Regularity of optimal sets for some functional involving eigenvalues of an operator in divergence form

In this paper we consider minimizers of the functional$\min \{{\lambda }_1(\mathrm{\Omega })+\cdots +{\lambda }_k(\mathrm{\Omega })+\mathrm{\Lambda }|\mathrm{\Omega }|,:\mathrm{\Omega }\subset D\text{ open}\}$ where $D\subset {\mathbb{R}}^d$ is a bounded open set and where $0<{\lambda }_1(\mathrm{\Omega })\le \cdots \le {\lambda }_k(\mathrm{\Omega })$ are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets ${\mathrm{\Omega }}^{⁎}$ have finite perimeter and that their free boundary $\partial {\mathrm{\Omega }}^{⁎}\cap D$ is composed of a regular part, which is locally the graph of a $C^{1,\alpha }$-regular function, and a singular part, which is empty if $d<d^{⁎}$, discrete if $d=d^{⁎}$ and of Hausdorff dimension at most $d-d^{⁎}$ if $d>d^{⁎}$, for some $d^{⁎}\in \{5,6,7\}$.     

Synthesis of nano-polycrystalline diamond from glassy carbon at pressures up to 25 GPa

ABSTRACT

Nano-polycrystalline diamond (NPD) with various grain sizes has been synthesized from glassy carbon at pressures 15–25?GPa and temperatures 1700–2300°C using multianvil apparatus. The minimum temperature for the synthesis of pure NPD, below which a small amount of compressed graphite was formed, significantly increased with pressure from ～1700°C at 15?GPa to ～1900°C at 25?GPa. The NPD having grain sizes less than ～50?nm was synthesized at temperatures below ～2000°C at 15?GPa and ～2300°C at 25?GPa, above which significant grain growth was observed. The grain size of NPD decreases with increasing pressure and decreasing temperature, and the pure NPD with grain sizes less than 10?nm is obtained in a limited temperature range around 1800–2000°C, depending on pressure. The pure NPD from glassy carbon is highly transparent and exhibits a granular nano-texture, whose grain size is tunable by selecting adequate pressure and temperature conditions.     

工艺因素对金属封装外引线弯曲疲劳的影响

考察了金属封装外壳制造工艺对外引线弯曲疲劳的影响,发现电镀镍是导致外引线弯曲次数明显减少的最主要工艺步骤,且随镀镍层厚度的增加,弯曲次数减少。此外还讨论了外引线的氢含量和晶粒度对引线抗疲劳能力的影响。     

Roles of SiH4 and SiF4 in growth and structural changes of poly-Si films

The structural properties of polycrystalline silicon films, prepared by plasma enhanced chemical vapor deposition system, with different flow rates of SiH₄/SiF₄ mixtures at 300 °C were investigated. This study indicates that the low hydrogen coverage on the growing surface, under optimum fluorine radicals, will be leaded to an improvement of crystallized area as compared with case of high hydrogen coverage surface. Moreover, the studies of the role of SiH₄ and SiF₄ radicals show that the SiH₄ radicals are important in the nucleation and growth of grains. However, SiF₄ radicals are effective in the structural change of grain boundaries regions and by this way, in the present system, establish the growth of grains under the dominant 〈1 1 0〉 direction. The stress investigation indicates that addition of high flow rate of SiF₄ in amorphous film, results in the nearly stress free films. Finally, we found that the changes in g-value reflect the changes in the intrinsic compressive and tensile stress in the both polycrystalline and amorphous silicon films.     

The microstructure of Cu films deposited by the self-ion assisted technique

The microstructures of Cu films deposited by the self-ion assisted, partially ionized beam (PIB) deposition technique under two different accelerating potentials, 0 KeV and 6 KeV, are compared. The 6 KeV film shows a bimodal (111) fiber and (100) fiber texture with an abundance of twin boundaries and a relatively large average grain size with a typical lognormal distribution. The 0 KeV film consists of small, mostly (111) oriented grains with islands of abnormally large (100) grains. The controlling factors for the abnormal growth of the (100) grains are discussed in relation to the observed microstructures, showing that all factors necessary for abnormal (100) growth are present in the films.     

Co-Segregation Effects on Boundary Migration

We analyze the effect of co-segregation on the mobility of grain boundaries within the framework of the impurity drag theory originally proposed by Cahn and Lücke and Stüwe for an ideal solution. The new derivation extends this model to the case where there are two types of impurities (or three components in the alloy). Since the resultant expression for the boundary mobility is complicated, numerical solutions were obtained for several cases to show how co-segregation affects the boundary mobility. Depending on the relative diffusivities of the two impurities which are both attracted to the boundary, the mobility may either increase or decrease with increasing concentration of one of the impurities. When one of the impurities is attracted to the boundary and the other repelled from the boundary, increasing the concentration of the attractive impurity can lead to a sharp decrease in the boundary mobility.     

On the application of slip boundary condition on curved boundaries

Hydrodynamic simulations of sloshing phenomena often involve the application of slip boundary condition at the wetted surfaces. If these surfaces are curved, the ambiguous nature of the normal vector in the discretized problem can interfere with the application of such a boundary condition. Even the use of consistent normal vectors, preferred from the point of view of conservation, does not assure good approximation of the continuum slip condition in the discrete problem, and non‐physical recirculating flow fields may be observed. As a remedy, we consider the Navier slip condition, and more successfully, the so‐called BC‐free boundary condition. Copyright © 2004 John Wiley & Sons, Ltd.     

A virtual boundary method with improved computational efficiency using a multi‐grid method

The flow around spherical, solid objects is considered. The boundary conditions on the solid boundaries have been applied by replacing the boundary with a surface force distribution on the surface, such that the required boundary conditions are satisfied. The velocity on the boundary is determined by extrapolation from the flow field. The source terms are determined iteratively, as part of the solution. They are then averaged and are smoothed out to nearby computational grid points. A multi‐grid scheme has been used to enhance the computational efficiency of the solution of the force equations. The method has been evaluated for flow around both moving and stationary spherical objects at very low and intermediate Reynolds numbers. The results shows a second order accuracy of the method both at creeping flow and at Re=100. The multi‐grid scheme is shown to enhance the convergence rate up to a factor 10 as compared to single grid approach. Copyright © 2004 John Wiley & Sons, Ltd.     

激光结晶a-Si:H SOI离子注入和快速退火

本文对激光结晶a-Si∶H SOI结构砷注入和快速退火行为作了研究.a-Si∶H激光结晶有Lp-LCR,OD,FCR-2,FCR-1四个结晶区.用剖面电镜观察了结晶区的结构.扩展电阻测量表明Lp-LCR区中有两种扩散机制,即杂质在晶粒体内扩散和沿缺陷扩散.OD区中有三种扩散形式,除有上述两种以外,还有沿缺陷的扩散.首次比较了沿晶界和缺陷的扩散速度.