Dynamics of invariant solutions of the DNA model using Lie symmetry approach

The utilization of the Lie group method serves to encapsulate a diverse array of wave structures. This method, established as a robust and reliable mathematical technique, is instrumental in deriving precise solutions for nonlinear partial differential equations (NPDEs) across a spectrum of domains. Its applications span various scientific disciplines, including mathematical physics, nonlinear dynamics, oceanography, engineering sciences, and several others. This research focuses specifically on the crucial molecule DNA and its interaction with an external microwave field. The Lie group method is employed to establish a five-dimensional symmetry algebra as the foundational element. Subsequently, similarity reductions are led by a system of one-dimensional subalgebras. Several invariant solutions as well as a spectrum of wave solutions is obtained by solving the resulting reduced ordinary differential equations (ODEs). These solutions govern the longitudinal displacement in DNA, shedding light on the characteristics of DNA as a significant real-world challenge. The interactions of DNA with an external microwave field manifest in various forms, including rational, exponential, trigonometric, hyperbolic, polynomial, and other functions. Mathematica simulations of these solutions confirm that longitudinal displacements in DNA can be expressed as periodic waves, optical dark solitons, singular solutions, exponential forms, and rational forms. This study is novel as it marks the first application of the Lie group method to explore the interaction of DNA molecules.

Existence of common fuzzy fixed points via fuzzy F-contractions in b-metric spaces

The main goal of this study is to establish common fuzzy fixed points in the context of complete b-metric spaces for a pair of fuzzy mappings that satisfy F-contractions. To strengthen the validity of the derived results, non-trivial examples are provided to substantiate the conclusions. Moreover, prior discoveries have been drawn as logical extensions from pertinent literature. Our findings are further reinforced and integrated by the numerous implications that this technique has in the literature. Using fixed point techniques to approximate the solutions of differential and integral equations is very useful. Specifically, in order to enhance the validity of our findings, the existence result of the system of non-linear Fredholm integral equations of second-kind is incorporated as an application.

FEM simulations for double diffusive transport mechanism hybrid nano fluid flow in corrugated enclosure by installing uniformly heated and concentrated cylinder

Generation of fluid flow due to simultaneous occurrence of heat and mass diffusions caused by buoyancy differences is termed as double diffusion. Pervasive applications of such diffusion arise in numerous natural and scientific systems. This article investigates double diffusion in naturally convective flow of water-based fluid saturated in corrugated enclosure and containing hybrid nano particles composed of Copper (Cu) and Alumina (Al2O3). Impact of uniformly applied magnetic field is also accounted. To produce thermosolutal convective potential circular cylinder of constant radius is also adjusted by providing uniform temperature and concentration distributions. Finite element approach is capitalized to provide solution of utilized governing equations by utilizing Multiphysics COMSOL software. Wide-range of physical parameters are incorporated to depict their influence on associated distributions (velocity, temperature and concentration). Interesting physical quantities like Nusselt number, Sherwood numbers are also calculated against involved sundry parameters. It is note worthily observed that maximum strength of stream lines [Formula: see text] is 3.3 at [Formula: see text] and drops to 1.2 when [Formula: see text] is increased to 0.04. Furthermore, in the hydrodynamic case (Ha = 0), it is observed that the velocity field exhibits an increasing trend compared to the hydromagnetic case [Formula: see text] which is proved from the attained values of stream-function i.e., [Formula: see text] (in the absence of a magnetic field) and [Formula: see text] (in the presence of a magnetic field). It is revealed from the statistics of Nusselt number that increase in volume fraction of nano particles from 0 to 0.4, heat flux coefficient upsurges up to 7% approximately. Since, present work includes novel physical aspects of thermosolutal diffusion generated due to induction of hybrid nanoparticles in water contained in corrugated enclosure, so this study will provide innovative thought to the researchers to conduct research in this direction.