• Structural Engineering and Mechanics
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• 제88권3호
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• pp.239-249
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• 2023

The Radial Point Interpolation Method (RPIM) has been proposed to overcome the difficulties associated with the use of the Radial Basis Functions (RBFs). The RPIM has the following properties: Simple implementation in terms of boundary conditions as in the Finite Element Method (FEM). A less expensive CPU time compared to other collocation meshless methods such as the Moving Least Square (MLS) collocation method. In this work, we propose an adaptive high-order numerical algorithm based on RPIM to simulate the thermoviscoplastic behavior of a material mixing observed in the Friction Stir Welding (FSW) process. The proposed adaptive meshfree RPIM algorithm adapts well to the geometric and physical data by choosing a good shape parameter with a good precision. Our numerical approach combines the RPIM and the Asymptotic Numerical Method (ANM). A numerical procedure is also proposed in this work to automatically determine an improved shape parameter for the RBFs. The efficiency of the proposed algorithm is analyzed in comparison with an iterative algorithm.

• Advances in nano research
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• 제16권4호
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• pp.427-434
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• 2024

Latest advancement in field of fluid dynamics has taken nanofluid under consideration which shows large thermal conductance and enlarges property of heat transformation in fluids. Motivated by this, the key aim of the current investigation scrutinizes the influence of thermal radiation and magnetohydrodynamic on the laminar flow of an incompressible two-dimensional Williamson nanofluid over an inclined surface in the presence of motile microorganism. In addition, the impact of heat absorption/generation and Arrhenius activation energy is also examined. A mathematical modeled is developed which stimulate the physical flow problem. By using the compatible similarities, we transfer the governing PDEs into ODEs. The analytic approach based on Homotopy analysis method is introduced to impose the analytic solution by using Mathematica software. The impacts of distinct pertinent variable on velocity profiles are investigated through graphs.

• 호남수학학술지
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• 제37권1호
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• pp.135-147
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• 2015

Owing to the notion of a normal adjacency for a digital product in [8], the study of product properties of digital topological properties has been substantially done. To explain a normal adjacency of a digital product more efficiently, the recent paper [22] proposed an S-compatible adjacency of a digital product. Using an S-compatible adjacency of a digital product, we also study product properties of digital topological properties, which improves the presentations of a normal adjacency of a digital product in [8]. Besides, the paper [16] studied the product property of two digital covering maps in terms of the $L_S$- and the $L_C$-property of a digital product which plays an important role in studying digital covering and digital homotopy theory. Further, by using HS- and HC-properties of digital products, the paper [18] studied multiplicative properties of a digital fundamental group. The present paper compares among several kinds of adjacency relations for digital products and proposes their own merits and further, deals with the problem: consider a Cartesian product of two simple closed $k_i$-curves with $l_i$ elements in $Z^{n_i}$, $i{\in}\{1,2\}$ denoted by $SC^{n_1,l_1}_{k_1}{\times}SC^{n_2,l_2}_{k_2}$. Since a normal adjacency for this product and the $L_C$-property are different from each other, the present paper address the problem: for the digital product does it have both a normal k-adjacency of $Z^{n_1+n_2}$ and another adjacency satisfying the $L_C$-property? This research plays an important role in studying product properties of digital topological properties.

• Advances in nano research
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• 제10권3호
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• pp.221-234
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• 2021

During the previous few years, phenomenon of bioconvection along with the use of nanoparticles showed large number of applications in technological and industrial field. This paper analyzed the bioconvection phenomenon in magnetohydrodynamic boundary layer flow of a Powell-Eyring nanoliquid past a stretchable cylinder with Cattaneo-Christov heat flux. In addition, the impacts of chemical reaction and heat generation/absorption parameter are considered. By the use of appropriate transformation, the governing PDEs (nonlinear) have been transformed and formulated into nonlinear ODEs. The resulting nonlinear ODEs subjected to relevant boundary conditions are solved analytically through homotopy analysis method which is programmed in Mathematica software. Graphical and numerical results versus physical quantities like velocity, temperature, concentration and motile microorganism are investigated under the impact of physical parameters. It is noted that velocity profile enhances as the curvature parameter A and Eyring-Powell fluid parameter M increases but a decline manner for large values of buoyancy ratio parameter Nr and bio-convection Rayleigh number Rb. In the presence of Prandtl number Pr, Eyring-Powell fluid parameter M and heat absorption parameter ��, temperature profile decreases. Nano particle concentration profile increases for increasing values of magnetic parameter Ha and thermophoresis parameter Nt. The motile density profile has revealed a decrement pattern for higher values of bio-convection Lewis number Lb and bio-convection peclet number Pe. This study may find uses in bio-nano coolant systems, advance nanomechanical bio-convection energy conversion equipment's, etc.