Kaushik Dehingia

This work proposes a new mathematical model incorporating allelopathy into the dynamic interaction between phytoplankton and zooplankton populations. The proposed nonlinear system is formulated to investigate how allelopathic effects influence the long-term behavior of the aquatic ecosystem. We first establish the model’s basic mathematical properties, including the existence, positivity, and boundedness of solutions, to ensure biological relevance. The equilibrium points of the system are then determined, and their local stability is also investigated. Furthermore, conditions for Hopf bifurcation are derived to examine the emergence of periodic oscillations in population dynamics. Numerical simulations are carried out to support the analytical results and illustrate the influence of model parameters on system behavior. The findings indicate that allelopathic interactions can significantly affect the stability and coexistence of phytoplankton and zooplankton populations, providing valuable insights into aquatic ecosystem dynamics.

This paper presents a mathematical prey-predator model to investigate the intricate, non-linear relationships between phytoplankton, zooplankton, and fish in a marine ecosystem. The model incorporates fundamental ecological processes, including logistic phytoplankton growth, zooplankton grazing on phytoplankton, and fish predation on zooplankton. Additionally, we consider the impact of extreme environmental pressures, including a fear effect, on the marine ecosystem. First, we examine the positivity and boundedness of the proposed model. Furthermore, all the equilibrium points are determined, and the local stability of the system is analyzed around each equilibrium point. The research also explores the impact of rising environmental pressure on population sizes among species. It concludes that greater environmental pressure could drive the system to extinction via a branch point bifurcation. Minimal environmental pressure will destabilize the system via a Hopf bifurcation. We also explore the impact of the fear cost on the zooplankton population and conclude that greater fear costs can cause system instability via another Hopf bifurcation. Theoretical calculations are confirmed by numerical simulations carried out using Mathematica and MATLAB software.

Despite the purely inorganic Cu2AgBiI6 double perovskite being promising in thermal and moisture stability and environment friendly, the poor charge separation and non-radiative carrier recombination hamper its photo conversion efficiency (PCE). In this work, a ferroelectric polymer P(VDF-TrFE) is employed in the perovskite film of a solar cell with a co-crystalline process. The ferroelectric behavior of the perovskite film after the incorporation of P(VDF-TrFE) polymer is analyzed using Piezoresponse Force Microscopy (PFM). Through the ferroelectric polarization effect, both the short-circuit current (Jsc) and open-circuit voltage (Voc) are significantly enhanced and consequently, the PCE is increased to 1.92%.

Despite the purely inorganic Cu2AgBiI6 double perovskite being promising in thermal and moisture stability and environment friendly, the poor charge separation and non-radiative carrier recombination hamper its photo conversion efficiency (PCE). In this work, a ferroelectric polymer P(VDF-TrFE) is employed in the perovskite film of a solar cell with a co-crystalline process. The ferroelectric behavior of the perovskite film after the incorporation of P(VDF-TrFE) polymer is analyzed using Piezoresponse Force Microscopy (PFM). Through the ferroelectric polarization effect, both the short-circuit current (Jsc) and open-circuit voltage (Voc) are enhanced significantly enhanced. Consequently, the PCE is increased to 1.92%, which is one of the highest PCE recorded till date in Cu-based perovskite solar cells.

In this study, we review several existing works on mathematical modeling and optimal control strategies based on differential equations for controlling CO2 emissions. Global warming and climate change are among the most pressing issues of the twenty-first century. The CO2 emissions from various anthropogenic and natural sources enhance the global average temperature by trapping a significant amount of heat in the inner layer of Earth’s atmosphere. Several mitigation strategies have been proposed to reduce CO2 concentration. However, due to economic and budgetary limitations, optimal control theory is widely adopted in mathematical modeling to design economically feasible strategies for reducing CO2 concentration in the atmosphere while minimizing the implementation cost. Optimization theory plays an integral role in environmental mathematical modeling by identifying effective strategies for controlling CO2 emission along with economic development. This study illustrates the need for further investigation through the development and analysis of more mathematical models to understand the dynamical interaction between CO2 emissions and various natural and anthropogenic sources. Also, the implementation and evaluation of various control strategies are required for effectively mitigating CO2 emissions. Moreover, the existing literature makes limited use of fractional-order differential equations in this domain. The adoption of this framework enables a more comprehensive characterization of the dynamics of carbon dioxide within the environment, as it captures memory-dependent processes that are not adequately described by the classical integer-order models.

The flow of copper (Cu), silver (Ag), titanium oxide (TiO2), copper oxide (CuO) nanoparticles with water as a base fluid in the presence of a high magnetic field in a vertical rectangular duct are examined in this research. The duct's left and right walls are kept at various steady temperatures and concentrations. The temperature, velocity, and nanoparticle concentration fields are all described by the transport equations. The second-order upwind method, an explicit finite-difference method (EFDM), is used to discretize the coupled nonlinear Navier-Stokes equations. To examine the heat transfer efficiency of this nanofluid, we nondimensionalized the governing equations and obtained solutions using an explicit numerical scheme. MATLAB code is used to perform computational steps. We have plotted the velocity, temperature, and concentration fields for different values of the magnetohydrodynamic (MHD) flow parameters, including the thermal Grashof number (Gr), solutal Grashof number (Gc), Hartmann number (Ha), electrical field load parameter (E), Brinkman number (Br), and nanoparticle volume fraction (ϕ).