Boundary knot method for 2D and 3D Helmholtz and convection-diffusion problems under complicated geometry

The boundary knot method (BKM) of very recent origin is an inherently meshless, integration-free, boundary-type, radial basis function collocation technique for the numerical discretization of general partial differential equation systems. Unlike the method of fundamental solutions, the use of non-singular general solution in the BKM avoids the unnecessary requirement of constructing a controversial artificial boundary outside the physical domain. The purpose of this paper is to extend the BKM to solve 2D Helmholtz and convection-diffusion problems under rather complicated irregular geometry. The method is also first applied to 3D problems. Numerical experiments validate that the BKM can produce highly accurate solutions using a relatively small number of knots. For inhomogeneous cases, some inner knots are found necessary to guarantee accuracy and stability. The stability and convergence of the BKM are numerically illustrated and the completeness issue is also discussed.

含瓦斯“试样”突出现象的RFPA^2D数值模拟

运用新近开发的岩石破坏过程分析ＲＦＰＡ＾２Ｄ（Ｒｏｃｋ Ｆａｉｌｕｒｅ Ｐｒｏｃｅｓｓ Ａｎａｌｙｓｉｓ）系统，以含瓦斯煤岩的破坏过程分析为例，通过对含瓦斯煤岩突出孕育机制及其声发射的数值模拟，说明了数值模拟方法给含瓦斯煤岩空出机制及其预测理论的发展所带来的新契机，数值模拟再现了含瓦斯煤岩突出的发生、发展过程，模拟结果表明，复杂的瓦斯煤岩断裂，突出现象可能是一些简单机理的演化结果。

An Extension of 2D Janbu’s Generalized Procedure of Slices for 3D Slope Stability Analysis II—Numerical Method and Applications

This paper provides a numerical approach on achieving the limit equilibrium method for 3D slope stability analysis proposed in the theoretical part of the previous paper. Some programming techniques are presented to ensure the maneuverability of the method. Three examples are introduced to illustrate the use of this method. The results are given in detail such as the local factor of safety and local potential sliding direction for a slope. As the method is an extension of 2D Janbu's generalized procedure of slices (GPS), the results obtained by GPS for the longitudinal sections of a slope are also given for comparison with the 3D results. A practical landslide in Yunyang, the Three Gorges, of China, is also analyzed by the present method. Moreover, the proposed method has the advantages and disadvantages of GPS. The problem frequently encountered in calculation process is still about the convergency, especially in analyzing the stability of a cutting corner. Some advice on discretization is given to ensure convergence when the present method is used. However, the problem about convergency still needs to be further explored based on the rigorous theoretical background.

岩石剪切破坏过程的RFPA~(2D)数值模拟

运用岩石破裂与失稳过程分析RFPA2D系统,对岩石剪切破裂过程进行了数值模拟研究。将剪切岩石视为非均匀弹-脆岩石材料,模拟结果再现了岩石剪切滑动形成从变形到破坏直至失稳的全过程,剪断面是滑动形成的主要形式,并首先在试样一端出现,然后再形成由一端及里的剪断面扩展直至另一端最后产生剪断面破坏贯通,形成统一的滑动面,岩石剪切破裂面分形维数还对应着剪断面的粗糙程度和力学行为。

2D Kinetics and Forced Dissociation of Selectin-ligand Bindings

Cell adhesion is crucial to many pathophysiological processes, such as inflammatory reaction and tumor metastasis. It is mediated by specific interactions between receptors and ligands, and provides the physical linkages among cells. For example, interactions between selectins and glycoconjugate ligands mediate leukocyte initially tethering to and subsequently rolling on vascular surfaces in sites of inflammation or injury, which is determined by their fast kinetic rates. To mediate cell adhesion, the interacting receptors and ligands must anchor to apposing surfaces of two cells or a cell and the substratum, i.e. , the so-called two-dimensional (2D) binding, which differs from interactions in the fluid phase, i.e. , the three-dimensional (3D) binding. How structural variations and surface environments of interacting molecules affect their 2D kinetics, and how external forces manipulate their dissociation has little been known quantitatively, and nowadays attracts more and more attentions.

Parametric Analysis for Monitoring 2D Kinetics of Receptor-Ligand binding

Thermal fluctuation approach is widely used to monitor association kinetics of surface-bound receptor-ligand interactions. Various protocols such as sliding standard deviation (SD) analysis (SSA) and Page's test analysis (PTA) have been used to estimate two-dimensional (2D) kinetic rates from the time course of displacement of molecular carrier. In the current work, we compared the estimations from both SSA and modified PTA using measured data from an optical trap assay and simulated data from a random number generator. Our results indicated that both SSA and PTA were reliable in estimating 2D kinetic rates. Parametric analysis also demonstrated that such the estimations were sensitive to parameters such as sampling rate, sliding window size, and threshold. These results furthered the understandings in quantifying the biophysics of receptor-ligand interactions.

Inductively coupled plasma etching in fabrication of 2D InP-based photonic crystals

The authors developed an inductively coupled plasma etching process for the fabrication of hole-type photonic crystals in InP. The etching was performed at 70 degrees C using BCl3/Cl-2 chemistries. A high etch rate of 1.4 mu m/min was obtained for 200 nm diameter holes. The process also yields nearly cylindrical hole shape with a 10.8 aspect ratio and more than 85 degrees straightness of the smooth sidewall. Surface-emitting photonic crystal laser and edge emitting one were demonstrated in the experiments.

Optical interleaver based on directional coupler in a 2D photonic crystal slab with triangular lattice of air holes

A small-size optical interleaver based on directional coupler in a 2D photonic crystal slab with triangular lattice of air holes is designed and theoretically simulated using plane wave expansion and finite-difference time-domain method. The interleaver is formed by two parallel and identical photonic crystal slab waveguides which are separated by three rows of air holes. The coupling region is designed below the light line to avoid vertical radiation. The simulated results show that the coupling coefficient is increased and the final length of the interleaver is decreased by enlarging the radius of the middle row of air holes. The transmission properties are analyzed after the interleaver's structure is optimized, and around 100 GHz channel spacing can be got when the length of the interleaver is chosen as 40.5 mu m. (c) 2006 Elsevier B.V. All rights reserved.

Theoretical analysis about the influence of channel layer thickness on the 2D electron gas and its distribution in InP-based high-electron-mobility transistors

The principle of high-electron-mobility transistor (HEMT) and the property of two-dimensional electron gas (2DEG) have been analyzed theoretically. The concentration and distribution of 2DEG in various channel layers are calculated by numerical method. Variation of 2DEG concentration in different subband of the quantum well is discussed in detail. Calculated results show that sheet electron concentration of 2DEG in the channel is affected slightly by the thickness of the channel. But the proportion of electrons inhabited in different subbands can be affected by the thickness of the channel. When the size of channel lies between 20-25 nm, the number of electrons occupying the second subband reaches the maximum. This result can be used in parameter design of materials and devices.

Size quantization effects in InAs self-assembled islands on InP(001) at the onset of 2D-to-3D transition

Photoluminescence spectroscopy has been used to investigate self-assembled InAs islands in InAlAs grown on InP(0 0 1) by molecular beam epitaxy, in correlation with transmission electron microscopy. The nominal deposition of 3.6 monolayers of InAs at 470 degrees C achieves the onset stage of coherent island formation. In addition to one strong emission around 0.74 eV, the sample displaces several emission peaks at 0.87, 0.92. 0.98, and 1.04 eV. Fully developed islands that coexist with semi-finished disk islands account for the multipeak emission. These results provide strong evidence of size quantization effects in InAs islands. (C) 1999 Elsevier Science B.V. All rights reserved.

液体多脉冲及2D NMR实验的计算机模拟

现代多脉冲及2D NMR技术是过去十年中发展起来的崭新的NMR实验方法。计算机模拟做为NMR实验的强有力分析手段已日益受到重视。国内这方面工作开展得尚很少；国外发表的工作主要采用的是数字模拟，存在分析结果不够直观、物理意义不够清晰等缺陷。本论文工作采用乘积算符方法研制出对分析多脉冲及2D NMR实验普适的模拟程序PROPER；在乘积算符基础上，针对磁等性自旋体系，提出了实用的对称化乘积算符及多量子积算符方法。一、多脉冲及2D NMR实验的计算机模拟 1. 采用乘积算符方法在本所PDP－11／23微机上研制了多脉冲及2D NMR实验的模拟程序PROPER。该程序对不超过4核（I ＝ 1／2）的同核及异核弱耦合自旋体系非选择性脉冲序列的分析是普遍适用的。受计算机内存的限制，PROPER程序所能处理的脉冲序列脉冲间隔数目一般不超过10。2. 应用PROPER模拟程序对INEP和DEPT脉冲序列进行了分析比较；特别对BIRD脉冲序列的各种相位变型进行了模拟分析，给出了分析结果，分析过程中考虑了影响BIRD作用效果的同核耦合因素。应用结果表明，PROPER程序计算正确、迅速、给出的模拟结果较通常的数字模拟方法简单、直观、物理意义清楚，便于分析。由于采用算符模拟，结果的输出打印比较费时。目前，PROPER程序正在改进和完善之中。二、多脉冲及2D NMR实验的密度算符描述 1. 针对磁等性自旋（I ＝ 1／2）体系，首次提出了对称化乘积算符描述方法。在通常的乘积算符基础上，引入了对称化乘积算符，并对其数理基础进行了详细论证。推导了算符循环对易关系决定的Liourill-Von Neumann方程的解，给出了算符间普遍存在的循环对易关系及其相应的演化公式。据此，以InS(I = 1/2, S = 1/2; n = 2,3)自旋体系为例，对DEPT脉冲序列进行了分析；结果表明，该方法较通常的乘积算符方法对磁等性自旋体系的分析要简单、实用，且物理意义更加明确。由于该方法涉及较多的算符对易关系，因此不易计算机编程。2. 在对称化乘积算符基础上引入了多量子积算符的概念。以In(I = 1/2; n = 2,3)体系为例，给出了两者的互换关系。推导出了具有标量耦合作用的两组合粒子体系普适的多量子积算符环对易关系及相应的演化解析式。多量子积算符方法可望将1／2－自旋磁等性组合粒子表象与自旋大于1／2的单粒子表象统一起来，并为计算机模拟提供新的数学方法。该方法尚有待于进一步研究。