某些半线性波动方程均匀化的矫正

本文处理具有H_0~1初值的半线性热方程均匀化的矫正问题．     

基于渐进均匀化的平纹编织复合材料低速冲击多尺度方法

针对平纹编织复合材料低速冲击响应和损伤问题,提出了一种多尺度分析方法. 首先, 建立微观尺度单胞模型,引入周期性边界条件,采用最大主应力失效准则和直接刚度退化模型表征纤维丝和基体的损伤起始与演化,预测了纤维束的弹性性能和强度性能. 其次,将这些性能参数代入介观尺度单胞模型,基于Hashin和Hou的混合失效准则以及连续介质损伤模型对介观尺度单胞进行6种边界条件下的渐进损伤模拟.然后采用渐进均匀化方法,以介观尺度单胞为媒介预测了0$^\circ$和90$^\circ$子胞的性能参数,并建立平纹编织复合材料的子胞模型,进而扩展成为材料的宏观尺度低速冲击模型. 在此基础上,研究了平纹编织复合材料低速冲击下的力学响应与损伤特征.结果表明:宏观冲击仿真和试验吻合较好, 验证了多尺度方法的正确性;最大接触力、材料吸能和分层面积均随冲击能量的增大而增大,分层损伤轮廓逐渐从椭圆形向圆形转化;基体拉伸和压缩损伤的长轴方向分别与子胞材料主方向正交和一致,损伤面积前者远大于后者.      

考虑蜂窝高度效应的蜂窝夹芯板稳定性分析

蜂窝芯层等效弹性参数因受表板影响与其高度紧密相关,而传统蜂窝夹芯板稳定性模型未对其加以考虑。本文基于精化锯齿层合板理论,建立了蜂窝夹芯板稳定性模型。模型借助于解析均匀化方法获取蜂窝芯层等效模量,并因引入该方法而能够反映由蜂窝高度改变引起的蜂窝芯子等效模量变化对屈曲载荷产生的影响,即捕捉到了蜂窝芯子的高度效应。以四边简支蜂窝夹芯方板受单向面内压缩载荷作用为例进行了算例分析。算例结果表明,蜂窝芯子高度效应在蜂窝高度较低时明显,随着蜂窝高度增加,高度效应逐渐减弱。此外,高度效应在蜂窝芯层厚度比例较大时明显,随着蜂窝芯层厚度比例的持续下降,高度效应减弱直至消失。     

A model of a homogenized cavity corresponding to a multinozzle droplet generator for continuous ink-jet printers

We modelize the behavior of a vibrating fluid cavity. Small nozzles are uniformly distributed in one direction on a side of the cavity. By means of asymptotic expansion in powers of the smallest dimension of the cavity, including boundary layer terms, we get the convergence of the solution of the three-dimensional problem, as well as the convergence of the solution of the “homogenized” three-dimensional problem towards the solution of the same two-dimensional problem. Numerical experiments have been carried out in order to illustrate the previous theoretical results. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 821–842, 1998     

一类拟线性抛物方程的均匀化

本文研究具有振荡系数的二阶抛物方程δｔｂ（ｕ）－δｘｉ（αｉｊ（ｘ／ε）δｘｊｕ＋αｉ（ｂ（ｕ）））＝ｆ（ｂ（ｕ））的渐近性态。由于函数ｂ（ｕ）的导函数ｂ‘（ｕ）允许为非线性函数，并可在ｕ＝０处退化，研究了均匀化问题通常的能量方法在这里行不通。     

小周期复合材料热传导问题的双尺度渐近展开及收敛性分析

利用双尺度渐近展开和均匀化思想讨论了小周期复合材料的热传导问题,得到了具有高阶震荡系数的抛物型方程的渐近展开式,并证明了当Ω为R~2中的光滑的区域时渐近展开式在空间L~2(0,T;H~1(Ω))中具有较好的收敛性.     

Discrete stochastic approximations of the Mumford–Shah functional

We propose a new Γ-convergent discrete approximation of the Mumford–Shah functional. The discrete functionals act on functions defined on stationary stochastic lattices and take into account general finite differences through a non-convex potential. In this setting the geometry of the lattice strongly influences the anisotropy of the limit functional. Thus we can use statistically isotropic lattices and stochastic homogenization techniques to approximate the vectorial Mumford–Shah functional in any dimension.     

Drug nanocrystals for the formulation of poorly soluble drugs and its application as a potential drug delivery system

Formulation of poorly soluble drugs is a general intractable problem in pharmaceutical field, especially those compounds poorly soluble in both aqueous and organic media. It is difficult to resolve this problem using conventional formulation approaches, so many drugs are abandoned early in discovery. Nanocrystals, a new carrier-free colloidal drug delivery system with a particle size ranging from 100 to 1000 nm, is thought as a viable drug delivery strategy to develop the poorly soluble drugs, because of their simplicity in preparation and general applicability. In this article, the product techniques of the nanocrystals were reviewed and compared, the special features of drug nanocrystals were discussed. The researches on the application of the drug nanocrystals to various administration routes were described in detail. In addition, as introduced later, the nanocrystals could be easily scaled up, which was the prerequisite to the development of a delivery system as a market product.     

A stochastic model for fronts in porous media

We analyze a stochastic model for the motion of fronts in two-phase fluids and derive upscaled equations for the capillary pressure. This extends results of [11], where the same law for the capillary pressure was derived under an assumption on typical explosion patterns. With the work at hand we remove that assumption and show that in the stochastic case the upscaled equations hold almost surely.