Sturm-Liouville边值问题解的非存在性、存在性和多重性结果

本文研究下述Sturm-Liouville边值问题利用Schauder不动点定理、上下解方法和Leray-Schauder映射度理论,获得了解的非存在性、存在性和多重性结果.其中一些是全新的结果,另一些则扩展、改进和完善了由Erbe,Wang,Hai,Lee和Lin所获得的结果.     

Thermally tuned optical fiber for true time delay generation

A new technique for generating a continuous range of true time delay values is introduced. Heating optical fiber in order to change the effective index of the guided mode produces time delays. A 45-m section of single-mode silica fiber is demonstrated to produce a continuous range of time delay values from 0 to 211 ps over a temperature tuning range of 50°C (30–80°C). A thermal time delay factor is introduced and found to be 0.096 ps/m°C for Corning LEAF fiber. A 7.66-m section of multimode Lucina polymer fiber is demonstrated to produce a range of time delay values from 0 to 32 ps over a temperature tuning range of 30°C (30–60°C). The thermal time delay factor for this fiber is −0.1427 ps/m°C.     

Patterned nucleation control in vacuum deposition of organic molecules

We report a generally applicable method to pattern organic molecules on mesoscopic scales. In our method, organic molecular beam deposition was conducted on substrate surfaces prepatterned with materials to which the organic molecules have larger binding energies in comparison to the substrate. Fully uniform nucleation control at these predefined locations can be achieved by an appropriate selection of the growth parameters including temperature and deposition rate. The physical mechanisms involved are studied by Monte Carlo simulations and stand in good agreement with the experimental findings.     

Multiphonon Bundle Emission in a Strong-Coupling Cavity Optomechanical System

Nonclassical effects in mesoscopic systems have attracted much attention recently. In this paper, it is shown that multiphonon bundle emission can be observed in a strong-coupling cavity optomechanical system. Theoretical analysis shows that when the driving field is adjusted to nth-order sideband excitation, the coupling between the cavity mode and the vibrational mode leads to super-Rabi oscillations, and finally results in an n-phonon bundles emission. Based on the current technology, this process can work in a wide range of parameters. Numerical simulation confirms the validity of the derivation. It is thought that this physical mechanism broadens the applications of cavity optomechanical system in realm of quantum phononics, such as in quantum metrology and phonon laser.     

井内流动与传热的三维耦合数值模型

钻井过程中,井内的压力、流场及温度分布是钻井作业必需的重要参数。本文提出了一个描述井内流动和传热的三维数学模型,用SIMPLER方法获得了该数学模型的数值解。该数值模型考虑了温度、压力对钻井液的流变性、密度以及各种介质的热物理参数的影响。现场试验数据与数值模拟结果的对比表明：本文提出的数学模型及采用的数值计算方法是可行的。     

空间理性八节点块体元

推导出空间八节点块体理性有限元列式，采用具有直到三次多项式的空间问题的微分方程的解作为插值的近似函数，数例结果表明空间理性八节点块体元的有效性。     

稀薄气固两相流的数值分析

本文用拉格朗日方法对稀薄气固两相流进行了数值分析,着重讨论有颗粒存在时,颗粒对气流速度分布的影响。计算的实例与实验结果比较,有着很好的吻合。     

压电材料椭圆夹杂界面开裂问题的电弹性耦合解

本文研究了在反平面剪切和面内电场的共同作用下，压电材料椭圆夹杂的界面开裂问题，假定夹杂是刚性的导体，采用复变函数保角变换和级数展开方法，可确定压电材料基体的复势表达式，进而求得夹杂界面开裂的电弹性耦合的能量释放率。     

Wall boundary conditions for high-order finite-difference schemes in computational aeroacoustics

High-order finite-difference schemes are less dispersive and dissipative but, at the same time, more isotropic than low-order schemes. They are well suited for solving computational acoustics problems. High-order finite-difference equations, however, support extraneous wave solutions which bear no resemblance to the exact solution of the original partial differential equations. These extraneous wave solutions, which invariably degrade the quality of the numerical solutions, are usually generated when solid-wall boundary conditions are imposed. A set of numerical boundary conditions simulating the presence of a solid wall for high-order finite-difference schemes using a minimum number of ghost values is proposed. The effectiveness of the numerical boundary conditions in producing quality solutions is analyzed and demonstrated by comparing the results of direct numerical simulations and exact solutions.This work was supported by the NASA Lewis Research Center Grant NAG 3-1267 and in part by the NASA Langley Research Center Grant NAG 1-1479 and the Florida State University through time granted on its Cray-YMP Supercomputer.     

On the Elastic Field of a Shpherical Inhomogeneity with an Imperfectly Bonded Interface

This study is devoted to the development of a unified and explicit elastic solution to the problem of a spherical inhomogeneity with an imperfectly bonded interface. Both tangential and normal displacement discontinuities at the interface are considered and a linear interfacial condition, which assumes that the tangential and the normal displacement jumps are proportional to the associated tractions, is adopted. The elastic disturbance due to the presence of an imperfectly bonded inhomogeneity is decomposed into two parts: the first is formulated in terms of an equivalent nonuniform eigenstrain distributed over a perfectly bonded spherical inclusion, while the second is formulated in terms of an imaginary Somigliana dislocation field which models the interfacial sliding and normal separation. The exact form of the equivalent nonuniform eigenstrain and the imaginary Somigliana dislocation are fully determined in this paper.