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.     

Effect of nonlinear electrodynamics on shadows of slowly rotating black holes

In this study, we investigate the effect of nonlinear electrodynamics on the shadows of charged, slowly rotating black holes with the presence of a cosmological constant. Rather than the null geodesic of the background black hole spacetime, the trajectory of a photon, as a perturbation of the nonlinear electrodynamic field, is governed by an effective metric. The latter can be derived by analyzing the propagation of a discontinuity of the electromagnetic waveform. Subsequently, the image of the black hole and its shadow can be evaluated using the backward ray-tracing technique. We explore the properties of the resultant black hole shadows of two different scenarios of nonlinear electrodynamics, namely, the logarithmic and exponential forms. In particular, the effects of nonlinear electrodynamics on the optical image are investigated, as well as the image's dependence on other metric parameters, such as the black hole spin and charge. The resulting black hole image and shadow display rich features that potentially lead to observational implications.     

Manipulating Nonlinear Photocurrent from Interlayer Coupling in Bilayer Metamaterials for Polarized Terahertz Generation

Polarized terahertz (THz) wave generation is of great significance for chiral and anisotropic sensing applications. However, how to manipulate amplitude, polarization, and ellipticity of the THz generation is still a fundamental challenge. Herein, polarized THz wave generation is achieved from a bilayer metamaterial consisting of T-shaped structure (TSS) and split resonator rings (SRRs) by combining Maxwell and hydrodynamic equations. The elliptically polarized THz wave can be synthetized directly from horizontally and vertically polarized THz components due to the orthogonal nonlinear photocurrents along the arm-directions of TSS and SRRs, respectively. Besides, the ellipticity and the orientation angle of the THz polarization ellipse can be modulated by the twist angle between the SRRs and TSS layers. The maximum ellipticity can reach 0.34 while the orientation angle is tunable from −0.45 to 0.48π by tuning the twist angle. This work proposes an interlayer coupling method for the polarized THz sources based on metamaterials in potential circular dichroism and chiral sensing applications.     

静电波对磁化等离子体的共振加热的理论及数值模拟研究

利用多标度展开得到了更一般的静电波与磁化等离子体回旋运动间的共振条件；通过数值模拟证实了理论分析，发现分数频率同样可以产生共振加热；发现加热效果即使对于相同频率的波，也不是随驱动波的振幅单调增强，而是存在一些优势振幅，即在特定频率特定振幅下有特别好的加热效果. 关键词： 等离子体 共振加热 非线性动力学     

连续动力系统时间序列的非线性检验

用相位随机化的替代数据方法，研究了连续混沌动力系统时间序列的非线性检验判定.研究发现，在不同的采样情况下，混沌时间序列的非线性特性检验有所差异，尤其对于过采样时间序列，往往会出现虚假的判断结果.针对过采样时间序列，最好采用能够反映非线性特征的参数，作为检验统计量进行检验判断. 关键词： 替代数据 关联维数 连续时间序列 非线性检验     

强激光腔镜温升对腔几何参数和远场光强的影响

 利用交替方向隐式有限差分法分析了高能激光器虚共焦非稳腔反射镜的温度场及热变形的数值计算方法。以单晶硅为例,计算了反射镜由于吸收激光能量而形成的温度场分布以及由此引起的热变形对谐振腔几何结构参数的影响,并在此基础上数值模拟了热畸变情况下正支虚共焦非稳腔的远场光强分布。计算结果表明:在激光束辐照的开始阶段,温升场主要集中在激光束辐照的中心区域内,在整个镜面上远未拉平,由此引起的厚度方向温升分布也是如此,很不均匀。     

Λ型三能级原子系统中Raman跃迁增强的Kerr非线性效应

在理论上研究了Λ型三能级原子系统Raman跃迁中的线性和非线性极化率.研究表明: Raman 跃迁中，如果原子完全被抽运到与控制光作用的基态时，将导致介质对探针光的线性极化率 为零，而三阶非线性极化率不为零.通过减小原子两基态间的无辐射衰减速率γ_{12，可以极大地增强交叉Kerr非线性效应.}     

大学生学习成绩分析及相应的差异教学策略

以SPSS、Origin为主要数据分析工具,对某大学化工学院本科生期末考试成绩进行分析。对降序排列的平均学分绩点一元拟合曲线的残差进行了拟合,对其拟合函数进行求导,发现可以将样本按照20%、50%、30%的比例分为3个集团。通过层次聚类也得到类似的结果。不同集团的学生的学分获得率的组成、标准偏差分布明显不同。重要的专业基础课程在学生学习集团的形成中起到了重要的作用,基于统计结果,建议针对不同集团学生的学习特点应采取相应的差异化教学策略。     

DYNAMICAL CHARACTER FOR A PERTURBED COUPLED NONLINEAR SCHRODINGER SYSTEM

The dynamical character for a perturbed coupled nonlinear Schrodinger system with periodic boundary condition was studied. First, the dynamical character of perturbed and unperturbed systems on the invariant plane was analyzed by the spectrum of the linear operator. Then the existence of the locally invariant manifolds was proved by the singular perturbation theory and the fixed-point argument.     

固态氢分子基质隔离高分辨光谱实验装置及其应用

建立了用傅立叶变换红外光谱和中红外差频激光光谱方法研究氢基质隔离光谱的测量装置. 作为装置的测试, 观测了3 cm长的固态氢分子晶体在1-5 μm波段的吸收光谱. 并用中红外差频激光测量其在2410 cm-1附近的W0(0)(v=0→0, J=6→0)谱线的高分辨精细结构. 通过在低温基片上喷溅沉积氢分子晶体薄膜的方法, 对氢基质隔离的CO2分子的高分辨红外吸收光谱进行了研究.