A method to fit composite exponential decay curves by reduction of the searching space dimension

A new method for fitting composite exponential decay curves is described. The main feature of the method is the prior transformation of the data set, allowing a very significant reduction of the number of parameters to be estimated by a final nonlinear least-squares fit. No starting estimation of fitting parameters is required. Some criteria are discussed for an optimum choice in the number of exponential terms in the signal. Examples of application of the method to simulated data sets including pseudorandom errors are shown.     

Determination of the dispersion curve of the refractive index by the stockwell transform

The determination of dispersion curves by the Stockwell transform (ST) is proposed. The required numerical data for dispersion curves are produced from the transmittance signal by the ST. The obtained data are then used to estimate the unknown dispersion parameters in Cauchy's formula using the genetic algorithm method through the minimisation problem based on the least-squares curve fitting. The results have shown that the dispersion curve obtained from the ST produced more improved outcomes than those obtained from the continuous wavelet transform.     

Measurement of surface temperature and emissivity by a multitemperature method for Fourier-transform infrared spectrometers

Surface temperatures are estimated with high precision based on a multitemperature method for Fourier-transform spectrometers. The method is based on Planck's radiation law and a nonlinear least-squares fitting algorithm applied to two or more spectra at different sample temperatures and a single measurement at a known sample temperature, for example, at ambient temperature. The temperature of the sample surface can be measured rather easily at ambient temperature. The spectrum at ambient temperature is used to eliminate background effects from spectra as measured at other surface temperatures. The temperatures of the sample are found in a single calculation from the measured spectra independently of the response function of the instrument and the emissivity of the sample. The spectral emissivity of a sample can be measured if the instrument is calibrated against a blackbody source. Temperatures of blackbody sources are estimated with an uncertainty of 0.2-2 K. The method is demonstrated for measuring the spectral emissivity of a brass specimen and an oxidized nickel specimen.     

基于移动最小二乘法的曲线曲面拟合

建立了一种基于移动最小二乘(MovingLeast-Squares,MLS)法的曲线曲面拟合方法。这种方法对传统的最小二乘(LS)法的作了比较大的改进,使生成的曲线曲面具有精度高、光滑性好等许多优点。详细介绍了移动最小二乘法的原理、应用和特点,并且给出了使用移动最小二乘法进行曲线曲面拟合的程序设计流程。最后给出了曲线拟合和空间散乱数据曲面拟合算例,将拟合结果与最小二乘拟合结果作了比较,分析了MLS拟合曲线曲面的光滑性和拟合质量,表明了该方法的优越性和有效性。     

Quantitative analysis of low-field NMR signals in the time domain

Two novel methods are described for direct quantitative analysis of NMR free induction decay (FID) signals. The methods use adaptations of the generalized rank annihilation method (GRAM) and the direct exponential curve resolution algorithm (DECRA). With FID-GRAM, the Hankel matrix of the sample signal is compared with that of a reference mixture to obtain quantitative data about the components. With FID-DECRA, a single-sample FID matrix is split into two matrices, allowing quantitative recovery of decay constants and the individual signals in the FID. Inaccurate results were obtained with FID-GRAM when there were differences between the frequency or transverse relaxation time of signals for the reference and test samples. This problem does not arise with FID-DECRA, because comparison with a reference signal is unnecessary. Application of FID-DECRA to 19F NMR data, which contained overlapping signals from three components, gave concentrations comparable to those derived from partial least squares (PLS) analysis of the Fourier transformed spectra. However, the main advantage of FID-DECRA was that accurate (<5% error) and precise (2.3% RSD) results were obtained using only one calibration sample, whereas with PLS, a training set of 10 standard mixtures was used to give comparable accuracy and precision.     

Deconvolution of kinetic decays and fitting of multiple exponential decay curves by the linear prediction method

A method based on linear prediction (LP) theory is employed in analyzing multiple exponential decay signals. A generalized LP method is also proposed to determine true system response in deconvolution problems when the convoluted signals have a decay time comparable to the duration of excitation pulse. These LP methods linearize the least-squares fit and require no prior knowledge of the exact number of the decaying exponents.     

Energy transfer and luminescence studies of Pr, Yb co-doped lead borate glass

Lead borate glass samples doped with the tripositive lanthanide ions Pr³⁺ and Yb³⁺ were synthesized by the conventional melting-quenching method. The luminescence properties and energy transfer process from Pr³⁺ to Yb³⁺ were investigated. Upon ultraviolet excitation, the room temperature luminescence decay curve of a sample containing only a low concentration of Pr³⁺ exhibited monoexponential decay from ¹D₂ with the lifetime 37 μs, without emission from ³P₀. The room temperature Pr³⁺ emission intensity decreased with the increase of Yb³⁺ mole ratio in the glass. Under the excitation of 454.5 nm at 10 K, a broad red emission band centered at 605 nm, and an NIR emission band at 995 nm were observed in the co-doped lead borate glass, originating from Pr³⁺ and Yb³⁺ ions, respectively. The decay curves of the ¹D₂ emission from Pr³⁺ with addition of Yb³⁺ in lead borate glass show non-monoexponential character, and are best described by a stretched exponential function. The average ¹D₂ decay time decreases considerably with the addition of Yb³⁺ in the glass. Decay curve fitting using a modified Inokuti-Hirayama expression indicates dipole-dipole energy transfer from Pr³⁺ to Yb³⁺, which is consistent with the expected cross-relaxation scheme. There is a good agreement of the estimated overall energy transfer efficiency obtained from the integrals under the normalized decay curves, or from the lifetimes fitted by the stretched exponential function, or from the average decay times.     

The Characteristic Curves of Water

In 1960, E. H. Brown defined a set of characteristic curves (also known as ideal curves) of pure fluids, along which some thermodynamic properties match those of an ideal gas. These curves are used for testing the extrapolation behaviour of equations of state. This work is revisited, and an elegant representation of the first-order characteristic curves as level curves of a master function is proposed. It is shown that Brown’s postulate—that these curves are unique and dome-shaped in a double-logarithmic p, T representation—may fail for fluids exhibiting a density anomaly. A careful study of the Amagat curve (Joule inversion curve) generated from the IAPWS-95 reference equation of state for water reveals the existence of an additional branch.     

建立EPE和蜂窝纸板串联组合本构模型的方法

目的 寻求建立EPE和蜂窝纸板串联组合本构模型的方法,为其他串联组合衬垫本构模型的建立提供参考依据.方法 通过静态压缩试验得到EPE的应力-应变曲线和蜂窝纸板的应力-应变曲线,利用三次Bezier曲线分别拟合其试验曲线,根据拟合曲线求EPE和蜂窝纸板串联组合的应力-应变曲线.结果 EPE和蜂窝纸板的拟合曲线与其各自的试验曲线有很好的吻合度,用同样的方法拟合得到的串联组合的应力-应变曲线与基于其各自的本构模型计算得到的串联组合的应力-应变曲线亦很好地吻合.结论 利用文中方法得到串联组合本构模型是可行的,为缓冲包装设计提供了参考依据.     

Orthogonal LS-PLS approach to ship fuel-speed curves for supporting decisions based on operational data

The shipping industry relies on ship fuel-speed curves to describe the fuel consumption (and CO₂ emissions levels) per hour as a function only of the vessel’s speed over ground, based on dedicated test data. However, they are affected by additional factors in real cases. In this article, a novel method is developed elaborating the orthogonal least-squares partial least-squares (LS-PLS) approach to enhance fuel-speed curves accuracy when information is available on additional factors from multi-sensor systems. Through real data examples, the approach is shown capable of detecting anomalies in CO₂ emission levels and testing the effectiveness of ship energy efficiency initiatives.     

RATE-DEPENDENT DEFORMATION AND FRACTURE OF α-TITANIUM

Aspects of combined rate-dependent deformation and crack growth in α-titanium at room temperature are examined. Results are presented for tests carried out on pre-cracked three point loaded single edge notch bend and compact tension specimens subjected to constant crack opening displacement rates and constant load. Curves of the ratio of the reference stress to the yield stress as a function of the ratio of the plastic displacement to specimen width are found to be different for different rates. The stress difference between continuously loaded curves and curves obtained from load relaxation tests (“relaxed” curves) is found to be similar to uniaxial results. Earlier uniaxial tests show that the “relaxed” curve represents a boundary below which no further creep takes place. The pre-cracked specimen constant load curves cross the “relaxed” curve, even though the contribution from crack growth to the overall deformation is found to be small. Sustained load crack growth is observed to take place under contained yielding conditions and the sustained load resistance curves are found to be different for different reference stresses.     

Forgetting and the Ageing of Scientific Publications

In this paper, I will argue that the process of ageing in scientific publications on the one hand, and the process of obsolescence and forgetting to which all kinds of phenomena, people and events are exposed on the other, develop with the same speed. Whereas in the literature on the subject it is stated that the speed of the ageing of scientific literature is exponential, it is shown that the decay from 'age 4' is best described by an inverse function, as was already brought to light in reference to forgetting of people and events as measured by the frequencies of calendar years in large text corpora. The empirical bases are SCI data as presented by Nakamoto and various files of reference data collected by the author. It is shown that the decay curve of the reference frequencies from 'age 4' backwards is independent of time.     

A bell-shape pulse generator

A simple circuit for forming the function Y=exp(-X² /2) is described. The original curve is approximated with three quadratic parabolas using the method of least-squares estimation. The approximation function is generated through analog integration of a linear voltage with appropriate shape     

Pre- and post-irradiation fading of 6LiF:Mg,Ti (TLD-600) exposed to thermal neutrons

The results of (6)LiF:Mg,Ti (TLD-600) glow peaks fading after irradiation by thermal neutrons, as a function of pre- and post-irradiation times up to 3 months, are presented. The measured glow curves were analysed using the computerised glow curve deconvolution and region of integration methods, to study the decay characteristics of each individual peak and the sum of selected peak areas in the glow curve. The results confirm a high stability for the sum of peaks 4 + 5 and 6 + 7, whereas peaks 2 and 3 have a dominant contribution to the fading effect.     

Determination of depth-dose curves in beta dosimetry

In beta dosimetry, the absorbed dose rate changes rapidly with the depth in a given medium. Its knowledge is essential for the full characterisation of the beta reference fields and the evaluation of the response of beta detectors. This work presents a general formalism for the precise determination of beta depth-dose curves by means of ionisation chamber measurements. An extrapolation chamber is not required. The formalism is appropriate for the determination of the full range depth-dose curve of up to 10 mm depth and more, when all electrons are stopped. Particular care was taken for the determination of the correction factors for the ISO 6980 reference fields, which are the most common beta reference fields. The formalism is proved experimentally: The depth-dose curves of all beta sources available at the Physikalisch-Technische Bundesanstalt (PTB) were determined and compared with the curves published in ISO 6980, yielding an excellent agreement. The presented formalism reflects the state-of-the-art of depth-dose measurements at the PTB.     

Non-equilibrium Dynamics of Interacting Tunneling States in Glasses

After the temporary application of a strong electric bias field to a glass sample at temperatures in the milli-Kelvin range its dielectric constant is increased and then decays slowly back to its equilibrium value. We studied these dielectric non-equilibrium properties of the polyester glass Mylar and the borosilicate glass BK7 as a function of bias field and temperature. We find that the decay to equilibrium depends on the duration of the applied bias field substantially only if the sample has been biased for several thousand seconds or longer. The decay curves after shorter bias field applications are influenced rather by the rate by which the field has been changed. Following the ”dipole gap” theory¹ we assume that the observed excess dielectric response originates in the non-equilibrium dynamics of tunneling states (TSs) that are strongly coupled. Our analysis of the data within the framework of strongly coupled pairs of TSs indicates three competing equilibrium destroying processes, leading to the observed dynamics. Obviously the energy relaxation rate of TSs depends on the bias field since it changes the energy splitting of TSs by coupling to their dipole moments. In addition, a quick enough field sweep can drive TSs non-adiabatically between their energy eigen-states yielding sweep rate dependent decay times. The third process results in decay times independent of temperature and the bias field sweep rate and duration. We propose a picture where the field lifts the tunneling particle in potential wells beyond its original double well as the cause of the third contribution. The decay towards equilibrium is by quantum mechanical tunneling. Moreover, our observations indicate that below a material dependent temperature the relaxation of TSs is caused primarily by interactions between them. PACS numbers: 61.43.Fs, 05.70.Ln, 66.35.+a, 77.22.-d     

New robust bilinear least squares method for the analysis of spectral-pH matrix data

A new second-order multivariate method has been developed for the analysis of spectral-pH matrix data, based on a bilinear least-squares (BLLS) model achieving the second-order advantage and handling multiple calibration standards. A simulated Monte Carlo study of synthetic absorbance-pH data allowed comparison of the newly proposed BLLS methodology with constrained parallel factor analysis (PARAFAC) and with the combination multivariate curve resolution-alternating least-squares (MCR-ALS) technique under different conditions of sample-to-sample pH mismatch and analyte-background ratio. The results indicate an improved prediction ability for the new method. Experimental data generated by measuring absorption spectra of several calibration standards of ascorbic acid and samples of orange juice were subjected to second-order calibration analysis with PARAFAC, MCR-ALS, and the new BLLS method. The results indicate that the latter method provides the best analytical results in regard to analyte recovery in samples of complex composition requiring strict adherence to the second-order advantage. Linear dependencies appear when multivariate data are produced by using the pH or a reaction time as one of the data dimensions, posing a challenge to classical multivariate calibration models. The presently discussed algorithm is useful for these latter systems.     

Information-processing method of ground-based atmospheric remote sensing: the effective instrument function method

A new method for atmospheric remote sensing from the ground is described. The nonlinear deconvolution method and the reference effective instrument function are used to increase the spectral resolution. The nonlinear least-squares method is used to retrieve the atmospheric parameter profile. This method can increase the measurable altitude of remote sensing and improve the precision of atmospheric inversion.     

Establishment of accuracy limits and standards for comparative thermal conductivity measurements

New techniques have been developed for reducing thermal conductivity data from thermal comparative measurements. The first of these techniques is based on making a Taylor-series expansion of the stack centerline temperature profile. The result is an expression giving the ratio of sample to reference conductivities at any temperature as a function of measured quantities, the stack thermocouple readings and stack element thicknesses. The conventional formula presently used to reduce comparative conductivity data is shown to be a special result of the general analysis. A second technique involves the use of linear least-squares (LS) techniques to derive both the sample and the reference conductivities from the measured data. The LS technique provides the coefficients for a polynomial temperature expansion of the reference and sample conductivities directly. Use of the new techniques is illustrated in a reduction of some comparative data on the conductivities of Pyrex 7740 and Pyroceram 9606. It is shown that a highly self-consistent pair of conductivity functions can be derived for these two commonly used reference materials if the conductivity vs temperature relation for Pyrex is modified slightly from its recommended value. The Pyroceram conductivity results from the comparative measurements are in good agreement with a conductivity derived from pulse diffusivity and differential scanning calorimetry measurements and also in good agreement with the recommended Pyroceram conductivity function.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

运用数学拟合方法绘制动态冲击缓冲曲线的研究

提出了一个研究发泡聚乙烯缓冲曲线的方法。该方法使用压力-能量曲线来研究缓冲包装用发泡聚乙烯的动态缓冲性能。由于获得动态缓冲曲线需要大量的冲击实验和有效的数据,该方法是获得同种材料在多种厚度、多种跌落高度条件下的动态缓冲曲线的简便方法。该方法能够提供充足的数据,并为缓冲包装设计提供最大加速度、静应力和缓冲系数的参考。