An efficient multi-grid method for TV minimization problems

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.

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Competition for Light Interception in Cotton Populations of Different Densities

Agronomy ◽

10.3390/agronomy11010176 ◽

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.

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A two-grid method for level-set based topology optimization with GPU-acceleration

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2020.113336 ◽

2021 ◽

Vol 389 ◽

pp. 113336

Author(s):

Yixin Li ◽

Bangjian Zhou ◽

Xianliang Hu

Keyword(s):

Topology Optimization ◽

Level Set ◽

Grid Method ◽

Gpu Acceleration

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An Algorithm for Nonparametric Estimation of a Multivariate Mixing Distribution with Applications to Population Pharmacokinetics

Pharmaceutics ◽

10.3390/pharmaceutics13010042 ◽

2020 ◽

Vol 13 (1) ◽

pp. 42

Author(s):

Walter M. Yamada ◽

Michael N. Neely ◽

Jay Bartroff ◽

David S. Bayard ◽

James V. Burke ◽

...

Keyword(s):

Drug Development ◽

Population Pharmacokinetics ◽

Empirical Bayes ◽

Applied Mathematics ◽

Grid Method ◽

Bayes Estimation ◽

Population Pharmacokinetic ◽

Support Points ◽

Primal Dual ◽

Log Normal

Population pharmacokinetic (PK) modeling has become a cornerstone of drug development and optimal patient dosing. This approach offers great benefits for datasets with sparse sampling, such as in pediatric patients, and can describe between-patient variability. While most current algorithms assume normal or log-normal distributions for PK parameters, we present a mathematically consistent nonparametric maximum likelihood (NPML) method for estimating multivariate mixing distributions without any assumption about the shape of the distribution. This approach can handle distributions with any shape for all PK parameters. It is shown in convexity theory that the NPML estimator is discrete, meaning that it has finite number of points with nonzero probability. In fact, there are at most N points where N is the number of observed subjects. The original infinite NPML problem then becomes the finite dimensional problem of finding the location and probability of the support points. In the simplest case, each point essentially represents the set of PK parameters for one patient. The probability of the points is found by a primal-dual interior-point method; the location of the support points is found by an adaptive grid method. Our method is able to handle high-dimensional and complex multivariate mixture models. An important application is discussed for the problem of population pharmacokinetics and a nontrivial example is treated. Our algorithm has been successfully applied in hundreds of published pharmacometric studies. In addition to population pharmacokinetics, this research also applies to empirical Bayes estimation and many other areas of applied mathematics. Thereby, this approach presents an important addition to the pharmacometric toolbox for drug development and optimal patient dosing.

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Three-body recombination calculations with a two-body mapped grid method

Physical Review A ◽

10.1103/physreva.103.032817 ◽

2021 ◽

Vol 103 (3) ◽

Author(s):

T. Secker ◽

J.-L. Li ◽

P. M. A. Mestrom ◽

S. J. J. M. F. Kokkelmans

Keyword(s):

Grid Method ◽

Three Body ◽

Body Recombination

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Kinematic characteristics of longitudinal double folding wings

The Aeronautical Journal ◽

10.1017/aer.2021.52 ◽

2021 ◽

pp. 1-25

Author(s):

L. Tiegang ◽

C. Guoguang ◽

L. Shuai

Keyword(s):

Angular Velocity ◽

Structural Model ◽

Initial Conditions ◽

Aerodynamic Force ◽

Model Simulation ◽

Lagrange Equation ◽

Grid Method ◽

Weapon Systems ◽

Folding Wing ◽

Double Folding

ABSTRACT A folding wing is a tactical missile launching device that needs to be miniaturised to facilitate storage, transportation, and launching; save missile and transportation space; and improve the combat capability of weapon systems. This study investigates the aeroelastic characteristics of the secondary longitudinal folding wing during the unfolding process. First, the Lagrange equation is used to establish the structural dynamics model of the folding wing, the kinematics characteristics during the deformation process are analysed, and the unfolding movement of the folding wing is obtained using the dynamic equations in the process. Then, the generalised unsteady aerodynamic force is calculated using the dipole grid method, and the multi-body dynamics equation of the folding wing is obtained. The initial angular velocity required for the deployment of the folding wing is analysed through structural model simulation, and the influence of the initial angular velocity on the opening process is studied. Finally, aeroelastic flutter analysis is performed on the folding wing, and the physical model of the folding wing verified experimentally. Results show that the type of aeroelastic response is sensitive to the initial conditions and the way the folding wing opens.

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