Vol. 16, No. 1 (2027): Regular Issue

The purpose of the study is to examine effect of throughflow in Rayleigh-B{é}nard setup taking micropolar fluid in enclosures. Linear and non-linear stability analysis of the problem is carried out by deriving the Lorenz model considering Fourier-series representation. In this study, three different enclosure types — shallow $(hb)$ are examined, where $h$ - height and $b$ - breadth of the enclosure. According to the study, shallow enclosure is more stable than square and tall enclosure. On the other hand heat transport is more in tall enclosure. It is also observed that, system is stable in anti-gravity and unstable in pro-gravity conditions. Thus, the onset of convection can be controlled by adjusting the suction injection effects. Graphs are plotted to study and demonstrate the effects of micropolar fluid characteristics on Rayleigh-number and average Nusselt number.

The purpose of this research is the analytical solution of unsteady natural convective flow of a viscous incompressible fluid, which flows over an isothermally heated infinite vertical cylinder. Uniform magnetic field is applied in the direction perpendicular to the cylinder and normal to the direction of the flow. Considering that the pressure is uniform in the whole flow field. The closed-form solutions of the governing dimensionless unsteady coupled linear boundary layer equations are obtained in terms of Bessel functions and modified Bessel functions by Laplace transform method. Velocity and skin-friction profiles are analyzed graphically for different values of Ekman number and magnetic parameter along with the temperature profiles and Nusselt number. The nonlinear regression using Variance analysis (ANOVA) is conducted to the determine the impact of each parameter on the Nusselt number and predicted the optimal values for the Nusselt number. The present study has considered only Newtonian fluids. Future studies will address non-Newtonian liquids.

The investigation was conducted on the peristaltic transport of Newtonian fluid via a curved tube. The entire research has been focused beneath long wavelength and low Reynolds number approximations. This type of research explains the phenomenon of food bolus swallowing through a hiatus hernia-affected oesophagus. The axial and radial velocities, reflux limit expressions, and pressure have been calculated using Mathematica. The pressure differences are found to grow with wave curvature and amplitude but decrease with inclination angle, wall thickness change, and distance from the central line. The effect of curvature on pressure difference and the relationship between pressure and average flow rate have also been obtained. This new mathematical study will certainly provide some new insights into the analysis of the hiatus hernia affected oesophagus.

The initial-boundary value problems (IBVPs) for the Korteweg-de Vries (KdV) equation on the interval $(0, q)$, where $q$ is a large positive number, are solved by the Inverse Scattering Method (ISM). By virtue of the appropriate setup of the associated scattering problem (SP), the fundamental equation in this inverse SP (ISP) is reduced to a system of linear algebraic equations. The known function in this equation describes only the discrete spectrum of the SP. The solution of this system completely describes the whole family of recovered potentials $y(x, t)$ in the linear Schrödinger equation (LSEq). By the unique solvability of the ISP, the recovered potential $y(x, t)$ is a solution of the considered IBVP. A class of various scattering data (SD) sets is derived from various pairs of prescribed initial and boundary conditions. A class $G$ of solutions of IBVPs on the interval $(0, q)$ is constructed from the class of various SD sets of SPs. The class of Bäcklund transformations (BTs) linking each solution of the IBVP in the class $G$ with its corresponding common solution of linear equations of the Lax pair is derived.

A six-compartment fractional model of hepatitis B was developed to analyze the transmission mechanisms of the infection, also taking into account the impact of the media on the population. Its biological validity was confirmed from an epidemiological point of view. The basic reproduction number, $ R_0 $, was determined using the new generation matrix method. A study of the asymptotic behavior around the equilibrium points showed that the model undergoes a transcritical bifurcation when $R_0 = 1,$ thus establishing $R_0$ as a critical threshold influencing the evolution of the epidemic. Fractional-order optimal control was applied, incorporating time-evolving prevention and treatment strategies. The results, validated by simulations using realistic parameters, revealed that the fractional approach offers superior performance. The application of prevention and treatment measures led to a progressive reduction in the number of cases and a decrease in the epidemic peak. The analysis was extended to a stochastic framework, incorporating white noise, to study the stochastic stability of the endemic equilibrium point. In addition, sensitivity indices were used to identify key parameters influencing $R_0,$, facilitating the development of disease control strategies. Numerical simulations corroborated the theoretical results obtained.

Malaria is a significant global health issue, particularly impacting infants and contributing to high mortality rates. The WHO report revealed that malaria control efforts in 2023 suffered from a $4 billion funding shortfall, receiving less than half of the $8.3 billion needed to meet global targets. An intermittent preventive treatment (IPT) program effectively prevents malaria, but no optimal cost-control approach has yet been studied with an IPT program. So, we present an optimal control model for malaria control that incorporates four key control parameters: preventing vertical transmission, an IPT program, treatment, and vector control. We categorize interventions into four groups to evaluate the effectiveness of malaria control: Group 1: single control; Group 2: two controls combined; Group 3: three controls combined; and Group 4: all four controls combined. We obtain that the IPT is the most effective and most cost-effective intervention in Group 1. In Group 2, the combination of IPT and vector control is the most effective, while the combination of vertical transmission prevention and IPT is the most cost-effective. In Group 3, the most effective strategy is the combination of IPT, treatment, and vector control, whereas the most cost-effective strategy is the combination of prevention of vertical transmission, IPT, and treatment. When all four controls are implemented together, we get the highest efficacy index of 97.32%. We obtain that the IPT program is the core control parameter in the most effective and economical policy among all four groups. This research aims to assist policymakers in developing effective malaria control strategies and to allocate resources efficiently for maximum impact.

Investigating the rotating convective instability of a magnetically-influenced Jefferey nanofluid is the goal of this work. For both stationary and oscillatory convection, a variety of parameters are graphically evaluated, including the Jeffery parameter ($\lambda$), Taylor number ($Ta$), nanoparticle Rayleigh number ($R_n$), adjusted diffusivity ratio ($N_A$), Lewis number ($Le$), and Hartman number ($Ha^2$). The impact of these parameters on stability analysis in the two forms of convection are investigated. The governing equations of the research are solved through the use of normal modes in both linear and weakly nonlinear analyses. By using these analyses, critical Rayleigh numbers for the beginning of oscillatory and stationary instability are found. The differential eigenvalue problem is solved using a one-term Galerkin technique in linear theory, whereas multiple scales analysis is used to study the weakly nonlinear theory.

This work studies a class of fractional nonlocal semilinear integro-differential control systems of order $\alpha \in (1,2)$ in Hilbert spaces. The dynamics are described by Caputo derivatives with nonlocal initial conditions. Using resolvent operators for fractional evolution equations, we provide sufficient conditions for the existence and uniqueness of mild solutions through the Banach fixed point theorem. The analysis assumes Lipschitz continuity and linear growth of the nonlinear term, boundedness of the associated operators, and admissibility of the control operator. An optimal control problem with a quadratic cost functional on a convex admissible control set is then considered. By applying minimizing sequence techniques, reflexivity of the control space, and weak lower semicontinuity arguments, the existence of an optimal control is established. An example for validation is included in the paper to further support the theoretical findings.

In this paper, we investigate the effect of gravity modulation on Darcy–Brinkman bioconvection in a porous medium saturated with a Newtonian fluid containing gyrotactic microorganisms. A weakly nonlinear stability analysis is performed to examine the oscillatory mode of convection under low-amplitude modulation. Heat transport is quantified using the mean Nusselt number, evaluated through a complex Ginzburg–Landau equation (CGLE). The CGLE is derived from a solvability condition at the lowest order of the perturbation parameter. The results are presented graphically to illustrate the impact of system parameters on bioconvection. Both the Vadasz number and the modulation amplitude are found to have a significant influence on heat transfer. Conversely, an increase in the modified bioconvection Rayleigh–Darcy number and cell eccentricity leads to a decrease in heat transfer. It is also found that the convective transport process is more strongly influenced by the irregular shapes of microorganisms than by spherical-shaped ones. Gravity modulation is found to be effective in controlling heat transfer, highlighting the role of external modulation in regulating transport processes within the system.

A four--degree--of--freedom nose landing gear (NLG) system is investigated, which has two time delays in the torsional and lateral bending damping of the strut. By applying a combination of numerical computations and qualitative theory of delay differential equations, the local stability of the trivial equilibrium is analyzed with three different time delay cases. It is further shown that the NLG system undergoes stability switches as the time delays vary, and these stability switches correspond to Hopf bifurcation points at critical time delays. Additionally, numerical results indicate that the NLG system exhibits various irregular motion transitions as the time delays increase, including periodic, multiperiodic, and even chaotic motions. These results highlight the profound impact of time delays on the shimmy amplitude, which leads to a detrimental effect on the stability of the NLG system. The analytical findings provide a theoretical insight into the stability design of NLG systems in the field of engineering applications.

Since the 1980s, HIV/AIDS has evolved from an acute epidemic into a manageable chronic condition, yet approximately 39 million people worldwide live with HIV, highlighting persistent gaps in epidemic control. In this research work, We develop a compartmental model of HIV/AIDS transmission incorporating pre-exposure prophylaxis (PrEP), post-exposure prophylaxis (PEP), condom usage, and antiretroviral treatment (ART). Mathematical analysis shows local asymptotic stability when the basic reproduction number $(R_{0H}) < 1$. The model exhibits backward bifurcation with imperfect prophylaxis, where endemic states persist even when $R_{0H} < 1$; this vanishes at 100% efficacy. Sensitivity analysis identified natural death rate, HIV-to-AIDS progression, contact rate, and AIDS-to-treatment progression as most influential parameters. Calibrated with South African data (2010-2023), the model predicts 28% reduction in new infections by 2033. Simulations show that high condom efficacy $(>80\%)$ combined with PrEP, PEP, and ART could reduce transmission by 75%, demonstrating the effectiveness of integrated prevention strategies.

Low-frequency underwater noise is a critical factor affecting ship stealth, which can be effectively mitigated by enhancing low-frequency vibration isolation and implementing chaotization control. This paper proposes a new cross-shaped quasi-zero-stiffness (C-QZS) structure to upgrade the traditional vibration isolation floating raft system (VIFRS). A nonlinear time-delay feedback controller is then introduced to induce chaos in the vibration responses. The specific research include: 1) establishing a dynamic model of the controlled C-QZS VIFRS and evaluating the low-frequency isolation performance of the C-QZS structure. 2) calculating the simple coded dispersion entropy (SCDE) of system responses to analyze the impacts of control parameters and excitation forces on controller performance. and 3) comparing the present study with the conventional nonlinear VIFRS. Results demonstrate that the C-QZS-based system outperforms its counterpart in chaotizing low-frequency vibration line spectra, requiring less energy input, exhibiting higher robustness, and achieving superior low-frequency isolation, thus better meeting practical engineering requirements.

We model the effect of vaccination on an epidemic by applying a discrete-time dynamical system defined by a nonlinear operator on the 3D simplex. Our study is conducted using a discrete susceptible-infected-recovered model with vaccination (SVIR). Our research focuses on the dynamical properties of this operator and the results obtained enable real-time forecasting. We find all fixed points and demonstrate that each fixed point is of non-hyperbolic type. Moreover, we show that every orbit approaches a fixed point.

This study investigates a discrete-time ecological system with one prey and two predators, incorporating modified Leslie-Gower (LG) type growth for the top predator. The system explores the intricate dynamics arising from the unique ecological interactions within the predator-prey framework. Notably, one predator is entirely reliant on the prey, while the top predator contends with a pronounced scarcity of its primary food source. This scarcity imposes constraints on the top predator's growth, leading to a complex interplay of population dynamics. Additionally, the growth of the middle predator is influenced by a fear effect induced by the top predator. The present study systematically explores various fixed points, delineating their stability dynamics and establishing threshold values for key parameters. Feasibility, local stability conditions of equilibria, and a comprehensive set of sufficient conditions for the global stability of the interior equilibrium point are identified. Analytical investigations uncover the existence of periodic points and one-parameter Hopf bifurcations. Furthermore, the research delves into the parameter ranges associated with different bifurcations, including a comprehensive examination of a two-parameter bifurcation scenario. The simultaneous impact of fear effect and intraspecific competition is explored, revealing a novel pattern in three-dimensional space. Two-parameter stability regions shed light on the system's complexity, highlighting the top predator's pivotal role in determining long-term species densities, contrary to the traditional emphasis on prey dependence. The study concludes by discussing the presence of chaos and its hybrid control within this ecological context.

This paper investigates the approximate controllability of a class of heterogeneous nonlinear networked systems, where each node may be affected by nonlinear perturbations of the Hölder type. We relax the exact controllability requirements and focus on establishing sufficient conditions under which approximate controllability holds. Using the Schauder's fixed point theorem, we establish conditions ensuring the system can be steered arbitrarily close to any desired final state. Numerical examples illustrate the theoretical findings.