Least-squares Fitting Research Articles

Quantum cascade laser measurements of CH4 linestrength and temperature-dependent self-broadening and narrowing parameters at 7.16 µm

Absorption lineshapes for 10 CH4 transitions in the v2 and v4 band were measured at high-resolution in a thermodynamically-controlled optical cell using a quantum cascade laser near 7.16 µm. Linestrength, self-broadening, -narrowing, pressure-shift coefficients and their temperature dependence were recorded over a temperature and pressure range of 290–1050 K and 3–80 kPa, respectively. Voigt, Rautian, speed-dependent Voigt profiles were least-squares fit to the measured absorption spectra to determine the best-fit lineshape parameters. Significant collisional-narrowing and speed-dependent effects were observed but no line mixing behaviour was found in pure CH4 at the experimental conditions. The self-pressure-shift coefficients were found to change signs from negative to positive with increasing temperature and the Frost's formula fit well their temperature dependence for the studied transitions. The measured spectra provided tests of the CH4 line lists near 1397 cm−1 released in HITEMP 2020 and the recorded spectroscopic parameters compared well with the values in the database. Several weak transitions excluded from the HITEMP database were observed at elevated temperatures with the line positions given here. The analyses of uncertainties in all the measured spectroscopic parameters were also demonstrated in this work.

Lipid profiling using Raman and a modified support vector machine algorithm.

Lipid droplets are dynamic organelles that play important cellular roles. They are composed of a phospholipid membrane and a core of triglycerides and sterol esters. Fatty acids have important roles in phospholipid membrane formation, signaling, and synthesis of triglycerides as energy storage. Better non-invasive tools for profiling and measuring cellular lipids are needed. Here we demonstrate the potential of Raman spectroscopy to determine with high accuracy the composition changes of the fatty acids and cholesterol found in the lipid droplets of prostate cancer cells treated with various fatty acids. The methodology uses a modified least squares fitting (LSF) routine that uses highly discriminatory wavenumbers between the fatty acids present in the sample using a support vector machine algorithm. Using this new LSF routine, Raman micro-spectroscopy can become a better non-invasive tool for profiling and measuring fatty acids and cholesterol for cancer biology.

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis.

The ARL Spectral Fitting application provides a free, publicly accessible, and fully transparent method for performing Franck-Condon Lineshape Analysis (FCLSA) on spectral data, in addition to CIE color coordinate determination and basic spectral processing. While some of the features may be found in commercial software or in programs made byacademic research groups, we believe that ARL Spectral Fitting is the only application that possesses all three of the aforementioned attributes. This program is intended as a standalone, GUI-based application for use by an average laboratory researcher without requiring any coding knowledge or proprietary software. In addition to the standalone executable hosted on ARL GitHub, the associated MATLAB files are available for use and further development. FCLSA augments the information found in luminescence spectra, providing meaningful insight into the relationship between the ground and excited states of a photoluminescent species. This insight is achieved by modeling spectra with two versions (modes) of an equation that are characterized by either four or six parameters, depending on which mode is used. Once optimized, the value of each of these parameters can be used to gain insight into the molecule, as well as to perform further analysis (for example, the free energy content of the excited-state molecule). This application provides tools for easy by-hand fitting of imported data, as well as two methods for optimizing this fit-damped least-squares fitting, powered by the Levenberg-Marquardt algorithm, and derivative-free fitting utilizing the Nelder-Mead simplex algorithm. Furthermore, estimations of sample color can be performed and reported in CIE and RGB coordinates.

3D finite-element modeling of effective elastic properties for fracture density and multiscale natural fractures

AbstractNatural fractures are usually multiscale in size, orientations and distribution, resulting in complex anisotropic characteristics. Analytical methods for quantifying the associated effective elastic properties are based on some assumptions, such as dilute fracture concentration and regular-shaped fractures, which do not occur in actual reservoirs. Here, we conduct anisotropic finite-element modeling of effective elastic properties of complex fractured rocks using the least-square fitting method. The algorithm is developed for a 3D case and validated by classical effective medium theories for models with different fracture densities. The results of the 3D numerical method agree well with the theoretical predictions at low fracture density. The model also considers the interactions among fractures to calculate equivalent stiffness tensors at high fracture density. Three 2D fracture models are simulated to demonstrate the basic behavior of stress interactions and their effect on the overall elasticity under different fracture densities. We applied the developed model to 3D natural fractures built from a real outcrop, and we found that the fracturing pattern significantly affects the effective anisotropy properties. The resultant P-wave phase velocities as functions of the incidence angle and frequency are anisotropic. This study provides a great potential to calculate equivalent stiffness tensors and anisotropic properties of 3D multiscale natural fractures.

High-temperature dual-species (CO/NH3) detection using calibration-free scanned-wavelength-modulation spectroscopy at 2.3 μm

A dual-species sensor based on scanned-wavelength-modulation spectroscopy (scanned-WMS) with the 2f/1f detection is developed for calibration-free CO and NH3 detection in high-temperature environments. A 2.3 μm distributed feedback (DFB) diode laser was used to exploit the CO and NH3 lines centred at 4300.7 cm−1 and 4301.13 cm−1, respectively. The DFB laser was scanned across the target absorption lines at 100 Hz with fast sinusoidal modulation at 5 kHz. The spectral fitting strategy was employed to least-square fit the simulated and measured WMS-2f/1f spectra. The integrated absorbance of target transitions inferred from the scanned-WMS-2f/1f spectral fitting was used to determine the species concentration. The performance of the developed sensor was validated by simultaneously measuring species concentrations under various temperatures (300–700 K) and at 1 atm in a high-temperature gas cell. The noise equivalent absorption (NEA) coefficient of 3.5 × 10-6 cm−1 for CO and 4.9 × 10-7 cm−1 for NH3 was achieved at 700 K with an absorption path length of 20 cm. The developed dual-species sensor has the potential to be applied in the exhaust of practical combustion systems such as NH3 monitoring for NOx abatement in selective catalytic reduction (SCR) aftertreatment and CO sensing for optimizing combustor efficiency.

Configuration Mixing for Po Isotopes within the Interacting Boson Model-2

We analyze a sequence of 194−204Po isotopes, using the Configuration Mixing (CM) Interacting Boson Model 2 (IBM-2). We set the parameters of Hamiltonian using a least-square fit for the known energy levels, electrical transition rates B(E2), and quadruple moments Q(2+1) for the first excited states. We have a good agreement with the experimental values for all the observables tested, and we infer that the feature of the shape coexistence is concealed in the isotopes of Po, just as in the isotopes of Os and Pt.

Navigation using carrier Doppler shift from a LEO constellation: TRANSIT on steroids

A new global navigation concept is studied that relies on carrier Doppler shift measurements from a large LEO constellation. This system could provide an alternative to pseudorange-based GNSS. The concept uses a high-fidelity model of received carrier Doppler shift. This model is used in a point-solution batch filter that simultaneously estimates eight unknowns: the three position vector components, receiver clock offset, three velocity vector components, and receiver clock offset rate. The filter uses eight or more measured Doppler shifts in its least-squares fit. A generalized Geometric Dilution of Precision (GDOP) analysis indicates that absolute position accuracies on the order of 1-5 meters and absolute velocity accuracies on the order of 0.01 m/sec to 0.05 m/sec may be achievable if the range-rate precision of the Doppler shift measurements is 0.01 m/sec. These accuracies are comparable to current pseudorange-based GNSS. Clock offset accuracy is on the order of 0.0001 to 0.0010 sec 1-.

On the Structure and Kinematics of an Algerian Eddy in the Southwestern Mediterranean Sea

An Algerian Eddy, anticyclonic vortex generated by the instability of the Algerian Current in the southwestern Mediterranean Sea, is studied using data provided by drifters (surface currents), Argo floats (temperature and salinity profiles), environmental satellites (absolute dynamic topography maps and ocean color images) and operational oceanography products. The eddy was generated in May 2018 and lasted as an isolated vortex until November 2018. Its morphology and kinematics are described in June–July 2018 when drifters were trapped in its core. During that period, the eddy was slowly moving to the NE (~2 km/day), with an overall diameter of about 200 km (slowly growing with time) and maximal surface swirl velocity of ~50 cm/s at a radius of ~50 km. Geostrophic currents derived from satellite altimetry data compare well with low-pass filtered drifter velocities, with only a slight overestimation, which is expected as its maximum vorticity corresponds to a small Rossby number of ~0.6. Satellite ocean color images and some drifters show that the eddy has an elliptical spiral structure. The looping tracks of the drifters trapped in the eddy were analyzed using two statistical methods: least-squares ellipse fitting and wavelet ridge analysis, revealing a typical eccentricity of about 0.5, a wide range of inclination and a rotation period between 3 and 10 days. Clusters of drifters on the northeastern limb of the eddy were also considered to estimate divergence and vorticity. The results indicate convergence (divergence) and downwelling (upwelling) at scales of 20–50 km near the northeastern (northwestern) edge of the eddy, in agreement with the quasi-geostrophic theory. Vertically, the eddy extends mostly down to 250 m depth, with a warm, low-salinity and low-density signature and with geostrophic currents near 50 cm/s in the top layer (down to ~80 m) reducing to less than 10 cm/s near 250 m. Near the surface, colder water is advected into it.

CFD modelling and grid uncertainty analysis of the free-falling water entry of 2D rigid bodies

The open source Computational Fluid Dynamics (CFD) library, OpenFOAM, is utilized to simulate the water impact of two-dimensional wedges and ship bow sections. For the free falling cases, the predicted results are validated against existing experimental data, and the parameter study is performed regarding the number of cells, time step, and width of the water domain applied in the numerical models. Grid uncertainty analysis for the CFD results is performed with a constant Courant–Friedrichs–Lewy number, to assess the consistency and accuracy of the CFD solver in solving the present problem. Three uncertainty estimation methods are compared on the peak slamming forces and pressures: Correction Factor (Cf), Factor of Safety (Fs), and Least-squares Fit (Lf) based approaches. All three of them can provide reliable uncertainty estimation for CFD simulations, as long as the right mesh configuration has been used. The variations of pressure distribution on wedge sections with various deadrise angles and initial entry velocities are analyzed. To examine the capability of the tool to predict the slamming loads for a section with roll motions two cases are simulated: one considering a free roll motion and another with constant roll angles. The predicted slamming loads are compared with the available experimental data and other numerical results.

Determination of anisotropy constants via fitting of magnetic hysteresis to numerical calculation of Stoner–Wohlfarth model

Anisotropy constants of magnetic materials are typically determined through angle-resolved Ferromagnetic Resonance (ar-FMR) and torque magnetometry, which can be time consuming measurements, thus limiting their utility. The Stoner–Wohlfarth model can be used to numerically fit measured magnetic hysteresis curves to more easily determine these anisotropy constants. To demonstrate this, 10 nm bct FexCoyMnz single-crystal films grown by molecular beam epitaxy on MgO(001) substrates were investigated. The hysteresis behavior measured by vibrating sample magnetometry was least-squares fit against numerically calculated hysteresis curves generated from the Stoner–Wohlfarth model to extract the anisotropy constants. The cubic anisotropy of different compositions of FeCoMn films was at ∼104 J/m3, which is on the same order of magnitude of bct Fe and Co thin films measured by ar-FMR and torque magnetometry techniques.

Evaluation and Comparative Study of Cell Balancing Methods for Lithium-Ion Batteries Used in Electric Vehicles

Vehicle manufacturers positioned electric vehicles (EVs) and hybrid electric vehicles (HEVs) as reliable, safe and environmental friendly alternative to traditional fuel based vehicles. Charging EVs using renewable energy resources reduce greenhouse emissions. The Lithium-ion (Li-ion) batteries used in EVs are susceptible to failure due to voltage imbalance when connected to form a pack. Hence, it requires a proper balancing system categorised into passive and active systems based on the working principle. It is the prerogative of a battery management system (BMS) designer to choose an appropriate system depending on the application. This study compares and evaluates passive balancing system against widely used inductor based active balancing system in order to select an appropriate balancing scheme addressing battery efficiency and balancing speed for E-vehicle segment (E-bike, E-car and E-truck). The balancing systems are implemented using “top-balancing” algorithm which balance the cells voltages near the end of charge for better accuracy and effective balancing. The most important characteristics of the balancing systems such as degree of imbalance, power loss and temperature variation are determined by their influence on battery performance and cost. To enhance the battery life, Matlab-Simscape simulation-based analysis is performed in order to fine tune the cell balancing system for the optimal usage of the battery pack. For the simulation requirements, the battery model parameters are obtained using least-square fitting algorithm on the data obtained through electro chemical impedance spectroscopy (EIS) test. The achieved balancing time of the passive and active cell balancer for fourteen cells were 48 and 20 min for the voltage deviation of 30 mV. Also, the recorded balancing time was 215 and 42 min for the voltage deviation of 200 mV.

Catalog of averaged magnetic phase curves of stars

Some stars show variability of the longitudinal components of their global magnetic fields, mainly resulting from rotation. Recently, a lot of new observational data have accumulated for various types of stars. To summarize information about magnetic variability, we present the second version of the catalog of average magnetic phase curves. The curves are obtained from literary data and as a result of observations from SAO RAS telescopes. A total of 357 stars of various spectral types were studied based on data that was published before the end of August 2020. Magnetic Ap and Bp stars make up the most numerous subset in the catalog (224 objects). The phase curves were obtained by least-squares fit of the simple sine wave or double sine wave, which are presented in uniform form. The parameters of variability of these objects are presented in tabular form; the upper limits of observed magnetic fields of various types are indicated. The information is presented in a convenient form for verification of various kinds of theoretical models. For clarity and ease of use, phase dependences are presented in graphic form in 514 figures. Periods of variability are defined or refined for a number of stars. The created catalog allows the estimation of the limits of the observed magnetic field variability for various types of stars and the estimation of the energy of the magnetic fields of stars. The catalog will be useful for the development of observation programs. The catalog facilitates the study of the orientation of the axes of rotation of stars in space, the investigation of the interactions of magnetic fields of stars with the interstellar medium, and the “magnetic braking” mechanism. This catalog also permits the study of the orientation of the orbits of planets for some stars with planets and planetary systems.

Evaluation and Comparative Study of Cell Balancing Methods for Lithium-Ion Batteries Used in Electric Vehicles

Vehicle manufacturers positioned electric vehicles (EVs) and hybrid electric vehicles (HEVs) as reliable, safe and environmental friendly alternative to traditional fuel based vehicles. Charging EVs using renewable energy resources reduce greenhouse emissions. The Lithium-ion (Li-ion) batteries used in EVs are susceptible to failure due to voltage imbalance when connected to form a pack. Hence, it requires a proper balancing system categorised into passive and active systems based on the working principle. It is the prerogative of a battery management system (BMS) designer to choose an appropriate system depending on the application. This study compares and evaluates passive balancing system against widely used inductor based active balancing system in order to select an appropriate balancing scheme addressing battery efficiency and balancing speed for E-vehicle segment (E-bike, E-car and E-truck). The balancing systems are implemented using “top-balancing” algorithm which balance the cells voltages near the end of charge for better accuracy and effective balancing. The most important characteristics of the balancing systems such as degree of imbalance, power loss and temperature variation are determined by their influence on battery performance and cost. To enhance the battery life, Matlab-Simscape simulation-based analysis is performed in order to fine tune the cell balancing system for the optimal usage of the battery pack. For the simulation requirements, the battery model parameters are obtained using least-square fitting algorithm on the data obtained through electro chemical impedance spectroscopy (EIS) test. The achieved balancing time of the passive and active cell balancer for fourteen cells were 48 and 20 min for the voltage deviation of 30 mV. Also, the recorded balancing time was 215 and 42 min for the voltage deviation of 200 mV.

Metodología de MCM Alchimia ejemplos resueltos de estimación de incertidumbre asistida por computadora

MCM Alchimia is a free and multilingual desktop application, which runs on Windows. It is available to download from the Internet. This application implements the processes indicated in the Guide to the Expression of Uncertainty in Measurement (GUM) and the Supplement 1 of this document, easily obtaining measurement results and associated expanded uncertainty, with a detailed uncertainty budget according to GUM, and a summary of statistical parameters of the simulated sample obtained by Monte Carlo Method (MCM). This work establishes an intuitive and rapid guide for estimating measurement uncertainties by GUM and MCM methods with the software MCM Alchimia, through discussion of five examples from document JCGM 100: 2008 and three from JCGM 101: 2008. Some features and algorithms of the software are explained in detail. Particularly, functions and tools that are not available in other similar software applications, for example, the estimation of uncertainties in test models that involve the use of least-square fittings. In addition, more intuitive approaches to some problem than those suggested in the JCGM guides are shown, discussing different features available in the software to perform an easy data treatment of complex measurement models.

Voltammetric and electrochemical impedance analysis of poly(bisphenol A) supported poly(3,4-ethylenedioxythiophene) layers deposited on gold – the effects of thickness distribution, overoxidation and non-stationarity

The present study describes the preparation and electrochemical characterization of poly(bisphenol A) (poly(BPA)) supported poly(3,4-ethylenedioxythiophene) (PEDOT) modified gold electrodes.Cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) were used to characterize the electrochemistry of the Au | PEDOT | 0.1 mol/dm3 H2SO4(aq.) and Au | [poly(BPA)/PEDOT] | 0.1 mol/dm3 H2SO4(aq.) electrodes before and after overoxidation. Scanning electron microscopy (SEM) was used for the study of the structure/morphology of the polymer coatings.Similarly to overoxidized PEDOT modified electrodes, time evolution of the electrochemical properties of the poly(BPA)/PEDOT films could be observed after overoxidation. The four-dimensional (4D) analysis method (i.e., a post-experimental mathematical/analytical procedure to overcome the problems caused by non-stationarity) and complex nonlinear least-squares (CNLS) fitting has been used for the estimation of the impedance parameters corresponding to different time instants after overoxidation of the [poly(BPA)/PEDOT] film.The deviations of the impedance responses from the purely capacitive behavior predicted at low frequencies by the theoretical models could be well explained solely by the assumption of uneven film thickness. It has been found that the impedance model, which takes into account the film thickness distribution gives a good description of the impedance data, both before and after overoxidation.According to the results, after the electrochemical deposition of poly(BPA) on the PEDOT layer the resulting [poly(BPA)/PEDOT] modified electrode becomes more resistant against the negative effects of overoxidation.

Quantifying the Tetrad Effect, Shape Components, and Ce\u2013Eu\u2013Gd Anomalies in Rare Earth Element Patterns

Plots of chondrite-normalised rare earth element (REE) patterns often appear as smooth curves. These curves can be decomposed into orthogonal polynomial functions (shape components), each of which captures a feature of the total pattern. The coefficients of these components (known as the lambda coefficients—lambda ) can be derived using least-squares fitting, allowing quantitative description of REE patterns and dimension reduction of parameters required for this. The tetrad effect is similarly quantified using least-squares fitting of shape components to data, resulting in the tetrad coefficients (tau ). Our method allows fitting of all four tetrad coefficients together with tetrad-independent lambda curvature. We describe the mathematical derivation of the method and two tools to apply the method: the online interactive application BLambdaR, and the Python package pyrolite. We show several case studies that explore aspects of the method, its treatment of redox-anomalous REE, and possible pitfalls and considerations in its use.

Estimating Real-Time qPCR Amplification Efficiency from Single-Reaction Data.

Methods for estimating the qPCR amplification efficiency E from data for single reactions are tested on six multireplicate datasets, with emphasis on their performance as a function of the range of cycles n1–n2 included in the analysis. The two-parameter exponential growth (EG) model that has been relied upon almost exclusively does not allow for the decline of E(n) with increasing cycle number n through the growth region and accordingly gives low-biased estimates. Further, the standard procedure of “baselining”—separately estimating and subtracting a baseline before analysis—leads to reduced precision. The three-parameter logistic model (LRE) does allow for such decline and includes a parameter E0 that represents E through the baseline region. Several four-parameter extensions of this model that accommodate some asymmetry in the growth profiles but still retain the significance of E0 are tested against the LRE and EG models. The recursion method of Carr and Moore also describes a declining E(n) but tacitly assumes E0 = 2 in the baseline region. Two modifications that permit varying E0 are tested, as well as a recursion method that directly fits E(n) to a sigmoidal function. All but the last of these can give E0 estimates that agree fairly well with calibration-based estimates but perform best when the calculations are extended to only about one cycle below the first-derivative maximum (FDM). The LRE model performs as well as any of the four-parameter forms and is easier to use. Its proper implementation requires fitting to it plus a suitable baseline function, which typically requires four–six adjustable parameters in a nonlinear least-squares fit.

Phase transitions of ScOOH under high pressure

ABSTRACT In-situ X-ray diffraction measurements of ScOOH were conducted under high pressure and temperature conditions up to 11 GPa and 900 K to understand its phase transitions. As the pressure increased, α-ScOOH, InOOH-type ScOOH, and YbOOH-type ScOOH were observed. The experimental results indicate that the boundaries between α-ScOOH and InOOH-type ScOOH, and between InOOH-type and YbOOH-type ScOOH are represented by the following linear equations: P(GPa) = (0.0009 ± 0.0015) × [T(K) – 700] + 4.33 ± 0.04 and P(GPa) = (–0.0029 ± 0.0002) × [T(K) – 800] + 8.1 ± 0.3, respectively. By using a least-squares fit of the second-order Birch–Murnaghan equation of state (EoS) to the experimental compression data, the EoS parameters of the three phases of ScOOH at 400 K were obtained. The volume change of the transition from α-ScOOH to InOOH-type ScOOH is ∼3.9% at 4 GPa and 400 K, while the volume change of the transition from InOOH-type to YbOOH-type ScOOH is ∼7.6% at 9 GPa and 400 K.

Estimating Curie-point depths using both wavelet-based and Fourier spectral centroid methods in the western Pacific marginal seas

SUMMARY The Curie-point depth is an important magnetic parameter for studying the geological structure and thermal evolution of the lithosphere. In this study, we first apply wavelet transform to the centroid method, and compare it with the conventional Fourier spectral centroid method based on a 3-D fractal magnetization model. We find that the Fourier transform method is suitable for estimating smaller Curie-point depths (less than 20 km), whereas the wavelet transform method has better accuracy in estimating large Curie-point depths (more than 30 km). The application of both methods to the western Pacific magnetic anomalies from the Earth Magnetic Anomaly Grid of 2-arcmin resolution (EMAG2) proves their reliability and comparability. Our results show small Curie-point depths in areas with active magmatism and high heat flow, like mid-ocean ridges and island arcs of subduction zones, but large Curie-point depths in sedimentary basins and forearcs of subduction zones with low surface heat flow. We wrote our Curie-point depth inversion software CPDINV using FORTRAN language, which includes completed modules of minimum-curvature gridding, projection, wavelet and Fourier transforms, least-squares fitting and depth estimation.

TMF: A GNSS Tropospheric Mapping Function for the Asymmetrical Neutral Atmosphere

Tropospheric mapping function plays a vital role in the high precision Global Navigation Satellites Systems (GNSS) data processing for positioning. However, most mapping functions are derived under the assumption that atmospheric refractivity is spherically symmetric. In this paper, the pressure, temperature, and humidity fields of ERA5 data with the highest spatio-temporal resolution available from the European Centre for Medium-range Weather Forecast (ECMWF) were utilized to compute ray-traced delays by the software WHURT. Results reveal the universal asymmetry of the hydrostatic and wet tropospheric delays. To accurately represent these highly variable delays, a new mapping function that depends on elevation and azimuth angles—Tilting Mapping Function (TMF)—was applied. The basic idea is to assume an angle between the tropospheric zenith direction and the geometric zenith direction. Ray-traced delays served as the reference values. TMF coefficients were fitted by Levenberg–Marquardt nonlinear least-squares method. Comparisons demonstrate that the TMF can improve the MF-derived slant delay’s accuracy by 73%, 54% and 29% at the 5° elevation angle, against mapping functions based on the VMF3 concept, without, with a total and separate estimation of gradients, respectively. If all coefficients of a symmetric mapping function are determined together with gradients by a least-square fit at sufficient elevation angles, the accuracy is only 6% lower than TMF. By adopting the b and c coefficients of VMF3, TMF can keep its high accuracy with less computational cost, which could be meaningful for large-scale computing.