Concentration-cancellation for the velocity fields in two dimensional incompressible fluid flows

We show that the weak-L ² limit of a sequence of solutions of the two dimensional incompressible Euler equation is still a solution, provided that a (strong) concentration set for the reduced defect measure has locally finite one dimensional Hausdorff measure in space and time.     

A Stochastic Analysis of a Staffing Problem

Consider an organization with several categories of staff, each having a specified number of members. The age of entry into service and the age of retirement are both specified. Withdrawals occur at time-independent rates. Under this set-up, the authors have computed the maximum ages at which promotions should take place, assuming that the staff members continuing at various ages are random. Some illustrative calculations have been carried out.     

基于远场的拼接光栅压缩池的设计

 利用傅里叶光学方法得到了失调拼接光栅压缩池输出光束的远场振幅表达式，建立了分析拼接光栅的各种误差的理论模型，得到了拼接误差对脉冲的影响是附加相位延迟和角度偏转。在要求远场的一倍衍射极限区域的积分能量分布达到理想情况下的90％的条件下，对于含有口径为40 cm、脉宽为0.1~10 ps脉冲的系统进行分析并分别得到了各种误差的容限。     

Molecular dynamics simulation of processing using AFM pin tool

A three-dimensional molecular dynamics (MD) model is utilized to investigate the effect of tool geometry on the deformation process of the workpiece and the nature of deformation process at the atomic-scale. Results show that different states exist between the atomic force microscope (AFM) pin tool and the workpiece surface, i.e. the non-wear state, the ploughing state, the state in which ploughing is dominant and the state in which cutting plays a key role. A relationship between the deformation process of the workpiece and the potential energy variation is presented. The potential energy variation of atoms in different deformed regions in the workpiece such as plastically deformed region, elastically deformed region and the mixed deformation region is different. The features of variations of potential energy are discussed.     

Three Electrons in a Two-Dimensional Parabolic Trap: The Relative Motion Solution

In agreement with the Kohn theorem the relative motion (rel) of three electrons in a two-dimensional parabolic trap separates from the centre-of-mass (CM) motion. By introducing new coordinates the Hamiltonian for relative motion in the approximation of non-interacting electrons can be taken to the normal form. The eigenstates of the normalized Hamiltonian are products of the Fock-Darwin states for normal modes. The energy levels for relative motion are obtained by diagonalizing the exact Hamiltonian in the eigenbasis for the non-interacting case. In this basis the interaction matrix elements can be obtained in the analytical form. Since the rank of the Hamiltonian matrix is significantly reduced, the calculations are faster and more accurate than those for the full (CM + rel) motion. This advantage is especially important for the calculations of excited states and the analysis of energy spectra.     

Khillah extract as inhibitor for acid corrosion of SX 316 steel

The inhibitive effect of the extract of khillah (Ammi visnaga) seeds, on the corrosion of SX 316 steel in HCl solution was determined using weight loss measurements as well as potentiostatic technique. It was found that the presence of the extract reduces markedly the corrosion rate of steel in the acid solution. The inhibition efficiency increases as the extract concentration is increased. The inhibitive effect of khillah extract was discussed on the basis of adsorption of its components on the metal surface. Negative values were calculated for the energy of adsorption indicating the spontaneity of the adsorption process. The formation of insoluble complexes as a result of interaction between iron cations and khellin, which present in the extract, was also discussed.     

Wavelength and power monitoring of DWDM systems using scanning F–P filter calibrated with a F–P laser

A novel technique to overcome the long-term drift and hysteresis of a scanning Fabry–Perot filter was developed and applied to wavelength and power monitoring of DWDM system. By using the comb peaks generated by a temperature-stabilized, near threshold-biased Fabry–Perot diode laser as wavelength reference for the scanning Fabry–Perot filter, wavelength and power measurement accuracy of better than ±10 pm and 0.2 dB, respectively, were achieved.     

Primal cutting plane algorithms revisited

Dual fractional cutting plane algorithms, in which cutting planes are used to iteratively tighten a linear relaxation of an integer program, are well-known and form the basis of the highly successful branch-and-cut method. It is rather less well-known that various primal cutting plane algorithms were developed in the 1960s, for example by Young. In a primal algorithm, the main role of the cutting planes is to enable a feasible solution to the original problem to be improved. Research on these algorithms has been almost non-existent.  In this paper we argue for a re-examination of these primal methods. We describe a new primal algorithm for pure 0-1 problems based on strong valid inequalities and give some encouraging computational results. Possible extensions to the case of general mixed-integer programs are also discussed.     

Structural evolution in amorphous silicon and germanium thin films.

The structural evolution in amorphous silicon and germanium thin films has been investigated by high-resolution transmission electron microscopy (HRTEM) in conjunction with autocorrelation function (ACF) analysis. The results established that the structure of as-deposited semiconductor films is of a high density of nanocrystallites embedded in the amorphous matrix. In addition, from ACF analysis, the structure of a-Ge is more ordered than that of a-Si. The density of embedded nanocrystallites in amorphous films was found to diminish with annealing temperature first, then to increase. The conclusions also corroborate well with the results of diminished medium-range order in annealed amorphous films determined previously by a variable coherence microscopy method.     

Structural-acoustic coupling effect on the nonlinear natural frequency of a rectangular box with one flexible plate

The nonlinear natural frequency of a rectangular box, which consists of one flexible plate and five rigid plates, is studied in this paper. The flexible plate is assumed to vibrate like a simple piston. The behavior of the structural-acoustic coupling between the flexible plate and the air cavity is analyzed by using the proposed finite element modal method. The system finite element equation is reduced and expressed in terms of the modal coordinates with small degrees of freedom by using the proposed reduction method. The system nonlinear stiffness matrix representing the large amplitude vibration can be transformed to be a constant modal matrix. The natural frequencies are determined by using the harmonic balance method to solve the eigenvalue equations of the structural-acoustic system. The effect of the cavity depth on the natural frequencies and convergence studies are discussed in detail.