The spectral analysis and exponential stability of a bi‐directional coupled wave‐ODE system

In this paper, an unstable linear time invariant (LTI) ODE system is stabilized exponentially by the PDE compensato—a wave equation with Kelvin‐Voigt (K‐V) damping. Direct feedback connections between the ODE system and wave equation are established: The velocity of the wave equation enters the ODE through the variable v_t(1,t); meanwhile, the output of the ODE is fluxed into the wave equation. It is found that the spectrum of the system operator is composed of two parts: point spectrum and continuous spectrum. The continuous spectrum consists of an isolated point , and there are two branches of asymptotic eigenvalues: the first branch approaches to , and the other branch tends to ?∞. It is shown that there is a sequence of generalized eigenfunctions, which forms a Riesz basis for the Hilbert state space. As a consequence, the spectrum‐determined growth condition and exponential stability of the system are concluded.     

A priori bounds and multiplicity for fully nonlinear equations with quadratic growth in the gradient

We consider fully nonlinear uniformly elliptic equations with quadratic growth in the gradient, such as

$?F(x,u,Du,D^{2}u)=\lambda c(x)u+〈M(x)Du,Du〉+h(x)$

in a bounded domain with a Dirichlet boundary condition; here $\lambda \in \mathbb{R}$, $c,h\in L^p(\mathrm{\Omega })$, $p>n\ge 1$, $c?0$ and the matrix M satisfies $0<{\mu }_{1}I\le M\le {\mu }_{2}I$. Recently this problem was studied in the “coercive” case $\lambda c\le 0$, where uniqueness of solutions can be expected; and it was conjectured that the solution set is more complex for noncoercive equations. This conjecture was verified in 2015 by Arcoya, de Coster, Jeanjean and Tanaka for equations in divergence form, by exploiting the integral formulation of the problem. Here we show that similar phenomena occur for general, even fully nonlinear, equations in nondivergence form. We use different techniques based on the maximum principle.We develop a new method to obtain the crucial uniform a priori bounds, which permit to us to use degree theory. This method is based on basic regularity estimates such as half-Harnack inequalities, and on a Vázquez type strong maximum principle for our kind of equations.     

大尺寸电阻加热式碳化硅晶体生长热场设计与优化

大尺寸低缺陷碳化硅(SiC)单晶体是功率器件和射频(RF)器件的重要基础材料,物理气相传输(physical vapor transport, PVT)法是目前生长大尺寸SiC单晶体的主要方法。获得大尺寸高品质晶体的核心是通过调节组分、温度、压力实现气相组分在晶体生长界面均匀定向结晶,同时尽可能减小晶体的热应力。本文对电阻加热式8英寸(1英寸=2.54 cm)碳化硅大尺寸晶体生长系统展开热场设计研究。首先建立描述碳化硅原料受热分解热质输运及其多孔结构演变、系统热输运的物理和数学模型,进而使用数值模拟方法研究加热器位置、加热器功率和辐射孔径对温度分布的影响及其规律,并优化热场结构。数值模拟结果显示,通过优化散热孔形状、保温棉的结构等设计参数,电阻加热式大尺寸晶体生长系统在晶锭厚度变化、多孔介质原料消耗的情况下均能达到较低的晶体横向温度梯度和较高的纵向温度梯度。     

Progress in DNA Aptamers as Recognition Components for Protein Functional Regulation

Proteins play a central role in all domains of life, and precise regulation of their activity is essential for understanding the related biological processes and therapeutic functions. Nucleic acid aptamers, the molecular recognition components derived from systematic evolution of ligands by exponential enrichment(SELEX), can specifically identify proteins with antibody-like recognition characteristics and help to regulate their activity. This minireview covers the SELEX-based selection of protein-binding aptamers, membrane protein analytical techniques based on aptamer-mediated target recognition, aptamer-mediated functional regulation of proteins, including membrane receptors and non-membrane proteins(thrombin as a model), as well as the potential challenges and prospects regarding aptamer-mediated protein manipulation, aiming to supply some useful information for researchers in this field.     

Two solutions for a singular elliptic equation with critical growth at infinity

We look for positive solutions for the singular equation $-\Delta u-\frac{1}{2}\left(x\cdot \nabla u\right)=\mu h\left(x\right)u^{q-1}+\lambda u+u^{(N+2)/(N-2)},\text{in }{\mathbb{R}}^N,$ where $N\ge 3$, $\lambda >0$, $\mu >0$ is a parameter, $0<q<1$ and $h$ has some summability properties. By using a perturbation method and critical point theory, we obtain two solutions when $max\{1,N/4\}<\lambda <N/2$ and the parameter $\mu >0$ is small.     

Compressibility of random walker trajectories on growing networks

We find that the simple coupling of network growth to the position of a random walker on the network generates a traveling wave in the probability distribution of nodes visited by the walker. We argue that the entropy of this probability distribution is bounded as the network size tends to infinity. This means that the growth of a space coupled to a random walker situated in it constrains its dynamics to a set of typical random walker trajectories, and walker trajectories inside the growing space are compressible.     

Initial boundary value problem for a class of strongly damped semilinear wave equations with logarithmic nonlinearity

This paper deals with the initial boundary value problem for strongly damped semilinear wave equations with logarithmic nonlinearity $u_{tt}-\Delta u-\Delta u_t={\phi }_p\left(u\right)log\left|u\right|$ in a bounded domain $\Omega \subset {\mathbb{R}}^n$. We discuss the existence, uniqueness and polynomial or exponential energy decay estimates of global weak solutions under some appropriate conditions. Moreover, we derive the finite time blow up results of weak solutions, and give the lower and upper bounds for blow-up time by the combination of the concavity method, perturbation energy method and differential–integral inequality technique.     

Al2O3衬底无催化剂生长GaN纳米线及其光学性能

采用一种绿色的等离子增强化学气相沉积法,以Al2O3为衬底, Ga金属为镓源, N2为氮源,在不采用催化剂的情况下,成功制备获得了结晶质量良好的GaN纳米线.研究表明,生长温度可显著调控GaN纳米线的形貌,当反应温度为950℃时,生长出的GaN微米片为六边形;当反应温度为1000℃时,生长出了长度为10-20μm的超长GaN纳米线.随着反应时间增加, GaN纳米线的长度增加. GaN纳米线内部存在着压应力,应力大小为0.84 GPa.同时,也进一步讨论了GaN纳米线无催化剂生长机制. GaN纳米线光致发光结果显示, GaN纳米线缺陷较少,结晶质量良好,在360 nm处有一个较为尖锐的本征发光峰,可应用于紫外激光器等光电子器件.本研究结果将为新型光电器件低成本绿色制备提供一个可行的技术方案.