scholarly journals Hybrid Newton–Successive Substitution Method for Multiphase Rachford-Rice Equations

Entropy ◽  
2018 ◽  
Vol 20 (6) ◽  
pp. 452
Author(s):  
Ran Gao ◽  
Xiaolong Yin ◽  
Zhiping Li
Keyword(s):  
Substitution Method ◽  
Successive Substitution

Series solutions for boundary value problems using a symbolic successive substitution method

1999 ◽  
Vol 23 (3) ◽  
pp. 287-296 ◽  
Author(s):  
Venkat R. Subramanian ◽  
Bala S. Haran ◽  
Ralph E. White
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Series Solutions ◽  
Substitution Method ◽  
Successive Substitution

scholarly journals SOLUTIONS IN EXPLICIT FORM FOR DETERMINING THE HYDRAULIC RESISTANCE COEFFICIENT FOR TURBULENT FLOW

2019 ◽  
Vol 9 (4) ◽  
pp. 39-46
Author(s):  
Maxim Nikolaevich NIKITIN ◽  
Tatyana Sergeevna SOLOVYOVA ◽  
Olga Vladimirovna SHLYAHTINA
Keyword(s):  
Comparative Analysis ◽  
Computational Complexity ◽  
Turbulent Flow ◽  
Iterative Solution ◽  
Resistance Coefficient ◽  
Explicit Solutions ◽  
Substitution Method ◽  
Relative Roughness ◽  
Acceptable Accuracy ◽  
Successive Substitution

A comparative analysis of explicit solutions of the Colebrook-White equation is carried out. The median values of relative deviations, coefficients of determination and computational complexities for each approximation were obtained. The results of the iterative solution of the Colebrook-White equation by successive substitution method were used as the intrinsic solution. Approximations by B. Eck and A.R. Vatankhah were identified as the most effective in terms of computational complexity. It was shown that widely used approximations by P.R.H. Blasius, A.D. Altshul and J. Nikuradze although simple, provide acceptable accuracy only within restricted ranges of Reynolds and relative roughness.

scholarly journals Monte Carlo method with control variate for integral equations

2018 ◽  
Vol 22 (4) ◽  
pp. 1765-1771
Author(s):  
Yi Tian
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Integral Equations ◽  
Solution Process ◽  
Fredholm Integral Equations ◽  
Substitution Method ◽  
Control Variate ◽  
Successive Substitution

This paper combines the successive substitution method and Monte Carlo method with a control variate to solve Fredholm integral equations of the second kind. Some examples are gives to elucidate the solution process and the results reveal the efficiency of the method.

An accelerated successive substitution method for calculation of saturation pressure of multicomponent fluids

1992 ◽  
Vol 72 ◽  
pp. 15-24 ◽  
Author(s):  
D.-H. Xu ◽  
A. Danesh ◽  
A.C. Todd
Keyword(s):  
Saturation Pressure ◽  
Substitution Method ◽  
Successive Substitution

An accelerated successive substitution method for single stage flash calculations

1988 ◽  
Vol 66 (2) ◽  
pp. 291-296 ◽  
Author(s):  
Anup K. Gupta ◽  
P. R. Bishnoi ◽  
N. Kalogerakis
Keyword(s):  
Single Stage ◽  
Substitution Method ◽  
Successive Substitution

scholarly journals Solid-Phase “Self-Hydrolysis” of [Zn(NH3)4MoO4@2H2O] Involving Enclathrated Water—An Easy Route to a Layered Basic Ammonium Zinc Molybdate Coordination Polymer

Molecules ◽  
2021 ◽  
Vol 26 (13) ◽  
pp. 4022
Author(s):  
Kende Attila Béres ◽  
István E. Sajó ◽  
György Lendvay ◽  
László Trif ◽  
Vladimir M. Petruševski ◽  
...  
Keyword(s):  
Coordination Polymer ◽  
Solid Phase ◽  
Water Molecules ◽  
Temperature Dependent ◽  
Dynamic Interactions ◽  
Ammonia Release ◽  
Successive Substitution ◽  
Red Dye ◽  
Hydrolysis Of ◽  
Zinc Molybdate

An aerial humidity-induced solid-phase hydrolytic transformation of the [Zn(NH3)4]MoO4@2H2O (compound 1@2H2O) with the formation of [(NH4)xH(1−x)Zn(OH)(MoO4)]n (x = 0.92–0.94) coordination polymer (formally NH4Zn(OH)MoO4, compound 2) is described. Based on the isostructural relationship, the powder XRD indicates that the crystal lattice of compound 1@2H2O contains a hydrogen-bonded network of tetraamminezinc (2+) and molybdate (2−) ions, and there are cavities (O4N4(μ-H12) cube) occupied by the two water molecules, which stabilize the crystal structure. Several observations indicate that the water molecules have no fixed positions in the lattice voids; instead, the cavity provides a neighborhood similar to those in clathrates. The @ symbol in the notation is intended to emphasize that the H2O in this compound is enclathrated rather than being water of crystallization. Yet, signs of temperature-dependent dynamic interactions with the wall of the cages can be detected, and 1@2H2O easily releases its water content even on standing and yields compound 2. Surprisingly, hydrolysis products of 1 were observed even in the absence of aerial humidity, which suggests a unique solid-phase quasi-intramolecular hydrolysis. A mechanism involving successive substitution of the ammonia ligands by water molecules and ammonia release is proposed. An ESR study of the Cu-doped compound 2 (2#dotCu) showed that this complex consists of two different Cu2+(Zn2+) environments in the polymeric structure. Thermal decomposition of compounds 1 and 2 results in ZnMoO4 with similar specific surface area and morphology. The ZnMoO4 samples prepared from compounds 1 and 2 and compound 2 in itself are active photocatalysts in the degradation of Congo Red dye. IR, Raman, and UV studies on compounds 1@2H2O and 2 are discussed in detail.

Separate magnitude and phase measurement of passive two-terminal networks by the substitution method

1973 ◽  
Vol 16 (8) ◽  
pp. 1209-1211
Author(s):  
L. �. Degtyar' ◽  
Z. I. Zelikovskii
Keyword(s):  
Phase Measurement ◽  
Substitution Method
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