3D reconstruction of single rising bubble in water using digital image processing and characteristic matrix

Reconstructing the shape of a bubble will lay a firm foundation for further description of the dynamic characteristics of bubbly flow, especially for a single rising bubble or separate bubbles whose interaction could be neglected. In this case, the rising bubble is usually simulated as an ellipsoid consisting of two semi-eUipsoids up and down. Thus the projected image of a bubble consists of two semi-ellipses. In this paper, a method for reconstructing the ellipsoid bubble model is described following digital image processing, using the Hough transform in 2D ellipse parameter extraction which could cover most of the bubble edge points in the image. Then a method based on characteristic symmetric matrix is described to detect 3D bubble ellipsoid model parameters from 2D ellipse parameters of projection planes. This method can be applied to bubbles rising with low-velocity in static flow field much in conformity with the projection theory and the shape variation of the rising bubble. This method does not need to solve nonlinear equation sets and provides an easy way to calculate the characteristic matrix of a space ellipsoid model for deformed bubble. For bubble application, two assumed conditions and a calibration factor are proposed to simplify calculation and detection. Errors of ellipsoid center and three axes are minor. Errors of the three rotation angles have no negative effect on further study on bubbly flow.

Effect of Metal Contact and Rapid Thermal Annealing on Electrical Characteristics of Graphene Matrix

Development of graphene field effect transistors （GFETs） faces a serious challenge of graphene interface to the dielectric material. A single layer of intrinsic graphene has an average sheet resistance of the order of 1-5 kΩ/□. The intrinsic nature of graphene leads to higher contact resistance yielding into the outstanding properties of the material. We design a graphene matrix with minimized sheet resistance of 0.185 kΩ/□ with Ag contacts. The developed matrices on silicon substrates provide a variety of transistor design options for subsequent fabrication. The graphene layer is developed over 400 nm nickel in such a way as to analyze hypersensitive electrical properties of the interface for exfoliation. This work identifies potential of the design in the applicability of few-layer GFETs with less process steps with the help of analyzing the effect of metal contact and post-process anneMing on its electrical fabrication.

Computation of Jordan Chains by Generalized Characteristic Matrices

In this paper, we introduce a method to define generalized characteristic matrices of a defective matrix by the common form of Jordan chains. The generalized characteristic matrices can be obtained by solving a system of linear equations and they can be used to compute Jordan basis.

DYNAMIC CHARACTERISTICS ON PRECISION NC LATHE BASED ON MULTI-BODY SYSTEM THEORY

Based on multi-body system theory and the mainshafl system of precision NC lathe as object investigated, it is treated as a coupled rigid-flexible multi-body system which is made up of some rigid and elastic bodies in an especial linking mode. And a dynamic model is established, The problems of computing vibration characteristics are resolved by using multi-body system transfer matrix method, Resutts show that the mainshaft system of NC lathe is in the stable and reliable working area all the time. The method is simple and easy, the idea is clear. In addition, the method can be easily used and popularized in the other multi-body system.

Mathematical Description of Acousto-Optic Tunable Filter Orthogonal Polarizing Method

The transfer function of the optical splitting system of the acousto-optic tunable filter （AOTF） is deduced to be a reference to optical design. The characteristic matrix （ transfer function） of AOTF is used to describe quantitatively the characters of polarization elements in the orthogonal polarizing system. According to the characteristic matrix, the included angle of polarizer＇s transmission direction and polarization analyzer＇s transmission direction should be 90°. As a result the signal to noise ratio increased about 20 times though the light intensity was reduced to 54.3%,because both the transmittances of polarizer and polarization analyzer are 0. 74, which is an intrinsic character. The orthogonal polarizing method is an effective method to get rid of the influence of zero order light and improve the spectrum resolution and signal-to-noise ratio.

CHARACTERISTIC MATRICES AND SIMILARITY OF TIME-VARYING LINEAR DIFFERENTIAL SYSTEMS

In this paper, we discuss foe characteristic matrices and similarity of timevarying linear differential systems with emphasis on the relationship of similarityand characteristic matrices of the systems, obtaining the necessary and sufficientcondition for a matrix bein characteristic matrix, the necessary and sufficientcondition for time-varying linear systems being similar and the necessary andsufficient condition for a time-varying linear system being similar to a blockdiagonai system. We improve one of t,he main results of [4].

A SPLIT-CHARACTERISTIC FINITE ELEMENT MODEL FOR 1-D UNSTEADY FLOWS

An efficient and accurate solution algorithm was proposed for 1-D unsteady flow problems widely existing in hydraulic engineering. Based on the split-characteristic finite element method, the numerical model with the Saint-Venant equations of 1-D unsteady flows was established. The assembled f＇mite element equations were solved with the tri-diagonal matrix algorithm. In the semi-implicit and explicit scheme, the critical time step of the method was dependent on the space step and flow velocity, not on the wave celerity. The method was used to eliminate the restriction due to the wave celerity for the computational analysis of unsteady open-channel flows. The model was verified by the experimental data and theoretical solution and also applied to the simulation of the flow in practical river networks. It shows that the numerical method has high efficiency and accuracy and can be used to simulate 1-D steady flows, and unsteady flows with shock waves or flood waves. Compared with other numerical methods, the algorithm of this method is simpler with higher accuracy, less dissipation, higher computation efficiency and less computer storage.

Finite p-groups with a minimal non-abelian subgroup of index p(Ⅲ)

This paper finishes the classification of three-generator finite p-groups G such that Φ(G) Z(G).This paper is a part of classification of finite p-groups with a minimal non-abelian subgroup of index p, and partly solves a problem proposed by Berkovich(2008).