Least-squares Procedure Research Articles

A SHALLOW WATER MODEL BY FINITE POINT METHOD

In this paper, "finite point method" (FPM) is presented for modeling 2D shallow water flow problem. The method is based on the use of a weighted least-square approximation procedure, incorporating QR factorization and an iterative adjustment of local approximation parameters. The stabilization of the convective term in this present work is derived from the approximate Riemann solver proposed by Roe. The present method is shown to produce competitive accuracy in the comparisons with the analytical solutions and the well-known Galerkin characteristic-based split (CBS) algorithm.

Strong variable linear polarization in the cool active star II Peg

Abstract Magnetic fields of cool active stars are currently studied polarimetrically using only circular polarization observations. Including linear polarization in the reconstruction of stellar magnetic fields allows more information about the magnetic field to be extracted and significantly improves the reliability of stellar magnetic field maps. The goal of this study is to initiate systematic observations of active stars in all four Stokes parameters and to identify cool stars for which linear polarization can be detected at a level sufficient for Zeeman–Doppler Imaging (ZDI). Four active RS CVn binaries, II Peg, HR 1099, IM Peg and σ Gem, were observed with the ESPaDOnS spectropolarimeter at the Canada–France–Hawaii Telescope during a time period from 2012 February to 2013 January. The least-squares deconvolution procedure was applied to derive mean polarization profiles of all four Stokes parameters. Linear polarization was detected in all four stars in at least one observation. At the same time, II Peg showed an exceptionally strong and highly variable linear polarization signature throughout all observations. This establishes II Peg as the first promising target for ZDI in all four Stokes parameters and suggests the feasibility of such an analysis with existing equipment for at least a few of the most active cool stars.

Silane Radical Cation: A Theoretical Account on the Jahn–Teller Effect at a Triple Degeneracy

An ab initio quantum dynamics study is performed to examine the complex nuclear motion underlying the first photoelectron band of the silane molecule due to Jahn-Teller distortion via T2⊗(e+t2+t2) coupling. The problem is investigated by employing a quadratic vibronic coupling model for the Hamiltonian. All sheets of the required potential energy surface are established through extensive electronic structure calculations using the multireference configuration-interaction method. They cover at most two dimensions of the full 9D coordinate space, with the parameters defining the model Hamiltonian being determined by a least-squares fitting procedure. The results are compared with the available experimental data and discussed in relation to those obtained for the methane radical cation. The quadratic couplings of Jahn-Teller active vibrational modes are found to have a crucial role on the irregular vibronic structure, intensity of the spectral excitations, and overall width of the first photoelectron band of the title molecule. The impact of large amplitude motions on the vibronic structure and dynamics of the first photoelectron band has also been examined by varying their linear coupling parameters up to ±10%.

Autoxidation and Oxygen Binding Properties of Recombinant Hemoglobins with Substitutions at the αVal-62 or βVal-67 Position of the Distal Heme Pocket

The E11 valine in the distal heme pocket of either the α- or β-subunit of human adult hemoglobin (Hb A) was replaced by leucine, isoleucine, or phenylalanine. Recombinant proteins were expressed in Escherichia coli and purified for structural and functional studies. (1)H NMR spectra were obtained for the CO and deoxy forms of Hb A and the mutants. The mutations did not disturb the α1β2 interface in either form, whereas the H-bond between αHis-103 and βGln-131 in the α1β1 interfaces of the deoxy α-subunit mutants was weakened. Localized structural changes in the mutated heme pocket were detected for the CO form of recombinant Hb (rHb) (αV62F), rHb (βV67I), and rHb (βV67F) compared with Hb A. In the deoxy form the proximal histidyl residue in the β-subunit of rHb (βV67F) has been altered. Furthermore, the interactions between the porphyrin ring and heme pocket residues have been perturbed in rHb (αV62I), rHb (αV62F), and rHb (βV67F). Functionally, the oxygen binding affinity (P50), cooperativity (n50), and the alkaline Bohr Effect of the three α-subunit mutants and rHb (βV67L) are similar to those of Hb A. rHb (βV67I) and rHb (βV67F) exhibit low and high oxygen affinity, respectively. rHb (βV67F) has P50 values lower that those reported for rHb (αL29F), a B10 mutant studied previously in our laboratory (Wiltrout, M. E., Giovannelli, J. L., Simplaceanu, V., Lukin, J. A., Ho, N. T., and Ho, C. (2005) Biochemistry 44, 7207-7217). These E11 mutations do not slow down the autoxidation and azide-induced oxidation rates of the recombinant proteins. Results from this study provide new insights into the roles of E11 mutants in the structure-function relationship in hemoglobin.

Deformation of the benzene ring upon fluorination: equilibrium structures of all fluorobenzenes

Born−Oppenheimer equilibrium structure (r BO e) estimates are reported for benzene and all 12 possible fluorobenzenes, based on geometry optimizations performed at the coupled cluster level of electronic structure theory including single and double excitations augmented by a perturbational estimate of the effects of connected triple excitations [CCSD(T)] and Gaussian basis sets of at least triple zeta quality. Furthermore, accurate semiexperimental equilibrium (r SE e) structures are determined for C6H6, C6H5F, and 1,2- and 1,3-difluorobenzene. They are obtained through a least-squares structural refinement procedure based on equilibrium rotational constants of as many isotopologues as feasible, determined by correcting experimental vibrationally averaged ground-state rotational constants with computed ab initio vibration–rotation interaction constants and electronic g-factors, and using a few structural constraints based on the best r BO e estimates. The r BO e and r SE e equilibrium structures are in excellent agreement with each other for the four semirigid molecules but in almost all cases they differ significantly from previously determined equilibrium structure estimates based on rotational spectroscopy or gas electron diffraction. The nature of deformations of the benzene ring induced by a single fluorine substitution can be characterized as follows: (a) the strongest effect is the pushing of the ipso carbon atom toward the ring center resulting in a deformation at the ipso [by +2.7(1)°] and ortho [−1.7(1)°] CCC angles, (b) a simultaneous decrease in the ortho CC bond length of the benzene ring by 0.009 Å and (c) a decrease of all the CH bond lengths. Additivity relations concerning the F substitution effects are obtained based on the equilibrium structures of all possible fluorobenzenes.

Least-Squares-Based Iterative Multipath Super-Resolution Technique

In this paper, we investigate the multipath resolution problem for direct sequence spread spectrum signals. To resolve multipath components arriving within a very short interval, we propose a new multipath super-resolution algorithm based on the iterative least-squares method. The proposed least-squares-based iterative multipath super-resolution (LIMS) algorithm exploits a triangular shaped auto-correlation function (ACF) of the pseudo-noise (PN) sequence and simplifies the least-squares parameter estimation procedure using iterative and algebraic operations. This results in an algorithm demanding low computational load with a high multipath resolution capability. It is also discussed that the LIMS algorithm can be applied for recursive multipath tracking of source localization systems, such as the global navigation satellite systems (GNSS). Simulation results show that the LIMS algorithm maintains its good performance even in a low [(C)/(N0)] or severe multipath interference conditions.

Performance Evaluation of Aqueous Carbonation for Steelmaking Slag: Process Chemistry

Accelerated carbonation of BOF slag in an RPB is a viable method for CO2 capture due to its high mass transfer rate. However, the process chemistry of carbonation of BOF slag is not well-determined due to their complex compositions. In this investigation, the quantitative X-ray diffraction was utilized to determine the mechanism of carbonation reaction in an RPB. Rietveld refinement, which aims to minimize the difference between the experimental and refined XRD patterns by a least-square procedure, is performed to quantify the crystallized mineral. In addition, changes of physico-chemical properties of BOF slags before and after carbonation were evaluated.

Precision Parts Parallelism Error on-Line Detection Based on the CCD Imaging System

In order to meet the requirement of high precision and high efficiency in parts detection, the paper made the research on parts shape-position error on-line detection, put forward a new detection method about parts detection, applied the CCD imaging techniques into the machining quality on-line detection of parts, detected the edge points of parts image by making use of wavelet transformation and Hough transformation, fit the points using least-squares procedure and got the equation of line accurately, realized the non-contact detection of surface quality of parts. Experiment shows that the new method can detect parallelism error more accurately and effectively compared to the artificial detection method.

Crank-Nicolson split least-squares procedure for nonlocal reactive flow in porous media

In this paper, we introduce a Crank-Nicolson split least-squares Galerkin finite element procedure for parabolic integro-differential equations, arising in the modeling of nonlocal reactive flows in porous media. By selecting the least-squares functional properly, the procedure can be split into two independent sub-procedures, one of which is for the primitive unknown and the other is for the flux. By carefully choosing projections, we get optimal order H1(Ω) and L2(Ω) norm error estimates for u and sub-optimal (L2(Ω))d norm error estimate for σ with second-order accuracy in time increment. The numerical examples are given to testify the efficiency of the introduced scheme.

Hydrothermal synthesis and crystal structure of novel bis(6-carboxypyridine-2-carboxylato-κ3 O 2,N,O 6)nickel(II) trihydrate, Ni(Hpydc)2·3H2O

The synthesis and crystal structure of the compound bis(6-carboxypyridine-2-carboxylato-κ(3)O(2),N,O(6))nickel(II) trihydrate, Ni(Hpydc)(2)·3H(2)O, with a supramolecular network is reported (H(2)pydc is pyridine-2,6-dicarboxylic acid). The compound has been prepared by hydrothermal methods. The crystal structure has been solved by direct methods using single-crystal X-ray diffraction data collected at 293 K and refined by full-matrix least-squares procedures to a final R value of 0.0323 for 2779 observed reflections. The compound has distorted octahedral geometry around the metal centre. The complex contains two identical singly ionized ligand molecules. The nickel(II) is bonded to four O atoms and two N atoms from the tridentate ligand molecules, which are nearly perpendicular to each other. Hydrogen-bonded interactions create a three-dimensional supramolecular porous network. The supramolecular structure accounts for the porous structure of the compound as is evident from the Brunauer, Emmett & Teller (BET) surface area of 80 m(2) g(-1). Thermal degradation of the compound shows that lattice water molecules give stability to the crystal structure.

The phase diagrams and Pitzer model representations for the system KCl + MgCl2 + H2O at 50 and 75°C

The solubilities in the KCl-MgCl2-H2O system were determined at 50 and 75°C and the phase diagrams and the diagram of refractive index vs composition were plotted. Two invariant point, three univariant curves, and three crystallization zones, corresponding to potassium chloride, hexahydrate (MgCl2 · 6H2O) and double salt (KCl · MgCl2 · 6H2O) showed up in the phase diagrams of the ternary system, The mixing parameters θK, Ca and ΨK, Ca, Cl and equilibrium constant K sp were evaluated in KCl-MgCl2-H2O system by least-squares optimization procedure, in which the single-salt Pitzer parameters of KCl and MgCl2 β(0), β(1), β(2), and C ϕ were directly calculated from the literature. The results obtained were in good agreement with the experimental data.

Essentials of the self-organizing map

The self-organizing map (SOM) is an automatic data-analysis method. It is widely applied to clustering problems and data exploration in industry, finance, natural sciences, and linguistics. The most extensive applications, exemplified in this paper, can be found in the management of massive textual databases and in bioinformatics. The SOM is related to the classical vector quantization (VQ), which is used extensively in digital signal processing and transmission. Like in VQ, the SOM represents a distribution of input data items using a finite set of models. In the SOM, however, these models are automatically associated with the nodes of a regular (usually two-dimensional) grid in an orderly fashion such that more similar models become automatically associated with nodes that are adjacent in the grid, whereas less similar models are situated farther away from each other in the grid. This organization, a kind of similarity diagram of the models, makes it possible to obtain an insight into the topographic relationships of data, especially of high-dimensional data items. If the data items belong to certain predetermined classes, the models (and the nodes) can be calibrated according to these classes. An unknown input item is then classified according to that node, the model of which is most similar with it in some metric used in the construction of the SOM. A new finding introduced in this paper is that an input item can even more accurately be represented by a linear mixture of a few best-matching models. This becomes possible by a least-squares fitting procedure where the coefficients in the linear mixture of models are constrained to nonnegative values.

Investigation of the free volume and ionic conducting mechanism of poly(ethylene oxide)-LiClO4 polymeric electrolyte by positron annihilating lifetime spectroscopy

The positron annihilation lifetime and ionic conductivity are each measured as a function of organophilic rectorite (OREC) content and temperature in a range from 160 K to 300 K. According to the variation of ortho-positronium (o-Ps) lifetime with temperature, the glassy transition temperature is determined. The continuous maximum entropy lifetime (MELT) analysis clearly shows that the OREC and temperature have important effects on o-Ps lifetime and free volume distribution. The experimental results show that the temperature dependence of ionic conductivity obeys the Vogel—Tammann—Fulcher (VTF) and Williams—Landel—Ferry (WLF) equations, implying a free-volume transport mechanism. A linear least-squares procedure is used to evaluate the apparent activation energy related to the ionic transport in the VTF equation and several important parameters in the WLF equation. It is worthwhile to notice that a direct linear relationship between the ionic conductivity and free volume fraction is established using the WLF equation based on the free volume theory for nanocomposite electrolyte, which indicates that the segmental chain migration and ionic migration and diffusion could be explained by the free volume theory.

Material Balance Adjustement in Raw Material Processing

Circuit of one processing plant was studied in order to adjust the mass balance. The granulometric composition of the streams that belong to grinding and classifying processes was analyzed, while the chemical content was determined only at the streams related to separation process. Three connection matrixes are considered in this paper, one corresponding to the size fraction equations, the second corresponding to the chemical content measurements and the third, the solid flow rate balance. The technique used consisted of filtering all the data by a weighted least-squares procedure. Then running the output data in a custom designed feature of the computer program MATLAB. The raw data was then corrected and the different missing assays calculated and presented here.

Multinuclear Magnetic Resonance Crystallographic Structure Refinement and Cross-Validation Using Experimental and Computed Electric Field Gradients: Application to Na2Al2B2O7

An NMR crystallographic method is presented for the refinement of structures using electric field gradient (EFG) tensors measured using solid-state NMR spectroscopy and those calculated using the projector-augmented wave DFT method. As the calculated EFG data often overestimate the experimental data, the former are scaled to yield optimal agreement for a test set of compounds having highly accurate NMR data. A least-squares optimization procedure is then performed to minimize the difference between the experimental and the scaled calculated EFG tensors. This procedure yields high-quality crystal structures comparable to those obtained from pure DFT energy minimizations, as judged by their rmsd from single-crystal X-ray structures, and is based on experimental observables. Further improvement is obtained by simultaneously refining the structures against the experimental EFG tensor parameters and optimizing the lattice energy with DFT. We use this hybrid experimental–theoretical approach to refine the crystal structure of Na2Al2B2O7, a member of an important family of nonlinear optical materials, which has been the focus of study due to its tendency to form stacking faults. The resulting structures are subjected to a systematic cross-validation process using experimental 23Na, 11B, 17O, and 27Al EFG and chemical shift data, thereby demonstrating the validity of our strategy. This approach may be useful for the refinement of crystal structures of intrinsically polycrystalline materials for which typically only low quality structures are obtainable through traditional diffraction-based methods.

Critique and Improvement of a One-Dimensional Semianalytical Model of a Direct Methanol Fuel Cell

Abstract A constructive critique and a suite of proposed improvements for a recent one-dimensional semianalytical model of a direct methanol fuel cell are presented for the purpose of improving the predictive ability of the modeling approach. The model produces a polarization curve for a fuel cell system comprised of a single membrane-electrode assembly, based on a semianalytical one-dimensional solution of the steady-state methanol concentration profile across relevant layers of the membrane electrode assembly. The first improvement proposed is a more precise numerical solution method for an implicit equation that describes the overall current density, leading to better convergence properties. A second improvement is a new technique for identifying the maximum achievable current density, an important piece of information necessary to avoid divergence of the implicit-equation solver. Third, a modeling improvement is introduced through the adoption of a linear ion-conductivity model that enhances the ability to better match experimental polarization-curve data at high current densities. Fourth, a systematic method is advanced for extracting anodic and cathodic transfer-coefficient parameters from experimental data via a least-squares regression procedure, eliminating a potentially significant parameter estimation error. Finally, this study determines that the methanol concentration boundary condition imposed on the membrane side of the membrane-cathode interface plays a critical role in the model’s ability to predict the limiting current density. Furthermore, the study argues for the need to carry out additional experimental work to identify more meaningful boundary concentration values realized by the cell.

Raman tensor analysis of hexagonal polyoxymethylene and its application to study the molecular arrangement in highly crystalline electrospun nanofibers

The orientation dependence in space of Raman-active vibrations in the hexagonal structure of polyoxymethylene (POM) is discussed in terms of Raman tensor elements as intrinsic physical parameters of the lattice. The variation of polarized intensity for the A1 and the E1 vibrational modes with respect to the POM molecular orientation is systematically studied, from both theoretical and experimental viewpoints, according to the symmetry assignments of each vibrational mode. A set of working equations including the Raman selection rules associated with the A1 and the E1 modes and the orientation distribution function are explicitly formulated and validated by means of a least-square fitting procedure on experimental data. In addition, an approach based on the introduction of orientation distribution functions is applied to quantitatively assess and compare on a statistical base the molecular orientation of two different types of electrospun POM nanofibers. Copyright © 2012 John Wiley & Sons, Ltd.

Rotational spectra of rare isotopic species of fluoroiodomethane: Determination of the equilibrium structure from rotational spectroscopy and quantum-chemical calculations

Supported by accurate quantum-chemical calculations, the rotational spectra of the mono- and bi-deuterated species of fluoroiodomethane, CHDFI and CD(2)FI, as well as of the (13)C-containing species, (13)CH(2)FI, were recorded for the first time. Three different spectrometers were employed, a Fourier-transform microwave spectrometer, a millimeter/submillimter-wave spectrometer, and a THz spectrometer, thus allowing to record a huge portion of the rotational spectrum, from 5 GHz up to 1.05 THz, and to accurately determine the ground-state rotational and centrifugal-distortion constants. Sub-Doppler measurements allowed to resolve the hyperfine structure of the rotational spectrum and to determine the complete iodine quadrupole-coupling tensor as well as the diagonal elements of the iodine spin-rotation tensor. The present investigation of rare isotopic species of CH(2)FI together with the results previously obtained for the main isotopologue [C. Puzzarini, G. Cazzoli, J. C. López, J. L. Alonso, A. Baldacci, A. Baldan, S. Stopkowicz, L. Cheng, and J. Gauss, J. Chem. Phys. 134, 174312 (2011); G. Cazzoli, A. Baldacci, A. Baldan, and C. Puzzarini, Mol. Phys. 109, 2245 (2011)] enabled us to derive a semi-experimental equilibrium structure for fluoroiodomethane by means of a least-squares fit procedure using the available experimental ground-state rotational constants together with computed vibrational corrections. Problems related to the missing isotopic substitution of fluorine and iodine were overcome thanks to the availability of an accurate theoretical equilibrium geometry (computed at the coupled-cluster singles and doubles level augmented by a perturbative treatment of triple excitations).

Iron speciation in ancient Attic pottery pigments: a non-destructive SR-XAS investigation

The present work reports a detailed investigation on the speciation of iron in the pigments of decorated pottery fragments of cultural heritage relevance. The fragments come from the Gioiosa Guardia archaeological site in the area of the `Strait of Messina' (Sicily, Southern Italy), and date back to VI-V century BC. The purpose of this study is to characterize the main pigmenting agents responsible for the dark-red coloration of the specimens using non-destructive analytical techniques such as synchrotron radiation X-ray absorption spectroscopy (SR-XAS), a well established technique for cultural heritage and environmental subjects. Absorption spectra were collected at the Fe K-edge on the Italian beamline for absorption and diffraction (BM8-GILDA) at the European Synchrotron Radiation Facility in Grenoble (France). In order to determine the speciation of Fe in the samples, principal component analysis and least-squares fitting procedures were applied to the near-edge part of the absorption spectra (XANES). Details on the local structure around the Fe sites were obtained by analyzing the extended part of the spectra (EXAFS). Furthermore, an accurate determination of the average Fe oxidation state was carried out through analysis of the pre-edge peaks of the absorption spectra. Samples resulted composed of an admixture of Fe(2)O(3) (hematite or maghemite) and magnetite (Fe(3)O(4)), occurring in different relative abundance in the dark- and light-colored areas of the specimens. The results obtained are complementary to information previously obtained by means of instrumental neutron activation analysis, Fourier transform infrared absorbance and time-of-flight neutron diffraction.

COVMAP: a new algorithm for structure model optimization in theEXPOpackage

A new procedure (COVMAP) has been developed with the aim of recovering the full structure from very poor models, such as those provided by direct methods in unfavorable conditions. The procedure is based on the concept of covariance between points of an electron density map, mathematically set out by the authors in a recent paper:i.e.the density at one point depends on the density at another point of the map if their covariance is not vanishing. This concept suggested a procedure of electron density modification that uses pairs of model peaks to restrict the region where the density modification should be applied. Such modified densities lead to additional peaks, which in turn are submitted to two other important phasing tools present inEXPO2011, the resolution bias minimization and weighted least-squares procedures, which relocate, refine or reject these peaks. The procedure is cyclic and often leads to the correct structure even if the starting model is very poor.