Novel implementation of homogenization method to predict effective properties of periodic materials

Representative volume element （RVE） method and asymptotic homogenization （AH） method are two widely used methods in predicting effective properties of pe- riodic materials. This paper develops a novel implementa- tion of the AH method, which has rigorous mathematical foundation of the AH method, and also simplicity as the RVE method. This implementation can be easily realized using commercial software as a black box, and can use all kinds of elements available in commercial software to model unit cells with rather complicated microstructures, so the model may remain a fairly small scale. Several examples were car- fled out to demonstrate the simplicity and effectiveness of the new implementation.

某三级甲等公立医院数字减影设备的成本效益分析

目的对公立医院数字减影血管造影(digital subtraction angiography,DSA)设备进行成本效益分析,结合社会效益评价,为设备采购和管理提供科学依据。方法采用投资回收期法、投资收益率法、量本利分析法和净现值法对数字减影设备进行成本效益分析,运用模糊数学法建模和指标评分法进行社会效益评价。结果公立医院数字减影设备包括DSA数字血管造影机、DSA全数字化平板探测器血管造影机、血管造影X线系统,其中:血管造影X线系统投资收益率最高为19.07%,投资回收期仅2.80年,运行效益评价为优秀;DSA全数字化平板探测器血管造影机A的经济指标最低,原因在于其业务量仅达保本工作量的83.91%,但其社会效益评分最高(C值为7.3)。结论公立医院在采购和管理数字减影等大型设备时需进行充分的成本效益分析论证,兼顾公立医院的公益性和科研属性,实行经济效益和社会效益双评价。

Penalty model for delay of bidding section construction period in South-to-North Water Diversion Eastern Route Project from perspective of programs

According to the multi-project and program management theory, this paper analyzes the program generation principle and establishes a program based on progress goals. On the basis of the present situation of calculation of penalty for delay of the bidding section construction period with the critical path method, we studied the effects of contractor-induced delay of the bidding section construction period in detail, including the effects on the construction period of the bidding section itself, the earliest start times of the next bidding section and other subsequent bidding sections, and the construction period of the program, and then constructed a penalty model for delay of the bidding section construction period from the perspective of programs. Using the penalty model, we conducted a practical analysis of penalty for delay of the construction period of the Baoying station program in the South-to-North Water Diversion Project. The model can help determine the amount of penalty for delay of the construction period in bidding sections scientifically and reasonably,

Analysis of the periodic solutions of a smooth and discontinuous oscillator

In this paper, the periodic solutions of the smooth and discontinuous （SD） oscillator, which is a strongly irra- tional nonlinear system are discussed for the system having a viscous damping and an external harmonic excitation. A four dimensional averaging method is employed by using the complete Jacobian elliptic integrals directly to obtain the perturbed primary responses which bifurcate from both the hyperbolic saddle and the non-hyperbolic centres of the un- perturbed system. The stability of these periodic solutions is analysed by examining the four dimensional averaged equa- tion using Lyapunov method. The results presented herein this paper are valid for both smooth （e 〉 0） and discontin- uous （ce = 0） stages providing the answer to the question why the averaging theorem spectacularly fails for the case of medium strength of external forcing in the Duffing system analysed by Holmes. Numerical calculations show a good agreement with the theoretical predictions and an excellent efficiency of the analysis for this particular system, which also suggests the analysis is applicable to strongly nonlinear systems.

Unstable and exact periodic solutions of three-particles time-dependent FPU chains

For lower dimensional Fermi–Pasta–Ulam（FPU） chains, the α-chain is completely integrable and the Hamiltonian of the β-chain can be identified with the H′enon–Heiles Hamiltonian. When the strengths α, β of the nonlinearities depend on time periodically with the same frequencies as the natural angular frequencies, the resonance phenomenon is inevitable. In this paper, for certain periodic functions α（t） and β（t） with resonance frequencies, we give the existence and stability of some nontrivial exact periodic solutions for a one-dimensional αβ-FPU model composed of three particles with periodic boundary conditions.

A Note on Homogenization of Parabolic Equation in Perforated Domains

We are concerned with a class of parabolic equations in periodically perforated domains with a homogeneous Neumann condition on the boundary of holes.By using the periodic unfolding method in perforated domains, we obtain the homogenization results under the conditions slightly weaker than those in the corresponding case considered by Nandakumaran and Rajesh（Nandakumaran A K, Rajesh M. Homogenization of a parabolic equation in perforated domain with Neumann boundary condition. Proc. Indian Acad. Sci.（Math. Sci.）, 2002, 112（1）： 195–207）. Moreover,these results generalize those obtained by Donato and Nabil（Donato P, Nabil A. Homogenization and correctors for the heat equation in perforated domains. Ricerche di Matematica L. 2001, 50： 115–144）.

Short-Term Period Variation of Relative Sunspot Numbers

We use wavelet transform to analyze the daily relative sunspot number series over solar cycles 10-23. The characteristics of some of the periods shorter than - 600-day are discussed. The results exhibit not only the variation of some short periods in the 14 solar cycles but also the characteristics and differences around solar peaks and valley years. The short periodic components with larger amplitude such as ～27, ～ 150 and ～360-day are obvious in some solar cycles, all of them are time-variable, also their lengths and amplitudes are variable and intermittent in time. The variable characteristics of the periods are rather different in different solar cycles.

Design of BLDCM Driving and Control System for Motorized Treadmill

To satisfy the requirement of developing a new generation of motorized treadmill for a famous domestic manufacturer, a brushless DC motor （BLDCM） driving and control system for motorized treadmill is developed. High integration and reliability of this system are ensured under the condition that intelligent power module （IPM） is used and the protection module is included. Periodic current control method is applied to reduce the average current flowing through the armature winding of the motor when the treadmill is required to start with low speed while large load is added. Piecewise proportion-integration-differentiation （PID） control algorithm is applied to solve the problem of speed fluctuation when impulse load is added. The motorized treadmill of a new generation with the driving and control system has the advantages of high reliability, good speed stability, wide timing scope, low cost, and long life-span. And it is very promising for practical applications.

Theoretical aspects of selecting repeated unit cell model in micromechanical analysis using displacement-based finite element method

Repeated Unit Cell（RUC）is a useful tool in micromechanical analysis of composites using Displacement-based Finite Element（DFE）method,and merely applying Periodic Displacement Boundary Conditions（PDBCs）to RUC is almost a standard practice to conduct such analysis.Two basic questions arising from this practice are whether Periodic Traction Boundary Conditions（PTBCs,also known as traction continuity conditions）are guaranteed and whether the solution is independent of selection of RUCs.This paper presents the theoretical aspects to tackle these questions,which unify the strong form,weak form and DFE method of the micromechanical problem together.Specifically,the solution’s independence of selection of RUCs is dealt with on the strong form side,PTBCs are derived from the weak form as natural boundary conditions,and the validity of merely applying PDBCs in micromechanical Finite Element（FE）analysis is proved by referring to its intrinsic connection to the strong form and weak form.Key points in the theoretical aspects are demonstrated by illustrative examples,and the merits of setting micromechanical FE analysis under the background of a clear theoretical framework are highlighted in the efficient selection of RUCs for Uni Directional（UD）fiber-reinforced composites.

High temperature-sensitivity sensor based on long period fiber grating inscribed with femtosecond laser transversal-scanning method

We propose a high temperature-sensitive long period fiber grating（LPFG） sensor fabricated by using the femtosecond laser transversal-scanning method. The femtosecond pulses scan over the whole fiber core and some part of the cladding region; the modified regions are more extended. It is found that the LPFG-I fabricated by the transversal-scanning method shows higher temperature sensitivity and better temperature uniformity than that of LPFG-II written by the femtosecond laser point-by-point method. The LPFG-I with a temperature sensitivity of 75.96 pm/°C in the range of 25°C–400°C is measured. Moreover, in the range from 400°C to 800°C, a higher temperature sensitivity of 148.64 pm/°C and good linearity of 0.99 are achieved, while the temperature sensitivity of LPFG-II is only 95.55 pm/°C. LPFG-I exhibits better temperature characteristics, which, to the best of our knowledge, has the highest sensitivity in silica fiber temperature sensors.

A Novel Method of Edge Filter Linear Demodulation Using Long Period Grating in Fiber Sensor System

A novel method of linear demodulation based on edge filter is presented. An experimental system is built up in which LPG is used as the edge filter. We achieve linear demodulation with a bandwidth of 5nm.

SPECTRAL METHOD FOR ZAKHAROV EQUATION WITH PERIODIC BOUNDARY CONDITIONS

This paper describes the spectral method for numerically solving Zakharov equation with periodicboundary conditions. This method is spectral method for spatial variable and difference method fortime variable. We make error estimation of approximate solution and prove the convergence of spectralmethod. We had given the convergence rate. Also, we prove the stability of approximate method forinitial values.

Effect of sample size on the response of DEM samples with a realistic grading

This paper shows that for DEM simulations of triaxial tests using samples with a grading that is repre- sentative of a real soil, the sample size significantly influences the observed material response. Four DEM samples with identical initial states were produced： three cylindrical samples bounded by rigid wails and one bounded by a cubical periodic cell, When subjected to triaxial loading, the samples with rigid boundaries were more dilative, stiffer and reached a higher peak stress ratio than the sample enclosed by periodic boundaries. For the rigid-wall samples, dilatancy increased and stiffness decreased with increasing sample size, The periodic sample was effectively homogeneous, The void ratio increased and the contact density decreased close to the rigid walls, This heterogeneity reduced with increasing sample size. The positions of the critical state lines （CSLs） of the overall response in e-log p＇ space were sensitive to the sample size, although no difference was observed between their slopes. The critical states of the interior regions of the rigid-wall-bounded samples approached that of the homogeneous periodic sample with increasing sample size. The ultimate strength of the material at the critical state is independent of sample size.

Prediction of vibrations induced by trains on line 8 of Beijing metro

This paper mainly discusses the problem of ground-borne vibrations due to the planned line 8 of Beijing metro which passes under the National Measurement Laboratory.A lot of vibration sensitive equipments are placed in the laboratory.It is therefore necessary to study the impact of vibrations induced by metro trains on sensitive equipments and important to propound a feasible vibration mitigation measure.Based on the coupled periodic finite element-boundary element (FE-BE) method,a 3D dynamic track-tunnel-soil interaction model for metro line 8 has been used to predict vibrations in the free field induced by trains running at variable speeds between 30 km/h and 80 km/h.Four types of track structures commonly used on the Beijing metro network have been considered:(1) high resilience direct fixation fasteners,(2) Vanguard fasteners,(3) a floating slab track and (4) a floating ladder track.For each of these track types,the vibration isolation efficiency has been compared.The results of the numerical study can be used to predict vibrations in nearby buildings and to decide upon effective vibration countermeasures.

Loaded-frequency selective surface

A new frequency-selective surface(FSS)with loadings is introduced in this paper and analyzed by way of period moment methods(PMMs).The simulated results show that FSS may operate in different bands and especially generate a large reduction in the resonant frequency for a fixed unit cell size through different loadings.This provides a new orientation in the development for FSS.Practical circuits are fabricated,and the measured results agree well with the simulated results.

BIFURCATIONS AND NEW EXACT TRAVELLING WAVE SOLUTIONS OF THE COUPLED NONLINEAR SCHRDINGER-KdV EQUATIONS

By using the method of dynamical system, the exact travelling wave solutions of the coupled nonlinear Schrdinger-KdV equations are studied. Based on this method, all phase portraits of the system in the parametric space are given. All possible bounded travelling wave solutions such as solitary wave solutions and periodic travelling wave solutions are obtained. With the aid of Maple software, the numerical simulations are conducted for solitary wave solutions and periodic travelling wave solutions to the coupled nonlinear Schrdinger-KdV equations. The results show that the presented findings improve the related previous conclusions.