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In this paper, we use the sub-ODE method to analyze soliton solutions for the renowned nonlinear Klein-Gordon model (NLKGM). This method provides a variety of soliton solutions, including three positive solitons, three Jacobian elliptic function solutions, bright solitons, dark solitons, periodic solitons, rational solitons and hyperbolic function solutions. Applications for these solitons can be found in optical communication, fiber optic sensors, plasma physics, Bose-Einstein condensation and other areas. We also study some numerical solutions by using forward, backward, and central difference techniques. Moreover, we discuss variational integrators (VIs) using the projection technique for NLKGM. We develop a numerical solution for NLKGM using the discrete Euler lagrange equation, the Lagrangian and the Euler lagrange equation. At the end, in various dimensions, covering 3D, 2D, and contour, we will also plot several graphs for the obtained NLKGM solutions. A contour plot is a type of graphic representation that displays a three-dimensional surface on a two-dimensional plane by using contour lines. Each contour line in the plotted function represents one of the function's constant values, mapping the function's value across the plane. This model has been studied across multiple soliton solutions using various methods in the open literature, but this model for VIs and finite deference scheme (FDS) is the first time it has been studied. Within the various numerical techniques accessible for solving Hamiltonian systems, variational integrators distinguish themselves because of their symplectic quality. Here are some of the symplectic properties: symplectic orthogonality, energy conservation, area preservation, and structure preservation. [ABSTRACT FROM AUTHOR]

Carbon nanomaterials have received increasing attention in drug-delivery applications because of their distinct properties and structures, including large surface areas, high conductivity, low solubility in aqueous media, unique chemical functionalities, and stability at the nano-scale size. Particularly, they have been used as nano-carriers and mediators for anticancer drugs such as Cisplatin, Camptothecin, and Doxorubicin. Cancer has become the most challenging disease because it requires sophisticated therapy, and it is classified as one of the top killers according to the World Health Organization records. The aim of the current work is to study and investigate the mechanism of combination between single-walled carbon nanotubes (SWCNTs) and fullerene derivatives (C N -[OH] β ) as mediators, and anticancer agents for photodynamic therapy directly to destroy the infected cells without damaging the normal ones. Here, we obtain a bio-medical model to determine the efficiency of the usefulness of Doxorubicin (DOX) as an antitumor agent conjugated with SWCNTs with variant radii r and fullerene derivative (C N -[OH] β ). The two sub-models are obtained mathematically to evaluate the potential energy arising from the DOX–SWCNT and DOX-(C N -[OH] β ) interactions. DOX modelled as two-connected spheres, small and large, each interacting with different SWCNTs (variant radii r) and fullerene derivatives C N -[OH] β , formed based on the number of carbon atoms (N) and the number of hydroxide molecules (OH) (β), respectively. Based on our obtained results, we find that the most favorable carbon nanomaterial is the SWCNT (r = 15.27 Å), followed by fullerene derivatives C N -(OH) 22 , C N -(OH) 20 , and C N -(OH) 24 , with minimum energies of −38.27, −33.72, −32.95, and −29.11 kcal/mol. [ABSTRACT FROM AUTHOR]

Fullerenes have generated a great deal of interest in recent years, due to their properties and potential applications in many fields, including medicine. In this paper, we study an antiviral fullerene compound which may be used to treat the human immunodeficiency virus (HIV). We formulate a mathematical model which can describe the interaction energy between the C $$_{60}$$ antiviral compounds and the HIV. In particular, this paper predicts the energy and force arising from the interaction between HIV active region and the antiviral molecule which is attached to the external surface of a fullerene C $$_{60}$$ . These interactions are calculated based on the structure of the antiviral molecules. Our results show that the binding of fullerene C $$_{60}$$ to the antiviral molecules increases the efficiency of the compound to prohibit the activity of HIV. [ABSTRACT FROM AUTHOR]

The wedge geometry is a cornerstone in thermal transport mechanism, sepcially in scenarios involving fluid flow over surfaces. The current study emphasizes the melting heat transport mechanism in a Graphene oxide nanofluid over a Falkner‐Skan wedge geometry in the presence of multiple features of infinite shear rate accompanied with variable thermal transport characteristics and activation energy. Additionally, Cross model incorporated in the sytem, which predicts accurate behavior of intricate flow for better thermal simulation. The flow is governed by framed set of partial differential equations based on Naver stokes relations. A highly nonlinear system is altered in simplified non dimensional form using similarity variables. Numerical simulations are performed by an efficient MATLAB (bvp4c) solver scheme and the results of emerging parameters are compiled via different pictorial and tabular representations. The higher values of velocity ratio and melting heat parameter boost up the heat transfer rate over the Falkner‐Skan wedge geometry, whereas Brownian motion of nanofluid molecules arises by thermophoresis which declines the concentration profile. Numeric growth in the values of Schmidt number reduce the mass diffusivity, which declines the fluid temperature distribution. Likewise, Increasing value of Prandtl number causes reduction in thermal conductivity and produces temperature fall. It is worth noting that, this computational assessment is crucial in thermal processes because the results derived from this analysis enable the optimization of designs for better performance, efficiency, and control in practical applications. [ABSTRACT FROM AUTHOR]

AbstractA study is conducted on the unsteady motion of a free convective flow of second grade fluid, energy transfer, and Darcy’s law over an oscillatory smooth vertical plate. The study compares two different approaches in developing a fractional model: the Caputo-Fabrizio operator with nonsingular kernel and the constant proportional Caputo fractional operator with Fourier’s and Fick’s laws. By applying the Laplace method and transforming the provided set of equations into nondimensional form, we obtained semi-analytical results and presented these results through graphical analysis. The study examines how different flow parameters, including the fractional parameters, affect the velocity, mass, and heat profiles of the physical system. The results suggest that the physical model using constant proportional Caputo derivative leads to higher temperature, stronger concentration, and increased velocity compared to the Caputo-Fabrizio model. This highlights the importance of selecting an appropriate fractional model when studying complex physical systems. It is also depicted from the whole analysis that field variables with novel hybrid fractional derivative constant proportional Caputo exhibits a more effective and declining tendency than Caputo-Fabrizio. [ABSTRACT FROM AUTHOR]