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Journal articles on the topic 'Refinement method'

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Published: 4 June 2021

Last updated: 1 February 2022

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1

David, William I. F. "On the equivalence of the Rietveld method and the correlated integrated intensities method in powder diffraction." Journal of Applied Crystallography 37, no. 4 (July 17, 2004): 621–28. http://dx.doi.org/10.1107/s0021889804013184.

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The Rietveld method is the most straightforward and statistically correct approach for the refinement of crystal structure parameters from powder diffraction data. The equivalent two-stage approach, involving the refinement of structural parameters based on integrated intensities extracted using the Pawley method, is extremely useful in circumstances such as the global optimization methods of structure determination, where a great many refinements need to be performed very quickly. The equivalence is emphasized in a simple mathematical relationship between the goodness of fits obtained in Rietveld, Pawley and correlated integrated intensities refinements. A rationale is given for determining the estimated standard deviations for structural variables from powder diffraction data.

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B�rger, Egon. "The ASM Refinement Method." Formal Aspects of Computing 15, no. 2-3 (November 1, 2003): 237–57. http://dx.doi.org/10.1007/s00165-003-0012-7.

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3

Zeitler, Todd R., and Brian H. Toby. "Parallel processing for Rietveld refinement." Journal of Applied Crystallography 35, no. 2 (March 22, 2002): 191–95. http://dx.doi.org/10.1107/s0021889802000109.

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A method for speeding Rietveld refinements using parallel computing is presented. The method can be applied to most, if not all, Rietveld refinement programs. An example implementation for the Los AlamosGeneral Structure Analysis System(GSAS) package is described. Using a cluster with seven processors, least-squares refinements are completed 2.5 to 5 times faster than on an equivalent single-processor computer.

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HAH, ZOO-HWAN, HYUN-JUNG KIM, and SUNG-KIE YOUN. "A HIERARCHICALLY SUPERIMPOSING LOCAL REFINEMENT METHOD FOR ISOGEOMETRIC ANALYSIS." International Journal of Computational Methods 11, no. 05 (October 2014): 1350074. http://dx.doi.org/10.1142/s0219876213500746.

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In isogeometric analysis, the tensor-product form of Nonuniform Rational B-spline (NURBS) represents spline surfaces. Due to the nature of the tensor-product, the local refinement in isogeometric analysis has many issues to be resolved. Attempts have been made in this regard, such as T-splines and hierarchical approaches. In this work, a local refinement method for isogeometric analysis based on a superimposing concept is proposed. Local refinements are performed by superimposing hierarchically-created finer overlay meshes onto the regions of high error rather than a change of analysis basis (from NURBS to some other spline space). To employ the superimposing concept as a local refinement strategy in isogeometric analysis, a hierarchical framework to construct overlay meshes is developed, and compatibility conditions across the interfacial boundaries of different levels of meshes is discussed. Through numerical examples, the effectiveness and validity of the proposed method are demonstrated.

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Sato, T. "Maximum-entropy method: phase refinement." Acta Crystallographica Section A Foundations of Crystallography 48, no. 6 (November 1, 1992): 842–50. http://dx.doi.org/10.1107/s0108767392005336.

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6

Patterson, Michael A., William W. Hager, and Anil V. Rao. "Aphmesh refinement method for optimal control." Optimal Control Applications and Methods 36, no. 4 (February 28, 2014): 398–421. http://dx.doi.org/10.1002/oca.2114.

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7

Dessalew, Gashaye, Tesfaye Kebede, Gurju Awgichew, and Assaye Walelign. "Refinement of Multiparameters Overrelaxation (RMPOR) Method." Journal of Mathematics 2021 (August 23, 2021): 1–10. http://dx.doi.org/10.1155/2021/2804698.

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In this paper, we present refinement of multiparameters overrelaxation (RMPOR) method which is used to solve the linear system of equations. We investigate its convergence properties for different matrices such as strictly diagonally dominant matrix, symmetric positive definite matrix, and M-matrix. The proposed method minimizes the number of iterations as compared with the multiparameter overrelaxation method. Its spectral radius is also minimum. To show the efficiency of the proposed method, we prove some theorems and take some numerical examples.

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Høier, R., C. R. Birkeland, R. Holmestad, and K. Marthinsen. "Three-phase structure invariants and structure factors determined with the quantitative convergent-beam electron diffraction method." Acta Crystallographica Section A Foundations of Crystallography 55, no. 2 (March 1, 1999): 188–96. http://dx.doi.org/10.1107/s0108767398008903.

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Quantitative convergent-beam electron diffraction is used to determine structure factors and three-phase structure invariants. The refinements are based on centre-disc intensities only. An algorithm for parameter-sensitive pixel sampling of experimental intensities is implemented in the refinement procedure to increase sensitivity and computer speed. Typical three-beam effects are illustrated for the centrosymmetric case. The modified refinement method is applied to determine amplitudes and three-phase structure invariants in noncentrosymmetric InP. The accuracy of the results is shown to depend on the choice of the initial parameters in the refinement. Even unrealistic starting assumptions and incorrect temperature factor lead to stable results for the structure invariant. The examples show that the accuracy varies from 1 to 10° in the electron three-phase invariants determined and from 0.5 to 5% for the amplitudes. Individual phases could not be determined in the present case owing to spatial intensity correlations between phase-sensitive pixels. However, for the three-phase structure invariant, stable solutions were found.

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9

Ida, Takashi, and Fujio Izumi. "Analytical method for observed powder diffraction intensity data based on maximum likelihood estimation." Powder Diffraction 28, no. 2 (April 16, 2013): 124–26. http://dx.doi.org/10.1017/s0885715613000195.

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A new methodology based on maximum likelihood estimation for structure refinement using powder diffraction data is proposed. The method can not only optimize the parameters adjusted in Rietveld refinement but also parameters to specify errors in a model for statistical properties of the observed intensity. The results of structure refinements with relation to fluorapatite Ca5(PO4)3F, anglesite PbSO4, and barite BaSO4 are demonstrated. The structure parameters of fluorapatite and barite optimized by the new method are closer to single-crystal data than those optimized by the Rietveld method, while the structure parameters of anglesite, whose values optimized by the Rietveld method are already in good agreement with the single-crystal data, are almost unchanged by the application of the new method.

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10

Krause, Lennard, Benedikt Niepötter, Christian J. Schürmann, Dietmar Stalke, and Regine Herbst-Irmer. "Validation of experimental charge-density refinement strategies: when do we overfit?" IUCrJ 4, no. 4 (May 24, 2017): 420–30. http://dx.doi.org/10.1107/s2052252517005103.

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A cross-validation method is supplied to judge between various strategies in multipole refinement procedures. Its application enables straightforward detection of whether the refinement of additional parameters leads to an improvement in the model or an overfitting of the given data. For all tested data sets it was possible to prove that the multipole parameters of atoms in comparable chemical environments should be constrained to be identical. In an automated approach, this method additionally delivers parameter distributions ofkdifferent refinements. These distributions can be used for further error diagnostics,e.g.to detect erroneously defined parameters or incorrectly determined reflections. Visualization tools show the variation in the parameters. These different refinements also provide rough estimates for the standard deviation of topological parameters.

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11

Audu, KJ, YA Yahaya, KR Adeboye, and UY Abubakar. "Refinement of Extended Accelerated Over-Relaxation Method for Solution of Linear Systems." NIGERIAN ANNALS OF PURE AND APPLIED SCIENCES 4, no. 1 (August 19, 2021): 53–61. http://dx.doi.org/10.46912/napas.226.

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Given any linear stationary iterative methods in the form z^(i+1)=Jz^(i)+f, where J is the iteration matrix, a significant improvements of the iteration matrix will decrease the spectral radius and enhances the rate of convergence of the particular method while solving system of linear equations in the form Az=b. This motivates us to refine the Extended Accelerated Over-Relaxation (EAOR) method called Refinement of Extended Accelerated Over-Relaxation (REAOR) so as to accelerate the convergence rate of the method. In this paper, a refinement of Extended Accelerated Over-Relaxation method that would minimize the spectral radius, when compared to EAOR method, is proposed. The method is a 3-parameter generalization of the refinement of Accelerated Over-Relaxation (RAOR) method, refinement of Successive Over-Relaxation (RSOR) method, refinement of Gauss-Seidel (RGS) method and refinement of Jacobi (RJ) method. We investigated the convergence of the method for weak irreducible diagonally dominant matrix, matrix or matrix and presented some numerical examples to check the performance of the method. The results indicate the superiority of the method over some existing methods.

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Tahiri, Ahmed. "A multilevel local mesh refinement with the PCD Method." Boletim da Sociedade Paranaense de Matemática 39, no. 1 (October 7, 2020): 213–25. http://dx.doi.org/10.5269/bspm.40222.

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We propose in this contribution a successive local mesh refinement with the PCD method. The multilevel local refinement improves the accuracy and gives a better precision, locally and globally, with a lower computational costs particularly if the considered problem has an anomaly. Here we present how a successive local mesh refinement can be handled. We conclude by presenting numerical experiments to show the interest of a multilevel local mesh refinement for the 2D diffusion equation.

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Soleimanian, V., and S. R. Aghdaee. "Comparison methods of variance and line profile analysis for the evaluation of microstructures of materials." Powder Diffraction 23, no. 1 (March 2008): 41–51. http://dx.doi.org/10.1154/1.2888763.

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A comparison of different methods of X-ray diffraction analysis for the determination of crystallite size and microstrain; namely, line profile analysis, Rietveld refinement, and three approaches based on the variance method, is presented. The analyses have been applied to data collected on a ceria sample prepared by the IUCr Commission on Powder Diffraction. In the variance method, split Pearson VII, the Voigt function, and its approximation pseudo-Voigt function were fitted to X-ray diffraction line profiles. Based on the fitting results, the variances of line profiles were calculated and then the crystallite size and root mean square strain were obtained from variance coefficients. A SS plot of Langford as well as a Fourier analysis and Rietveld refinement have been carried out. The average crystallite size and microstrain were determined. The values of area-weighted domain size determined from the variance method are in agreement with those obtained from line profile analysis within a single (largest) standard uncertainty, and the volume-weighted domain sizes derived from the SS plot, Fourier size distribution, and Rietveld refinement agree within a single standard uncertainty. The results of rms strain calculated from variance and Pearson VII shape function and those from Rietveld refinements fall within a single esd. However, the variance method in conjunction with pseudo-Voigt and Voigt functions produce rms strains substantially larger than those determined from line profile analysis and Rietveld refinements.

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14

Kulkarni, Rekha P., and N. Gnaneshwar. "Spectral refinement using a new projection method." ANZIAM Journal 46, no. 2 (October 2004): 203–24. http://dx.doi.org/10.1017/s1446181100013791.

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AbstractIn this paper we consider two spectral refinement schemes, elementary and double iteration, for the approximation of eigenelements of a compact operator using a new approximating operator. We show that the new method performs better than the Galerkin, projection and Sloan methods. We obtain precise orders of convergence for the approximation of eigenelements of an integral operator with a smooth kernel using either the orthogonal projection onto a spline space or the interpolatory projection at Gauss points onto a discontinuous piecewise polynomial space. We show that in the double iteration scheme the error for the eigenvalue iterates using the new method is of the order of , where h is the mesh of the partition and k = 0, 1, 2,… denotes the step of the iteration. This order of convergence is to be compared with the orders in the Galerkin and projection methods and in the Sloan method. The error in eigenvector iterates is shown to be of the order of in the new method, in the Galerkin and projection methods and in the Sloan method. Similar improvement is observed in the case of the elementary iteration. We show that these orders of convergence are preserved in the corresponding discrete methods obtained by replacing the integration by a numerical quadrature formula. We illustrate this improvement in the order of convergence by numerical examples.

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André, Pascal, Christian Attiogbé, and Arnaud Lanoix. "A tool-assisted method for the systematic construction of critical embedded systems using Event-B." Computer Science and Information Systems 17, no. 1 (2020): 315–38. http://dx.doi.org/10.2298/csis190501042a.

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Embedded control systems combine digital and physical components, leading to complex interactions and even complexity of their development. In [4] we proposed a method to build such complex systems in a systematic way. The overall method starts from an abstract model of the physical environment of the considered system and its controller. The method consists in a sequence of refinement steps, in the spirit of Event-B, that gradually introduces design details from an abstract level, until more concrete levels. Two main refinement processes are distinguished: one to capture the global model, the other to detail it; we provide through the method the guidelines to accompany these two refinement processes. But there were a lack of assistance tools. The designers need to be assisted by tools to guide them, to automate partially the refinements and to help in proving more easily model properties. We illustrate the method with the landing gear system case study and choosing the Event-B tool Rodin for illustration; we make it explicit the tools requirements for such a general method and, we introduce a tool support to assist the user in applying the method in combination with standard Event-B tool such as Rodin.

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16

Balić-Žunić, T. "Quantitative powder diffraction phase analysis with a combination of the Rietveld method and the addition method." Powder Diffraction 17, no. 4 (December 2002): 287–89. http://dx.doi.org/10.1154/1.1523872.

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The Rietveld method can be combined with the addition method to determine the absolute quantities of the phases treated by Rietveld refinement plus the quantity of phase(s) not treated by it (amorphous or unobserved). If q is the added proportion of a defined phase already present in the sample, and a1 and a2 its relative proportions as determined by Rietveld refinement prior and after the addition, the proportion of the amorphous (untreated) phase(s) in the original sample is calculated as xo=[a2−(1−q)a1−q]/(1−q)(a2−a1). The absolute quantities of the phases treated by Rietveld refinement are then determined by a correction for the content of the amorphous phase(s), or they can be calculated directly from specific equations. The advantage of the method is that no new variables are introduced in the refinement when the added standard already is a part of the original mixture.

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17

Kim, Sojeong, and Sukhoon Lee. "Clustered Noise Filtering Based Trajectory Refinement Method." Journal of Korean Institute of Information Technology 18, no. 3 (March 31, 2020): 11–20. http://dx.doi.org/10.14801/jkiit.2020.18.3.11.

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18

White, Thomas A. "Post-refinement method for snapshot serial crystallography." Philosophical Transactions of the Royal Society B: Biological Sciences 369, no. 1647 (July 17, 2014): 20130330. http://dx.doi.org/10.1098/rstb.2013.0330.

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A post-refinement procedure has been devised for ‘snapshot’ diffraction data consisting entirely of partially recorded reflections, each diffraction pattern from a crystal in an orientation unrelated to the others. Initial estimates of the diffraction geometry are used to calculate initial partialities, which are then used to scale the entire dataset together to produce initial estimates of the fully integrated intensities. The geometrical parameters for each pattern are then refined to maximize the agreement between these estimates and the calculated intensities in each pattern, and the procedure repeated iteratively. The performance of the procedure was investigated using simulated data and found to yield a significant improvement in the data quality.

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19

Hori, Masayoshi, Takayuki Nomura, Masaharu Shimakura, Shuichi Takashima, and Eiji Masumoto. "Refinement of resin transfer molding (RTM) method." Advanced Composite Materials 6, no. 3 (January 1997): 255–59. http://dx.doi.org/10.1163/156855197x00120.

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20

Miel, George. "Iterative refinement of the method of moments." Numerical Functional Analysis and Optimization 9, no. 11-12 (January 1988): 1193–200. http://dx.doi.org/10.1080/01630568808816280.

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21

Park, Sung-Kee, and In So Kweon. "Refinement method for structure from stereo motion." Electronics Letters 38, no. 10 (2002): 453. http://dx.doi.org/10.1049/el:20020304.

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22

ZOU, Xiao-Xiang. "A Vertex Refinement Method for Graph Isomorphism." Journal of Software 18, no. 2 (2007): 213. http://dx.doi.org/10.1360/jos180213.

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23

Said, Mar Yah, Michael Butler, and Colin Snook. "A method of refinement in UML-B." Software & Systems Modeling 14, no. 4 (December 14, 2013): 1557–80. http://dx.doi.org/10.1007/s10270-013-0391-z.

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Liu, Jian, Ziyuan Ouyang, Chunlai Li, and Yongliao Zou. "Refinement of a lunar FeO mapping method." Chinese Journal of Geochemistry 26, no. 1 (March 2007): 98–104. http://dx.doi.org/10.1007/s11631-007-0098-3.

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25

Riemslag, F. C. C., H. F. E. Verduyn Lunel, and H. Spekreijse. "The electrooculogram: A refinement of the method." Documenta Ophthalmologica 73, no. 4 (December 1989): 369–75. http://dx.doi.org/10.1007/bf00154492.

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Bernardin, Frédéric, Mireille Bossy, Claire Chauvin, Philippe Drobinski, Antoine Rousseau, and Tamara Salameh. "Stochastic downscaling method: application to wind refinement." Stochastic Environmental Research and Risk Assessment 23, no. 6 (October 7, 2008): 851–59. http://dx.doi.org/10.1007/s00477-008-0276-9.

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Kumar, Avishek, Michael F. Thorpe, and Sefika Banu Ozkan. "Novel Physics-Based Protein Structure Refinement Method." Biophysical Journal 104, no. 2 (January 2013): 229a. http://dx.doi.org/10.1016/j.bpj.2012.11.1291.

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28

Ammons, Bruce A., and Madhukar Vable. "An HR-method of mesh refinement for boundary element method." International Journal for Numerical Methods in Engineering 43, no. 6 (November 30, 1998): 979–96. http://dx.doi.org/10.1002/(sici)1097-0207(19981130)43:6<979::aid-nme451>3.0.co;2-j.

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Knöbelreiter, Patrick, and Thomas Pock. "Learned Collaborative Stereo Refinement." International Journal of Computer Vision 129, no. 9 (June 20, 2021): 2565–82. http://dx.doi.org/10.1007/s11263-021-01485-5.

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AbstractIn this work, we propose a learning-based method to denoise and refine disparity maps. The proposed variational network arises naturally from unrolling the iterates of a proximal gradient method applied to a variational energy defined in a joint disparity, color, and confidence image space. Our method allows to learn a robust collaborative regularizer leveraging the joint statistics of the color image, the confidence map and the disparity map. Due to the variational structure of our method, the individual steps can be easily visualized, thus enabling interpretability of the method. We can therefore provide interesting insights into how our method refines and denoises disparity maps. To this end, we can visualize and interpret the learned filters and activation functions and prove the increased reliability of the predicted pixel-wise confidence maps. Furthermore, the optimization based structure of our refinement module allows us to compute eigen disparity maps, which reveal structural properties of our refinement module. The efficiency of our method is demonstrated on the publicly available stereo benchmarks Middlebury 2014 and Kitti 2015.

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30

Wei, Yong Qi, Wu Yao, and Wei Wang. "Effects of Internal Standards and Peak Profile Functions on Quantitative XRD Phase Analysis of Cement and its Hydrates." Key Engineering Materials 492 (September 2011): 424–28. http://dx.doi.org/10.4028/www.scientific.net/kem.492.424.

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Quantitative X-Ray diffraction (QXRD) combined with the Rietveld refinement method allows direct determination of crystalline phase content of cement and its hydrates. However, relatively precise results need the correction of proper internal standards and the use of matched peak profile functions with masterly refinement strategies. The aim of this paper is to research and discuss effects of these factors on the quantitative phase analysis results. For this purpose, different internal standards and peak profile functions with corresponding refinement strategies were attempted in experiments and refinements. The results indicate that Al2O3as internal standard is more suitable for cement and its hydrates than ZnO, and the better peak profile function is CW function 2 rather than function 3 in GSAS.

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31

Enyew, Tesfaye Kebede, Gurju Awgichew, Eshetu Haile, and Gashaye Dessalew Abie. "Second-refinement of Gauss-Seidel iterative method for solving linear system of equations." Ethiopian Journal of Science and Technology 13, no. 1 (April 30, 2020): 1–15. http://dx.doi.org/10.4314/ejst.v13i1.1.

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Although large and sparse linear systems can be solved using iterative methods, its number of iterations is relatively large. In this case, we need to modify the existing methods in order to get approximate solutions in a small number of iterations. In this paper, the modified method called second-refinement of Gauss-Seidel method for solving linear system of equations is proposed. The main aim of this study was to minimize the number of iterations, spectral radius and to increase rate of convergence. The method can also be used to solve differential equations where the problem is transformed to system of linear equations with coefficient matrices that are strictly diagonally dominant matrices, symmetric positive definite matrices or M-matrices by using finite difference method. As we have seen in theorem 1and we assured that, if A is strictly diagonally dominant matrix, then the modified method converges to the exact solution. Similarly, in theorem 2 and 3 we proved that, if the coefficient matrices are symmetric positive definite or M-matrices, then the modified method converges. And moreover in theorem 4 we observed that, the convergence of second-refinement of Gauss-Seidel method is faster than Gauss-Seidel and refinement of Gauss-Seidel methods. As indicated in the examples, we demonstrated the efficiency of second-refinement of Gauss-Seidel method better than Gauss-Seidel and refinement of Gauss-Seidel methods.

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Chodkiewicz, Michał Leszek, Magdalena Woińska, and Krzysztof Woźniak. "Hirshfeld atom like refinement with alternative electron density partitions." IUCrJ 7, no. 6 (October 29, 2020): 1199–215. http://dx.doi.org/10.1107/s2052252520013603.

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Hirshfeld atom refinement is one of the most successful methods for the accurate determination of structural parameters for hydrogen atoms from X-ray diffraction data. This work introduces a generalization of the method [generalized atom refinement (GAR)], consisting of the application of various methods of partitioning electron density into atomic contributions. These were tested on three organic structures using the following partitions: Hirshfeld, iterative Hirshfeld, iterative stockholder, minimal basis iterative stockholder and Becke. The effects of partition choice were also compared with those caused by other factors such as quantum chemical methodology, basis set, representation of the crystal field and a combination of these factors. The differences between the partitions were small in terms of R factor (e.g. much smaller than for refinements with different quantum chemistry methods, i.e. Hartree–Fock and coupled cluster) and therefore no single partition was clearly the best in terms of experimental data reconstruction. In the case of structural parameters the differences between the partitions are comparable to those related to the choice of other factors. We have observed the systematic effects of the partition choice on bond lengths and ADP values of polar hydrogen atoms. The bond lengths were also systematically influenced by the choice of electron density calculation methodology. This suggests that GAR-derived structural parameters could be systematically improved by selecting an optimal combination of the partition and quantum chemistry method. The results of the refinements were compared with those of neutron diffraction experiments. This allowed a selection of the most promising partition methods for further optimization of GAR settings, namely the Hirshfeld, iterative stockholder and minimal basis iterative stockholder.

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Nishibori, Eiji, Tadakatsu Ogura, Shinobu Aoyagi, and Makoto Sakata. "Ab initiostructure determination of a pharmaceutical compound, prednisolone succinate, from synchrotron powder data by combination of a genetic algorithm and the maximum entropy method." Journal of Applied Crystallography 41, no. 2 (March 8, 2008): 292–301. http://dx.doi.org/10.1107/s0021889808001520.

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The structure of a pharmaceutical compound, prednisolone succinate, has been determined by a newly developed analytical method forab initiostructure determination and refinements from X-ray powder data. It consists of a genetic algorithm (GA) for the structure determination process and the maximum entropy method (MEM), including its variations, for the structure refinement process. The crystal structure of prednisolone succinate has two molecules in the asymmetric unit and the total number of degrees of freedom is 25. In the structure refinement process, the various kinds of MEM analyses, such as difference MEM and omit MEM, in addition to ordinary MEM, play crucial roles in obtaining a better structural model. The data used in the present study were collected at BL02B2, SPring-8, which allowed the use of a wided-spacing range,d> 1.0 Å. The reliability factors,RwpandRI, of the final structure analysis by Rietveld refinement are less than 0.013 and 0.048, respectively. The structure determined in the present study gives noCHECKCIFalert relating to the fundamental structure, such as interatomic distances and bond angles, even in chemical bonds involving H atoms.

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Cui, Weizhe, and Qichen Hao. "Comparing Q-Tree with Nested Grids for Simulating Managed River Recharge of Groundwater." Water 12, no. 12 (December 14, 2020): 3516. http://dx.doi.org/10.3390/w12123516.

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The use of rivers to recharge groundwater is a key water resource management method. High-precision simulations of the groundwater level near rivers can be used to accurately assess the recharge effect. In this study, we used two unstructured grid refinement methods, namely, the quadtree (Q-tree) and nested grid refinement techniques, to simulate groundwater movement under river recharge. We comparatively analyzed the two refinement methods by considering the simulated groundwater level changes before and after the recharge at different distances from the river and by analyzing the groundwater flow and model computation efficiency. Compared to the unrefined model, the two unstructured grid refinement models significantly improve the simulation precision and more accurately describe groundwater level changes from river recharge. The unstructured grid refinement models have higher calculation efficiencies than the base model (the global refinement model) without compromising the simulation precision too much. The Q-tree model has a higher simulation precision and a lower computation time than the nested grid model. In summary, the Q-tree grid refinement method increases the computation efficiency while guaranteeing simulation precision at a certain extent. We therefore recommended the use of this grid refinement method in simulating river recharge to the aquifers.

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Capelli, Silvia C., Hans-Beat Bürgi, Birger Dittrich, Simon Grabowsky, and Dylan Jayatilaka. "Hirshfeld atom refinement." IUCrJ 1, no. 5 (August 29, 2014): 361–79. http://dx.doi.org/10.1107/s2052252514014845.

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Hirshfeld atom refinement (HAR) is a method which determines structural parameters from single-crystal X-ray diffraction data by using an aspherical atom partitioning of tailor-madeab initioquantum mechanical molecular electron densities without any further approximation. Here the original HAR method is extended by implementing an iterative procedure of successive cycles of electron density calculations, Hirshfeld atom scattering factor calculations and structural least-squares refinements, repeated until convergence. The importance of this iterative procedure is illustratedviathe example of crystalline ammonia. The new HAR method is then applied to X-ray diffraction data of the dipeptide Gly–L-Ala measured at 12, 50, 100, 150, 220 and 295 K, using Hartree–Fock and BLYP density functional theory electron densities and three different basis sets. All positions and anisotropic displacement parameters (ADPs) are freely refined without constraints or restraints – even those for hydrogen atoms. The results are systematically compared with those from neutron diffraction experiments at the temperatures 12, 50, 150 and 295 K. Although non-hydrogen-atom ADPs differ by up to three combined standard uncertainties (csu's), all other structural parameters agree within less than 2 csu's. Using our best calculations (BLYP/cc-pVTZ, recommended for organic molecules), the accuracy of determining bond lengths involving hydrogen atoms from HAR is better than 0.009 Å for temperatures of 150 K or below; for hydrogen-atom ADPs it is better than 0.006 Å2as judged from the mean absolute X-ray minus neutron differences. These results are among the best ever obtained. Remarkably, the precision of determining bond lengths and ADPs for the hydrogen atoms from the HAR procedure is comparable with that from the neutron measurements – an outcome which is obtained with a routinely achievable resolution of the X-ray data of 0.65 Å.

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Guo, Biao, Zhong Bin Hou, Jun Hao Geng, and Gang Feng Wang. "Collaborative Refinement Method for Process Innovation Knowledge Network." Materials Science Forum 770 (October 2013): 320–23. http://dx.doi.org/10.4028/www.scientific.net/msf.770.320.

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Accumulating a large number of process innovation knowledge (PIK) is the prerequisite and basis for process innovation.PIK can be gradually refined by using. Hence, how to ensure the correctness of the PIK collaborative refinement is the basic work of knowledge accumulation. This paperproposes a construction method of PIK network by the imitating of biological neural network, and arefinement methodof PIKby the imitating of neural stimulation conduction. Because the refining processes are iterative, the refinement of process innovation needsa specificeditingmechanism and control mechanism, which allow multi-userto engage in collaborative editing and protect the consistency of collaborative editing result. Using the refinement method of PIK,it is possible to convert the discrete, rough knowledge into a PIK network that can effectively solve the process problems.

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Rodden, William P., Paul F. Taylor, and Samuel C. McIntosh. "Further Refinement of the Subsonic Doublet-Lattice Method." Journal of Aircraft 35, no. 5 (September 1998): 720–27. http://dx.doi.org/10.2514/2.2382.

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FUJITA, Ichiro. "Refinement of Optical Flow Method and its Evaluation." Journal of the Visualization Society of Japan 23, Supplement1 (2003): 25–28. http://dx.doi.org/10.3154/jvs.23.supplement1_25.

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YELLIN, Kentaro, Yoshiki SAITO, Takuma TAKAGI, Ichiro KIMURA, Masaya OTSUKI, Evgeny ISENKO, and Yasuyuki SHIMIZU. "REFINEMENT OF MPS METHOD FOR AVALANCHES USING SIMULATING." Journal of Japan Society of Civil Engineers, Ser. B1 (Hydraulic Engineering) 70, no. 4 (2014): I_433—I_438. http://dx.doi.org/10.2208/jscejhe.70.i_433.

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YAMAGUCHI, Tomiko, Hideyuki IKEDA, and Kazumasa NISHIO. "Simulation of Grain Refinement using Monte Carlo Method." JOURNAL OF THE JAPAN WELDING SOCIETY 81, no. 2 (2012): 90–95. http://dx.doi.org/10.2207/jjws.81.90.

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Cheng, Fang Hsuan, and Yu Pang Chang. "Refinement of Depth Estimation Method via Energy Minimization." Applied Mechanics and Materials 479-480 (December 2013): 839–43. http://dx.doi.org/10.4028/www.scientific.net/amm.479-480.839.

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t has been proposed in this paper an idea of refining depth map obtained according to local stereo matching. Energy was calculated based on the entire image, meanwhile, energy minimization concept was adopted, and the area obtained according to color segmentation algorithm was adopted too. The lower the energy of an image, the better depth quality will be generated. The color feature and depth value among different regions and their neighboring regions are used to define the relation between the smooth and occluded regions in the energy function. Then the region energy was calculated repeatedly until the change was insignificant or the number of iterations was reached. The corrected left and right view was used first to perform local stereo matching to get initial depth estimation. The color information of the left view was used to perform color segmentation, and then the segmented region and initial depth estimation were used to calculate the parameter of disparity plane for each region. This process was performed iteratively on the disparity plane, where a more reasonable depth map can be obtained while the energy cost is minimized. From the experimental result, it is proved that the depth map after refinement showed better object shape and smooth region density as compared to that of the initial depth map.

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Méry, Dominique. "A simple refinement-based method for constructing algorithms." ACM SIGCSE Bulletin 41, no. 2 (June 25, 2009): 51–59. http://dx.doi.org/10.1145/1595453.1595462.

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Anighoro, Andrew, and Giulio Rastelli. "BEAR, a Molecular Docking Refinement and Rescoring Method." Computational Molecular Bioscience 03, no. 02 (2013): 27–31. http://dx.doi.org/10.4236/cmb.2013.32004.

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Cheng, Qianyi, InSuk Joung, and Jooyoung Lee. "A Simple and Efficient Protein Structure Refinement Method." Journal of Chemical Theory and Computation 13, no. 10 (September 14, 2017): 5146–62. http://dx.doi.org/10.1021/acs.jctc.7b00470.

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Rius, J., and C. Miravitlles. "An atomicity-constrained least-squares phase-refinement method." Acta Crystallographica Section A Foundations of Crystallography 47, no. 5 (September 1, 1991): 567–71. http://dx.doi.org/10.1107/s0108767391004622.

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NOJIMA, Shishin, Tomotsugu SHIMOKAWA, Toshiyasu KINARI, and Sukenori SHINTAKU. "1113 Adaptive Mesh Refinement in the Quasicontinuum Method." Proceedings of Conference of Hokuriku-Shinetsu Branch 2007.44 (2007): 423–24. http://dx.doi.org/10.1299/jsmehs.2007.44.423.

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Liggett, W., K. ‐W Moon, and C. Handwerker. "An Experimental Method for Refinement of Solderability Measurement." Soldering & Surface Mount Technology 9, no. 2 (December 1, 1997): 14–21. http://dx.doi.org/10.1108/09540919710195181.

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An experimental method for measurement system improvement is presented and applied to development of a protocol for solderability measurement with a wetting balance. Protocol development is central to development of reliable monitoring systems for manufacturing. This paper illustrates the method with an experiment in which sets of nearly identical test leads, each with a different solderability, are obtained by steam ageing of hot‐solder‐dipped copper and then measured according to alternative protocols. The protocols entail different flux types and solder bath temperatures. This method can be used wherever solderability measurements are made and thus satisfies the need for in‐house refinement of wetting balance protocols.With the experimental method, one can both compare alternative measurement protocols and estimate the relative solderability of sets of test leads. The results of both depend on what feature of the wetting force curve one selects to portray solderability. The comparison of measurement protocols is based on what is variously called precision, sensitivity, or signal‐to‐noise ratio. The solderability estimates show that different physical properties of the test leads affect different parts of the wetting force curve, and that changes in the steam ageing procedure affect solderability in a generally predictable way.

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Meddahi, S. "A multidomain discretization method with local mesh refinement." IMA Journal of Numerical Analysis 19, no. 2 (April 1, 1999): 251–71. http://dx.doi.org/10.1093/imanum/19.2.251.

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Khan, R. T. A., J. Bashir, N. Iqbal, and M. Nasir Khan. "Crystal structure of LaVO3 by Rietveld refinement method." Materials Letters 58, no. 11 (April 2004): 1737–40. http://dx.doi.org/10.1016/j.matlet.2003.10.059.

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Pece, Arthur, and Anthony Worrall. "A statistically-based Newton method for pose refinement." Image and Vision Computing 16, no. 8 (June 1998): 541–44. http://dx.doi.org/10.1016/s0262-8856(98)00098-5.

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