Browsing by Author "Alok Kumar Agrawal"

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Effects of human population and forestry trees on the hydrologic cycle: A modeling-based study
(American Institute of Mathematical Sciences, 2025) Gauri Agrawal; Alok Kumar Agrawal; Arvind Kumar
The hydrologic cycle is increasingly disrupted due to the rising human population and the associated decline in forest trees. The rationale of this work was to address the disruption in the hydrologic cycle, which is caused by the dual adverse effects of human population growth: reducing forestry trees and diminishing clouds’ formation. The proposed model assumes that the density of forestry trees decreases due to harvesting activities to fulfill the resource demands of human population. Additionally, it posits that the transpiration from forestry trees contributes to an increased density of vapor clouds’ formation, while population growth adversely impacts the natural formation rate of vapor clouds. The model was analyzed by employing qualitative analysis, demonstrating the feasibility and stability of equilibrium solutions. Furthermore, to capture the consequences of environmental fluctuations on the model’s dynamics, the proposed deterministic model was extended to a stochastic framework. The analytical and numerical work sought to provide the directives for understanding and mitigating the adverse effects of human activities on the hydrologic cycle, promoting sustainable practices to restore ecological equilibrium. Results of the model analysis reveal that an increase in human population leads to a decline in both rainfall and forestry trees. However, reforestation with high–transpiration tree species can mitigate rainfall decline and restore balance to the hydrologic cycle. Moreover, the maximum density of forest trees is achieved when the utility of rain by the forest trees and the natural formation of vapor clouds are maximal. Also, the minimal anthropogenic hindrance in reducing the natural formation of vapor clouds, combined with the maximal efficiency of vapor clouds to naturally convert into raindrops, facilitates maximum rainfall. © 2025 the Author(s)
Modeling the impact of air and water pollutants emitted from industries on rainfall
(World Scientific, 2025) Gauri Agrawal; Alok Kumar Agrawal; Arvind Kumar Misra
Rainfall regulates the hydrological cycle on the planet Earth, sustains our ecological system, and provides fresh water to all living beings. In the recent past, a deterioration in rainfall has been observed due to the increased level of pollutants emitted by industries in the environment. The presence of these industrial pollutants in the environment affects the processes of evaporation, condensation, and nucleation, requisite in forming cloud droplets and raindrops. In formulating the model, we categorize the total emissions of industrial pollutants into surface water pollutants and atmospheric pollutants in the environment to assess their effect explicitly on rainfall. We presume the natural formation rate of cloud droplets as a decreasing function of surface water pollutants. It is further assumed that the density of cloud droplets decreases due to atmospheric pollutants; and the surface water pollutants in regional water bodies increase due to the leaching of atmospheric pollutants during rainfall. To analyze the formulated model system, we use the qualitative theory of differential equations. The equilibrium solution is obtained, and its stability properties are discussed. The numerical analysis is performed to substantiate the analytically obtained results of the formulated mathematical model. The obtained results clearly show that industrial pollutants emitted into the environment exert a negative impact on rainfall. © 2025 World Scientific Publishing Company.
Modeling the impacts of chemical substances and time delay to mitigate regional atmospheric pollutants and enhance rainfall
(Elsevier B.V., 2025) Gauri Agrawal; Alok Kumar Agrawal; Arvind Kumar Misra
Rainfall, a crucial process of the hydrological cycle, involves the condensation of atmospheric cloud droplets into raindrops that fall on the Earth's surface, providing essentials for human well-being and ecosystem. Research studies show that the condensation–nucleation process for forming raindrops is reduced due to atmospheric pollutants. In this scenario, introducing chemical substances may effectively mitigate regional atmospheric pollution, and reduced atmospheric pollution may lead to adequate rainfall. In the present research work, we analyze rainfall dynamics using a modeling approach with the incorporation of a time lag involved between measuring the data for atmospheric pollution and introducing chemical substances in the regional atmosphere. Here, we assume the formation rate of cloud droplets as a decreasing function of atmospheric pollutants. It is also assumed that introducing chemical substances reduces regional atmospheric pollution. Involving time delay as a bifurcation parameter, we analyze the stability, direction, and period of the bifurcating periodic solutions arising through Hopf bifurcation. Along with this, the presented numerical simulations corroborate the analytical results of our mathematical model. The modeling study reveals that the use of chemical substances in proportion to the concentration of atmospheric pollutants measured at time (t−τ) becomes crucial to mitigate the atmospheric pollutants because as time delay exceeds a threshold value, the system loses its stability and undergoes Hopf bifurcation. © 2025 Elsevier B.V.