring transitions with polar and non-polar nematic liquid crystals on incompletely oxidized silane substrates

The active oxygen gas arising from a plasma reactor is used to realize progressive chemical modifications onto silane coatings that could be particularly interesting as alignment layers for liquid crystal display applications. Depending on the oxygen density grafted onto the substrate, these alignment layers provide different zenithal anchoring angles, or pretilt angles, with anchoring transitions, for polar and non-polar nematic liquid crystals as 5CB and MBBA, respectively. The anchoring transitions are found to be smoother with the polar nematics. Such a behavior is discussed in terms of the differential wetting model by adding a cosine term to the interaction energy between the nematic and the substrate. A local justification is proposed for this symmetry breaking term. Received: 18 May 1998     

Binding of oppositely charged membranes and membrane reorganization

We consider the electrostatic interaction between two rigid membranes, with different surface charge densities of opposite sign, across an aqueous solution without added salt. Exact solutions to the nonlinear Poisson-Boltzmann equation are obtained and their physical meaning discussed. We also calculate the electrostatic contribution to the free energy and discuss the renormalization of the area per head group of the charged lipids arising from the Coulomb interaction. Received 13 October 1998     

芳香氮化物-CHCl3系列复合物密度泛函法研究

报道对芳香氮化物吡咯（Ｃ４Ｈ５Ｎ）、苯（Ｃ６Ｈ５ＮＨ２）、对位氯代吡啶（Ｃ５Ｈ４ＮＣｌ）、吡啶（Ｃ５Ｈ５Ｎ）及吡咯负离子（Ｃ４Ｈ４Ｎ＾－）与三氯甲烷（ＣＨＣｌ３）形成的系列弱作用复合物的理论计算结果。把复合物看作是一个超分子在密度泛函Ｂ３ＬＹＰ／６－３１１Ｇ（ｄ,ｐ）的水平上进行计算,探讨该系列复合物的稳定性规律、电荷转移及主要几何参数变化等规律,计算结果表明：此类芳香氮化物与三氯甲（ＣＨ３ｌ３）     

Hydrogen electrocatalysis.

A selection of recent theoretical and experimental studies on electrolytic hydrogen evolution is presented. It is demonstrated with well-defined model surfaces that this reaction is a very structure-sensitive process. Crystallographic orientation, defect density and surface composition are parameters that determine the local geometric and electronic surface structure, and are thus crucial for the electrocatalytic activity as characterised by the exchange current density. The observed trends can be understood within a recent theory by J. K. N?rskov et al., which is based on density functional calculations and which emphasises the impact of hydrogen chemisorption energies on the reaction rate, that is, on the exchange current density. The particular electrocatalytic activities of ultrathin metal films and of nanostructures are addressed.     

Charge profile of surface doped C60

We study the charge profile of a C₆₀-FET (field effect transistor) as used in the experiments of Sch?n, Kloc and Batlogg. Using a tight-binding model, we calculate the charge profile treating the Coulomb interaction in a mean-field approximation. At low doping, the charge profile behaves similarly to the case of a continuous space-charge layer and becomes confined to a single interface layer for doping higher than ∼ 0.3 electron (or hole) per C₆₀ molecule. The morahedral disorder of the C₆₀ molecules smoothens the structure in the density of states. Received 21 June 2001     

Why is nacre strong? Elastic theory and fracture mechanics for biocomposites with stratified structures

Nacre, stratified ceramic layers surrounded by organic matrix, is a tough material found inside certain seashells. We construct a coarse-grained elastic energy for such an anisotropic system and present an analytic solution for a notch crack normal to the stratified sheets. This analysis proves the reduction in stress concentration which was announced in our earlier work (P. G. de Gennes and K. Okumura, C. R. Acad. Sci. Paris 1, Ser. IV, 257 (2000)) and the related increase in toughness. Received 18 March 2000     

Confinement of polystyrene at interfaces: Consequences on chain orientation

The knowledge of the structure and orientation of polymer chains adsorbed at an interface could be of major importance to predict the level of interfacial interactions and adhesion that depend strongly on the properties of the interface formed between the two materials (polymer and substrate) brought into contact. In this work, we were interested to study thin films of atactic polystyrene after adsorption (spin‐coating) on two chemically different substrates (inert and OH‐grafted gold substrates). The main aim is to analyze the resulting anisotropy due to the confinement in a quasi‐bidimensional geometry, as well as to investigate the incidence of the interfacial interactions, potentially established between the polymer and the surface, on the chain organization. Our infrared spectroscopy results allowed us to access the adsorption model of polystyrene chains and to highlight the relation between chain orientation and interfacial acid–base interactions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1268–1276, 2006