The rate of convergence of a multiple grid method

1980 ◽  
pp. 164-184 ◽  
Author(s):  
P. Wesseling
Keyword(s):  
Rate Of Convergence ◽  
Grid Method

Products of 2 × 2 stochastic matrices with random entries

1986 ◽  
Vol 23 (04) ◽  
pp. 1019-1024
Author(s):  
Walter Van Assche
Keyword(s):  
Rate Of Convergence ◽  
Beta Distribution ◽  
Stopping Time ◽  
Stochastic Matrices

The limit of a product of independent 2 × 2 stochastic matrices is given when the entries of the first column are independent and have the same symmetric beta distribution. The rate of convergence is considered by introducing a stopping time for which asymptotics are given.

Grid Method for Accuracy Study of Micro Parts Manufacturing

2011 ◽  
Vol 3 (3) ◽  
pp. 263-269 ◽  
Author(s):  
E. Minev ◽  
K. Popov ◽  
R. Minev ◽  
S. Dimov ◽  
V. Gagov
Keyword(s):  
Grid Method ◽  
Micro Parts ◽  
Accuracy Study ◽  
Parts Manufacturing

Numerical Solution of a Nonlinear Diffusion Model for Soybean Hydration with Moving Boundary

2015 ◽  
Vol 11 (5) ◽  
pp. 587-595 ◽  
Author(s):  
Douglas J. Nicolin ◽  
Gisleine E. C. da Silva ◽  
Regina Maria M. Jorge ◽  
Luiz Mario M. Jorge
Keyword(s):  
Differential Equation ◽  
Diffusion Model ◽  
Nonlinear Diffusion ◽  
Numerical Scheme ◽  
Moving Boundary ◽  
Grid Method ◽  
Variable Diffusivity ◽  
Variable Space ◽  
Diffusive Fluxes ◽  
Moisture Profiles

Abstract Variable diffusivity and volume of the grains are taken into account in the diffusion model that describes mass transfer in soybean hydration. The variable space grid method (VSGM) was used to consider the increase in grain size, and the diffusivity was considered an exponential function of the moisture content. An equation for the behavior of the grain radius as a function of time was obtained by global mass balance over the soybean grain and the differential equation considered that the increase in radius happens due to the influence of the convective and diffusive fluxes at the surface of the grains. The model was solved by an explicit numerical scheme which presented satisfactory results. The results showed the behavior of moisture profiles obtained as a function of time and radial position and also showed how the grain radius increased with time and changed the solution domain of the diffusion equation.

scholarly journals Competition for Light Interception in Cotton Populations of Different Densities

Agronomy ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 176
Author(s):  
Huanxuan Chen ◽  
Xinxin Zhao ◽  
Yingchun Han ◽  
Fangfang Xing ◽  
Lu Feng ◽  
...  
Keyword(s):  
Spatial Competition ◽  
Grid Method ◽  
Spatial Arrangement ◽  
Light Interception ◽  
Agricultural Science ◽  
Shade Avoidance ◽  
Canopy Architecture ◽  
Growing Period ◽  
Plant Densities ◽  
Competition For Light

Modification of the cotton canopy results in shade avoidance and competition for light, which shows that density and spatial arrangement of cotton have a great impact on light interception. This experiment was conducted in 2018 and 2019 in the experimental field at the Institute of Cotton Research of Chinese Academy of Agricultural Science in Anyang city, Henan Province, China. Six plant densities of cotton variety SCRC28 were used to assess spatial competition for light in cotton populations during the whole growing period. Light interception data were collected and analyzed according to the spatial grid method and the extension of Simpson’s 3/8 rule. The results showed that at the bottom of the canopy, greater light interception was observed at high densities than at low densities, while in the external part of the layer of the canopy in the horizontal direction, low light interception was recorded at low densities. Leaf area, aboveground biomass and plant height were obviously correlated with light interception, and the cotton population with a higher density (8.7 plants m−2) performed best at the light interception competition, and with the highest yield. The results will provide guidance on light management through the optimization of the structure of the canopy to provide more solar radiation and a significant basis by which to improve the management of light and canopy architecture.

scholarly journals Central and Local Limit Theorems for Numbers of the Tribonacci Triangle

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 880
Author(s):  
Igoris Belovas
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Normal Distribution ◽  
Rate Of Convergence ◽  
Limit Theorems ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Constructive Proof ◽  
The Central Limit Theorem ◽  
Local Limit Theorems

In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of convergence to the limiting (normal) distribution, as well as a new proof of the local limit theorem for the numbers of the tribonacci triangle.

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