Muhammad Junaid-U-Rehman

This study investigates a detailed analytical and numerical investigation of a nonlinear two-degree-of-freedom (2DOF) mechanical oscillator subjected to parametric excitation, magnetic stiffness nonlinearities, and dry friction. The considered system consists of two coupled oscillators, both of which are connected to a rotating rectangular beam that induces a time-periodic stiffness variation. The Complex Averaging (CxA) method is employed to derive approximate analytical solutions, which are thoroughly validated through time-domain simulations and bifurcation analyses. The dynamic analysis reveals a rich spectrum of nonlinear behaviors, including periodic, quasi-periodic, and chaotic responses. Detailed bifurcation diagrams, Lyapunov exponent analysis, and Poincaré maps demonstrate the influence of nonlinear stiffness degree, mass symmetry, and frictional effects on system stability and response amplitude. The obtained results give a significant understanding of the dynamic behavior of coupled nonlinear systems and establish a conceptual framework for the development of complex vibration abatement strategies, energy harvesting devices, and advanced mechanical systems.

Lie symmetry analysis has been applied to the extended Boiti-Leon-Manna-Pempinelli (eBLMP) equation. This system illustrates the exchange of information between two waves with distinct dispersion characteristics. The optimal system of the corresponding Lie algebra has been constructed. The equation considered has been reduced into a simpler form for the computation of analytical solutions. The novelty of this research is the optimal system of subalgebras in one dimension using the adjoint action approach. To analyze and understand the eBLMP more clearly, graphs have been plotted. We have also found conservation laws

This paper exhibits a brief study of Marangoni convective, Activation energy, non-uniform heat generation, thermal-bioconvection and Oxytactic microorganisms, and time-dependent and stagnation point flow of MHD trihybrid nanofluid around a rotating sphere based on the extended model, referred to as the YOM (Yamada-Ota model) and XM (Xue model). The porous medium impact of Darcy-Forchheimer is included in the momentum equation. Some acceptable transformations are implemented to translate the governing system of PDEs (partial differential equations) and the relevant boundary conditions for computation. This model aims to evaluate the efficiency of two well-known trihybrid nanofluid models, Yamada-Ota and Xue. The shooting approach (BVP4C) is applied to derive the numerical estimates for the relevant differential expression system. The detailed analysis and simulation of trihybrid nanofluid flow patterns are facilitated by the variation in changing factors, which include temperature, velocity, concentration, and gyrotactic and Oxytactic microorganisms the profiles. The results indicate that the YOM performs significantly superior than the XM flow model in terms of heat transmission ability.

The [ ]-expansion scheme is used to execute many wave results for the partial differential equation, namely, the nonlinear extended quantum Zakharov–Kuznetsov (NLEQZK) equation which plays a significant role in mathematical physics, and this equation is accomplished in quantum electron–positron–ion magneto plasmas. The Lie approach is used to find the infinitesimal generators, and group invariant solutions, and help us to reduce the considered PDEs into ODEs. Then a planer dynamical system approach is used to see the existence of closed-form solutions. All possible phase portraits are obtained and the existence of electrostatic wave potentials is reported. Meantime, periodic and super-nonlinear electrostatic wave potentials are found for different initial value conditions with the help of the Runge–Kutta method. Moreover, new traveling wave patterns of the considered models are constructed and presented graphically. Then, the conserved vectors of the given physical model with the use of the multiplier scheme are presented.

Nonlinear chains of atoms (NCA) are complex systems with rich dynamics, that influence various scientific disciplines. The lie symmetry approach is considered to analyze the NCA. The Lie symmetry method is a powerful mathematical tool for analyzing and solving differential equations with symmetries, facilitating the reduction of complexity and obtaining solutions. After getting the entire vector field by using the Lie scheme, we find the optimal system of symmetries. We have converted assumed PDE into nonlinear ODE by using the optimal system. The new auxiliary scheme is used to find the Travelling wave solutions, while graphical behaviour visually represents relationships and patterns in data or mathematical models. The multiplier method enables the identification of conservation laws, and fundamental principles in physics that assert certain quantities remain constant over time.

Nonlinear chains of atoms(NCA) are complex systems with rich dynamics, influencing various scientific disciplines. Lie symmetry approach is considered to analyze the NCA. The Lie symmetry method is a powerful mathematical tool for analyzing and solving differential equations with symmetries, facilitating the reduction of complexity and obtaining solutions. After getting the entire vector field by using the Lie scheme, we find the optimal system of symmetries. Using the optimal system we have converted assumed PDE into nonlinear ODE. The new auxiliary scheme introduces novel approaches to complement existing techniques, enhancing accuracy and simplifying computations. Travelling wave solutions describe wave-like propagation in systems, while graphical behavior visually represents relationships and patterns in data or mathematical models. The multiplier method enables the identification of conservation laws, fundamental principles in physics that assert certain quantities remain constant over time. Understanding these concepts contributes to a deeper comprehension of nonlinear chains of atoms and their dynamics, fostering advancements in related fields.