二能级原子与逆场算符耦合系统的J-C模型

利用表象变换方法,对含逆场算符的J-C模型,分别在相互作用表象中和薛定谔表象中求出了系统的演化波函数,并讨论了失谐量为零时的拉比振动.     

DPSM technique for ultrasonic field modelling near fluid-solid interface

Distributed point source method (DPSM) is gradually gaining popularity in the field of non-destructive evaluation (NDE). DPSM is a semi-analytical technique that can be used to calculate the ultrasonic fields produced by transducers of finite dimension placed in homogeneous or non-homogeneous media. This technique has been already used to model ultrasonic fields in homogeneous and multi-layered fluid structures. In this paper the method is extended to model the ultrasonic fields generated in both fluid and solid media near a fluid-solid interface when the transducer is placed in the fluid half-space near the interface. Most results in this paper are generated by the newly developed DPSM technique that requires matrix inversion. This technique is identified as the matrix inversion based DPSM technique. Some of these results are compared with the results produced by the Rayleigh-Sommerfield integral based DPSM technique. Theory behind both matrix inversion based and Rayleigh-Sommerfield integral based DPSM techniques is presented in this paper. The matrix inversion based DPSM technique is found to be very efficient for computing the ultrasonic field in non-homogeneous materials. One objective of this study is to model ultrasonic fields in both solids and fluids generated by the leaky Rayleigh wave when finite size transducers are inclined at Rayleigh critical angles. This phenomenon has been correctly modelled by the technique. It should be mentioned here that techniques based on paraxial assumptions fail to model the critical reflection phenomenon. Other advantages of the DPSM technique compared to the currently available techniques for transducer radiation modelling are discussed in the paper under Introduction.     

An improved approximation for the Rayleigh wave equation

We derive a simple expression, which gives an approximate value of the Rayleigh wave velocity in an isotropic solid. This approximation is five times better than that given by Viktorov. The velocity equation can be easily inverted in order to obtain an accurate determination of the elastic constants. This procedure can be worthwhile for elastic microanalysis of bulk materials by scanning acoustic microscopy.     

Exact Boundary Synchronization by Groups for a Kind of System of Wave Equations Coupled with Velocities*

This paper deals with the exact boundary controllability and the exact boundary synchronization for a 1-D system of wave equations coupled with velocities. These problems can not be solved directly by the usual HUM method for wave equations, however, by transforming the system into a first order hyperbolic system, the HUM method for 1-D first order hyperbolic systems, established by Li-Lu(2022) and Lu-Li(2022), can be applied to get the corresponding results.     

Surface Acoustic Wave Characterization of Equivalent Young's Moduli for Patterned Films北大核心CSCD

Based on the equivalent elasticity theory for layered materials, the micro-mechanics equivalent models for single and dual damascene structures were established. The equivalent elastic constant of the patterned structure was introduced, to establish the propagation model for the surface acoustic waves propagating in the layered structure of the patterned film/ substrate, and the theoretical dispersion curves of the surface acoustic waves were calculated with Green’s function and the matrix method. The finite element method was used to calculate 24 numerical examples of damascene structures with different volume ratios, and the results were compared with those of the strain energy method. The results show that, the average relative errors of the equivalent Young’s moduli of the 300 nm-thick dual damascene film and the 100 nm-thick single damascene film are 2.06% and 2.27%, respectively. The research verifies the correctness of the equivalent patterned structure model and the feasibility of the surface acoustic wave method to characterize the mechanical properties of patterned films, and provides a reference for the development of suitable chemico-mechanical polishing technologies for patterned films under low pressure. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

基于深度学习的材料超声回波衰减预测方法

材料超声回波衰减是评价材料均匀一致性的常用方法, 针对具有复杂结构的航空发动机盘件难以进行材料底面超声回波衰减评价的问题, 本文提出了利用超声背散射波信号直接预测底面回波衰减的方法。采用10MHz聚焦探头进行超声背散射波数据的采集, 利用深度学习技术构建和训练模型,建立了基于深度学习的材料底面回波衰减预测方法, 同时讨论了采用不同信号形式的超声波信号分类识别模型的准确率差异。研究发现：基于深度学习技术可实现通过超声背散射波预测材料的底面回波衰减, 预测结果和实际底面回波衰减试验结果具有良好的一致性。     

Asymptotic stability of viscous contact wave to a radiation hydrodynamic limit model

This paper is concerned with the large time behavior of the solutions for 1D radiation hydrodynamic limit model without viscosity and its asymptotic stability of the viscous contact discontinuity wave under the smallness assumption of the strength of the contact wave and initial perturbations. The present pressure includes a fourth-order term about the absolute temperature from radiation effect which brings the main difficulty. Furthermore, the dissipative of the system is weaker for the lack of viscosity. All these make the problem more challenging. The prove is mainly based on the energy method, including normal and radial directions energy estimates.     

Cavitation-induced shock wave behaviour in different liquids

This paper follows our earlier work where a strong high frequency pressure peak has been observed as a consequence of the formation of shock waves due to the collapse of cavitation bubbles in water, excited by an ultrasonic source at 24 kHz. We study here the effects of liquid physical properties on the shock wave characteristics by replacing water as the medium successively with ethanol, glycerol and finally a 1:1 ethanol–water solution. The pressure frequency spectra obtained in our experiments (from more than 1.5 million cavitation collapsing events) show that the expected prominent shockwave pressure peak was barely detected for ethanol and glycerol, particularly at low input powers, but was consistently observed for the 1:1 ethanol–water solution as well as in water, with a slight shift in peak frequency for the solution. We also report two distinct features of shock waves in raising the frequency peak at MHz (inherent) and contributing to the raising of sub-harmonics (periodic). Empirically constructed acoustic pressure maps revealed significantly higher overall pressure amplitudes for the ethanol–water solution than for other liquids. Furthermore, a qualitative analysis revealed that mist-like patterns are developed in ethanol–water solution leading to higher pressures.     

Weakly nonlinear focused ultrasound in viscoelastic media containing multiple bubbles

To facilitate practical medical applications such as cancer treatment utilizing focused ultrasound and bubbles, a mathematical model that can describe the soft viscoelasticity of human body, the nonlinear propagation of focused ultrasound, and the nonlinear oscillations of multiple bubbles is theoretically derived and numerically solved. The Zener viscoelastic model and Keller–Miksis bubble equation, which have been used for analyses of single or few bubbles in viscoelastic liquid, are used to model the liquid containing multiple bubbles. From the theoretical analysis based on the perturbation expansion with the multiple-scales method, the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation, which has been used as a mathematical model of weakly nonlinear propagation in single phase liquid, is extended to viscoelastic liquid containing multiple bubbles. The results show that liquid elasticity decreases the magnitudes of the nonlinearity, dissipation, and dispersion of ultrasound and increases the phase velocity of the ultrasound and linear natural frequency of the bubble oscillation. From the numerical calculation of resultant KZK equation, the spatial distribution of the liquid pressure fluctuation for the focused ultrasound is obtained for cases in which the liquid is water or liver tissue. In addition, frequency analysis is carried out using the fast Fourier transform, and the generation of higher harmonic components is compared for water and liver tissue. The elasticity suppresses the generation of higher harmonic components and promotes the remnant of the fundamental frequency components. This indicates that the elasticity of liquid suppresses shock wave formation in practical applications.     

Method of measuring one-dimensional photonic crystal period-structure-film thickness based on Bloch surface wave enhanced Goos-Hänchen shift

This paper puts forward a novel method of measuring the thin period-structure-film thickness based on the Bloch surface wave (BSW) enhanced Goos-Hänchen (GH) shift in one-dimensional photonic crystal (1DPC). The BSW phenomenon appearing in 1DPC enhances the GH shift generated in the attenuated total internal reflection structure. The GH shift is closely related to the thickness of the film which is composed of layer-structure of 1DPC. The GH shifts under multiple different incident light conditions will be obtained by varying the wavelength and angle of the measured light, and the thickness distribution of the entire structure of 1DPC is calculated by the particle swarm optimization (PSO) algorithm. The relationship between the structure of a 1DPC film composed of TiO₂ and SiO₂ layers and the GH shift, is investigated. Under the specific photonic crystal structure and incident conditions, a giant GH shift, 5.1×10³ times the wavelength of incidence, can be obtained theoretically. Simulation and calculation results show that the thickness of termination layer and periodic structure bilayer of 1DPC film with 0.1-nm resolution can be obtained by measuring the GH shifts. The exact structure of a 1DPC film is innovatively measured by the BSW-enhanced GH shift.