关于Jacobsthal数和Jacobsthal-Lucas数的r-循环矩阵的行列式和逆

和 是n阶r-循环矩阵, 其中 , 是Jacobsthal数, , 是Jacobsthal-Lucas数, 研究得出了 和 的关于Jacobsthal数和Jacobsthal-Lucas数的行列式的值. 同时, 计算出了矩阵 和 的逆.     

Describing Hydrodynamic Particle Removal from Surfaces Using the Particle Reynolds Number

The fundamental processes related to the removal of fine particles from surfaces in a hydrodynamic flow field are not adequately understood. A critical particle Reynolds number approach is proposed to assess these mechanisms for fine particles when surface roughness is small compared to particle diameter. At and above the critical particle Reynolds number, particle removal occurs, while below the critical value, particles remain attached to a surface. The system under consideration consists of glass particles adhering to a glass surface in laminar channel flow. Our results indicate rolling is the removal mechanism, which is in agreement with the literature. Theoretical results of the critical particle Reynolds number model for rolling removal are in general agreement with experimental data when particle size distribution, particle and surface roughness, and system Hamaker constant are taken into account.     

金刚石镀膜装置中的等离子体参数测量

利用平行马赫探针和单探针对金刚石镀膜装置中的等离子体漂移速度、,离子密度及电子温度进行了测量,采用ＣｈｕｎｇＫｙｕ－Ｓｕｎ理论对平行马赫探针数据进行分析得到的马赫数为０．２８,电子温度为５ｅＶ,等离子体流速约为９８０ｍ．ｓ＾－１。单探针测行离子密度在１０＾１８～１０＾２０ｍ＾－３的范围内,电子温度在２－８ｅＶ的范围内。     

高功率激光稳定腔选模分析

讨论了在有限菲涅耳数时，稳定凹－凸腔的高功率激光选模特性，研究表明当稳定凹－凸腔工作在临近界稳区时，基模体积显著提高，具有良好的选模效果。     

Indentation studies on 〈1 0 0〉, 〈0 0 1〉 and 〈1 0 1〉 face of ammonium dihydrogen phosphate (ADP) single crystals: A novel nonlinear optical material

In the present work, Vickers microhardness measurements were carried out on different faces i.e. (1 0 0), (0 0 1) and (1 0 1) of ammonium dihydrogen phosphate (ADP) single crystals grown by slow evaporation solution technique at room temperature in the load ranging from 0.2 to 2 N. The obtained results show that the load independent hardness values are 0.8, 0.7 and 0.66 GPa, respectively at different faces of ADP crystal. From the crack length measurements, the fracture toughness values (K_c) was estimated using Evans and Anstis model and the present studies suggest that Evans model is more relevant when compared to Anstis model. The load variation of some mechanical properties viz. brittle index number (B_i) and yield strength (σ_y) for ADP have also been calculated for the first time.     

伏安特性实验中电压表的改进应用

改进了传统电压表的面板设计,使电压表不仅能测两端的电压,还能测量自身的电流.于是在测量元件的伏安特性实验中,使用该电压表可以不考虑被测器件电阻的大小,均采用电流表外接的接线方式,即让电压表分流.再利用电压表的电流测量功能,测出自身分流电流的大小,从而可以准确得出被测器件的电流与两端的电压.     

A first-order system approach for diffusion equation. II: Unification of advection and diffusion

In this paper, we unify advection and diffusion into a single hyperbolic system by extending the first-order system approach introduced for the diffusion equation [J. Comput. Phys., 227 (2007) 315–352] to the advection–diffusion equation. Specifically, we construct a unified hyperbolic advection–diffusion system by expressing the diffusion term as a first-order hyperbolic system and simply adding the advection term to it. Naturally then, we develop upwind schemes for this entire   system; there is thus no need to develop two different schemes, i.e., advection and diffusion schemes. We show that numerical schemes constructed in this way can be automatically uniformly accurate, allow O(h)$O(h)$ time step, and compute the solution gradients (viscous stresses/heat fluxes for the Navier–Stokes equations) simultaneously to the same order of accuracy as the main variable, for all Reynolds numbers. We present numerical results for boundary-layer type problems on non-uniform grids in one dimension and irregular triangular grids in two dimensions to demonstrate various remarkable advantages of the proposed approach. In particular, we show that the schemes solving the first-order advection–diffusion system give a tremendous speed-up in CPU time over traditional scalar schemes despite the additional cost of carrying extra variables and solving equations for them. We conclude the paper with discussions on further developments to come.     

The influence of cell geometry on the Godunov scheme applied to the linear wave equation

By studying the structure of the discrete kernel of the linear acoustic operator discretized with a Godunov scheme, we clearly explain why the behaviour of the Godunov scheme applied to the linear wave equation deeply depends on the space dimension and, especially, on the type of mesh. This approach allows us to explain why, in the periodic case, the Godunov scheme applied to the resolution of the compressible Euler or Navier–Stokes system is accurate at low Mach number when the mesh is triangular or tetrahedral and is not accurate when the mesh is a 2D (or 3D) cartesian mesh. This approach confirms also the fact that a Godunov scheme remains accurate when it is modified by simply centering the discretization of the pressure gradient.