基于无约束非线性优化算法的光强自相关函数拟合

在光子相关光谱(PCS)颗粒测量技术中非线性累积反演方法是一种重要的算法。采用无约束非线性优化算法对反演过程中相关曲线的拟合问题进行了分析和研究, 实现了从任意初始值开始获取最优非线性拟合解, 并给出了算法的实现步骤。采用此方法对50 nm, 100 nm, 200 nm和500 nm的标准聚苯乙烯乳胶颗粒的实测光强自相关函数数据进行了拟合, 并反演了颗粒粒径, 与其他曲线拟合算法相比, 本算法不但对初始值的依赖性小, 而且得到的颗粒粒径更接近乳胶颗粒的标称直径, 测量误差更小。     

基于奇异值分解的光子相关光谱滤波方法研究

针对光子相关光谱颗粒测量法在测量超细纳米颗粒时,容易受噪声影响,导致拟合误差较大的问题,提出了一种基于奇异值分解的光子相关光谱滤波方法。其处理步骤为:利用颗粒系的光强自相关函数数据构造Hankel矩阵H;对矩阵进行奇异值分解;根据奇异值的大小分布,确定噪声级别和重建参数r;从重建矩阵H1中提取经滤波后的光强自相数据,再通过传统方法进行拟合,得到颗粒的粒径分布。实验中采用30nm标准乳胶球单分散颗粒系,以及30nm和100nm标准乳胶球双分散颗粒系进行实验对比。结果证明:基于奇异值分解的光子相关光谱滤波法有效地提高了测量准确性。     

基于奇异值分解的光子相关光谱滤波方法研究

针对光子相关光谱颗粒测量法在测量超细纳米颗粒时,容易受噪声影响,导致拟合误差较大的问题,提出了一种基于奇异值分解的光子相关光谱滤波方法。其处理步骤为:利用颗粒系的光强自相关函数数据构造Hankel矩阵H;对矩阵进行奇异值分解;根据奇异值的大小分布,确定噪声级别和重建参数r;从重建矩阵H1中提取经滤波后的光强自相数据,再通过传统方法进行拟合,得到颗粒的粒径分布。实验中采用30nm标准乳胶球单分散颗粒系,以及30nm和100nm标准乳胶球双分散颗粒系进行实验对比。结果证明:基于奇异值分解的光子相关光谱滤波法有效地提高了测量准确性。     

图像动态光散射法纳米颗粒粒度分布反演算法研究

针对基于整体相关的图像动态光散射法(IDLS)测量颗粒粒径分布(PSD)问题,研究了全局搜索(GS)算法反演颗粒粒径分布,对峰值为79nm、多分布指数(PDI)为10%的单峰颗粒系和峰值分别为79nm与352nm、多分布指数均为10%的双峰颗粒系进行了反演数值仿真,结果表明全局搜索算法能较好地反演出颗粒粒径分布情况。以此为基础,对峰值为79nm的单峰分布颗粒系,峰值为79nm和352nm、79nm和482nm的两组双峰分布颗粒系进行了实验测量及算法对比研究,结果表明在单峰分布颗粒系下,相对于累积量法,全局搜索算法反演效果较好;在双峰分布颗粒系下,全局搜索算法与双指数法反演结果基本一致。由此可知,对于图像动态光散射颗粒粒径分布测量方法,全局搜索算法能够有效地反演出单峰分布和双峰分布颗粒系的颗粒粒径分布,是反演多分散颗粒系的一种有效方法。     

基于自回归模型的超细颗粒动态光散射模拟

为了获取超细颗粒动态散射光模拟信号, 在分析超细颗粒动态散射光信号特性的基础上, 通过建立动态光散射随机过程的自回归(AR)模型, 利用Levison-Durbin递推算法确定模型参数, 并给出了单峰、双峰分布颗粒信号模拟的模型阶数确定方法, 从而提出了一种基于AR模型的态光散射信号模拟方法。分别对50 nm, 300 nm, 1000 nm, 50 nm与1000 nm, 100 nm与500 nm, 300 nm与1000 nm的单峰、双峰分布颗粒在模型阶数分别为1, 1, 1, 57, 28, 40时进行了模拟, 得到的模拟信号的光强自相关函数与理论值吻合, 用累积法对单峰分布颗粒反演和双指数法对双峰分布颗粒反演, 相对误差分别小于0.58%和3.7%, 因此, 单峰分布颗粒信号模拟需一阶模型, 双峰分布颗粒信号模拟粒径不同所需阶数不同。     

L-M非线性拟合的TDLAS氧气测量研究

氧气浓度是工业生产过程中重要监测参数,采用可调谐二极管激光吸收光谱法(tunable diode laser absorption spectroscopy,TDLAS),结合波长调制技术,可以实现对现场氧气浓度的高精度在线监测,利用氧气位于760 nm处的特征吸收峰进行了氧气浓度的测量。由于激光具有很强的相干性,所以TDLAS技术的检测灵敏度受到光学干涉噪声的严重制约,特别在低浓度时,光学干涉引起的基线起伏使得提取吸收峰波形信号时出现较大误差,影响了TDLAS分析仪的监测灵敏度。针对这一情况,采用了Levenberg-Marquardt非线性拟合算法,并且利用了吸收谱线线型——洛伦兹线型的导数形式对波长调制后获得的二次谐波波形信号进行拟合,提取波形信息。另一方面Levenberg-Marquardt非线性拟合方法需要有大量的计算,为了使研制的TDLAS分析仪能够实现现场的实时监测,采用了支持浮点运算的DSP的C28系列芯片进行数据处理,实现仪器在现场实时监测的功能。实验结果表明,该算法能够有效提取二次谐波信号的吸收峰特征值、克服背景噪声影响,由算法反演得到的氧气浓度与实际浓度的线性比值为1.01,浓度测量的线性误差为1.18%。     

对多孔介质NMR实验弛豫时间分布的实现

报道了人工岩石样品--多孔介质的NMR实验的弛豫时间T₁的测量数据及其处理分析方法. 文中采用Levenberg-Marquardt(L-M)拟合技术, 对实验数据利用3种不同的模型进行拟合：单指数,双指数和多指数模型拟合,特别是多指数拟合的弛豫时间τ -分布曲线. 各种方法利用价值函数χ²进行对比, 与实验结果进行了比较.     

高浓度超细颗粒的后向光子相关光谱测量技术研究

针对光子相关光谱颗粒粒径测量法不能在线测量高浓度超细颗粒的问题,通过分析溶液浓度对光子相关光谱测量法的影响,设计了一种后向散射光路,提出了后向光子相关光谱测量法.实验采用50 nm、100 nm以及500 nm三种标准乳胶球颗粒,在不同的浓度下分别用两种方法进行了测试.结果证明,后向光子相关光谱测量法能有效抑制多重散射的影响,适用于高浓度超细颗粒粒径的在线测量.     

离子交换树脂法制备纳米ZnS

以Zn(NO3)2·6H2O为锌源,Na2S为硫源,采用强碱性阴离子交换树脂法制备了纳米ZnS,并对形成的ZnS纳米粒子进行了XRD、TEM表征.XRD表征计算结果表明样品约为粒径6-10nm的小颗粒,TEM表征结果可观察到样品为由6-10nm的小颗粒团聚而成的50-80nm的大颗粒组成的.     

激光诱导击穿光谱法定量分析水泥中的铜元素

为定量分析水泥中的铜(Cu)元素,根据激光诱导击穿光谱分析方法(Ll BS)的特点,建立了激光诱导击穿光谱分析系统。采用标准加入法为定标方法,制备了5个不同含铜量的水泥样品。根据LIBS谱图,以213.598 nm和219.958 nm作为分析线。应用Savitzky-Golary卷积平滑方法对光谱数据进行了预处理,比较了Guass、Lorentz和Voigt拟合方法对光谱曲线的拟合效果。对测量结果采用一元线性拟合建立了相应的定标曲线,213.598 nm和219.958 nm定标曲线的校正决定系数分别为0.994 8和0.986 4,平均相对误差分别为3.20%和5.78%。实验结果表明:213.598 nm作为分析线的准确度优于219.958 nm分析线,该方法能够满足水泥中Cu元素定量分析的要求。     

On the neglecting of higher‐order cumulants in EXAFS data analysis

The cumulant expansion is one of the most powerful and useful methods for EXAFS data analysis, in which the higher‐order cumulants allow to consider deviations from a simple Gaussian distribution. In this work, analytical expressions have been derived to show the effects of neglecting higher‐order cumulants in EXAFS analysis by the ratio method. The errors in the best‐fitting procedure owing to the omission of the higher‐order cumulants, as well as of the coordination number, can be determined.     

Detecting charge noise with a Josephson junction: a problem of thermal escape in presence of non-Gaussian fluctuations

Motivated by several experimental activities to detect charge noise produced by a mesoscopic conductor with a Josephson junction as on-chip detector, the switching rate out of its zero-voltage state is studied. This process is related to the problem of thermal escape in presence of non-Gaussian fluctuations. In the relevant case of weak higher than second order cumulants, an effective Fokker-Planck equation is derived, which is then used to obtain an explicit expression for the escape rate. Specific results for the rate asymmetry due to the third moment of current noise allow to analyze experimental data and to optimize detection circuits.     

Computation of Current Cumulants for Small Nonequilibrium Systems

We analyze a systematic algorithm for the exact computation of the current cumulants in stochastic nonequilibrium systems, recently discussed in the framework of full counting statistics for mesoscopic systems. This method is based on identifying the current cumulants from a Rayleigh-Schrödinger perturbation expansion for the generating function. Here it is derived from a simple path-distribution identity and extended to the joint statistics of multiple currents. For a possible thermodynamical interpretation, we compare this approach to a generalized Onsager-Machlup formalism. We present calculations for a boundary driven Kawasaki dynamics on a one-dimensional chain, both for attractive and repulsive particle interactions.     

Fixed point behavior of cumulants in the three-dimensional Ising universality class

High-order cumulants and factorial cumulants of conserved charges are suggested for the study of the critical dynamics in heavy-ion collision experiments. In this paper, using the parametric representation of the three-dimensional Ising model which is believed to belong to the same universality class as quantum chromo-dynamics, the temperature dependence of the second- to fourth-order (factorial) cumulants of the order parameter is studied. It is found that the values of the normalized cumulants are independent of the external magnetic field at the critical temperature, which results in a fixed point in the temperature dependence of the normalized cumulants. In finite-size systems simulated using the Monte Carlo method, this fixed point behavior still exists at temperatures near the critical. This fixed point behavior has also appeared in the temperature dependence of normalized factorial cumulants from at least the fourth order. With a mapping from the Ising model to QCD, the fixed point behavior is also found in the energy dependence of the normalized cumulants (or fourth-order factorial cumulants) along different freeze-out curves.     

Full counting statistics of phonon transport in disordered systems

The coherent potential approximation (CPA) within full counting statistics (FCS) formalism is shown to be a suitable method to investigate average electric conductance, shot noise as well as higher order cumulants in disordered systems. We develop a similar FCS-CPA formalism for phonon transport through disordered systems. As a byproduct, we derive relations among coefficients of different phonon current cumulants. We apply the FCS-CPA method to investigate phonon transport properties of graphene systems in the presence of disorders. For binary disorders as well as Anderson disorders, we calculate up to the 8-th phonon transmission moments and demonstrate that the numerical results of the FCS-CPA method agree very well with that of the brute force method. The benchmark shows that the FCS-CPA method achieves 20 times more speedup ratio. Collective features of phonon current cumulants are also revealed.     

Effect of dephasing on the current statistics of mesoscopic devices

We investigate the effects of dephasing on the current statistics of mesoscopic conductors with a recently developed statistical model, focusing, in particular, on mesoscopic cavities and Aharonov-Bohm rings. For such devices, we analyze the influence of an arbitrary degree of decoherence on the cumulants of the current. We recover known results for the limiting cases of fully coherent and totally incoherent transport and are able to obtain detailed information on the intermediate regime of partial coherence for a varying number of open channels. We show that dephasing affects the average current, shot noise, and higher order cumulants in a quantitatively and qualitatively similar way, and that consequently shot noise or higher order cumulants of the current do not provide information on decoherence additional or complementary to what can be already obtained from the average current.     

Structural investigations on an amorphous Se90Te10 alloy produced by mechanical alloying using EXAFS, cumulant expansion and RMC simulations

We investigated an amorphous Se(90)Te(10) alloy produced by mechanical alloying using two different approaches. First, we used extended x-ray absorption fine structure (EXAFS) spectroscopy and the cumulant expansion method using the Einstein model for the temperature dependence of the cumulants to obtain the cumulants C(*)(1), C(*)(2), and C(*)(3). From these, we found information about the structure of the alloy as well as the thermal and structural disorder, anharmonicity of the effective interatomic pair potentials, thermal expansion of the Se-Se and Se-Te bonds and asymmetry of the partial distribution functions g(Se-Se)(r) and g(Se-Te)(r). The cumulants C(*)(1), C(*)(2), and C(*)(3) also allowed us to reconstruct the g(EXAFS)(ij)(r,T) functions from EXAFS. Then, we made reverse Monte Carlo (RMC) simulations using the total structure factor S(K) obtained from synchrotron x-ray diffraction and the EXAFS oscillations χ(k) on the Se K edge as input data to obtain the g(RMC)(ij)(r) functions. Both methods furnished very similar g(ij)(r) functions, and the structural data obtained from them were also very similar. The results obtained from both methods showed the presence of Se-Te pairs indicating that there is alloying at the atomic level. In addition, we could not find any evidence of the presence of Te clusters in the alloy.     

Advances in theoretical and experimental XAFS studies of thermodynamic properties,anharmonic effects and structural determination of fcc crystals

Thermodynamic properties, anharmonic effects and structural determination of fcc crystals have been studied based on the theoretical and experimental Debye–Waller factors presented in terms of cumulant expansion up to the third order, thermal expansion coefficient, X-ray absorption fine structure (XAFS) spectra and their Fourier transform magnitudes. The advances in these studies are performed by the further development of the anharmonic correlated Einstein model primary only for approximating three first XAFS cumulants into the method using that all the considered theoretical and experimental XAFS parameters have been provided based on only the calculated and measured second cumulants. The obtained cumulants describe the anharmonic effects in XAFS contributing to the accurate structural determination. Numerical results for Cu are found to be in good agreement with the experimental values extracted by using the present advanced method and with those obtained by the other measurements.