Special points for two-dimensional Brillouin zone or Wigner–Seitz cell integrations

1980 ◽  
Vol 58 (4) ◽  
pp. 497-503 ◽  
Author(s):  
H. C. Chow ◽  
S. H. Vosko
Keyword(s):  
Least Squares ◽  
Brillouin Zone ◽  
Least Squares Method ◽  
Two Dimensional ◽  
Direct Solution ◽  
Large Numbers ◽  
Seitz Cell ◽  
Transcendental Equations ◽  
Sample Points ◽  
Special Points

Various methods of generating special point formulae for two–dimensional Brillouin zone or Wigner–Seitz cell integrations, useful for the calculation of surface properties, are compared. The direct solution of the coupled non-linear transcendental equations, which determine the special points and their weights, by means of a least squares method is found to be feasible for small numbers of sample points and yields the most efficient formulae. For large numbers of sample points the product Gauss–Chebychev method is most practical.

A modified tangent-gas approximation for two-dimensional steady flow

1958 ◽  
Vol 4 (6) ◽  
pp. 600-606 ◽  
Author(s):  
G. Power ◽  
P. Smith
Keyword(s):  
Least Squares ◽  
Steady Flow ◽  
Variational Approach ◽  
Least Squares Method ◽  
Two Dimensional ◽  
Subsonic Flows ◽  
Von Karman ◽  
Straight Line ◽  
Volume Relationship ◽  
Pressure Volume Relationship

A set of two-dimensional subsonic flows past certain cylinders is obtained using hodograph methods, in which the true pressure-volume relationship is replaced by various straight-line approximations. It is found that the approximation obtained by a least-squares method possibly gives best results. Comparison is made with values obtained by using the von Kármán-Tsien approximation and also with results obtained by the variational approach of Lush & Cherry (1956).

A crystallographic and spectroscopic study of mercury(II) dithiocarbamate

1981 ◽  
Vol 59 (18) ◽  
pp. 2746-2749 ◽  
Author(s):  
Chung Chieh ◽  
Sing Kwen Cheung
Keyword(s):  
Mass Spectrum ◽  
Spectroscopic Study ◽  
Least Squares ◽  
Least Squares Method ◽  
Two Dimensional ◽  
Polymeric Compound ◽  
Full Matrix ◽  
Space Group ◽  
Polymeric Networks ◽  
Ir Bands

Ammonium dithiocarbamate, H2NCS2NH4, decomposes easily but the anion forms a stable mercury(II) complex, the crystals of which are orthorhombic with a = 7.851(3), b = 17.565(7), c = 12.051(3) Å, and space group Pbca. The structure was solved by the Patterson method and refined by the full-matrix least-squares method to an R of 0.038 for 781 reflections. The structure consists of layers of two-dimensional polymeric networks. The dimeric subunits in the layer containing two each of mutually connected Hg atoms and dithiocarbamates are further linked by other bridging dithiocarbamates forming a sheet-like structure. Each Hg atom bonds to four S atoms from four separate dithiocarbamates with Hg—S distances of 2.499(4), 2.508(4), 2.533(4), and 2.629(4) Å. The ir bands observed were: ν(NH2), 3320, 3220, 3125; δ(NH2), 1600; ν(C—N), 1395; ρr(NH2), 1172; and v(C—S), 840 cm−1. The mass spectrum of this polymeric compound gave peaks corresponding to Hg, S2, CNH2, HNCS, S, CS2, S5, S4, S3, and S8 in the order of their intensities.

scholarly journals METODA ZANURZANIA REGRESJI W PRZYPADKU WYSTĘPOWANIA OBSERWACJI NIETYPOWYCH

2019 ◽  
Vol 20 (2) ◽  
pp. 83-92
Author(s):  
Małgorzata Kobylińska
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Least Squares Method ◽  
Regression Function ◽  
Maximum Depth ◽  
Two Dimensional ◽  
Structural Elements ◽  
Linear Regression Function ◽  
Regression Functions

This paper presents the application of the regression maximum depth for the estimation of linear regression function structural elements. For two-dimensional sets including untypical observations, regression functions were developed using the classical least squares method and a method based on the concept of observation depth measure in a sample. The effect of untypical observations on the estimated models has been noted.

Least-Squares Parameter Estimation for Catalyst Layer Agglomerate Models

2010 ◽  
Author(s):  
Peter Dobson ◽  
Marc Secanell
Keyword(s):  
Parameter Estimation ◽  
Fuel Cell ◽  
Least Squares ◽  
Least Squares Method ◽  
Structural Parameters ◽  
Catalyst Layer ◽  
Operating Conditions ◽  
Membrane Electrode ◽  
Two Dimensional

A framework is presented to estimate the micro-structural parameters of cathode fuel cell electrodes by means of a nonlinear least-squares method. This work represents the first attempt in the literature to characterize the structure of the catalyst layer by numerical parameter estimation using a two-dimensional membrane electrode assembly model with an ionomer-filled agglomerate catalyst layer approximation. The framework is developed by coupling a two-dimensional model to an optimization based least-squares algorithm in DAKOTA. The algorithm, NL2SOL, minimizes the sum-of-squares of the residuals for any number of data points and parameters. Employing the proposed methodology allows for accurate characterization of the electrode structure and quantification the quality of the curve fit. Extension of this methodology allows for parameter estimation as novel materials are incorporated into fuel cell construction. Results indicate that curves can be fit using micro-structural and electrochemical parameters consistent with values published in the literature. However, the quality of the fit deteriorates for large data sets over the entire range of operating conditions.

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