Automatic shape optimisation of pharmaceutical tablets using Partial Differential Equations

Ahmat, Norhayati; Castro, Gabriela; Ugail, Hassan

doi:10.1016/j.compstruc.2013.09.001

Cited by 12 publications

(8 citation statements)

References 28 publications

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“…The PDE method has become a familiar technique for designing surfaces [9] in many fields, especially in graphics, modelling [8], design analysis [2], and optimization [5]. A parametric surface 𝜒(𝑢, 𝑣) can be produced using this method, which depends on the solution of the elliptic PDE.…”

Section: Parametric Surface Based On the Pde Methodsmentioning

confidence: 99%

WITHDRAWN: The Surface Area of Red Blood Cell Via PDE Method

Ahmed

2024

Preprint

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Using the PDE method to calculate the surface area for shape of red blood cell is the aim of this paper, and this technique depends on the use of an elliptic PDE and four boundary conditions. For finding the surface area first all creating the vectors Xu and Xv from the given radius and height which are obtained from boundary conditions of PDE method, then finding the norm of cross product between Xu and Xv and finally finding double integration of the result of that norm to get the surface area.

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Section: Parametric Surface Based On the Pde Methodsmentioning

confidence: 99%

WITHDRAWN: The Surface Area of Red Blood Cell Via PDE Method

Ahmed

2024

Preprint

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“…Where Equation ( 17) and (18) found by differentiating equation ( 13), ( 14) and (15), with respect to 𝑢 and 𝑣 respectively [6].…”

Section: Parametric Surface Based On the Pde Methodsmentioning

confidence: 99%

Using PDE Method to Compute The Volume of the Lung

Ahmed

2024

Preprint

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The object of this paper is computing the volume for the shape of Lung which is designed by a technique depending on the use of an elliptic and four boundary conditions which is called PDE method. To calculate the volume of the Lung some steps needed, first from the given radius and height which are obtained from boundary conditions of PDE method finding the vectors X, Xu and Xv, after that finding the cross product between the vectors Xu and Xv, then calculate the dot product between vector X and the result of the cross product between the vectors Xu and Xv, and then evaluate double integration of the result of dot product, at last divide the result of integration by 3 to get the volume.

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“…The PDE method was originally introduced in the field of computer graphics in 1989 and it has been widely used as a surface modeling technology in many fields especially in graphics, design, design analysis and optimization [1]. This method produces a standardized surface χ(u, v) that is generated by a fourth degree elliptical PDE solution…”

Section: The Pde Methodsmentioning

confidence: 99%

Designing the Shape of Helicobacter Pylori Using the PDE Method

2020

JXAT

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Modeling the shape of Helicobacter pylori (H. pylori), by using partial differential equation (PDE) is the aim of this article. The development of this technique relied on the use of elliptic PDE and a set of four periodic boundary conditions. The PDE method can create engineering surfaces from a small number of parameters. Also, the shape of the surfaces, which is generated by the PDE method, depends on the representation of a boundary and can be easily changed since it is described by the data distributed around the boundaries. In this study, a PDE-based representation generated from H. pylori was designed using the MATLAB program. The results showed that the PDE method is suitable for representing the shape of Helicobacter pylori bacteria. Besides, the radius and height from Helicobacter pylori are used to obtain four equations. These equations can be used for future prediction in the modeling of Helicobacter pylori. In conclusion, the PDE method can produce smooth parametric surface representations of any particular form of bacteria.The study implies that the PDE method has the potential to create complex engineering surfaces.

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Automatic shape optimisation of pharmaceutical tablets using Partial Differential Equations

Cited by 12 publications

References 28 publications

WITHDRAWN: The Surface Area of Red Blood Cell Via PDE Method

WITHDRAWN: The Surface Area of Red Blood Cell Via PDE Method

Using PDE Method to Compute The Volume of the Lung

Designing the Shape of Helicobacter Pylori Using the PDE Method

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