Muhammad Bilal Riaz

An analytical and data-driven framework is developed to investigate the coupled fluid flow, heat transfer, and oxygen transport in the human anterior chamber. The proposed model describes buoyancy-driven aqueous humor (AH) flow in a hemispherical geometry incorporating thermal and oxygen transport, wall slip effects, and porous resistance associated with the trabecular meshwork. The coupled governing equations are solved analytically using the complementary function--particular integral (CF--PI) technique. The findings indicate that the forces of buoyancy play a crucial role in aqueous humor circulation and oxygen delivery within the anterior chamber. Although increase in Prandtl number and heat source parameter increases temperature distribution, increase in Schmidt number decreases the oxygen concentration since there will be decrease in mass diffusivity. Porous resistance inhibits fluid movement, and the motion of slips promotes near-wall velocity.Moreover, an Artificial Neural Network (ANN) model is created to predict flow, thermal, mass transfer properties. Predictions made by the ANN shows good agreement with the results of the analysis, which proves its suitability as an effective tool of surrogate modelling.Overall, the study provides insight into coupled convection–diffusion mechanisms governing intraocular transport and contributes to a better understanding of ocular physiology and oxygen delivery to non-vascular tissues, particularly the cornea.

The Ablowitz-Kaup-Newell-Segur (AKNS) water wave equation is a fundamental model for describing nonlinear wave propagation in various physical systems, including fluid dynamics, plasma physics, and nonlinear optics. Its higher-dimensional form provides a more realistic framework for understanding complex wave interactions in dispersive media. In this work, the [Formula: see text]-dimensional AKNS equation is studied from both analytical and dynamical perspectives. Analytical solutions of the governing equation are obtained using the modified Khater method, constructing different types of wave structures such as stationary and traveling profiles. These solutions illustrate the influence of nonlinearity and dispersion on the formation and evolution of coherent wave patterns. To further explore the system behavior, a detailed dynamical analysis is performed. The model is reduced to a system of ordinary differential equations, allowing the investigation of phase space dynamics through phase portraits, time series, Poincaré sections, bifurcation diagrams, and Lyapunov exponents. The results demonstrate a wide range of behaviors, including periodic, quasi-periodic, and chaotic motions, depending on the choice of system parameters. In particular, the system shows strong sensitivity to initial conditions and parameter variations, indicating the presence of complex and chaotic dynamics.

In this paper, to investigate exact optical soliton solutions and their dynamical properties for the paraxial wave model involving the M-fractional derivative. To achieve this, employ the improved modified Sardar sub-equation method, which provides a systematic and efficient analytical framework for constructing closed-form solutions of nonlinear fractional wave equations. The resulting fractional complex paraxial wave dynamical (FPWD) model is of considerable importance due to its wide applicability in nonlinear optics, optical fiber communications, quantum electronics, and plasma physics. The mathematical analysis reveals the existence of new solitary wave solutions that demonstrate complex nonlinear patterns that govern the system. The research discovers a needle-type soliton structure that operates within an M-fractional paraxial wave framework, thus differentiating itself from existing research, which uses classical and other fractional operators. The research displays three-dimensional surface plots and contour maps to enhance understanding of the obtained wave structures. The study assesses how essential parameters affect solution stabilityAQ through a sensitivity analysis, which shows solitons maintain their strength and operational behavior across various physical conditions.

Fractional derivatives have demonstrated a wide range of solutions beneficial for engineering, medical, and manufacturing sciences. Research on the use of fractional derivatives in fluid flow problems is still emerging, especially in analytical studies. In this paper, a mathematical model is developed to analyze the behavior of Casson fluid in heat and mass transfer processes within a magnetohydrodynamic (MHD) environment over an unsteady oscillating surface. Additionally, the numerical computation of fractional MHD Casson fluid flow for parallel surfaces subject to oscillating boundary conditions is discussed. The model utilizes a non-singular fractional derivative to solve fractional-order partial differential equations. By applying an appropriate transformation, these equations are converted into a dimensionless form. Subsequently, the finite difference method is employed to analyze the system’s behavior. A comprehensive parametric study is conducted to explore the effects of different physical parameters on the flow and thermal fields, and numerical simulations identify the fractional derivative operator that yields the most accurate and stable solutions. Furthermore, the model is solved using an ANN approach, and multiple cases are discussed for varying values of the fractional order parameter [ ]. This ANN-based analysis confirms the effectiveness of the fractional model in capturing the complex dynamics of MHD Casson fluid flow under oscillating boundary conditions.

In this paper, we proposed a general model for static spherically symmetric compact stars by incorporating anisotropic pressure and a modified Van der Waal (VdW) Equation of State (EoS). The inclusion of radiation density in the energy–momentum tensor, which provides a more realistic description of high-energy stellar interiors. The calculated solutions satisfy all necessary physical conditions like energy conditions, causality conditions and interior spacetime smoothly match with Vaidya exterior spacetime. The resulting key physical quantities such as density, pressure, mass, and redshift are stable and well-behaved throughout the stellar interior. The theoretical data correspond closely with observational constraints obtained from massive pulsars like PSR J0030+0451, PSR J0740+6620, and PSR J0348+0432. These findings highlight the significant role of radiation density in shaping the structure and stability of pulsars and support the applicability of the proposed model.

The article presents a performance analysis of the advanced adaptive control systems of traffic lights that are based on the advanced fuzzy logic. They include Modified Intuitionistic Fuzzy Logic Algorithm (MIFLA) and the Modified Interval Type-2 fuzzy logic (MIT2FL) at a four-leg intersection. In this article, there is an integration of these fuzzy models with the SUMO platform with respect to the weaknesses of the traditional fixed-time traffic lights, particularly in rapidly urbanizing areas. This will be to achieve a real-time dynamic control system. The simulation matrix was a grid of the nine scenarios in which the performance of the controllers was assessed to some extent, depending on the traffic and directional imbalances. The results reveal that the MIT2FL is more effective than the MIFLA and the Modified Webster benchmark. MIT2FL is less divergent, has shorter queuing times, and is more flexible. This occurs when the demand is high, and the traffic conditions are not proportional. This work is significant because it provides fuzzy logic controllers that can deal with uncertainty. It also creates a benchmarking model of a typical multi-scenario. Moreover, it gives the opportunity for reproducibility of the findings in real traffic implementation. The innovations will assist in making the city smarter and easier to move around. They manage congestion, delays, and improve the sustainability of smart traffic control.