高温应变下的晶界湮没机理的晶体相场法研究

应用晶体相场方法研究高温应变下的预熔化晶界位错湮没机理. 结果表明, 原预熔化晶界上的位错在应变作用下发生分离运动, 形成新晶界, 即亚晶界. 该过程的实质是生成了亚晶粒; 亚晶界的迁移过程的本质是亚晶粒长大、吞噬旧晶粒的过程; 亚晶界之间的湮没是亚晶粒完全吞噬旧晶粒过程的结束, 体系转变成为单个晶粒结构. 根据原子密度序参数沿x和y方向的投影值随应变量的变化特征, 可以揭示出高温应变作用下, 预熔化亚晶界相遇湮没的本质是两对极性相反的偶极子位错对发生二次湮没, 该湮没的微观过程是通过位错连续二次滑移湮没而实现的, 其湮没的速率较低温时的湮没速率要小许多.     

The Thin Film Equation with Non-Zero Contact Angle: A Singular Perturbation Approach

In this paper we consider the thin film equation with prescribed non-zero contact angle condition for a large class of mobility coefficients, in dimension 1. We prove the global in time existence of weak solutions by using a diffuse approximation of the free boundary condition. This approach, which can be physically motivated by the introduction of singular disjoining/conjoining pressure forces had been suggested in particular by Bertsch et al. in [11 Bertsch , M. , Giacomelli , L. , Karali , G. ( 2005 ). Thin-film equations with “partial wetting” energy: Existence of weak solutions . Phys. D 209 : 17 – 27 .[Crossref], [Web of Science ®] , [Google Scholar]].     

Explicit iteration and unbounded solutions for fractional integral boundary value problem on an infinite interval

By employing the monotone iterative technique, we not only establish the existence of the unique solution for a fractional integral boundary value problem on semi-infinite intervals, but also develop an explicit iterative sequence for approximating the solution and give an error estimate for the approximation, which is an important improvement of existing results.     

连接阻尼对弹性杆纵向碰撞响应的影响

分析了刚度和阻尼并存的一般边界条件下线弹性杆与刚体的纵向碰撞过程,得到了碰撞后第一个波动周期杆振动的位移、速度和应力的解析表达式,讨论了碰撞持续时间为2倍杆长与波速比的条件.将导出的解析表达式通过具体的算例代入计算,讨论了不同质量比、不同连接刚度条件下连接阻尼对于碰撞过程中杆中质点速度及应力响应的影响.研究表明,连接阻尼改变了受碰撞弹性杆的振动模式,连接阻尼影响着碰撞反射波速度和应力的突变幅度;连接阻尼增大,杆中速度和应力响应分布变平缓:在连接刚度较大的情况下,连接阻尼变化对于杆中质点速度和应力影响较大;碰撞持续时间与质量比、连接刚度、连接阻尼及杆长有关,与碰撞的初速度无关;在质量比较大的情况下,连接阻尼使得反射波到达杆碰撞端时,杆端的应力有显著的变化.     

有限空间中经典场的正则量子化

从离散的角度研究带边界的1+1维经典标量场和Dirac场的正则量子化问题. 与以往不同的是, 这里将时间和空间两个变量同时进行变步长的离散, 应用变步长离散的变分原理, 得到离散形式的运动方程、边界条件和能量守恒的表达式. 然后, 根据Dirac理论, 将边界条件当作初级约束, 将边界条件和内在约束统一处理. 研究表明, 采用此方法, 不仅在每个离散的时空格点上能够建立起Dirac括号, 从而可以完成该模型的正则量子化;而且, 该方法还保持了离散情况下的能量守恒.     

微平行管道内Eyring流体的电渗滑移流动

研究了微平行管道内非牛顿流体––Eyring 流体在外加电场力和压力作用下的电渗流动. 在考虑微尺度效应, 电场作用, 非牛顿特性, 滑移边界等情况下, 建立Eyring流体在微平行管道内电渗流动的力学模型. 通过解线性Possion-Boltzmann方程和Cauchy动量方程, 给出Eyring 流体速度分布的精确解和近似解析解, 并探讨了上述因素对电渗流动的影响. 将电场力和压力对于Eyring流体电渗流动的速度分布的影响进行了比较分析, 得到有意义的结果.     

Stabilization of transmission coupled wave and Euler–Bernoulli equations on Riemannian manifolds by nonlinear feedbacks

We consider the transmission system of coupling wave equations with Euler–Bernoulli equations on Riemannian manifolds. By introducing nonlinear boundary feedback controls, we establish the exponential and rational energy decay rate for the problem. Our proofs rely on the geometric multiplier method.     

The Green function for the mixed problem for the linear Stokes system in domains in the plane

We construct the Green function for the mixed boundary value problem for the linear Stokes system in a two‐dimensional Lipschitz domain.     

Application of transparent boundary conditions to high-order finite-difference schemes for the wave equation in waveguides

We propose a method for generating finite-difference approximations of transparent boundary conditions (TBCs) with the fourth and sixth order in space. It is based on the wave equation solution continuation extra two or three layers of grid points outside the computational domain to use them in central-difference operators on approaching the boundary. We present the theoretical background of the method, give estimates of computational resources, and discuss accuracy and stability results of numerical tests in 1D and 2D cases.     

Fully nonlinear singularly perturbed equations and asymptotic free boundaries

In this paper we study one-phase fully nonlinear singularly perturbed elliptic problems with high energy activation potentials, ζε(u) with ζε→δ₀⋅∫ζ. We establish uniform and optimal gradient estimates of solutions and prove that minimal solutions are non-degenerated. For problems governed by concave equations, we establish uniform weak geometric properties of approximating level surfaces. We also provide a thorough analysis of the free boundary problem obtained as a limit as the ε-parameter term goes to zero. We find the precise jumping condition of limiting solutions through the phase transition, which involves a subtle homogenization process of the governing fully nonlinear operator. In particular, for rotational invariant operators, F(D²u), we show the normal derivative of limiting function is constant along the interface. Smoothness properties of the free boundary are also addressed.