Mathematical Model for Simulating the Movement of Water Droplet on Artificial Leaf Surface

El-Ajou, Ahmad; Oqielat, Moa’ath N.; Ogilat, Osama; Al‐Smadi, Mohammed; Momani, Shaher; Alsaedi, Ahmed

doi:10.3389/fphy.2019.00132

Cited by 9 publications

(4 citation statements)

References 29 publications

(41 reference statements)

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“…The fractional derivative and integrals were recognized to be an efficient tool to describe the properties of complex dynamical processes more accurately than the standard integer derivative and integral [14,17,21,27,38]. Fractional partial differential equations (FPDEs) are a fascinating subject, because they are frequently used to explain a variety of phenomena in real-world situations, including signal processing control theory, fluid flow, potential theory, information theory, finance, and entropy [7,9,25,32]. Samko in 1993 [29] introduces the VOFDEs.…”

Section: Introductionmentioning

confidence: 99%

Solving fractional time-delay diffusion equation with variable-order derivative based on shifted Legendre–Laguerre operational matrices

2023

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This article adopts a novel technique to numerical solution for fractional time-delay diffusion equation with variable-order derivative (VFDDEs). As a matter of fact, the variable-order fractional derivative (VFD) that has been used is in the Caputo sense. The first step of this technique is constructive on the construction of the solution using the shifted Legendre–Laguerre polynomials with unknown coefficients. The second step involves using a combination of the collocation method and the operational matrices (OMs) of the shifted Legendre–Laguerre polynomials, as well as the Newton–Cotes nodal points, to find the unknown coefficients. The final step focuses on solving the resulting algebraic equations by employing Newton’s iterative method. To illustrate and demonstrate the technique’s efficacy and applicability, two examples have been provided.

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Section: Introductionmentioning

confidence: 99%

Solving fractional time-delay diffusion equation with variable-order derivative based on shifted Legendre–Laguerre operational matrices

2023

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“…Tong et al [30] used a volume-protecting technique to display drop streams by meta-balls. [11] presented a model for various drop transforming on a plane, and more works can be found in [3,10,[12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

“…None of the past ideas has been contained in mathematical models for a movement of beads on leaf surface as of not long ago this model is presented in [14,15] by the authors. Besides, they model a solitary drop movement on the Anthurium leaf.…”

Section: Introductionmentioning

confidence: 99%

Towards a Model for Simulating Collision of Multiple Water Droplets Flow Down a Leaf Surface

Oqielat¹

2022

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In the current article, a physics-based mathematical model is presented to generate realistic trajectories of water droplets across the Frangipani leaf surface and can be applied on any other kind of leaves, which is the first in the series of two articles that we are going to present the second article later on. In the second article, we will study the collision between the droplet and the liquid streak. The model has many applications in different scientific and engineering fields, such as modelling pesticide movements on leaves surfaces and modeling absorption and nutrition systems. The leaf surface consists of a triangular mesh structure that needs to be constructed using different techniques such as a well-known technique called EasyMesh method. The leaf surface is constructed using surface fitting techniques, such as finite elements methods and Clough-Tocher method, using a set of 3D real-world data points collected by a laser scanner, and the motion of the droplet on each triangle is calculated using a derived equation of motion. The motion of the droplet affected different forces, such as gravity and drag forces. Simulations of the model were verified using Matlab programming, and the results seemed to be real and capture the droplet motion very well.

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“…The application of surface fitting techniques to model the leaf surface is the main goal of the research given in this article, for instant, the application of water droplet or pesticide spreading on the leaf surface and modelling virtual plant; for more details, see (Dorr et al 2014;Lisa et al 2016;Oqielat et al 2011;El-Ajou et al 2019). Recently, many researchers have been interest in modelling leaves surfaces such as Kempthorne et al (2015a) applied the discrete smoothing D 2 -splines to model the cotton and wheat leaf.…”

Section: Introductionmentioning

confidence: 99%

Modelling leaf surface reconstruction using Bernstein polynomials method

Oqielat

2020

Comp. Appl. Math.

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In this research paper, we adapt for the first time Bernstein polynomials for reconstructing a continuous differentiable surfaces of a real leaf from 3D scanned data points. As such model is essential for modelling the plant architecture, fluid movement, and biological structure such as photosynthesis. To evaluate the accuracy of the proposed method, we apply it on a real scattered data points collected from a genuine Frangipani and Anthurium leaf surface using a laser scanner. We found that the Bernstein polynomials develop precise model of the leaf surface.

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Mathematical Model for Simulating the Movement of Water Droplet on Artificial Leaf Surface

Cited by 9 publications

References 29 publications

Solving fractional time-delay diffusion equation with variable-order derivative based on shifted Legendre–Laguerre operational matrices

Solving fractional time-delay diffusion equation with variable-order derivative based on shifted Legendre–Laguerre operational matrices

Towards a Model for Simulating Collision of Multiple Water Droplets Flow Down a Leaf Surface

Modelling leaf surface reconstruction using Bernstein polynomials method

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