Lifespan of classical discontinuous solutions to general quasilinear hyperbolic systems of conservation laws with small BV initial data: Rarefaction waves

In the present paper the author investigates the global structure stability of Riemann solutions for general quasilinear hyperbolic systems of conservation laws under small BV perturbations of the initial data, where the Riemann solution contains rarefaction waves, while the perturbations are in BV but they are assumed to be C¹$C^1$-smooth, with bounded and possibly large C¹$C^1$-norms. Combining the techniques employed by Li–Kong with the modified Glimm’s functional, the author obtains a lower bound of the lifespan of the piecewise C¹$C^1$ solution to a class of generalized Riemann problems, which can be regarded as a small BV perturbation of the corresponding Riemann problem. This result is also applied to the system of traffic flow on a road network using the Aw–Rascle model.     

Asymptotic behavior of global classical solutions to Goursat problem for quasilinear hyperbolic systems with small BV data

This paper is concerned with the asymptotic behavior of global C ¹ solutions of the Goursat problem for quasilinear hyperbolic systems. Based on the existence result on the global classical solution, we prove that when t tends to the infinity, the solution approaches a combination of Lipschitz continuous and piecewise C ¹ traveling wave solutions, provided that the C ¹ norm of the boundary data is bounded but possibly large, and the BV norm of the boundary data is sufficiently small. Applications include the 1D compressible Euler equations for Chaplygin gases.     

基于启发式分割算法的气候突变检测研究

气候系统的非线性、多层次性和非平稳性对气候突变的检测方法提出了较高的要求.基于t检 验将非平稳序列分割为多个不同尺度的自平稳子序列，Bernaola Galvan提出的启发式分割 算法(BG算法)，对非平稳时间序列的突变检测效果较好.在BG算法的基础上，通过理想时间 序列验证BG算法处理非平稳时间序列的有效性，并对近2000a北半球树木年轮距平宽度序列 基于不同层次的思想，检测和分析其中包含的各种尺度的气候突变事件，成功地区分不同尺 度的突变.定义的新物理量——突变密度的分析表明，自然因素作用的基础上，人为因素影 响的加剧可能导致近1000a来突变密集段和稀疏段分布失衡，这可能是全球变化的重要表现 之一. 关键词： 气候突变 均值段 突变密度 人为因素 全球变化     

钙钛矿结构中的简谐子软模

利用复合空间型方法,在自由边界条件下解出了钙钛矿结构有限尺寸晶体的简谐振动方程.计算结果给出了收敛的简谐子谱分布,并发现了许多简谐子软模.用这些软模花样说明了钛酸钡晶体冷却时发生具有a畴和c畴结构的铁电相变.理论表明铁电相变过程涉及屏蔽电荷的激发及其在界面的缓慢扩散,以最后得出各个电畴内部的均匀自发极化 关键词： 晶格动力学 简谐子 软模 钛酸钡     

On a Class of Quasilinear Elliptic Equations

We consider a class of quasilinear elliptic boundary problems, including the following Modified Nonlinear Schrödinger Equation as a special case: $$\begin{cases} ∆u+ \frac{1}{2} u∆(u^2)−V(x)u+|u|^{q−2}u=0 \ \ \ in \ Ω, \\u=0 \ \ \ \ \ \ \ ~ ~ ~ on \ ∂Ω, \end{cases}$$ where $Ω$ is the entire space $\mathbb{R}^N$ or $Ω ⊂ \mathbb{R}^N$ is a bounded domain with smooth boundary, $q∈(2,22^∗]$ with $2^∗=2N/(N−2)$ being the critical Sobolev exponent and $22^∗= 4N/(N−2).$ We review the general methods developed in the last twenty years or so for the studies of existence, multiplicity, nodal property of the solutions within this range of nonlinearity up to the new critical exponent $4N/(N−2),$ which is a unique feature for this class of problems. We also discuss some related and more general problems.     

Reservoir Engineering Strong Magnomechanical Entanglement via Dual-Mode Cooling

A hybrid cavity magnomechanical system to transfer the bipartite entanglements and achieve the strong microwave photon–phonon entanglement based on the reservoir engineering approach is constructed. The magnon mode is coupled to the microwave cavity mode via magnetic dipole interaction and to the phonon mode via magnetostrictive force (optomechanical-like). It is shown that the initial magnon-phonon entanglement can be transferred to the photon-phonon subspace in the case of these two interactions cooperating. In the reservoir-engineering parameter regime, the initial entanglement is directionally transferred to the photon-phonon subsystem, so a strong bipartite entanglement in which the magnon mode acts as the cold reservoir to effectively cool the Bogoliubov mode delocalized over the cavity and the mechanical deformation mode is obtained. Moreover, dual-mode cooling is realized by engineering the dissipation of photon and phonon modes within the target mode, which allows entanglement to be further enhanced. The results indicate that the steady-state entanglement is robust against temperature. The dual-mode cooling reservoir engineering scheme can potentially be extended to other three-mode quantum systems.     

A New Fluorescence Turn-On Probe for Aluminum(III) with High Selectivity and Sensitivity,and its Application to Bioimaging

The development of novel selective probes with high sensitivity for the detection of Al³⁺ is widely considered an important research goal due to the importance of such probes in medicine, living systems and the environment. Here, we describe a new fluorescent probe, N′-(4-diethylamino-2-hydroxybenzylidene)-2-hydroxybenzohydrazide (1), for Al³⁺. Probe 1 was evaluated in a solution of acetonitrile/water (1:1 v/v). Compared with previously reported probes for Al³⁺, probe 1 can be synthesized easily and in high yield. A Job plot confirmed that probe 1 is able to complex Al³⁺ in a 1:1 ratio, and the binding constant was determined to be 4.25×10⁸ m⁻¹. Moreover, the detection limit was as low as 6.7×10⁻⁹ m, suggesting that probe 1 has a high sensitivity. Common coexistent metal ions, such as K⁺, Co²⁺, Ca²⁺, Ba²⁺, Ni²⁺, Pb²⁺, Hg²⁺, Ce²⁺, Zn²⁺, Cd²⁺, Fe³⁺, showed little or no interference in the detection of Al³⁺ in solution, demonstrating the high selectivity of the probe. Finally, the ability of probe 1 to act as a fluorescent probe for Al³⁺ in living systems was evaluated in Gram-negative bacteria, Escherichia coli, and confocal laser scanning microscopy confirmed its utility. The results of this study suggest that 1 has appropriate properties to be developed for application as a fluorescent probe of Al³⁺ for use in biological studies.     

Conversion of phenylacetonitrile in supercritical alcohols within a system containing small volume of water

The reaction of phenylacetonitrile in supercritical methanol and ethanol in a system containing a small volume of water was studied. The effects of various operating conditions, such as reaction temperature, reaction time, the mole ratio of phenylacetonitrile/water/methanol or ethanol on the product yield were systematically investigated. The optimal yield of methyl phenylacetate for phenylacetonitrile in supercritical methanol in a system containing a small volume of water was 70 % at 583 K and 2.5 h. The optimal yield of ethyl phenylacetate for phenylacetonitrile in supercritical ethanol with a small volume of water was 80 % at 583 K and 1.0 h. At the same time, a feasible mechanism was proposed for phenylacetonitrile in supercritical methanol and ethanol in a system containing a small volume of water.