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.

3D Anisotropic Elastoplastic-Damage Model and its Application in Simulating the Behavior of Rock Materials

A 3D anisotropic elastoplastic-damage model was presented based on continuum damage mechanics theory. In this model, the tensor decomposition technique is employed. Combined with the plastic yield rule and damage evolution, the stress tensor in incremental format is obtained. The derivate eigenmodes in the proposed model are assumed to be related with the uniaxial behavior of the rock material. Each eigenmode has a corresponding damage variable due to the fact that damage is a function of the magnitude of the eigenstrain. Within an eigenmodes, different damage evolution can be used for tensile and compressive loadings. This model was also developed into finite element code in explicit format, and the code was integrated into the well-known computational environment ABAQUS using the ABAQUS/Explicit Solver. Numerical simulation of an uniaxial compressive test for a rock sample is used to examine the performance of the proposed model, and the progressive failure process of the rock sample is unveiled.

Improving Nucleation in the Fabrication of High-Quality 3D Macro-Porous Copper Film through The Surface-Modification of A Polystyrene Colloid-Assembled Template

A new approach is developed to the fabrication of high-quality three-dimensional macro-porous copper films. A highly-ordered macroporous copper film is successfully produced on a polystyrene sphere (PS) template that has been modified by sodium dodecyl sulfate (SDS). It is shown that this procedure can change a hydrophobic surface of PS template into a hydrophilic surface. The present study is devoted to the influence of the electrolyte solution transport on the nucleation process. It is demonstrated that the permeability of the electrolyte solution in the nanochannels of the PS template plays an important role in the chemical electrodeposition of high-quality macroporous copper film. The permeability is drastically enhanced in our experiment through the surface modi. cation of the PS templates. The method could be used to homogeneously produce a large number of nucleations on a substrate, which is a key factor for the fabrication of the high-quality macroporous copper film.

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.

3D simulation of the micro indentation process and relative problems research

In this paper the finite element method was used to simulate micro-scale indentation process. The several standard indenters were simulated with 3D finite element model. The emphasis of this paper was the differences between 2D axisymmetric cone model and

Numerical Simulation of 3D-Thermal Field with Phase Transformation

以激光熔凝表面强韧化处理为背景,应用空间的弹塑性有限单元和高精度的数值算法、同时考虑材料组织性能的变化来模拟材料的温度场。主要研究激光熔凝加工中瞬时温度场数值模拟,同时考虑相变潜热的影响,为第二步热应力场及残余应力的数值模拟做准备。最后用算例验证了模型的正确性,并给出了不同时刻温度场的分布。

3D Finite Volume Scheme for Czochralski Crystal Growth

A general three-dimensional model is developed for simulation of the growth process of silicon single crystals by Czochralski technique. The numerical scheme is based on the curvilinear non-orthogonal finite volume discretization. Numerical solutions show that the flow and temperature fields in the melt are asymmetric and unsteady for 8’’ silicon growth. The effects of rotation of crystal on the flow structure are studied. The rotation of crystal forms the Ekman layer in which the temperature gradient along solid/melt surface is small.

3D Finite Volume Scheme for Czochralski Single Crystal Growth

Czochralski (Cz) technique, which is used for growing single crystals, has dominated the production of single crystals for electronic applications. The Cz growth process involves multiple phases, moving interface and three-dimensional behavior. Much has been done to study these phenomena by means of numerical methods as well as experimental observations. A three-dimensional curvilinear finite volume based algorithm has been developed to model the Cz process. A body-fitted transformation based approach is adopted in conjunction with a multizone adaptive grid generation (MAGG) technique to accurately handle the three-dimensional problems of phase-change in irregular geometries with free and moving surfaces. The multizone adaptive model is used to perform a three-dimensional simulation of the Cz growth of silicon single crystals.Since the phase change interface are irregular in shape and they move in response to the solution, accurate treatment of these interfaces is important from numerical accuracy point of view. The multizone adaptive grid generation (MAGG) is the appropriate scheme for this purpose. Another challenge encountered is the moving and periodic boundary conditions, which is essential to the numerical solution of the governing equations. Special treatments are implemented to impose the periodic boundary condition in a particular direction and to determine the internal boundary position and shape varying with the combination of ambient physicochemical transport process and interfacial dynamics. As indicated above that the applications and processes characterized by multi-phase, moving interfaces and irregular shape render the associated physical phenomena three-dimensional and unsteady. Therefore a generalized 3D model rather than a 2D simulation, in which the governing equations are solved in a general non-orthogonal coordinate system, is constructed to describe and capture the features of the growth process. All this has been implemented and validated by using it to model the low pressure Cz growth of silicon. Accuracy of this scheme is demonstrated by agreement of simulation data with available experimental data. Using the quasi-steady state approximation, it is shown that the flow and temperature fields in the melt under certain operating conditions become asymmetric and unsteady even in the absence of extrinsic sources of asymmetry. Asymmetry in the flow and temperature fields, caused by high shear initiated phenomena, affects the interface shape in the azimuthal direction thus results in the thermal stress distribution in the vicinity, which has serious implications from crystal quality point of view.

Comparisons of static, quasi-static and dynamic 3D porous media scale network models for two-phase immiscible flow in porous media

A dynamic 3D pore-scale network model is formulated for investigating the effect of interfacial tension and oil-water viscosity during chemical flooding. The model takes into account both viscous and capillary forces in analyzing the impact of chemical properties on flow behavior or displacement configuration, while the static model with conventional invasion percolation algorithm incorporates the capillary pressure only. From comparisons of simulation results from these models. it indicates that the static pore scale network model can be used successfully when the capillary number is low. With the capillary increases due to the enhancement of water viscosity or decrease of interfacial tension, only the quasi-static and dynamic model can give insight into the displacement mechanisms.

The Effects of Visual Object Size in The Depth Perception in KM Mouse

Whether mice perceive the depth of space dependent on the visual size of object targets was explored when visual cues such as perspective and partial occlusion in space were excluded. A mouse was placed on a platform the height of which is adjustable. The platform located inside a box in which all other walls were dark exception its bottom through that light was projected as a sole visual cue. The visual object cue was composed of 4x4 grids to allow a mouse estimating the distance of the platform relative to the grids. Three sizes of grids reduced in a proportion of 2/3 and seven distances with an equal interval between the platform and the grids at the bottom were applied in the experiments. The duration of a mouse staying on the platform at each height was recorded when the different sizes of the grids were presented randomly to test whether the Judgment of the mouse for the depth of the platform from the bottom was affected by the size information of the visual target. The results from all conditions of three object sizes show that time of mice staying on the platform became longer with the increase in height. In distance of 20 similar to 30 cm, the mice did not use the size information of a target to judge the depth, while mainly used the information of binocular disparity. In distance less than 20 cm or more than 30 cm, however, especially in much higher distance 50 cm, 60 cm and 70 cm, the mice were able to use the size information to do so in order to compensate the lack of binocular disparity information from both eyes. Because the mice have only 1/3 of the visual field that is binocular. This behavioral paradigm established in the current study is a useful model and can be applied to the experiments using transgenic mouse as an animal model to investigate the relationships between behaviors and gene functions.

Molecular docking and 3D-QSAR study of pyranmycin derivatives against 16S rRNA A site

To understand pharmacophore properties of pyranmycin derivatives and to design novel inhibitors of 16S rRNA A site, comparative molecular field analysis (CoMFA) approach was applied to analyze three-dimensional quantitative structure-activity relationship (3D-QSAR) of 17 compounds. AutoDock 3.0.5 program was employed to locate the orientations and conformations of the inhibitors interacting with 16S rRNA A site. The interaction mode was demonstrated in the aspects of inhibitor conformation, hydrogen bonding and electrostatic interaction. Similar binding conformations of these inhibitors and good correlations between the calculated binding free energies and experimental biological activities suggest that the binding conformations of these inhibitors derived from docking procedure were reasonable. Robust and predictive 3D-QSAR model was obtained by CoMFA with q(2) values of 0.723 and 0.993 for cross-validated and noncross-validated, respectively. The 3D-QSAR model built here will provide clear guidelines for novel inhibitors design based on the Pyranmycin derivatives against 16S rRNA A site. (c) 2005 Elsevier B.V. All rights reserved.

First-principles prediction of the magnetism of 3d transition-metal-doped Rocksalt MgO

Using first-principles band structure methods, we have systematically studied the electronic structures, magnetic stabilities, and half-metal properties of 3d transition-metal (TM) doped Rocksalt MgO compounds TMMg3O4 (TM = V, Cr, Mn, Fe, Co, and Ni). The calculations reveal that only CrMg3O4 has a ferromagnetic stability among the six compounds, which is explained by double-exchange mechanism. The magnetic stability is affected by the doping concentration of TM if the top valance band is composed of partially occupied t(2g) states. In addition, CrMg3O4 is a half-metallic ferromagnet. The origins of half-metallic and ferromagnetic properties are explored. The Curie temperature (T-c) of CrMg3O4 is 182 K. And it is hard for CrMg3O4 to deform due to the large bulk modulus and shear modulus, so it is a promising spintronic material. Our calculations provide the first available information on the magnetic properties of 3d TM-doped MgO.

The formation and electronic structures of 3d transition-metal atoms doped in silicon nanowires

Using first-principles methods, we systematically study the mechanism of defect formation and electronic structures for 3d transition-metal impurities (V, Cr, Mn, Fe, and Co) doped in silicon nanowires. We find that the formation energies of 3d transition-metal impurities with electrons or holes at the defect levels always increase as the diameters of silicon nanowires decrease, which suggests that self-purification, i.e., the difficulty of doping in silicon nanowires, should be an intrinsic effect. The calculated results show that the defect formation energies of Mn and Fe impurities are lower than those of V, Cr, and Co impurities in silicon nanowires. It indicates that Mn and Fe can easily occupy substitutional site in the interior of silicon nanowires. Moreover, they have larger localized moments, which means that they are good candidates for Si-based dilute magnetic semiconductor nanowires. The doping of Mn and Fe atom in silicon nanowires introduces a pair of energy levels with t(2) symmetry. One of which is dominated by 3d electrons of Mn or Fe, and the other by neighboring dangling bonds of Si vacancies. In addition, a set of nonbonding states localized on the transition-metal atom with e symmetry is also introduced. (C) 2008 American Institute of Physics. [DOI: 10.1063/1.3000445]

First-principles study of the electronic structures and magnetic properties of 3d transition metal-doped anatase TiO2

We study the electronic structures and magnetic properties of the anatase TiO2 doped with 3d transition metals (V, Cr, Mn, Fe, Co, Ni), using first-principles total energy calculations based on density functional theory (DFT). Using a molecular-orbital bonding model, the electronic structures of the doped anatase TiO2 are well understood. A band coupling model based on d-d level repulsions between the dopant ions is proposed to understand the chemical trend of the magnetic ordering. Ferromagnetism is found to be stabilized in the V-, Cr-, and Co-doped samples if there are no other carrier native defects or dopants. The ferromagnetism in the Cr- and Co-doped samples may be weakened by the donor defects. In the Mn-, and Fe-doped samples, the ferromagnetism can be enhanced by the acceptor and donor defects, respectively.