Numerical-Value Perturbation Method with Application of Solving Convective-Diffusion Integral Equation

The convective--diffusion equation is of primary importance in such fields as fluid dynamics and heat transfer hi the numerical methods solving the convective-diffusion equation, the finite volume method can use conveniently diversified grids (structured and unstructured grids) and is suitable for very complex geometry The disadvantage of FV methods compared to the finite difference method is that FV-methods of order higher than second are more difficult to develop in three-dimensional cases. The second-order central scheme (2cs) offers a good compromise among accuracy, simplicity and efficiency, however, it will produce oscillatory solutions when the grid Reynolds numbers are large and then very fine grids are required to obtain accurate solution. The simplest first-order upwind (IUW) scheme satisfies the convective boundedness criteria, however. Its numerical diffusion is large. The power-law scheme, QMCK and second-order upwind (2UW) schemes are also often used in some commercial codes. Their numerical accurate are roughly consistent with that of ZCS. Therefore, it is meaningful to offer higher-accurate three point FV scheme. In this paper, the numerical-value perturbational method suggested by Zhi Gao is used to develop an upwind and mixed FV scheme using any higher-order interpolation and second-order integration approximations, which is called perturbational finite volume (PFV) scheme. The PFV scheme uses the least nodes similar to the standard three-point schemes, namely, the number of the nodes needed equals to unity plus the face-number of the control volume. For instanc6, in the two-dimensional (2-D) case, only four nodes for the triangle grids and five nodes for the Cartesian grids are utilized, respectively. The PFV scheme is applied on a number of 1-D problems, 2~Dand 3-D flow model equations. Comparing with other standard three-point schemes, The PFV scheme has much smaller numerical diffusion than the first-order upwind (IUW) scheme, its numerical accuracy are also higher than the second-order central scheme (2CS), the power-law scheme (PLS), the QUICK scheme and the second-order upwind(ZUW) scheme.

Integration of a photonic crystal polarization beam splitter and waveguide bend

In this work, we present the design of an integrated photonic-crystal polarization beam splitter (PC-PBS) and a low-loss photonic-crystal 60 waveguide bend. Firstly, the modal properties of the PC-PBS and the mechanism of the low-loss waveguide bend are investigated by the two-dimensional finite-difference time-domain (FDTD) method, and then the integration of the two devices is studied. It shows that, although the individual devices perform well separately, the performance of the integrated circuit is poor due to the multi-mode property of the PC-PBS. By introducing deformed airhole structures, a single-mode PC-PBS is proposed, which significantly enhance the performance of the circuit with the extinction ratios remaining above 20dB for both transverse-electric (TE) and transverse-magnetic (TM) polarizations. Both the specific result and the general idea of integration design are promising in the photonic crystal integrated circuits in the future. (C) 2009 Optical Society of America

The research and progress of micro-fabrication technologies of two-dimensional photonic crystal

The novel material of photonic crystal makes it possible to control a photon, and the photonic integration will have breakthrough progress due to the application of photonic crystal. It is based on the photonic crystal device that the photonic crystal integration could be realized. Therefore, we should first investigate photonic crystal devices based on the active and the passive semiconductor materials, which may have great potential application in photonic integration. The most practical and important method to fabricate two-dimensional photonic crystal is the micro-manufacture method. In this paper, we summarize and evaluate the fabrication methods of two-dimensional photonic crystal in near-infrared region, including electron beam lithography, selection of mask, dry etching, and some works of ours. This will be beneficial to the study of the photonic crystal in China.

Micro-mould method for self-assembling three-dimensional opal photonic crystals

By vertical sedimentation, silica micro-spheres were grown in different shapes of concave micro-zones which were etched on a (100) p-silicon substrate. The following were found: this method can effectively raise the quality of films by avoiding cracks; the geometry of the micro-zones affects the sediment of the film; regular hexagons and triangles best facilitate the growth of photonic crystals. This method is practical for its ability to fabricate self-assembly photonic crystals in previously designed small areas.

SELF-CONSISTENT TREATMENT OF 3-DIMENSIONAL - 2-DIMENSIONAL AND 2-DIMENSIONAL - 2-DIMENSIONAL RESONANT-TUNNELING IN DOUBLE-BARRIER STRUCTURES

By using a transfer-matrix method on the basis of two-dimensional (2D) Bloch sums in accordance with a tight-binding scheme, a self-consistent calculation on the resonant tunneling in asymmetric double-barrier structures is presented, in which contributions to resonant tunneling from both three-dimensional (3D) electrons in the contacts and 2D electrons in the spacer or accumulation layers are considered simultaneously. The charge buildup effect on the current versus voltage (I-V) curves is evaluated systematically, showing quantitatively how it results in the I-V bistability and enhanced differences between I-V curves for positive and negative bias in an asymmetric double-barrier structure. Special attention is focused on the interaction between 3D-2D and 2D-2D resonant-tunneling processes, including the suppression of 2D-2D resonant tunneling by the charge buildup in the well accompanying the 3D-2D resonant tunneling. The effects of the emitter doping condition (doping concentration, spacer thickness) on the presence of two types of quasi-2D levels in the emitter accumulation layers, and on the formation of a potential bulge in the emitter region, are discussed in detail in relation to the tunneling process.

A NEW METHOD FOR MEASURING THE EFFECTIVE DIFFUSION CONSTANT OF 2-DIMENSIONAL ELECTRONS IN THE PRESENCE OF MAGNETIC-FIELDS

The transient charge response Q(t) of a two-dimensional electron gas (2DEG) in GaAs/AlxGa1-xAs heterostructures to a small pulse of the gate voltage, applied between the top gate and source electrodes in a Corbino structure, was employed to directly measure the effective diffusion constant of a 2DEG in the quantum Hall regime. The measured diffusion constant D showed a drastic change as the magnetic field was swept through the integer fillings of the Landau levels.

U-transformation-finite element method in 3-dimensional analysis of orthotropic laminates

For an orthotropic laminate, an equivalent system with doubly cyclic periodicity is introduced. Then a 3-dimensional finite element model for the equivalent system is transformed into the unitary space, where the large finite element matrix equation is decoupled into some small matrix equations. Such a decoupling very efficiently reduces the computational effort. For an orthotropic laminate with four clamped edges, no exact elasticity solution is available, and the deflection values predicted by different methods have a considerable difference each other for a small length-to-thickness ratio. The present predictions are the largest because the present method is a full 3-dimensional finite element analysis without superfluous constraints. Illustrative numerical examples are presented to observe the distributions of stresses through the thickness of the laminates. (C) 2010 Elsevier Ltd. All rights reserved.

A new method for fabrication of three-dimensional polymer micropatterning - Microtransfer molding

Microtransfer molding (muTM) is a kind of soft lithography for polymer micropatterning. In muTM, a liquid prepolymer(or concentrated polymer solution) is applied to the patterned surface of an elastomeric mold and then brought into the contact with a substrate. After prepolymer is cured thermally or by UV light, the elastomeric mold is peeled away. A pattern is left on the surface of the substrate. In this study, similar to300 nm lines and three-dimensional patterns of PMMA and epoxy on planar and/or non-planar substrates are realized.

Applications of the method of three-dimensional projection of a molecule in quantitative structure-activity relationship of phenol derivatives

Five variables for phenol derivatives were calculated by molecular projection in three-dimensional space which were combined with eight quantum-chemical parameters and three Am indices. These variables were selected by using leaps-and-bounds regression analysis. Multiple linear regression analysis and artificial neural networks' were performed, and the results obtained by using. artificial neural networks are superior than that obtained by using multiple linear regression.

A method to construct a third-generation horseradish peroxidase biosensor: Self-assembling gold nanoparticles to three-dimensional sol-gel network

A novel method for fabrication of horseradish peroxidase biosensor has been developed by self-assembling gold nanoparticles to a thiol-containing sol-gel network. A cleaned gold electrode was first immersed in a hydrolyzed (3-mercaptopropyl)-trimethoxysilane (MPS) sol-gel solution to assemble three-dimensional silica gel, and then gold nanoparticles were chemisorbed onto the thiol groups of the sol-gel network. Finally, horseradish peroxidase (HRP) was adsorbed onto the surface of the gold nanoparticles. The distribution of gold nanoparticles and HRP was examined by atomic force microscopy (AFM). The immobilized horseradish peroxidase exhibited direct electrochemical behavior toward the reduction of hydrogen peroxide. The performance and factors influencing the performance of the resulting biosensor were studied in detail. The resulting biosensor exhibited fast amperometric response (2.5 s) to H2O2. The detection limit of the biosensor was 2.0 mumol L-1, and the linear range was from 5.0 mumol L-1 to 10.0 mmol L-1. Moreover, the studied biosensor exhibited high sensitivity, good reproducibility, and long-term stability.

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.