A hybrid finite element approach to modeling sound radiation from circular and rectangular ducts

A numerical model based on a hybrid finite element method is developed that seeks to join sound pressure fields in interior and exterior regions. The hybrid method is applied to the analysis of sound radiation from open pipes, or ducts, and uses mode matching to couple a finite element discretization of the region surrounding the open end of the duct to wave based modal expansions for adjoining interior and exterior regions. The hybrid method facilitates the analysis of ducts of arbitrary but uniform cross section as well the study of conical flanges and here a modal expansion based on spherical harmonics is applied. Predictions are benchmarked against analytic solutions for the limiting cases of flanged and unflanged circular ducts and excellent agreement between the two methods is observed. Predictions are also presented for flanged and unflanged rectangular ducts, and because the hybrid method retains the sparse banded and symmetric matrices of the traditional finite element method, it is shown that predictions can be obtained within an acceptable time frame even for a three dimensional problem.     

垂直于界面V型缺口尖端的应力奇异性及其应用

基于双材料垂直于界面V型缺口理论,给出了单一材料和双材料裂纹问题、V型缺口问题应力强度因子的统一定义,得到了应力外推法计算双材料K_I的公式,数值算例验证了本文方法的有效性.以双材料单向拉伸和三点弯曲模型为对象,深入研究了双材料中弹性模量、泊松比、缺口深度、缺口张角对缺口尖端奇异应力场的影响,获得了一定范围内各种参数变化对缺口尖端奇异应力场的影响规律,为异体材料形成的V型缺口在应力断料中的应用提供了必要的参考依据.     

两层液体Bénard-Marangoni对流的实验研究

采用粒子图像测速技术(PIV)对两层流体B(en)ard-Marangoni对流进行了实验研究.研究了各种不同厚度比下的临界对流模式,同时研究了在温差变大时向超临界对流模式转化过程.实验结果表明,界面张力对各种对流模式的形成和转变具有重要的作用.     

A combination of energy method and spectral analysis for study of equations of gas motion

There have been extensive studies on the large time behavior of solutions to systems on gas motions, such as the Navier-Stokes equations and the Boltzmann equation. Recently, an approach is introduced by combining the energy method and the spectral analysis to the study of the optimal rates of convergence to the asymptotic profiles. In this paper, we will first illustrate this method by using some simple model and then we will present some recent results on the Navier-Stokes equations and the Boltzmann equation. Precisely, we prove the stability of the non-trivial steady state for the Navier-Stokes equations with potential forces and also obtain the optimal rate of convergence of solutions toward the steady state. The same issue was also studied for the Boltzmann equation in the presence of the general time-space dependent forces. It is expected that this approach can also be applied to other dissipative systems in fluid dynamics and kinetic models such as the model system of radiating gas and the Vlasov-Poisson-Boltzmann system.      

Stochastic modeling of unresolved scales in complex systems

Model uncertainties or simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., ‘unresolved’) due to a lack in our understanding of these mechanisms or limitations in computational power. The impact of these unresolved scales on the resolved scales needs to be parameterized or taken into account. A stochastic scheme is devised to take the effects of unresolved scales into account, in the context of solving nonlinear partial differential equations. An example is presented to demonstrate this strategy. Dedicated to Professor Peter E. Kloeden on the occasion of his 60th birthday     

生物酶法制备1, 3-甘油二酯

近年来的研究表明,食用含有1,3-甘油二酯（1,3-DAG）的油脂可以降低脂肪积累、防止体重增加。但是天然存在的1,3-DAG很少,所以1,3-DAG的制备尤显重要。相对于化学法,生物酶法合成1,3-DAG具有反应条件温和、环境友好、产品质量好等优点,故近年来利用酶法合成1,3-DAG越来越受到关注。本文综述了国内外生物酶法制备1,3-DAG的相关研究进展,并指出降低酶的生产成本、延长酶的使用寿命等措施有助于促进生物酶法工业化生产1,3-DAG。     

Effect of Pressure on Electronic Structures and Optical Properties of Rocksalt InN

The electronic structures and optical properties of rocksalt indium nitride (InN) under pres-sure were studied using the first-principles calculation by considering the exchange and cor-relation potentials with the generalized gradient approximation. The calculated lattice con-stant shows good agreement with the experimental value. It is interestingly found that the band gap energy E_g at the Γ or X point remarkably increases with increasing pressure, but E_g at the L point does not increase obviously. The pressure coefficient of E_g is calculated to be 44 meV/GPa at the Γ point. Moreover, the optical properties of rocksalt InN were calculated and discussed based on the calculated band structures and electronic density of states.     

Friction phenomena in a two-dimensional Frenkel-Kontorova model

By using the molecular dynamic simulation method with a fourth-order Runge--Kutta algorithm, a two-dimensional dc- and ac-driven Frenkel--Kontorova (FK) model with a square symmetry substrate potential for a square lattice layer has been investigated in this paper. For this system, the effects of many different parameters on the average velocity and the static friction force have been studied. It is found that not only the amplitude and frequency of ac-driven force, but also the direction of the external driving force and the misfit angle between two layers have some strong influences on the static friction force. It can be concluded that the superlubricity phenomenon appears easily with a larger ac amplitude and lower ac frequency for some special direction of the external force and misfit angle.     

Inverse Filter of Chaos with Applications on Parameter Estimation

Linear filter may hide simple nonlinearity of chaotic dynamics, which would decrease the accuracy of parameter estimation, and reduce the effect of signal processing. Based on theoretical and experimental analysis, this paper provides a method to recover the dynamics. An example of radar data proves that the dynamics hidden in observed data can be found by inverse filter of chaos. It is also pointed out that inverse filter of chaos can be applied to mine inner regulation of some time series and estimate parameters of nonlinear models in data processing for radar. And the method is significant to clutter modeling.     

AN EFFECTIVE TWO-LEVEL CHANNEL FOR AN IMPURITY IN A SUPERLATTICE

The eigenstates and eigenspectrum of a charged particle in a one-dimensional semiconductor superlattice with an impurity under the action of a dc electric field are investigated employing the single-band tight-binding model. We find that the system undergoes a series of avoided crossings, at which resonant oscillations between the impurity and its nearest neighbour occur if appropriate conditions are met, suggesting an effective two-level approximation. This phenomenon shows that introducing an impurity in a perfect lattice provides a promising structure for the observation of terahertz radiation.