Analysis and algorithms for a regularized cauchy problem arising from a non-linear elliptic PDE for seismic velocity estimation

In the present work we derive and study a non-linear elliptic PDE coming from the problem of estimation of sound speed inside the Earth. The physical setting of the PDE allows us to pose only a Cauchy problem, and hence is ill-posed. However, we are still able to solve it numerically on a long enough time interval to be of practical use. We used two approaches. The first approach is a finite difference time-marching numerical scheme inspired by the Lax–Friedrichs method. The key features of this scheme is the Lax–Friedrichs averaging and the wide stencil in space. The second approach is a spectral Chebyshev method with truncated series. We show that our schemes work because of (i) the special input corresponding to a positive finite seismic velocity, (ii) special initial conditions corresponding to the image rays, (iii) the fact that our finite-difference scheme contains small error terms which damp the high harmonics; truncation of the Chebyshev series, and (iv) the need to compute the solution only for a short interval of time. We test our numerical schemes on a collection of analytic examples and demonstrate a dramatic improvement in accuracy in the estimation of the sound speed inside the Earth in comparison with the conventional Dix inversion. Our test on the Marmousi example confirms the effectiveness of the proposed approach.     

Measuring derived acoustic power of an ultrasound surgical device in the linear and nonlinear operating modes

Objective and motivationThe method for measuring derived acoustic power of an ultrasound point source in the form of a sonotrode tip has been considered in the free acoustic field, according to the IEC 61847 standard. The main objective of this work is measuring averaged pressure magnitude spatial distribution of an sonotrode tip in the free acoustic field conditions at different electrical excitation levels and calculation of the derived acoustic power at excitation frequency (f₀ ≈ 25 kHz). Finding the derived acoustic power of an ultrasonic surgical device in the strong cavitation regime of working, even in the considered laboratory conditions (anechoic pool), will enable better understanding of the biological effects on the tissue produced during operation with the considered device.Experimental methodThe pressure magnitude spatial distribution is measured using B&;K 8103 hydrophone connected with a B&;K 2626 conditioning amplifier, digital storage oscilloscope LeCroy Waverunner 474, where pressure waveforms in the field points are recorded. Using MATLAB with DSP processing toolbox, averaged power spectrum density of recorded pressure signals in different field positions is calculated. The measured pressure magnitude spatial distributions are fitted with the appropriate theoretical models.Theoretical approachesIn the linear operating mode, using the acoustic reciprocity principle, the sonotrode tip is theoretically described as radially oscillating sphere (ROS) and transversely oscillating sphere (TOS) in the vicinity of pressure release boundary. The measured pressure magnitude spatial distribution is fitted with theoretical curves, describing the pressure field of the considered theoretical models. The velocity and displacement magnitudes with derived acoustic power of equivalent theoretical sources are found, and the electroacoustic efficiency factor is calculated. When the transmitter is excited at higher electrical power levels, the displacement magnitude of sonotrode tip is increased, and nonlinear behaviour in loading medium appears, with strong cavitation activity produced hydrodynamically. The presence of harmonics, subharmonics and ultraharmonics as a consequence of stable cavitation is evident in the averaged power spectral density. The cavitation noise with continuous frequency components is present as a consequence of transient cavitation. The averaged pressure magnitude at the frequency components of interest (discrete and continous) in the field points is found by calculating average power spectral density of the recorded pressure waveform signal using the welch method. The frequency band of interest where average power spectral density is calculated is in the range from 15 Hz up to 120 kHz due to measurement system restrictions. The novelty in the approach is the application of the acoustic reciprocity principle on the nonlinear system (sonotrode tip and bubble cloud) to find neccessary acoustic power of the equivalent acoustic source to produce the measured pressure magnitude in the field points at the frequency components of interest.ResultsIn the nonlinear operating mode, the ROS model for the considered sonotrode tip is chosen due to the better agreement between measurement results and theoretical considerations. At higher excitation levels, it is shown that the averaged pressure magnitude spatial distribution of discrete frequency components, produced due to stable cavitation, can be fitted in the far field with the inverse distance law. The reduced electroacoustic efficiency factor, calculated at excitation frequency component as ratio of derived acoustic power with applied electrical power, is reduced from 40% in the linear to 3% in the strong nonlinear operating mode. The derived acoustic power at other frequency components (subharmonic, harmonic and ultraharmonic) is negligible in comparison with the derived acoustic power at excitation frequency.Discussion and conclusionsThe sonotrode tip and loading medium are shown in the strong cavitation regime as the coupled nonlinear dynamical system radiating acoustic power at frequency components appearing in the spectrum. The bubble cloud in the strong nonlinear operating mode decreases the derived acoustic power significantly at the excitation frequency.     

T1 THEOREM FOR BESOV SPACES ON NONHOMOGENEOUS SPACES

Suppose μ is a Radon measure on Rd, which may be non doubling. The only condition assumed on μ is a growth condition, namely, there is a constant Co ＞ 0 such that for all x ∈ supp(μ) and r ＞ 0,μ(B(x,r)) ≤ Corn, where 0 ＜ n ≤ d. We prove T1 theorem for non doubling measures with weak kernel conditions. Our approach yields new results for kernels satisfying weakened regularity conditions, while recovering previously known Tolsa's results. We also prove T1 theorem for Besov spaces on nonhomogeneous spaces with weak kernel conditions given in [7].     

多普勒漂移对超音速燃气流光辐射特性计算的影响

分析了超音速射流由于高速相对运动产生多普勒谱线漂移效应对光辐射特性计算的影响。通过采用逐线计算法对不同环境压力、气流温度、气流速度条件下超音速燃气射流在不同的红外光谱区(2.7微米谱带和4.3微米谱带)光辐射谱带积分强度的计算结果比较表明:多普勒漂移效应受环境总压影响最大,压力越大多普勒漂移的影响越小;随着温度升高多普勒漂移效应的影响降低;随着相对速度的增加,多普勒漂移效应的影响多数情况下是增加的。     

激光微区发射光谱分析法测定铝酸锶铕镝长余辉材料中的铕

激光微区发射光谱分析法结合CCD光学多道分析仪测定了SrAl2O4:Eu2 ,Dy3 长余辉材料中铕的含量,研究了该方法用于长余辉材料定量分析的准确性。实验中以Eu(Ⅱ)412.973nm为分析线,计算机拟合LogIf~Logc工作曲线,对Eu的分析结果表明:分析谱线相对强度RSD为4.3%,定量分析相对标准偏差RSD为7.4%,分析结果的平均值为2.13%;采用高温固相反应法制备SrAl2O4:Eu2 ,Dy3 长余辉材料,制备前后的Eu百分含量发生明显变化,高温合成后的长余辉材料中Eu百分含量明显增大。     

集成因子分析与卡尔曼滤波的计算光度分析方法

通过将因子分析与卡尔曼滤波法集成,提出一种多元光度分析新算法。该法运用因子分析法提取多组分化学体系量测数据矩阵中的因子构建卡尔曼滤波校正模型,以克服卡尔曼滤波法依赖于纯物质光谱建模的内在局限性。数值仿真及分析实验结果均表明,该法能获得准确可靠的计算分析结果,是一种有效的计算光度分析新算法。     

广义谱分解与亏损矩阵幂的算法

提出了亏损矩阵广义谱分解概念,所得广义特征矩阵具有类似若当链的性质AA(h)i=λiA(h)i+A(h+1)i.亏损矩阵可分解成A=∑si=1(λiA(0)i+A(1)i),由Am=∑si=1∑mh=0Chmλm-hiA(h)i可生成线性方程组,求出各A(h)i,进而计算A的较大次幂Am.介绍了广义谱分解在计算矩阵幂级数中的应用.     

膜厚监控系统的光谱宽度对窄带滤光片性能的影响

讨论了膜厚监控系统的光谱宽度对波分复用窄带滤光片特性的影响,分析了监控过程中所出现的信号异常现象,其主要原因是控制光光谱宽度以及控制波长与滤光片中心波长不一致,所以控制光光谱分辨率必须小于单个法布里-珀罗滤光片最后2层膜折转点波长宽度的一半,即对100GHz的滤光片,监控系统的光谱宽度必须小于0．2nm。一旦产生中心波长偏离,就必定产生厚度控制误差。讨论了高折射率膜和低折射率膜的信号变化规律,发现当中心波长比监控波长长时,虽然信号变化规律正确,但判读到极值时的膜厚变薄。中心波长偏离越长,厚度将越薄。而当中心波长比监控波长短时,信号将出现反转。中心波长越短,反转量越大。最后指出了监控误差对滤光片Tmax和半峰全宽的影响。     

影响光谱辐亮度标定因素的分析

在利用漫反射板标定光谱辐亮度的实验装置中,标准灯完全可以近似为点光源。通过对进入光谱仪的辐射通量的数值积分,可以对应求出仪器的实测光谱辐亮度的计算公式。计算表明,实测光谱辐亮度并不等于漫反射板表面的光谱辐亮度,而有一个随标定条件变化的微小差值。通过计算,对光谱仪与漫反射板的距离、光谱仪入射挟缝的光轴与漫反射板法线的夹角以及标准灯与漫反射板的距离等影响光谱仪标定的因素进行分析,得到了最佳的标定条件。讨论了理想标定情况、光谱仪视场趋于一点的极限情况和采用实际的双向反射分布函数已知的漫反射板标定时,实测光谱辐亮度的计算情况。     

中药色谱指纹图谱组分保留时间漂移的校准

基于光谱相关色谱方法判断复杂中药色谱指纹图谱的组分相关性,实现同一中药样本在不同实验条件下所得的色谱指纹图谱的相同组分的色谱保留时间漂移的局部最小二乘校正,为合理评价指纹图谱的品质提供较为实用的工具。