Scattering of SH-wave from interface cylindrical elastic inclusion with a semicircular disconnected curve

Scattering of SH wave from an interface cylindrical elastic inclusion with a semicircular disconnected curve is investigated. The solution of dynamic stress concentration factor is given using the Green＇s function and the method of complex variable functions. First, the space is divided into upper and lower parts along the interface. In the lower half space, a suitable Green＇s function for the problem is constructed. It is an essential solution of the displacement field for an elastic half space with a semi-cylindrical hill of cylindrical elastic inclusion while bearing out-plane harmonic line source load at the horizontal surface. Thus, the semicircular disconnected curve can be constructed when the two parts are bonded and continuous on the interface loading the undetermined anti-plane forces on the horizontal surfaces. Also, the expressions of displacement and stress fields are obtained in this situation. Finally, examples and results of dynamic stress concentration factor are given. Influences of the cylindrical inclusion and the difference parameters of the two mediators are discussed.

Dynamic behaviors of water contained in calcium-silicate-hydrate gel at different temperatures studied by quasi-elastic neutron scattering spectroscopy

The dynamic behaviors of water contained in calcium-silicate-hydrate（C-S-H） gel with different water content values from 10%to 30%（by weight）,are studied by using an empirical diffusion model（EDM） to analyze the experimental data of quasi-elastic neutron scattering（QENS） spectra at measured temperatures ranging from 230 K to 280 K.In the study,the experimental QENS spectra with the whole Q-range are considered.Several important parameters including the bound/immobile water elastic coefficient A,the bound water index BWI,the Lorentzian with a half-width at half-maximum（HWHM） Γ;（Q） and Γ;（Q）,the self-diffusion coefficients D;and D;of water molecules,the average residence times τ;and τ;,and the proton mean squared displacement（MSD）(u;) are obtained.The results show that the QENS spectra can be fitted very well not only for small Q（≤1 A;） but also for large Q.The bound/immobile water fraction in a C-S-H gel sample can be shown by the fitted BWI.The distinction between bound/immobile and mobile water,which includes confined water and ultra-confined water,can be seen by the fitted MSD.All the MSD tend to be the smallest value below 0.25 A;（the MSD of bound/immobile water） as the Q increases to 1.9 A;no matter what the temperature and water content are.Furthermore,by the abrupt changes of the fitted values of D;,τ;,and Γ;（Q）,a crossover temperature at 250 K,namely the liquid-to-crystal-like transition temperature,can be identified for confined water in large gel pores（LGPs） and/or small gel pores（SGPs） contained in the C-S-H gel sample with 30% water content.

3D scattering of obliquely incident plane SV waves by an alluvial valley embedded in a fluid-saturated, poroelastic layered half-space

The indirect boundary element method is used to study the 3D dynamic response of an infinitely long alluvial valley embedded in a saturated layered half-space for obli- quely incident SV waves. A wave-number transform is first applied along the valley＇s axis to reduce a 3D problem to a 2D plane strain problem. The problem is then solved in the section perpendicular to the axis of the valley. Finally, the 3D dynamic responses of the valley are obtained by an inverse wave-number transform. The validity of the method is con- firmed by comparison with relevant results. The differences between the responses around the valley embedded in dry and in saturated poroelastic medium are studied, and the effects of drainage conditions, porosity, soil layer stiffness, and soil layer thickness on the dynamic response are dis- cussed in detail resulting in some conclusions.

INVERSE SCATTERING BY AN INHOMOGENEOUS PENETRABLE OBSTACLE IN A PIECEWISE HOMOGENEOUS MEDIUM

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using the integral equation method. We then proceed to establish two tools that play important roles for the inverse problem： one is a mixed reciprocity relation and the other is a priori estimates of the solution on some part of the interfaces between the layered media. For the inverse problem, we prove in this paper that both the penetrable interfaces and the possible inside inhomogeneity can be uniquely determined from a knowledge of the far field pattern for incident plane waves.

Scattering of Tollmien-Schlichting waves as they pass over forward-/backward-facing steps

Forward-/backward-facing steps in boundary-layer flows are often seen in engineering applications, and they have potential impacts on laminar-turbulent transition through scattering of the oncoming instability modes(e.g., Tollmien-Schlichting(T-S) waves). This issue is studied in the present paper by applying a local scattering framework, which is a rather generic mathematical framework on describing the mode scattering process. In this framework, a high-Reynolds-number triple-deck formalism is employed, and a transmission coefficient, defined as the ratio of the asymptotic amplitude of the instability mode downstream of the step to that upstream, is introduced. Through the systematical study, it has been found that both the forward-and backward-facing steps have a destabilizing effect on the oncoming T-S waves in subsonic boundary layers, this effect increases with the height of the step and/or the frequency of the T-S wave, and a backward-facing step(BFS) always has a greater impact than a forward-facing step(FFS). These facts agree with most of the previous investigations.However, one numerical study(WORNER, A., RIST, U., and WAGNER, S. Humps/steps influence on stability characteristics of two-dimensional laminar boundary layer. AIAA Journal, 41, 192–197(2003)), which was based on an ad-hoc configuration, showed an opposite impact of an FFS. Through the investigation on the specific configuration, it is revealed that the wrong conclusion was drawn by misinterpreting the numerical results.

Analysis of the Linear Sampling Method for Boundary Reconstruction of Chiral Obstacle in Electromagnetic Scattering Problems

In this paper, we consider the inverse scattering by chiral obstacle in electromagnetic fields, and prove that the linear sampling method is also effective to determine the support of a chiral obstacle from the noisy far field data.

Computer Simulation of Transition Regimes of Solitons in Stimulated Raman Scattering with Excitation of Polar Optical Phonons

The system of nonlinear equations modeling the process of nonstationary stimulated Raman scattering (SRS) in noncentrosymmetric crystals for the waves on laser, Stokes, polariton, and phonon frequencies is investigated by using the numerical methods. The general case for amplitudes of waves that resulted in doubling of the number of equations is considered. It is shown that the application of the methods of finite differences to the computer simulation of transition regimes is completely consistent with the analytical results found for the asymptotical solutions in form of solitons. The obtained results also indicate that the laser pulses of Gaussian shape appearing at the boundary of nonlinear medium tend to become solitons of Lorentzian shape. It was also found that the formation of solitons occurs when the vibrations of optical phonons and that of electromagnetic wave were either in or out of phase. It is shown that all electromagnetic waves entering the medium with different speeds become solitons having the same speed. In the second part of the paper we considered the computer simulation of soliton stability with respect to small (weak) perturbations of all interacting waves. In the present paper we considered the case of evolution of those disturbances in the vicinity of peaks of solitons. The numerical analysis showed that in wide range of parameters the solitons were stable.

A Method for Calculating Bottom Backscattering Strength Using Omnidirectional Projector and Omnidirectional Hydrophone

A method of obtaining bottom backscattering strength by employing an omnidirectional projector and omnidirectional hydrophone is proposed. The backscattering strength is extracted from monostatic backscattering data. The method was adopted in an experiment conducted in the South Yellow Sea of China. The seafloor surface was relatively smooth and covered by a small quantity of shell fragments, as observed through a digital camera system. Sampling data showed that the main component of the sediment at this experimental site was fine sand. In this paper, we detail the calculation method. Preliminary results of backscattering strength as a function of grazing angle(20?–70?) in the frequency range of 6–24 kHz are presented. The measured backscattering strength increased with the grazing angle and changed more rapidly at large grazing angles(60?–70?). A comparison of the data at different frequencies reveals that the measured backscattering strength substantially rises with the increase of acoustic frequency. A fitting curve of Lambert's law against the measured data shows that the backscattering strength deviates from Lambert's law at large grazing angles.

Scattering of Oblique Surface Water Waves by Thin Vertical Barrier Over Undulating Bed Topography

The present study deals with the scattering of oblique surface water waves by small undulation on the bottom in the presence of a thin vertical barrier. Here, three different configurations of vertical barriers are investigated. Perturbation analysis is employed to determine the physical quantities, namely, the reflection and transmission coefficients. In this analysis, many different Boundary Value Problems (BVPs) are obtained out of which the first two bvps are considered. The zeroth order bvp is solved with the aid of eigenfunction expansion method. The first order reflection and transmission coefficients are derived in terms of the integrals by the method of the Green's integral theorem. The variation of these coefficients is plotted and analyzed for different physical parameters. Furthermore, the energy balance relation, an important relation in the study of water wave scattering, is derived and checked for assuring the correctness of the numerical results for the present problem.

Factors influencing electromagnetic scattering from the dielectric periodic surface

The scattering characteristics of the periodic surface of infinite and finite media are investigated in detail.The Fourier expression of the scattering field of the periodic surface is obtained in terms of Huygens’ s principle and Floquet’s theorem.Using the extended boundary condition method(EBCM) and T-matrix method, the scattering amplitude factor is solved,and the correctness of the algorithm is verified by use of the law of conservation of energy.The scattering cross section of the periodic surface in the infinitely long region is derived by improving the scattering cross section of the finite period surface.Furthermore, the effects of the incident wave parameters and the geometric structure parameters on the scattering of the periodic surface are analyzed and discussed.By reasonable approximation, the scattering calculation methods of infinite and finite long surfaces are unified.Besides, numerical results show that the dielectric constant of the periodic dielectric surface has a significant effect on the scattering rate and transmittance.The period and amplitude of the surface determine the number of scattering intensity peaks, and, together with the incident angle, influence the scattering intensity distribution.

Solution of two-dimensional scattering problem in piezoelectric/piezomagnetic media using a polarization method

Using a polarization method, the scattering problem for a two-dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated. To achieve the purpose, the polarization method for a two-dimensional piezoelectric/piezomagnetic ＂comparison body＂ is formulated. For simple harmonic motion, kernel of the polarization method reduces to a 2-D time-harmonic Green＇s function, which is obtained using the Radon transform. The expression is further simplified under conditions of low frequency of the incident wave and small diameter of the inclusion. Some analytical expressions are obtained. The analytical solutions for generalized piezoelectric/piezomagnetic anisotropic composites are given followed by simplified results for piezoelectric composites. Based on the latter results, two numerical results are provided for an elliptical cylindrical inclusion in a PZT-5H-matrix, showing the effect of different factors including size, shape, material properties, and piezoelectricity on the scattering cross-section.

Scattering of water waves by thin vertical plate submerged below ice-cover surface

The present paper is concerned with scattering of water waves from a vertical plate, modeled as an elastic plate, submerged in deep water covered with a thin uniform sheet of ice. The problem is formulated in terms of a hypersingular integral equation by a suitable application of Green＇s integral theorem in terms of difference of potential functicns across the barrier. This integral equation is solved by a collocation method using a finite series involving Chebyshev polynomials. Reflection and transmission coefficients are obtained numerically and presented graphically for various values of the wave number and ice-cover parameter.

Elastic scattering of sodium and cesium atoms at ultracold temperatures

The elastic scattering properties in a mixture of sodium and cesium atoms are investigated at cold and ultracold temperatures. Based on the accurate interatomic potential for the NaCs mixture, the interspecies s-wave scattering lengths, the effective ranges and the p-wave scattering lengths are calculated by the quantal method and the semiclassical method, respectively. The s-wave scattering lengths are 512.7a0 for the singlet state and 33.4a0 for the triplet state. In addition, the spin-change and elastic cross sections are also calculated, and the g-wave shape resonance is found in the total elastic cross sections.

银纳米线SERS快速高灵敏检测水中痕量Hg2+研究

水中痕量重金属汞离子(Hg^(2+))对人类健康会构成严重威胁,因此快速高灵敏检测水中痕量Hg^(2+)具有重要科学意义和实际应用价值。为实现这一目标,研究运用银纳米线(silver nanowires, AgNWs)作为表面增强拉曼散射(Surface-Enhanced Raman Scattering, SERS)基底来快速高灵敏检测水中痕量Hg^(2+)。用旋涂法制备了均匀分布的AgNWs基SERS基底,并用罗丹明6G(Rhodamine 6G,R6G)作为拉曼信标分子,以间接检测水中痕量Hg^(2+)。通过研究SERS活性、稳定性、重现性、选择性、AgNWs直径及pH值对其SERS活性的影响,用时域有限差分法(Finite Difference Time Domain, FDTD)模拟了AgNWs表面电场分布情况。结果显示,AgNWs基SERS基底具有良好的活性、优异的信号再现性、稳定性和选择性,SERS活性随着直径的增大而增强,对Hg^(2+)的检测限(Detection Of Limit, LOD)达10-11mol/L,远低于美国环境保护署(The U.S. Environmental Protection Agency, EPA)的饮用水Hg^(2+)浓度标准(10-8mol/L)。在低浓度范围内,SERS特征峰强度(R^(2)=0.9919)有良好的线性关系。FDTD模拟结果为试验结果提供了有力的理论支撑,可为水中检测痕量Hg^(2+)提供新策略,在环境监测中具有广阔的应用前景。

Measurement of the Nucleon Nucleon Scattering Length with the ESC04 Interaction

We have determined a value for the 1S0 neutron-neutron scattering length (ann). The scattering length result is presented for the extended-soft-core (ESC04) interaction. The value obtained in the present work is ann = -18.6249 fm. The method of solution of the radial Schr?dinger equation with nonlocal potential for nucleonnucleon pairs is described and the result is consistent with previous determinations of ann = -18.63 ± 0.10 (statistical) ± 0.44 (systematic) ± 0.30 (theoretical) fm. The nonlocal potentials are of the central, spin-spin, spin-or-bital, and tensor type. The analysis from the ESC04 interaction is done at energies 0 ￡ Tlab ￡ 350 MeV. We compare the present result with experimental S-wave phase shifts analysis and agreement is found.

Inverse Scattering Problem for the Schrodinger’s Equation

The analytic properties of the scattering amplitude are discussed. And, the representation of the potential by the scattering amplitude is obtained.

Diffraction of SH-waves by topographic features in a layered transversely isotropic half-space

Abstract： The scattering of plane SH-waves by topographic features in a layered transversely isotropic （TI） half-space is investigated by using an indirect boundary element method （IBEM）. Firstly, the anti-plane dynamic stiffness matrix of the layered TI half-space is established and the free fields are solved by using the direct stiffness method. Then, Green＇s functions are derived for uniformly distributed loads acting on an inclined line in a layered TI half-space and the scattered fields are constructed with the deduced Green＇s functions. Finally, the free fields are added to the scattered ones to obtain the global dynamic responses. The method is verified by comparing results with the published isotropic ones. Both the steady-state and transient dynamic responses are evaluated and discussed. Numerical results in the frequency domain show that surface motions for the TI media can be significantly different from those for the isotropic case, which are strongly dependent on the anisotropy property, incident angle and incident frequency. Results in the time domain show that the material anisotropy has important effects on the maximum duration and maximum amplitudes of the time histories.

磷钼杂多酸-罗丹明S体系的共振散射光谱研究

在0.14mol·dm^(-3)H_2SO_4介质中,PO_4^(3-),MoO_4^(2-)与罗丹明S形成磷钼杂多酸-罗丹明S三元缔合物,在610nm处产生一灵敏的共振散射(即瑞利散射)光谱峰,磷浓度在0.2～20μg·dm^(-3)范围内与共振散射光强度呈良好线性关系.实验结果表明,本法具有灵敏度高、选择性好等特点,用于水和茶叶试样中磷酸根的测定,结果与示波极谱法的测定结果一致.

铬天青S-铝(Ⅲ)-聚乙二醇4000体系的共振散射光谱及其应用

在pH5 0的NaAc HAc缓冲溶液及非离子表面活性剂聚乙二醇 40 0 0存在下 ,铬天青S与铝 (Ⅲ )形成络合物微粒体系 ,在 40 0nm和 5 30nm处出现两个较强的共振散射峰 .共振散射光强度与Al(Ⅲ )的浓度在 0 0 84— 0 84μg·ml- 1 范围内呈良好的线性关系 ,考察了适宜的反应条件及共存物质的影响 .建立了一个共振散射光谱测定水中Al的方法 ,其结果与分光光度法一致 .