Inverse determination of laser power on laser welding with a given width penetration by a modified Newton–Raphson method

2015 ◽  
Vol 65 ◽  
pp. 15-21 ◽  
Author(s):  
Quan Nguyen ◽  
Ching-yu Yang
Keyword(s):  
Laser Welding ◽  
Laser Power ◽  
Newton Raphson ◽  
Raphson Method

Determination of the Force Constants of Non-linear XY2 Molecules in the Gas-Phase by the GF Matrix Method

2004 ◽  
Vol 59 (9) ◽  
pp. 621-622 ◽  
Author(s):  
Fatih Ucun ◽  
Vesile Gūçlü
Keyword(s):  
Gas Phase ◽  
Condensed Phase ◽  
Matrix Method ◽  
Solid Phase ◽  
Force Constants ◽  
Matrix Solution ◽  
The Matrix ◽  
Newton Raphson ◽  
Raphson Method

The force constants of the internal coordinates of nonlinear XY2 molecules in the gas-phase were calculated by using the GF matrix method. The matrix solution was carried out by means a computer program built relative to the Newton-Raphson method and the calculations were listed in a table. The force constants of some molecules in the liquidand solid- phase were also found and compared with these ones, and it was seen that the force constants for more condensed phase are lower as in an agreement with having its lower frequency.

Determination of AGMA Geometry Factor J for Slotted External Spur Gears

1983 ◽  
Vol 105 (3) ◽  
pp. 305-311
Author(s):  
Y. P. Singh
Keyword(s):  
Direct Method ◽  
Mining Industry ◽  
Spur Gears ◽  
Input Output ◽  
Typical Application ◽  
Geometry Factor ◽  
Newton Raphson ◽  
A Direct Method ◽  
Raphson Method

This paper presents a direct method for determining the geometry factor J for slotted external spur gears. The location of maximum stressed point on the tooth profile where the stress parabola is tangent to the fillet curve has been determined by solving the resulting nonlinear equations using the sophisticated Newton-Raphson method. The semi-graphical procedure given in AGMA Standard [1] is not convenient for determining the geometry factory J of large gears used in grinding mill and kiln drives in the mining industry. Listing of the computer program and input-output point out for a typical application are presented.

Determination of Force Constants of Planar XY3 and Tetrahedral XY4 Molecules by the GF Matrix Method

2005 ◽  
Vol 60 (3) ◽  
pp. 183-186 ◽  
Author(s):  
Vesile Güçlü ◽  
Fatih Ucun
Keyword(s):  
Computer Program ◽  
Matrix Method ◽  
Force Constants ◽  
Internal Coordinates ◽  
The Matrix ◽  
Newton Raphson ◽  
Raphson Method

The force constants of the internal coordinates of planar XY3 and tetrahedral XY4 molecules were calculated using the GF matrix method. The matrix solutions were carried out by means of a computer program built relative to the Newton-Raphson method, and the calculations were listed in tables. For tetrahedral XY4 molecules having the same Y atom it was found that the force constants decrease with the increasing mass of the X atom, and this was attributed to the slowing of the molecule with increasing mass of the centre X atom.

scholarly journals Implementation of the Green-Ampt Infiltration Model: Comparative between different numerical solutions

2021 ◽  
Vol 22 (4) ◽  
pp. 645-658
Author(s):  
T. A. Mendes ◽  
S. F. Sousa Júnior ◽  
S. A. S. Pereira
Keyword(s):  
Numerical Solutions ◽  
Real Data ◽  
Lambert Function ◽  
Soil Permeability ◽  
Infiltration Process ◽  
Infiltration Model ◽  
Newton Raphson ◽  
The Difference ◽  
Raphson Method

The phenomena of infiltration and the percolation of water in the soil are of fundamental importance for the evaluation of runoff, groundwater recharge, evapotranspiration, soil erosion and transport of chemical substances in surface and groundwater. Within this context, the quantitative determination of the infiltration values is extremely important for the different areas of knowledge, in order to evaluate, mainly the surface runoff. Several types of changes in vegetation cover and topography result in significant changes in the infiltration process, making it necessary to use mathematical models to assess the consequences of these changes. Thus, this article aims to implement the Green-Ampt model using two numerical methods - Newton-Raphson method and W-Lambert function - to determine soil permeability parameters - K and matric potential multiplied by the difference between initial and of saturation - comparing them to the real data obtained in simulations using an automatic rainfall simulator from the Federal University of Goiás - UFG. The Green-Ampt model adjusted well to the data measured from the rain simulator, with a determination coefficient of 0.978 for the Newton-Raphson method and 0.984 for the W-Lambert function.

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