Weakly Nonlinear Geometric Optics for Hyperbolic Systems of Conservation Laws

We present a new approach to analyze the validation of weakly nonlinear geometric optics for entropy solutions of nonlinear hyperbolic systems of conservation laws whose eigenvalues are allowed to have constant multiplicity and corresponding characteristic fields to be linearly degenerate. The approach is based on our careful construction of more accurate auxiliary approximation to weakly nonlinear geometric optics, the properties of wave front-tracking approximate solutions, the behavior of solutions to the approximate asymptotic equations, and the standard semigroup estimates. To illustrate this approach more clearly, we focus first on the Cauchy problem for the hyperbolic systems with compact support initial data of small bounded variation and establish that the L ¹-estimate between the entropy solution and the geometric optics expansion function is bounded by O(?²), independent of the time variable. This implies that the simpler geometric optics expansion functions can be employed to study the behavior of general entropy solutions to hyperbolic systems of conservation laws. Finally, we extend the results to the case with non-compact support initial data of bounded variation.     

基于Cluster态和Bell态的任意三粒子态远程制备(英文)

本文提出了一个新颖的基于四粒子cluster态和Bell态制备任意三粒子远程制备方案.在发送者(Alice)对自己手中的粒子做正交完备测量,接受者(Bob)对自己手中的粒子做适当的幺正变换后,任意三粒子远程制备成功.对于Alice的两种不同的正交完备基测量的情况,分别计算了远程制备成功的概率.另外,本方案成功制备的概率在一般情况和一些特殊情况下是可以计算的.分析结果表明:在一般情况下,远程态制备可以以1/8的概率实现;但在一些特殊情况下,成功的概率可以提高到1/4、1/2,甚至1.     

Coupling dynamic analysis of a liquid-filled spherical container subject to arbitrary excitation

Using spherical coordinates, the coupling nonlin- ear dynamic system of a liquid-filled spherical tank, which can be excited discretionarily, is deduced by the H-O variational principle, and the viscous damping is introduced via the liquid dissipation function. The kinetic equations of the coupling system are deduced by the relationship between the velocity of liquid particles and the disturbed liquid surface equation. Normal differential equations are obtained through the Galerkin method. An equivalent mechanical model is developed for liquid sloshing in a spherical tank subject to arbitrary excitation. The fixed and slosh masses, as well as the spring and damping constants, are determined in such a way as to satisfy the principle of equivalence. Numerical simulations illustrate the theoretical results in this paper as well.     

Understanding the relationship between the structure of an organofunctional methoxysilane bilayer and its properties as adhesion primer for Zn-epoxidized rubber system

The structure of a new organofunctional methoxysilane bilayer system, which was found to improve the adhesion of epoxidized natural rubber (ENR) to zinc, is analyzed by High Resolution Electron Energy Loss and Infrared Reflection Absorption Spectroscopy. This bilayer is formed when zinc plate is successively dip-coated in water-alcohol solutions of γ-mercaptopropyltrimethoxysilane and aminopropyltrimethoxysilane. The optimal adhesion, obtained when both silane layers are cured at 110 °C, is due to the specific structure of this bilayer, which depends dramatically on the cure temperature of the first layer. From HREELS results under the conditions of an impact mechanism, it is shown that the surface density of NH₂ groups (which react with the epoxy groups of rubber and provide the adhesion of the whole system) is much higher when the γ-MPS layer is cured at 110 °C instead of 70 °C or room temperature. This high NH₂ group surface density is also confirmed by wettability measurements, which indicate a marked increase in the basic component of the surface energy at 110 °C. An IRRAS study of the γ-MPS layer deposited on zinc shows that up to 70 °C hydrolysis of the SiOCH₃ groups is poor, and becomes effective only after the zinc/γ-MPS layer is dipped in the basic APS solution. This makes the penetration of APS molecules across the γ-MPS layer easier and, consequently, amino groups can interact with zinc. Therefore, they are unavailable for a reaction with epoxy groups. In contrast, when the γ-MPS layer is cured at 110 °C or higher, hydrolysis of its SiOCH₃ groups begins and, simultaneously, lateral cross-linking occurs between SiOH groups. Under these conditions, penetration of the γ-MPS layer by APS molecules is hindered and lateral mixed cross-linking occurs at the interface γ-MPS/APS via the SiOH groups. This entails a greater density of pendant amino groups directed towards the surface, which enhances the practical adhesion of rubber to zinc.     

Bisplitting an Arbitrary <Emphasis Type="Italic">N</Emphasis>-Qubit State with a Class of Asymmetric Three-Qubit W States

We propose a tripartite scheme for bisplitting an arbitrary single-qubit quantum information (QI) by using a class of asymmetric three-qubit W state as quantum channels. In the scheme, the sender Alice first performs a Bell-state measurement on her two qubits and then publishes her measurement result via a public classical channel. Based on Alice’s message, if the two receivers Bob and Charlie collaborate together, they can retrieve the QI, i.e., they can deterministically recover the QI in one receiver’s site by first performing a two-qubit unitary operation and then executing a single-qubit unitary operation. Afterwards, we sketch the extension of the single-qubit QI splitting to an arbitrary N-qubit QI splitting.     

Structural analysis of glycosphingolipid analogues obtained by the saccharide primer method using CE‐ESI‐MS

A glycosphingolipid analogue (12‐azidododecyl β‐lactoside) as a saccharide primer has been shown to be useful for the synthesis of oligosaccharide libraries by mammalian cells. In the present study, CE‐ESI‐MS was employed to elucidate the structure of glycosphingolipid analogues derived from 12‐azidododecyl β‐lactoside (Lac‐C12N3) by mammalian cells. MDCK cells and COLO201 cells were cultured with Lac‐C12N3, and the glycosylated products secreted into the medium were collected and separated into acidic and neutral products by column chromatography. The acidic products could be directly analyzed by CE‐ESI‐MS, while the neutral products were converted to anionic derivatives via a reaction with propiolic acid. With this method, it was possible to analyze both acidic and neutral products glycosylated by MDCK cells and COLO201 cells at high sensitivity.     

A two-dimensional unstructured cell-centered multi-material ALE scheme using VOF interface reconstruction

We present a new cell-centered multi-material arbitrary Lagrangian–Eulerian (ALE) scheme to solve the compressible gas dynamics equations on two-dimensional unstructured grid. Our ALE method is of the explicit time-marching Lagrange plus remap type. Namely, it involves the following three phases: a Lagrangian phase wherein the flow is advanced using a cell-centered scheme; a rezone phase in which the nodes of the computational grid are moved to more optimal positions; a cell-centered remap phase which consists of interpolating conservatively the Lagrangian solution onto the rezoned grid. The multi-material modeling utilizes either concentration equations for miscible fluids or the Volume Of Fluid (VOF) capability with interface reconstruction for immiscible fluids. The main original feature of this ALE scheme lies in the introduction of a new mesh relaxation procedure which keeps the rezoned grid as close as possible to the Lagrangian one. In this formalism, the rezoned grid is defined as a convex combination between the Lagrangian grid and the grid resulting from condition number smoothing. This convex combination is constructed through the use of a scalar parameter which is a scalar function of the invariants of the Cauchy–Green tensor over the Lagrangian phase. Regarding the cell-centered remap phase, we employ two classical methods based on a partition of the rezoned cell in terms of its overlap with the Lagrangian cells. The first one is a simplified swept face-based method whereas the second one is a cell-intersection-based method. Our multi-material ALE methodology is assessed through several demanding two-dimensional tests. The corresponding numerical results provide a clear evidence of the robustness and the accuracy of this new scheme.     

一类格心型ALE有限体积格式方法

现在国内外流行的ALE有限体积格式基本上都基于交错网榕进行格式的离散.该类格武在进行重映时,速度、密度和能量需要分别进行重映计算,效率较低,而且由于速度在网格角点.而密度、能量在网格中心,重映时会出现动能和内能不协调现泉.本文在巳有格心型Lagrange有限体积格式研究的基础上,结合Abgrall R.等关于榕心型格式下的网格角点速度的计算方法,利用最小二乘法进行高阶插值多项式重构,构造了一类新的格心型的高精度Lagrangian有限体积格式,并结合有效的高精度ENO守恒重映方法,获得了一类格心型的高精度ALE有限体积格式.数值试验的结果说明本文的格式是有效的,高精度的,收敛的,并且避免了物理量的不协调现象.