Analytical study of the propagation of acoustic waves in a 1D weakly disordered lattice

This paper presents an analytical approach of the propagation of an acoustic wave through a normally distributed disordered lattice made up of Helmholtz resonators connected to a cylindrical duct. This approach allows to determine analytically the exact transmission coefficient of a weakly disordered lattice. Analytical results are compared to a well-known numerical method based on a matrix product. Furthermore, this approach gives an analytical expression of the localization length apart from the Bragg stopband which depends only on the standard deviation of the normal distribution disorder. This expression permits to study on one hand the localization length as a function of both disorder strength and frequency, and on the other hand, the propagation characteristics on the edges of two sorts of stopbands (Bragg and Helmholtz stopbands). Lastly, the value of the localization length inside the Helmholtz stopband is compared to the localization length in the Bragg stopband.     

Time-Reversed Dynamical Entropy and Irreversibility in Markovian Random Processes

A concept of time-reversed entropy per unit time is introduced in analogy with the entropy per unit time by Shannon, Kolmogorov, and Sinai. This time-reversed entropy per unit time characterizes the dynamical randomness of a stochastic process backward in time, while the standard entropy per unit time characterizes the dynamical randomness forward in time. The difference between the time-reversed and standard entropies per unit time is shown to give the entropy production of Markovian processes in nonequilibrium steady states.     

Localization of electromagnetic and acoustic waves in random media. Lattice models

We consider lattice versions of Maxwell's equations and of the equation that governs the propagation of acoustic waves in a random medium. The vector nature of electromagnetic waves is fully taken into account. The medium is assumed to be a small perturbation of a periodic one. We prove rigorously that localized eigenstates arise in a vicinity of the edges of the gaps in the spectrum. A key ingredient is a new Wegner-type estimate for a class of lattice operators with off-diagonal disorder.     

Acoustic wave propagation simulation in a poroelastic medium saturated by two immiscible fluids using a staggered finite-difference with a time partition method

Based on the three-phase theory proposed by Santos, acoustic wave propagation in a poroelastic medium saturated by two immiscible fluids was simulated using a staggered high-order finite-difference algorithm with a time partition method, which is firstly applied to such a three-phase medium. The partition method was used to solve the stiffness problem of the differential equations in the three-phase theory. Considering the effects of capillary pressure, reference pressure and coupling drag of two fluids in pores, three compressional waves and one shear wave predicted by Santos have been correctly simulated. Influences of the parameters, porosity, permeability and gas saturation on the velocities and amplitude of three compressional waves were discussed in detail. Also, a perfectly matched layer (PML) absorbing boundary condition was firstly implemented in the three-phase equations with a staggered-grid high-order finite-difference. Comparisons between the proposed PML method and a commonly used damping method were made to validate the efficiency of the proposed boundary absorption scheme. It was shown that the PML works more efficiently than the damping method in this complex medium. Additionally, the three-phase theory is reduced to the Biot’s theory when there is only one fluid left in the pores, which is shown in Appendix. This reduction makes clear that three-phase equation systems are identical to the typical Biot’s equations if the fluid saturation for either of the two fluids in the pores approaches to zero. Supported by the Key Program of the National Natural Science Foundation of China (Grant No. 10534040) and the National Natural Science Foundation of China (Grant No. 10674148)     

Finite Element Analysis of Maxwell's Equations in Dispersive Lossy Bi-Isotropic Media

In this paper, the time-dependent Maxwell's equations used to modeling wave propagation in dispersive lossy bi-isotropic media are investigated. Existence and uniqueness of the modeling equations are proved. Two fully discrete finite element schemes are proposed, and their practical implementation and stability are discussed.     

负折射介质中三阶非线性色散项对超短脉冲传输的影响

采用分步傅里叶法研究了三阶非线性色散项对超短脉冲传输的影响.通过模拟数值计算得出,在德鲁德模型频率选取的一定范围内,三阶非线性色散项对超短脉冲传输所造成的影响是不可忽略的.结果表明:三阶非线性色散项系数取负值时,在正常色散区超短脉冲不对称展宽,脉冲中心向前沿偏移;在零色散点超短脉冲不对称展宽程度加剧并在脉冲前沿形成振荡,脉冲中心向前沿偏移;在反常色散区超短脉冲不对称变窄,脉冲中心仍向前沿偏移.     

Radiative Transport in a Periodic Structure

We derive radiative transport equations for solutions of a Schrödinger equation in a periodic structure with small random inhomogeneities. We use systematically the Wigner transform and the Bloch wave expansion. The streaming part of the radiative transport equations is determined entirely by the Bloch spectrum, and the scattering part by the random fluctuations.     

本征态的局域化与增益介质中局域态的放大

用时域有限差分方法(FDTD)模拟了二维增益、非增益随机介质中的光学现象。在非增益介质中，观察到了局域态空间分布及其频率特征。在增益介质中，观察到局域态的放大过程。模拟结果显示非增益介质中的局域态相当于传统激光腔的腔模，随机激光是由局域态谐振产生的。     

电磁波在多层介质内的透射

导了多层介质中透射电磁波的电场振幅与介质表面入射电磁波场电场振幅之间的关系式，引入了一个母函数，通过微分可以生成介质各层中的透射波。     

Auto-correlation Properties of Scattering Light in Ultrasound-modulated Random Media

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Pattern Structure of Deterministic Displacement in Random Porous Media with Dispersion Effect

A new model-model of random porous mediz degradation via several fluid displacing,freezing,and thawing cycles is introduced and investigated in this paper.The fluid transport is based on the deterministic method with dispersion effect.The result shows that the topology and the geometry of the porous media have a strong effect on displacement processes.The cluster size of viscous fingering (VF) pattern in percolation cluster increases with the increase of iteration parameter n.When iteration parameter n≥10,VF pattern does not change with n.We find that the displacement fluid forms trapping regions in random porous media with dispersion effect.And the trapping regions will expand with the increasing of the iteration parameter n.When r (throat size)→1 and n≥5,the peak value of the distribution Nmat(r) increases as n increases,where Nmat(r) is the normalized distribution of throat sizes after different displacement-damages but before freezing.The peak value of the distribution Ninv(r) reaches a maximum when n≥10 and r=1,where Ninv(r) is the normalized distribution of the size of invaded throat.This result is different from invasion percolation.It is found that the sweep efficiency E increases along with the increasing of iteration parameter n and decreases with the network size L,and E has a minimum as L increases to the maximum size of lattice.The VF pattern in percolation cluster has one frozen zone and one active zone.     

Numerical simulation of laser-generated surface acoustic waves in the transparent coating on a substrate by the finite element method

The optimum finite element model in the system consisting of a transparent coating and an opaque substrate is established based on the analysis of two important parameters: meshing size and time step, and the stability of solution. Taking into account the temperature dependence of material properties, the transient temperature and temperature gradient field are obtained. According to the thermoelastic theory, this temperature gradient field can be taken as a buried bulk source to generate ultrasonic wave. The surface acoustic waves (SAWs) are obtained. The influence of the coating thickness on the SAWs is analyzed. The model provides a useful tool for the determination of modes which are generated by a laser source in transparent coating on opaque substrate. The surface skimming longitudinal wave exists for the multiple oscillations and it charges from unipolar waveforms to dipolar.     

脉冲在时域二次折射率介质中的传播

从空域与时域的相似性出发，把克尔介质近似为时域二次折射率介质，从而得到了脉冲在该介质中的解析形式，并给出了相应的时域传输矩阵。     

不同偏振飞秒激光经块状材料传输后的脉宽压缩

实验研究了线偏振和圆偏振状态下的飞秒强激光脉冲在块状材料中的传输过程。不同偏振的激光脉冲在传输过程中得到了不同程度的光谱展宽,经色散补偿后,脉冲时域宽度均得到了压缩。详细分析了压缩脉冲的脉宽以及啁啾情况与入射激光脉冲能量之间的关系,比较了飞秒激光在线偏振及圆偏振情况下的不同压缩效果。在线偏振入射光情况下得到了最短21fs的压缩脉冲宽度,在圆偏振情况下得到的最短脉冲宽度为22fs。实验结果表明,这种光谱展宽与色散补偿方式对圆偏振光同样适用,而且圆偏振的入射激光将更有利于对更高能量的脉冲进行压缩。在色散补偿量相同的情况下,压缩效果随入射脉冲能量变化的规律符合理论估计。     

Interaction of second sound with acoustic waves in solids

An expression has been derived for the collision operator for phonons in a solid, which is valid at very low temperatures. The set of coupled equations for the elastic deformation and the phonon density or second sound has been reduced to a simple tractable form and the dispersion equation for the coupled waves consisting of the acoustic modes and second sound has been derived. It is shown that only the longitudinal mode interacts with the second sound. It is also shown that as a result of the interaction with the second sound, the longitudinal velocity along the principal axis acquires a correction term that is proportional to bothγ ² andT ⁴. The author felicitates Prof. D S Kothari on his eightieth birthday and dedicates this paper to him on this occasion.     

Analytical Study of Nonlinear Dust Acoustic Waves in Two-Dimensional Dust Plasma with Dust Charge Variation

The nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation is analytically investigated by using the formally variable separation approach. New analytical solutions for the governing equation of this system have been obtained for dust acoustic waves in a dust plasma for the first time. We derive exact analytical expressions for the general case of the nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation.     

Analytical Study of Nonlinear Dust Acoustic Waves in Two-Dimensional Dust Plasma with Dust Charge Variation

The nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation is analytically investigated by using the formally variable separation approach. New analytical solutions for the governing equation of this system have been obtained for dust acoustic waves in a dust plasma for the first time. We derive exact analytical expressions for the general case of the nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation.     

Applications of the Dirac Form of the Maxwell Equations in Moving Dielectric Media

Maxwell equations in a resting and nonrelativisticly moving medium can be rewritten in a form of the Dirac equation. In the paper the formal analogy between an electron in the electromagnetic field and a photon in the dielectric medium has been used to consider three effects: Fresnel’s drag, mechanical Faraday effect (interpreted here as a procession of the photon spin) and Landau frequencies in a rotating medium. The third effect, up to my knowledge, is new. It predicts that only some discrete frequencies of light can propagate in a rotating medium.     

Analysis of Acoustic Domain Fluxes in a Piezoelectric Semiconductor n-CdS Measured by Brillouin Scattering Method

Acoustic fluxes constituting an acoustic domain in a piezoelectric semiconducting n-CdS were analyzed by Brillouin scattering method. Obtained results were as follows: 0.8 GHz and 2.0 GHz acoustic fluxes were faster than the sound velocity 1.75 × 10⁵ cm/s. The observed profile of the 2.0 GHz flux agreed fairly well with the simulated one performed numerically by KdV equation. The faster positions of the acoustic domain were formed by lower frequency acoustic fluxes and the slower positions understood by acoustic fluxes around maximum gain frequency generated first in a small signal regime.     

飞秒脉冲在共振介质中长距离演化过程研究

为研究飞秒脉冲在共振二能级原子介质中传播较长距离时的演化规律,用时域有限差分的方法数值模拟了5 fs脉冲载波与共振介质相互作用的麦克斯韦布洛赫方程。结果表明,5 fs脉冲的包络与载波的形状基本吻合,变化趋势大体一致,慢变振幅近似和旋转波近似不影响基本结论。在脉冲的谱宽远大于原子介质跃迁线形增宽的条件下,3.2π脉冲演化成2π双曲正割脉冲所经历的过程非常复杂,达到稳态所通过的空间长度大约是面积演化成稳态值所需要的长度的5×104倍。因此,在短距离的面积演化过程中,飞秒脉冲无法保持双曲正割的脉冲形状,只有经过很长的传播距离才能最终到达稳态,形成孤子解。同时,通过比较5 fs和50 fs脉冲的演化情况,得出结论,脉宽越短的脉冲达到稳态所经历的过程越复杂,需要通过的空间距离越长。