Semiclassical study of collision-induced predissociation: Comparison of the Landau-Zener model with the method of analytic continuation

Semiclassical calculations are carried out by two methods for the problem of collision-induced predissociation of electronically excited I₂. The first method is that of surface-hopping with the Landau-Zener model. The second method is similar to surface-hopping, except that analytic continuation of the adiabatic potential energy surfaces replaces the Landau-Zener model. Results of the calculations by the two methods compare favorably with each other and with experiment. The possible advantages of the second method are discussed.Camille and Henry Dreyfus Teacher-Scholar, Alfred P. Sloan Research Fellow.     

激光辐照下转动柱壳平均温度与破坏时间的工程估算

 推导了激光辐照下转动壳体平均温度沿壳体母线方向分布的解析公式。由于对高斯功率密度分布光束无法得到工程上实用的结果,对公式进行了解析拟合,仅由一个具有实际物理意义的拟合系数——分布因子确定了解析拟合公式的形式,明确了温度估算公式中各项的物理意义。解析拟合公式计算结果与数值模拟结果较为一致。作为温升估算方法的一个应用实例,推导了转动充压柱壳在激光辐照下破坏时间的解析公式,与数值计算结果吻合得较好。     

Extraordinary acoustic transmission,symmetry, blaschke products and resonators

The phenomenon of extraordinary acoustic transmission ( eat) in a resonator, which has recently been investigated experimentally, is studied theoretically. It is shown that the combination of a single propagating mode and a symmetry orthogonal to the direction of propagation for a resonator leads to eat. This is accomplished by decomposing the problem using symmetry, the Blaschke product and the properties of functions of a single complex variable which have modulus one on the real axis. The conditions of a resonator requires that the solution has singularities in the analytic extension to complex frequencies (resonances) and it is precisely near these resonances that we observe eat. The condition of a Blaschke product requires that there is a zero at the complex conjugate of the singularity and eat occurs when the solution on the real axis passes between these complex conjugate pairs of poles and zeros. A detailed numerical study of the problem is conducted and we show that once the single mode of propagation or the symmetry is broken then eat (at least perfect transmission) no longer holds generally.     

基于层次分析法的企业网络舆情危机应对评价研究

网络舆情危机应对评价是企业在新的舆论背景下研究危机应对的重点.采用定量和定性分析有机结合的层次分析法确定指标体系及权重,给出了企业网络舆情危机应对评价的步骤,并进行了评价验证.该评价体系为相关单位网络舆情危机应对评价提供一定的参考和指导.     

Numerical study for the electrified instability of viscoelastic cylindrical dielectric fluid film surrounded by a conducting gas

The linear electrohydrodynamic cylindrical instability of annular Walters B^′${\mathrm{B}}^{\prime }$ viscoelastic dielectric fluid layer surrounded by a conducting gas in the presence of radial electric field is investigated. The obtained dispersion relation is found to be complicated and cannot be treated theoretically easily. Two limiting cases of interest are investigated, when the inertia is dominant, and when both the kinematic viscosity and viscoelasticity are high, and the corresponding new stability conditions are obtained for both cases. We solve the eigenvalue problem numerically using the continuation method which gives better results than the classical non-linear solvers such as Newton and Secant methods. It is found that the applied radial electric field has a dual role on the stability of the considered system, depending of the chosen wavenumbers range. Both the kinematic viscoelasticity and liquid depth are found to have stabilizing effects, while both the kinematic viscosity and surface tension have destabilizing effects on the considered system. The stability or instability breaks down for critical wavenumber values at which the growth rate vanishes. The behaviors of both the maximum growth rate and the corresponding dominant wavenumber are discussed in detail corresponding to the effect of all physical parameters. Finally a comparison between the results obtained here for Walters B^′${\mathrm{B}}^{\prime }$ viscoelastic fluids, and those obtained here too if the fluid is replaced by a Rivlin–Ericksen viscoelastic one is achieved. The limiting cases of absence of electric field and/or kinematic viscoelasticity are also investigated in detail.     

模糊数学在企业创新能力评定中的应用

建立了企业创新的系统结构图,并利用模糊综合评价法建立了一个对企业创新能力进行评定的三级模糊综合评判的数学模型,采用层次分析法更加合理的确定了权重的分配,通过实例说明了该模型的使用方法,得到了更有效的结果.     

Mechanics of stretchable electronics on balloon catheter under extreme deformation

Stretchable electronics has been applied to balloon catheters for high-efficacy ablation, with tactile sensing integrated on the surface, to establish full and conformal contact with the endocardial surface for elimination of the heart sink caused by blood flow around their surfaces. The balloon of the catheter folds into uniform ‘clover’ patterns driven by the pressure mismatch inside (∼vacuum) and outside of the balloon (pressure ∼1 atm). The balloon catheter, on which microelectrodes and interconnects are printed, undergoes extreme mechanical deformation during its inflation and deflation. An analytic solution is obtained for balloon catheter inflation and deflation, which gives analytically the distribution of curvatures and the maximum strain in the microelectrodes and interconnects. The analytic solution is validated by the finite element analysis. It also accounts for the effect of inflated radius, and is very useful to the optimal design of balloon catheter.     

模糊广义判断矩阵的一致性检验及合成排序

决策评价过程中往往包含诸多不确定性、随机性和模糊性,广义判断下的ＡＨＰ－ＧＪＡＨＰ是一种广义ＡＨＰ,Ｆｕｚｚｙ 环境下的ＧＪＡＨＰ决策方法是应用集值统计的方法,在区间判断标度基础上确定模糊判断矩阵元素的正模糊数表示,并根据模糊集理论的扩展原理,求得Ｆｕｚｚｙ 环境下的模糊排序权值向量。本文给出模糊广义判断矩阵的一致性定义,讨论了各类判断形式条件下的一致性检验法与Ｆｕｚｚｙ 环境下递阶层次结构中的合成排序问题     

Distributions and analytic continuation of Dirichlet series

This is the second in a series of three papers; the other two are “Summation Formulas, from Poisson and Voronoi to the Present” [Progr. Math. 220 (2004) 419-440] and “Automorphic Distributions, L-functions, and Voronoi Summation for GL(3)” (preprint). The first paper is primarily expository, while the third proves a Voronoi-style summation formula for the coefficients of a cusp form on . The present paper contains the distributional machinery used in the third paper for rigorously deriving the summation formula, and also for the proof of the GL(3)×GL(1) converse theorem given in the third paper. The primary concept studied is a notion of the order of vanishing of a distribution along a closed submanifold. Applications are given to the analytic continuation of Riemann's zeta function, degree 1 and degree 2 L-functions, the converse theorem for GL(2), and a characterization of the classical Mellin transform/inversion relations on functions with specified singularities.