充水有限长圆柱薄壳声散射:Ⅰ.理论

研究水中充水有限长圆柱薄壳的声散射。采用弹性薄壳理论结合边界条件导出了有限长圆柱薄壳倾斜入射时散射声场的解析解,内部充水的作用反映在系统总阻抗中增加了内部流体阻抗。数值计算表明,在反向散射声场中,刚性散射部分仅在正横附近有比较大的贡献,而斜入射时起主要作用的是弹性散射部分。散射波相速度频散曲线的计算表明,与内部真空的情况相比内部充水后除正横附近的纵波和剪切波以外,增加了一组内部流体引起的附加波,其对散射声场贡献非常重要。在计算的频率-角度谱图中,内部流体附加波呈现"碗"形共振曲线。      

充水有限长圆柱薄壳声散射:Ⅱ.实验

从实验和理论上研究了充水有限长圆柱薄壳的声散射。实验采用指向性尖锐的宽带收发合置换能器,发射宽带调频信号和单频窄脉冲信号进行测量,所得结果分别在时域和频域上与理论计算结果相对比,证明其吻合程度很好。理论和实验的结果表明,内部充水圆柱壳在频域上增加了一组由内部流体负载引起的附加波的共振;而在时域上增加了一系列由于声波在壳体内来回反射产生的"回音廊"式回波。频率-角度图中"碗"形亮线出现分簇的原因解释为前几种模式"回音廊"式回波叠加的结果。      

Pressure and temperature dependence of the structure of liquid Sn up to 5.3 GPa and 1373 K

Pressure and temperature dependence of the structure of liquid Sn has been measured up to 5.3?GPa and 1373?K using multi-angle energy-dispersive X-ray diffraction in Paris–Edinburgh cell. Under nearly isobar condition at ～1?GPa, liquid Sn displays a normal behavior with gradual structural changes with temperature up to 1373?K. Under isothermal compressions at 850 and 1373?K, however, the structure factors of liquid Sn both show a turn-over at ～3?GPa in the height of the first diffraction peak. According to the hard sphere cluster model, the structure of liquid Sn may be viewed as two different types of clusters. Below ～3?GPa, it is shown that the packing fraction of the dominant cluster (occupying ～0.94 fraction) changes with compression, while above ～3?GPa, the packing fractions and the hard sphere diameters of both clusters start to influence the structure, causing significant changes with increasing pressure. Our results suggest that the compression behavior of liquid Sn changes from localized densification only in one cluster below ～3?GPa to homogeneous structural changes in both clusters above ～3?GPa.     

Pressure-induced isostructural phase transition and correlation of FeAs coordination with the superconducting properties of 111-type Na(1-x)FeAs

The effect of pressure on the crystalline structure and superconducting transition temperature (T(c)) of the 111-type Na(1-x)FeAs system using in situ high-pressure synchrotron X-ray powder diffraction and diamond anvil cell techniques is studied. A pressure-induced tetragonal to tetragonal isostructural phase transition was found. The systematic evolution of the FeAs(4) tetrahedron as a function of pressure based on Rietveld refinements on the powder X-ray diffraction patterns was obtained. The nonmonotonic T(c)(P) behavior of Na(1-x)FeAs is found to correlate with the anomalies of the distance between the anion (As) and the iron layer as well as the bond angle of As-Fe-As for the two tetragonal phases. This behavior provides the key structural information in understanding the origin of the pressure dependence of T(c) for 111-type iron pnictide superconductors. A pressure-induced structural phase transition is also observed at 20 GPa.     

Gelfand Factor Rings and Weak Zariski Topologies

Let R be any ring with identity. Let N(R) (resp. J(R)) denote the prime radical (resp. Jacobson radical) of R, and let Spec _r (R) (resp. Spec _l (R), Max _r (R), Prim _r (R)) denote the set of all right prime ideals (resp. all left prime ideals, all maximal right ideals, all right primitive ideals) of R. In this article, we study the relationships among various ring-theoretic properties and topological conditions on Spec _r (R) (with weak Zariski topology). The following results are obtained: (1) R/N(R) is a Gelfand ring if and only if Spec _r (R) is a normal space if and only if Spec _l (R) is a normal space; (2) R/J(R) is a Gelfand ring if and only if every right prime ideal containing J(R) is contained in a unique maximal right ideal.     

Finding the Maximum Eigenvalue of Essentially Nonnegative Symmetric Tensors via Sum of Squares Programming

Finding the maximum eigenvalue of a tensor is an important topic in tensor computation and multilinear algebra. Recently, for a tensor with nonnegative entries (which we refer it as a nonnegative tensor), efficient numerical schemes have been proposed to calculate its maximum eigenvalue based on a Perron–Frobenius-type theorem. In this paper, we consider a new class of tensors called essentially nonnegative tensors, which extends the concept of nonnegative tensors, and examine the maximum eigenvalue of an essentially nonnegative tensor using the polynomial optimization techniques. We first establish that finding the maximum eigenvalue of an essentially nonnegative symmetric tensor is equivalent to solving a sum of squares of polynomials (SOS) optimization problem, which, in its turn, can be equivalently rewritten as a semi-definite programming problem. Then, using this sum of squares programming problem, we also provide upper and lower estimates for the maximum eigenvalue of general symmetric tensors. These upper and lower estimates can be calculated in terms of the entries of the tensor. Numerical examples are also presented to illustrate the significance of the results.     

Global Quadratic Minimization over Bivalent Constraints: Necessary and Sufficient Global Optimality Condition

In this paper, we establish global optimality conditions for quadratic optimization problems with quadratic equality and bivalent constraints. We first present a necessary and sufficient condition for a global minimizer of quadratic optimization problems with quadratic equality and bivalent constraints. Then we examine situations where this optimality condition is equivalent to checking the positive semidefiniteness of a related matrix, and so, can be verified in polynomial time by using elementary eigenvalues decomposition techniques. As a consequence, we also present simple sufficient global optimality conditions, which can be verified by solving a linear matrix inequality problem, extending several known sufficient optimality conditions in the existing literature.     

Analysis of circumferential waves on a water-filled cylindrical shell

The formation of scattering field from a water-filled cylindrical shell was studied. The analytic solutions of scattering field are derived using elastic thin shell theory and Sommerfeld-Watson Transformation(SWT) method.Complex wave-number poles of circumferential waves are found numerically,the phase speed and attenuation of circumferential waves between the situation of a hollow cylindrical shell and a water-filled cylindrical shell are compared. The synthesis of backscattering form functions which are sum of specular reflection component and circumferential waves is consistent with normal mode result.The calculated echo sequences of additional fluid circumferential waves are compared with experimental results. The results show that richer resonance peaks appeared in the backscattering form functions of a water-filled cylindrical shell and the formation of echo’s structure are due to re-radiation effects of additional fluid circumferential waves.     

狭义相对论中的与门佯谬

提出了一个所谓“与门佯谬”问题,并利用狭义相对论进行了详细的分析和计算,消除和此佯谬。