Exactness of SWKB for shape invariant potentials

The supersymmetry-based semiclassical method (SWKB) is known to produce exact spectra for conventional shape invariant potentials. In this paper we prove that this exactness follows from their additive shape invariance.     

消光式核壳二聚体传感器的设计与光谱特性分析

根据ITO/Au纳米核壳二聚体粒子在生物医学领域的应用合理性,设计了一种实时检测生物液体的核壳二聚体探针消光式传感器;由偶极子理论推导出输出波长与外界环境折射率关系;利用MATLAB设计ITO/Au纳米核壳二聚体粒子结构;采用软件DDSCAT7.3结合离散偶极近似法,利用二聚体有效半径模拟计算了300~950nm可见光到红外光波段不同核壳比、二聚体间距、以及不同介质折射率的消光光谱;根据传感芯片折射率与偶极共振、耦合八级共振的响应关系得出ITO/Au二聚体的折射率灵敏特性。与传统Ag/Au核壳纳米粒子相比,ITO/Au纳米核壳二聚体结构引入了可作为传感芯片灵敏性自参考参数的耦合八级共振峰,同时ITO/Au二聚体结构的折射率灵敏度可达到419nm/RIU。这些工作及其结果对制作消光式传感器具有重要的意义。     

受限亚音速气流中倒置悬臂壁板静气弹稳定性的理论及实验研究

板壳结构在航空航天、高速列车、能量采集等诸多工程领域已经得到了广泛应用. 将悬臂壁板倒置于轴向气流中并在壁板周围流场中设置刚性壁面可有效地调控壁板的失稳速度, 是俘能器优化设计的重要措施之一. 但针对刚性壁面作用下亚音速气流中倒置悬臂壁板的失稳机制仍需要开展深入研究. 本文以受限亚音速气流中倒置的二维悬臂壁板为对象, 以理论分析及风洞实验为手段, 研究了单侧刚性壁面效应对倒置悬臂壁板静态失稳特性的影响规律. 在理论分析中, 首先应用镜像函数法来处理壁面约束条件, 基于算子理论研究获得了以Possio积分方程为表征的壁板气动力, 壁面效应实际表征为一包含移位Tricomi算子的复合算子; 然后将壁板失稳方程的求解问题转化为定区间上的函数逼近问题; 最后, 依据Wererstrass定理并利用最小二乘法求解该最优函数, 以获得系统的失稳临界参数. 在试验研究中依据压杆稳定原理设计了壁板静态失稳的测试方法并完成了风洞实验. 理论分析结果表明, 壁板会发生发散(静气动弹性)失稳, 临界动压随壁板与壁面间距的增加而增大并最终趋于稳定(无壁面情况); 通过理论与风洞实验结果的对比分析, 验证了本文气动力及理论分析的适用性及准确性. 针对倒置悬臂壁板结构的气动弹性失稳问题, 本文提出的方法不涉及系统方程的离散及特征值求解问题, 而是将其转化为了定区间上的函数逼近问题进行求解, 这为弹性结构静气动弹性失稳问题的研究提供了一个可行的新思路.      

正电子冲击下氦电离三重微分截面的理论计算

我们发展了一种正电子碰撞原子电离的畸变波Born近似方法， 在这个方法中，正负电子偶素通道通过一个ab initio的光学势附加到入射粒子和靶的相互作用势上，且通道对电离作用被第一次被考虑在正电子碰撞原子电离的过程中. 应用这个方法计算了在50 eV入射能量范围氦的电离的三重微分截面，计算结果和实验数据很好的符合.     

Meshless acoustic analysis using a weakly singular Burton-Miller boundary integral formulation

The Burton-Miller boundary integral formulation is solved by a complex variable boundary element-free method (CVBEFM) for the boundary-only meshless analysis of acoustic problems with arbitrary wavenumbers. To regularize both strongly singular and hypersingular integrals and to avoid the computation of the solid angle and its normal derivative, a weakly singular Burton-Miller formulation is derived by considering the normal derivative of the solid angle and adopting the singularity subtraction procedures. To facilitate the implementation of the CVBEFM and the approximation of gradients of the boundary variables, a stabilized complex variable moving least-square approximation is selected in the meshless discretization procedure. The results show the accuracy and efficiency of the present CVBEFM and reveal that the method can produce satisfactory results for all wavenumbers, even for extremely large wavenumbers such as k = 10 000.     

Global approximation to arbitrary cost functions: A Bayesian approach with application to US banking

This paper proposes and estimates a globally flexible functional form for the cost function, which we call Neural Cost Function (NCF). The proposed specification imposes a priori and satisfies globally all the properties that economic theory dictates. The functional form can be estimated easily using Markov Chain Monte Carlo (MCMC) techniques or standard iterative SURE. We use a large panel of U.S. banks to illustrate our approach. The results are consistent with previous knowledge about the sector and in accordance with mathematical production theory.     

Estimates for Divergence Velocities of Axially Moving Orthotropic Thin Plates

Some models for axially moving orthotropic thin plates are investigated analytically via methods of complex analysis to derive estimates for critical plate velocities. The linearized Kirchhoff plate theory is used, and the energy forms of steady-state models are considered with homogeneous and inhomogeneous tension profiles in the cross direction of the plate. With the help of the energy forms, some limits for the divergence velocity of the plate are found analytically. In numerical examples, the derived lower limits for the divergence velocity are analyzed for plates with small flexural rigidity.     

Invariant discrete flows

In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself.     

桉树杂交种与其亲本的近红外光谱判别

研究桉树控制授粉后目标性状的基因作用方式是探索其基因重组规律的重要内容。常规的数量统计分析精度往往不高,而DNA分析的专业要求高,且费时费力。该研究利用近红外光谱(NIRs)研究不同基因型桉树杂交种、亲本及杂交种与亲本间近红外光谱信息的关系,探索NIRs用于桉树杂交种与其亲本判别的可行性和准确性。以控制授粉的桉树亲本及其杂交F1代材料为对象,每种基因型从各自田间试验分别选取10个单株,采集树冠中上部新鲜健康叶片。用手持式近红外仪Phazir Rx(1624)采集桉树杂交种与其亲本叶片的NIRs信息。每单株选10片完全生理成熟的健康叶片,避开叶脉扫描其正面光谱5次,以50条NIRs信息的均值代表单个叶片的NIRs信息,最终每个基因型获得10条NIRs信息。对原始NIRs采用二阶多项式S.G一阶导数预处理。预处理后的NIRs用于多元统计分析,首先对桉树杂交亲本和子代样本进行主成分分析(PCA),直观展示不同基因型的分类情况。然后运用簇类独立软模式(SIMCA)和偏最小二乘判别分析(PLS-DA)两种有监督的判别模式验证NIRs用于桉树杂交种与其亲本树种的分类判别效果。PCA结果显示,不同的亲本间、杂交种间及杂交种与亲本间样本的主因子得分可以清晰地将各基因型分开。SIMCA模式判别分析中,桉树杂交种样本到亲本PCA模型的样本距离显示,待判别样本能够形成单独的聚类,且能直观反映两者的遗传相似。PLS-DA判别结果显示,桉树杂交亲本的PLS模型能通过预测其杂交子代的响应变量将其与亲本准确分开。结果表明,桉树叶片的NIRs信息可以准确地反映桉树杂交子代遗传信息的传递规律,NIRs判别模型可以准确地将各种基因型予以区分。因此,NIRs信息不仅可用于桉树杂交种和纯种的定性判别,还可以分析桉树基因重组过程中加性遗传效应的大小,从而为桉树遗传基础分析及其育种改良研究提供理论支撑。     

An approach of dynamic mesh adaptation for simulating 3‐dimensional unsteady moving‐immersed‐boundary flows

In this paper, we present an approach of dynamic mesh adaptation for simulating complex 3‐dimensional incompressible moving‐boundary flows by immersed boundary methods. Tetrahedral meshes are adapted by a hierarchical refining/coarsening algorithm. Regular refinement is accomplished by dividing 1 tetrahedron into 8 subcells, and irregular refinement is only for eliminating the hanging points. Merging the 8 subcells obtained by regular refinement, the mesh is coarsened. With hierarchical refining/coarsening, mesh adaptivity can be achieved by adjusting the mesh only 1 time for each adaptation period. The level difference between 2 neighboring cells never exceeds 1, and the geometrical quality of mesh does not degrade as the level of adaptive mesh increases. A predictor‐corrector scheme is introduced to eliminate the phase lag between adapted mesh and unsteady solution. The error caused by each solution transferring from the old mesh to the new adapted one is small because most of the nodes on the 2 meshes are coincident. An immersed boundary method named local domain‐free discretization is employed to solve the flow equations. Several numerical experiments have been conducted for 3‐dimensional incompressible moving‐boundary flows. By using the present approach, the number of mesh nodes is reduced greatly while the accuracy of solution can be preserved.