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Abstract In the modern digital sphere, graph theory is a significant field of research that has a great deal of significance. It finds widespread application in computer science, robotic directions, and chemistry. Additionally, graph theory is used in robot network localization, computer network problems and the formation of various chemical structures for networks. Moreover, it finds uses in exploring diffusion mechanisms and scheduling aircraft as well. The present research project examines and concentrates on the edge version of metric dimension of the Concealed Non-Kekuléan Benzenoid Hydrocarbon, Polythiophene, Backbone DNA network and Bakelite networks. All the mentioned networks have constant edge metric dimension except Bakelite network, as demonstrated by the results. If we talk about the applications of these networks, Polythiophene are used to treat prion disorders. It is also capable of detecting metal ions. The concept of Bakelite, which finds applications in the jewelry, electrical, cookware, sports, and clock industries, had an impact on the invention of modern polymers. The functions of DNA include information encoding, replication, mutation, and recombination gene expression.

The impact of nonlinear heat source and activation energy on magnetized Synovial trihybrid nanofluid Marangoni convective flow across a sheet combining two viscosity models is investigated in this study. Heat sources, activation energy, and conditions of local thermal non-equilibrium (LTNE) are all considered in the modelling. Based upon energy equations, the LTNE model provides unique heat transport for both liquid and solid phases. This leads to the utilization of different temperature profiles for the fluid and solid phases in this work. A trihybrid fluid is created by combining the basic fluid blood with MWCNT (multi-wall carbon nanotubes), SWCNT (single-wall carbon nanotubes) and sliver nanoparticle. This study significant potential in several fields. The effects of parameters on friction between joints are examined, which aids in the analysis of the lubricant nature of Synovial trihybrid nanofluid. A significant finding of the current work is that the thermal profiles decrease with higher values of the Concentration-dependent viscosity parameter, but the velocity profile increases. An increase in the inter-phase heat transfer characteristic raises the liquid phase's thermal profile while lowering the solid phase's thermal profile.

The impact of heat generation and activation energy on the Darcy-Forchheimer flow of magnetized fluid with nanoparticles in the condition of blood flowing arteries is being investigated by researchers from all over the world in an effort to understand the heat transmission component for the treatment of numerous diseases. The assessment of heat transmission has been made with the enclosure of influence like the viscous dissipation, heat source, Joules heating, and thermal radiation. Utilized is a tetra hybrid nanofluid made up of silver (Ag), gold (Au), titanium oxide (TiO2), coper (Cu), and Blood as the base fluid. The main justification for the use of gold, copper, and silver nanoparticles as drug delivery nanomaterials is their potential for drug transport and imaging. The purpose of the presented model is to assess the performance of the well-known tetra hybrid nanofluid models developed by Yamada-Ota and Xue. The main PDE are transformed into ODE via similarity renovations, and these ODE are then numerically solved using the MATLAB built-in bvp4c scheme. The arteries' internal temperature rises as a result of thermal radiation and viscous dissipation. The velocity and thermal distributions show an increasing behavior with greater variations in the flow parameter. The Yamada-Ota model outperforms the Xue tetra hybrid nanofluid model in terms of heat transmission effectiveness.

Thin-film photovoltaic (PV) technology offers an economically viable and flexible way to harness solar energy. Using a material that absorbs more solar light than silicon significantly reduces material consumption and costs. Solar cells based on the kesterite mineral structure and its alloys stand out from other thin-film solar cells due to their earth-abundance and non-toxicity. Incorporating plasmonic nanoparticles in the kesterite absorber layer opens a promising path of enhancing light trapping efficiency. Again, the main losses in solar cells result from the incomplete utilization of the solar spectrum. The otherwise unused sub-bandgap photons can be utilized by adding an upconverting layer on a solar cell. This paper demonstrates a theoretical design and performance analysis of a high-efficiency kesterite solar cell by incorporating titanium nitride (TiN) plasmonic bowtie nanoparticles (NPs) and an upconverter layer. We compared the optical characteristics of various shapes and sizes of nanoparticles to find the optimum solar cell efficiency. The 100 nm thick bowtie-shaped NP had the highest power conversion efficiency, η of 24.80% and had the open circuit voltage Voc=0.59V, and short circuit current density, Jsc = 45.43 mA/cm2. The absorbed power for bowtie-shaped TiN NP incorporation enhanced the average absorption from ∼61% to ∼88% for the kesterite layer. For 100 nm thickness, the absorption enhancement, g, was greater than 1 for the whole spectral range, and the maximum value was ∼1.2. Incorporating a yttrium aluminum garnet upconverter layer increased the solar cell efficiency to ∼27.44.%.

The purpose of this study is to simulate thermal flows via quasi-Newtonian modeling by employing Finite Element Methods (FEM), as well as Newton Multigrid Solvers (NMS). A heated rotating cylinder is exposed to an inflowing fluid stream in a channel to facilitate the thermal energy transfer in the fluid. The NMS may be more easily parallelized as a result of an excessive number of degrees of freedom. The discretization of a dimensionless system of partial differential equations that are to be solved over an extensive computational domain is accomplished by using the higher-order stable finite element pair. Temporal discretization is performed using a 2nd order Crank-Nicolson scheme. By applying the Newton method, the discretized nonlinear system of algebraic equations is transformed into a linear form. To compute the linearized subproblems that arise from each nonlinear sweep, a geometric multigrid approach has been put in place. The whole framework has been implemented in an open-source finite element software Featflow. It has been deduced that in a clockwise rotation of the cylinder, more fluid will move from above the cylinder, and when it is rotated in an anticlockwise direction, more fluid will move from bottom side of the cylinder. In addition to this, there is a correlation between an increase in the rotational parameter ω and a reduction in both the lift coefficient CL and drag coefficient CD. The benchmark values of CD and CL fits very well with the available data for certain special cases of this study.

Recent years have been marked by a significant increase in interest in solving nonlinear equations that arise in various fields of natural science. This trend is associated with the creation of a new method of mathematical physics. The present study is devoted to the analysis of the propagation of m-nonlinear viscoelastic waves equations in an unbounded domain. The physical properties are determined by the equations of the linear theory of viscoelasticity. This article shows the main effect and interaction between the different weak and strong damping terms on the behavior of solutions. We found, under a novel condition on the kernel functions, an energy decay rate by using an appropriate energy estimates.