Singly Periodic Solutions of the Allen-Cahn Equation and the Toda Lattice

The Allen-Cahn equation ? Δu = u ? u ³ in ?² has family of trivial singly periodic solutions that come from the one dimensional periodic solutions of the problem ?u″ =u ? u ³. In this paper we construct a non-trivial family of singly periodic solutions to the Allen-Cahn equation. Our construction relies on the connection between this equation and the infinite Toda lattice. We show that for each one-soliton solution to the infinite Toda lattice we can find a singly periodic solution to the Allen-Cahn equation, such that its level set is close to the scaled one-soliton. The solutions we construct are analogues of the family of Riemann minimal surfaces in ?³.     

Limit Cycles Bifurcating from a k-dimensional Isochronous Center Contained in ?n with k ? n

The goal of this paper is double. First, we illustrate a method for studying the bifurcation of limit cycles from the continuum periodic orbits of a k-dimensional isochronous center contained in ℝ ⁿ with n ⩾ k, when we perturb it in a class of differential systems. The method is based in the averaging theory. Second, we consider a particular polynomial differential system in the plane having a center and a non-rational first integral. Then we study the bifurcation of limit cycles from the periodic orbits of this center when we perturb it in the class of all polynomial differential systems of a given degree. As far as we know this is one of the first examples that this study can be made for a polynomial differential system having a center and a non-rational first integral. The first and third authors are partially supported by a MCYT/FEDER grant MTM2005-06098-C01, and by a CIRIT grant number 2005SGR-00550. The second author is partially supported by a FAPESP–BRAZIL grant 10246-2. The first two authors are also supported by the joint project CAPES–MECD grant HBP2003-0017.     

Theoretical Studies on the Reactions of 1,1,2,2,3,3,4‐Heptafluorocyclopentane with Hydroxyl and Hydrogen Free Radicals

1,1,2,2,3,3,4‐Heptafluorocyclopentane (F7A) has considerable potential to be a new halon replacement due to its environmental friendliness and low‐toxicity. However, the reaction processes of F7A with hydroxyl and hydrogen free radicals, which are of great importance for investigating its fire suppression mechanisms, are still unclear. In this paper, ab inito and density functional theory are used to deduce the possible reaction pathways for the reactions of F7A with hydroxyl and hydrogen free radicals at the CCSD/cc‐pVDZ//B3LYP/6‐311++G (d,p) level of theory. Two distinct reaction pathways including ten elementary reaction channels for F7A with hydroxyl free radical, and five distinct reaction pathways including twenty elementary reaction channels for F7A with hydrogen free radical are investigated. The geometries, vibrational frequencies and reaction energy barriers are also determined. Based on the calculated results, the possible reaction mechanisms are proposed and discussed. The most feasible reaction channel for F7A with hydroxyl free radical is that leads to CH(OH)CH₂(CF₂)₃+·F, and the most feasible reaction channel for F7A with hydrogen free radical is that leads to (CF₂)₃CH₂CH·+HF. The study is helpful to further study its fire suppression mechanisms and promote it to be a new generation of halon replacement.     

通过赝反伽伐尼反应实现金纳米粒子模块替换

通过可控的方式精确调控纳米粒子的结构仍是一个富有挑战性和鼓舞人心的课题.尽管单原子或两、三个金属原子的精细调控已经在金纳米粒子中实现,涉及三个以上金属原子的取代（模块取代）还没有报道.本工作报道了环己硫醇配体保护的Au₄₈（CHT）₂₆的合成及其通过赝反伽伐尼过程的模块取代.单晶结构揭示模块取代的产物与母体团簇共用一个相似的Au₃₁（CHT）₁₂主体,但剩余部分不同（Au₆（CHT）₁₁ vs.Au₁₆（CHT）₁₄）.一个有趣的发现是模块取代抑制了Au₄₈（CHT）₂₆的光热过程,却增强了它的发射,赋予了所合成团簇更好的双（多）功能应用潜力.光热效应的减弱和发射的增强也暗示了这两种作用能够彼此至少部分转化,对于研究这两种效应之间的相互影响也具有重要的启示.     

Influence of aspect ratio and arrangement direction on the shear behavior of ellipsoids

This work studies the macroscopic and microscopic behaviors of ellipsoids under triaxial tests using 3D discrete element method (DEM) simulation. To avoid the boundary effect, a novel stress servo-controlled periodic boundary condition is proposed to maintain the confining pressure of samples during testing. The shape features of ellipsoids are investigated, including the aspect ratio of elongated/oblate ellipsoids and the initial arrangement directions of ellipsoids. The macroscopic properties of ellipsoidal particle samples, such as the deviatoric stress, volumetric strain, internal friction angle, as well as dilatancy angles are explored. Elongated and oblate ellipsoids with varying aspect ratios are investigated for the occurrence of stick-slips. In addition, it is demonstrated that the initial arrangement direction has a significant impact on the coordination number and contact force chains. The corresponding anisotropy coefficients of the entire contact network are analyzed to probe the microscopic roots of macroscopic behavior.     

STM针尖诱导构筑-置换两步法制备Pt表面纳米结构

STM“Jump-to-contact”针尖诱导表面纳米构筑是目前水溶液中具有最高分辨率的一种表面纳米构筑技术.然而,一些金属因其具有较高的内聚能而难以发生针尖原子向表面的转移,限制了该技术的广泛应用.本文建立了以STM构筑-置换两步法获得不能直接利用“Jump-to-contact”原理进行构筑的金属表面纳米团簇阵列,利用STM针尖“Jump-to-contact”诱导在Au(111)表面构筑Cu纳米团簇阵列,然后通过Pt-Cu置换的方法,制备出Au(111)表面的Pt纳米团簇阵列.     

Barrier Dispersion-Based Coatings Containing Natural and Paraffin Waxes

Petroleum, synthetic, and natural waxes have been used as hydrophobic bases for dispersions intended for use as barrier coatings for packaging paper. Oil-in-water dispersions with alkaline pH were prepared by a two-step homogenization procedure containing paraffin wax, with various characteristics, the Fischer–Tropsch synthesis product or beeswax. The size of the dispersed particles determined by dynamic light scattering depended on the type of hydrophobic base used and was in the range of 350–440 nm. The ability of dispersion particles in aggregation driven by electrostatic attraction, evaluated by Zeta potential analysis by electrophoretic light scattering, was from −26 to −50 mV. Static multiply light scattering was used for 30 days of stability assessment and helped to select the dispersion with a Sarawax SX70 wax base as the most stable. Dispersions were further used for coating the backing of kraft paper by the Meyer rod method. Coated paper with an applied coating of 6 g/m² had very good hydrophobic properties (Cobb60 < 4 g/m²), sufficient strength properties, and air permeation, which enabled its application as a packaging material. The dispersions based on Sarawax SX70 wax were evaluated as the best coating for Mondi ProVantage Kraftliner 125 g/m² backing paper. Good hydrophobic properties and strength properties indicate the possibility of using the SX70-based wax dispersion coating as a replacement for PFAS coatings in some applications.     

Flow physics of normal and abnormal bioprosthetic aortic valves

Flow physics of transvalvular flows in the aorta with bioprosthetic valves are investigated using computational modelling. For the efficient simulations of flow-structure-interaction in transvalvular flows, a simplified, reduced degree of freedom valve model is employed with a sharp interface immersed boundary based incompressible flow solver. Simulations are performed for normal as well as abnormal valves with reduced leaflet motion that models the effect of early leaflet thrombosis. The structure of the aortic jet and the hemodynamic stresses on the aortic wall are analysed to understand the hemodynamic impacts and possible long-term clinical implications of sub-clinical, reduced leaflet motion. The simulation results have shown that the reduced leaflet motion tilts the direction of aortic jet and generates stronger flow separation and re-attachment on the aortic wall downstream from the reduced motion leaflets. The modified flow pattern increases the wall pressure fluctuation and average wall shear stress on the downstream aortic wall, and results in the asymmetric oscillatory shear index distributions, which may have long-term clinical implications such as aortic wall damage and remodelling.     

Asymptotic approximations for Bloch waves and topological mode steering in a planar array of Neumann scatterers

We study the canonical problem of wave scattering by periodic arrays, either of infinite or finite extent, of Neumann scatterers in the plane; the characteristic lengthscale of the scatterers is considered small relative to the lattice period. We utilise the method of matched asymptotic expansions, together with Fourier series representations, to create an efficient and accurate numerical approach for finding the dispersion curves associated with Floquet–Bloch waves through an infinite array of scatterers. The approach lends itself to direct scattering problems for finite arrays and we illustrate the flexibility of these asymptotic representations on topical examples from topological wave physics.     

周期性管柱信道的声波通信技术研究综述

井下声波通信技术利用周期性管柱信道实时传输声波数据,相比于其他通信方式,具有适应性好、复杂度低、传输效率高等优点,在随钻地质导向、油水井监测等方面有广阔的应用前景,是发展智能油田的关键技术之一。本文主要综述上世纪90年代以来关于信道物理模型、信道容量、声信号调制与接收方法等关键问题的研究历程,并对通信系统的设计要点与国内外相关产品的现场应用进行梳理,为后续的技术改进提供依据。