On 3D Lagrangian Navier–Stokes α Model with a Class of Vorticity-Slip Boundary Conditions

This paper concerns the 3-dimensional Lagrangian Navier–Stokes α model and the limiting Navier–Stokes system on smooth bounded domains with a class of vorticity-slip boundary conditions and the Navier-slip boundary conditions. It establishes the spectrum properties and regularity estimates of the associated Stokes operators, the local well-posedness of the strong solution and global existence of weak solutions for initial boundary value problems for such systems. Furthermore, the vanishing α limit to a weak solution of the corresponding initial-boundary value problem of the Navier–Stokes system is proved and a rate of convergence is shown for the strong solution.     

Existence of Weak Solutions for a Two-dimensional Fluid-rigid Body System

We consider the problem of a rigid body immersed in an inviscid incompressible fluid in two dimensional space. The motion of the fluid is described by the incompressible Euler equations and the motion of the rigid body is governed by the balance of linear and angular momentum. A global weak solution is obtained, without any assumption on the weighted norm of the initial vorticity.     

流动注射能量转移化学发光法测定2-氨基丁酸

在碱性条件下 ,N 溴代琥珀酰亚胺 (NBS)氧化 2 氨基丁酸 ,反应能量激发共存的荧光物质 ,产生化学发光。基于此 ,建立了一种测定痕量 2 氨基丁酸的流动注射化学发光分析方法。 2 氨基丁酸浓度在 3.0×1 0 -4～ 0 .1g/L范围内与化学发光强度呈良好的线性关系 ;对 5mg/L的 2 氨基丁酸进行 1 1次平行测定 ,相对标准偏差 (RSD)为 2 .0 % ;根据IUPAC建议 ,计算出 2 氨基丁酸检出限 (3σ)为 8× 1 0 -5g/L。将本法用于化学去龋剂中 2 氨基丁酸含量的测定 ,结果满意     

CdTe nanocrystals sensitized chemiluminescence and the analytical application

It was found that the mixing of CdTe semiconductor nanocrystals (NCs) with luminol in the presence of KMnO₄ can induce a great sensitized effect on chemiluminescence (CL) emission. When the concentration of luminol, KMnO₄ and NaOH were fixed at 1 μM, 1 μM and 0.05 M, respectively, the most excellent performance can be obtained for the CdTe NCs sensitized CL. By means of CL and photoluminescence spectra, we suppose the enhanced CL signals resulted from the accelerated luminol CL induced by the oxidized species of CdTe NCs. Based on the finding, using thioglycolic acid-capped CdTe NCs as label and immunoglobulin G (IgG) as a model analyte, a CL immunoassay protocol for IgG content detection was developed. The strong inhibition effect of phenol compounds on luminol-KMnO₄-CdTe NCs CL system was also observed. All these findings demonstrated the possibility of semiconductor nanocrystals induced chemiluminescence to be utilized for more practical applications.     

Vanishing viscosity limit for the 3D magnetohydrodynamic system with a slip boundary condition

This work investigates the solvability, regularity and vanishing viscosity limit of the 3D viscous magnetohydrodynamic system in a class of bounded domains with a slip boundary condition.     

Needle and seed segmentation in intra-operative 3D ultrasound-guided prostate brachytherapy

In order to guide the needle to the correct location in 3D US-guided brachytherapy, the needle is continuously tracked as it is being inserted. A pre-scan before the needle insertion and a post-scan after the needle insertion are subtracted to obtain a difference image containing the needle. The image is projected along two orthogonal directions approximately perpendicular to the needle, and the 3D needle is reconstructed from the segmented needles in the two projected images. The seeds implanted with the needle are located in the cropped volume along the needle. Thus, the seeds are segmented using a tri-bar model and 3D line segment patterns. Finally, the positions of the seeds are determined using a peak detection technique. Experiments with agar and turkey/chicken phantoms as well as patient data demonstrated that our needle segmentation technique could segment the needle in near real-time with an accuracy of 0.6 mm in position and 1.0 degrees in orientation. The true-positive rate for seed segmentation is 100% for the agar phantom and 93% for the chicken phantom. The average distance to manual seed segmentation was 1.0mm for the agar phantom and 1.7 mm for the chicken phantom.     

Global subsonic and subsonic-sonic flows through infinitely long axially symmetric nozzles

In this paper, we establish existence of global subsonic and subsonic-sonic flows through infinitely long axially symmetric nozzles by combining variational method, various elliptic estimates and a compensated compactness method. More precisely, it is shown that there exist global subsonic flows in nozzles for incoming mass flux less than a critical value; moreover, uniformly subsonic flows always approach to uniform flows at far fields when nozzle boundaries tend to be flat at far fields, and flow angles for axially symmetric flows are uniformly bounded away from π/2; finally, when the incoming mass flux tends to the critical value, subsonic-sonic flows exist globally in nozzles in the weak sense by using angle estimate in conjunction with a compensated compactness framework.     

On Transonic Shocks in a Nozzle with Variable End Pressures

In the book, Courant and Friedrichs (Supersonic Flow and Shock Waves. New York: Interscience Publishers, 1948) described the following transonic shock phenomena in a de Laval nozzle: Given the appropriately large receiver pressure p _r , if the upstream flow is still supersonic behind the throat of the nozzle, then at a certain place in the diverging part of the nozzle a shock front intervenes and the gas is compressed and slowed down to subsonic speed. The position and the strength of the shock front are automatically adjusted so that the end pressure at the exit becomes p _r . When the end pressure p _r varies and lies in an appropriate scope, in general, it is expected that a curved transonic shock is still formed in a nozzle. In this paper, we solve this problem for the two-dimensional steady Euler system with a variable exit pressure in a nozzle whose divergent part is an angular sector. Both existence and uniqueness are established. Supported by the National Natural Science Foundation of China (No.10571082) and the National Basic Research Programm of China (No.2006CB805902). Supported in part by Zheng Ge Ru Foundation, and Hong Kong RGC Earmarked Research Grants CUHK4028/04P, CUHK4040/06P and RGC Central Allocation Grant CA05/06.SC01.     

Propagation of flat-topped beams

The propagation of flat-topped beams passing through paraxial ABCD optical system is investigated based on the propagation formulas of Gaussian beam. The focal shift of focused coherent flat-topped beam is also studied in detail. Analytical expressions of the M² factor and the far-field intensity distribution for flat-topped beams are derived on the basis of second-order moments.