Direct-search methods in data fitting: Application to Mössbauer spectroscopy

Summary An algorithm based on the direct search of parameter optimization without evaluating derivatives is discussed. It consists of a slightly modified version of the Hooke and Jeeves method, optimized in velocity, in order to give quick rensponses also on personal computers. In the present work it has been applied to the minimization of a sum of squares, common case in data fitting. An application to M?ssbauer spectroscopy is presented.     

Monte-Carlo拟合算法及其在电子动量谱学实验数据处理中应用的研究

介绍了一种新的Monte-Carlo曲线拟合算法,由于新算法具有比其他迭代算法拟合更加稳定的优势,解决了电子动量谱学实验数据处理中遇到的电离能谱能峰叠加引起的拟合效果不佳的问题.利用VB语言编写的基于以上方法的拟合程序处理CF2Br2分子的动量谱学实验数据,与基于Levenberg-Marquardt算法的PeakFit软件处理的结果进行比较,结果明显优于后者,并由此明确的重新指认了之前动量谱学方法无法指认的CF2Br2分子的价壳层最外四个轨道4b2,2a2,4b1和6a1的排序,肯定了Hartree-Fock和外价壳层格林函数方法(OVGF)的理论计算结果,而修正了光电子谱学实验的指认.     

A weighted least squares method for circle fitting to frequency response data

Despite the recent development of powerful multi-degree of freedom curve fitting programs the advent of the microcomputer has meant that there is still scope for improvement of simpler single degree of freedom models. A weighted least squares curves fitting method, based on a well known conformal mapping, is described. This method is shown to have important theoretical advantages over some established methods.     

Discrete ambiguities in phase-shift analysis

In two practical examples (α-³He and α-α scattering) we investigate to what extent the elastic amplitude above the first inelastic threshold, determined from phase-shift analysis, is subject to ambiguity. We find that it is extremely difficult to determine the correct physical amplitude uniquely.     

Geometric model-based fitting algorithm for orientation-selective PELDOR data

Pulsed electron–electron double resonance (PELDOR or DEER) spectroscopy is frequently used to determine distances between spin centres in biomacromolecular systems. Experiments where mutual orientations of the spin pair are selectively excited provide the so-called orientation-selective PELDOR data. This data is characterised by the orientation dependence of the modulation depth parameter and of the dipolar frequencies. This dependence has to be taken into account in the data analysis in order to extract distance distributions accurately from the experimental time traces. In this work, a fitting algorithm for such data analysis is discussed. The approach is tested on PELDOR data-sets from the literature and is compared with the previous results.     

作图法求解实验方程要注意的问题

通过分析实验方程参数不确定度的实例，指出了作图法注解实验方程应注意的几个问题。     

Quantum algorithm for total least squares data fitting

The total least squares (TLS) method is widely used in data-fitting. Compared with the least squares fitting method, the TLS fitting takes into account not only observation errors, but also errors from the measurement matrix of the variables. In this work, the TLS problem is transformed to finding the ground state of a Hamiltonian matrix. We propose quantum algorithms for solving this problem based on quantum simulation of resonant transitions. Our algorithms can achieve at least polynomial speedup over the known classical algorithms.     

Real-time full spectrum fitting of beam-based Doppler broadening data

A full spectrum fitting code, developed and used by the Bath positron group to compute the fractions of positrons annihilated from surface, defect and bulk states as a function of incident positron energy, is described. To date, the most useful application of the code has been in studies of ion-implanted silicon, being particularly useful in the observation of the formation of oxygen-divacancy complexes. The advantages and limitations of the code are discussed.     

Online multi-parameter phase-curve fitting and application to a large corpus of asteroid photometric data

We apply the new H,G₁₂ and H,G₁,G₂ phase functions to a large corpus of asteroid photometric data. We make use of low-precision (generally rounded to 0.1 mag) and low-accuracy (rms magnitude uncertainties of ±0.2-0.3 mag) data obtained from the Minor Planet Center and modified at Lowell Observatory. We find (1) a correlation between G₁,G₂ values derived for asteroid families and albedos; (2) G₁₂ homogeneity in families. In addition, we make available an online Java applet (titled Asteroid Phase Function Analyzer). The applet may be used to compute asteroid absolute magnitudes and slope parameters using three different phase functions: the H,G, H,G₁,G₂, and H,G₁₂. The tool also includes non-Gaussian error analysis using Monte Carlo methods. The applet is available at http://asteroid.astro.helsinki.fi/astphase/.     

Three comments on single impurity-molecule spectroscopy

Three issues of interest in the present stage of development of single impurity-molecule spectroscopy (SIMS) are discussed: (i) prospects of SIMS in quantum informatics, (ii) the possibility of SIMS realization by measuring the surface enhanced Raman scattering in solids, and (iii) concentration effects in SIMS and in persistent spectral hole burning.     

Truncation of continuum ambiguities in phase-shift analysis

The continuum ambiguity in the determination of phase shifts from scattering data consists of a family of amplitudes which have in general an infinite number of partial waves. In practical computations, however, the partial wave series is necessarily truncated. We discuss the relation of the resulting (truncated) amplitudes to those representing the true continuum ambiguity. In particular, we show that each of the latter is approximated increasingly well, as the cut-off tends to infinity, uniformly inside an ellipse in the cos plane.     

Amplitude ambiguities in pion absorption on the diproton

A classification is given of, and intra-relationships are derived between amplitudes which yield identical spin-summed differential cross sections and vector polarizations for one of the nucleons emitted in pion absorption on the diproton. To accomplish this, a formal correspondence is established between the amplitude for pion absorption on the diproton and the amplitude for pion nucleon elastic scattering, and the well-known Minami ambiguity for the latter is generalized.Paper dedicated to the memory of Michael Moravcsik, whose untimely death terminated a very useful exchange of ideas onamplitude ambiguities, a subject on which he had been a leading authority. His remarks and observations provided me with a better, deeper insight into the topic of this paper     

Antiferromagnetic fluctuations in heavy fermion CePdSn according to Mössbauer spectroscopy data

The transition from single-ion Kondo-behavior to the magnetically ordered state in the heavy fermion intermetallic compound CePdSn is studied using ¹¹⁹Sn Mössbauer spectroscopy. It is found that the temperature evolution of the experimental spectra can be described well by a two-level relaxation model of the same particles. This allows one to treat the spin-slip model of the magnetic structure of CePdSn as the decomposition of the total volume of the sample into antiferromagnetic domains.     

Ion-molecular interactions in solutions of methanesulfonic acid in diethylamine according to IR spectroscopy data

The methanesulfonic acid (MSA)-diethylamine (DEA) binary liquid system is studied over the entire range of compositions at 30°C by using multiple frustrated total internal reflection IR spectroscopy. Solutions with acid: base equimolar ratio contain only 1 : 1 ion pairs. Upon adding the acid, a MSA molecule abstracts an anion from the 1 : 1 complex to produce a protonated DEA and an (H₃C(O₂)SO…H…OS(O₂)CH₃)⁻ anion with a strong H bond: (C₂H₅)₂(H)NH⁺ · OS(O₂)CH₃⁻ + HOS(O₂)CH₃ ↔ (C₂H₅)₂(H)NH⁺ + (H₃C(O₂)SO…H…OS(O₂)CH₃)⁻. This equilibrium is shifted to the left. The 1 : 1 complex is present in solutions even at an significant excess of the acid. To protonate the complex, it is required at least two MSA molecules. Under conditions of an excess of the base, DEA molecules do not solvate the 1 : 1 complex. The solution separates into two phases, composed of (C₂H₅)₂(H)NH⁺ · OS(O₂)CH₃⁻ complexes and pure DEA.     

光反馈腔衰荡光谱技术中的数据处理

在光反馈式腔衰荡光谱技术中,光谱数据的处理因一种特殊的光谱纹波现象而变得困难。以6 590.8~6 591.6 cm-1光谱范围内水汽分子的光反馈式腔衰荡光谱为基础,根据光谱纹波效应的特性分析结果,提出了一种简单的数据处理方法。利用该方法确定了6 590.871 cm-1处水汽分子吸收谱线的线宽约为0.100 3 cm-1,这与Hitran数据库提供的线宽结果仅有0.002 cm-1的误差,充分验证了该方法的有效性。     

由色散数据求氢波长的三次样条插值法和直线化拟合法

介绍了三次样条插值的基本概念及运用Matlab求三次样条插值的方法,并将该方法应用到氢原子光谱实验中,应用直线拟合方法求出了氢原子光谱的波长.