Abstract

To reduce the pollution from the atmosphere or polluted cities like the capital city Delhi of India, use of artificial rain is a solution. In this paper, we have proposed and analyzed a nonlinear mathematical model to reduce the pollution level by rain making. In the proposed model five variables are considered, namely; (i) number density of water vapor, (ii) number density of cloud drops, (iii) number density of raindrops, (iv) cumulative concentration of aerosols, and (v) concentration of pollutant particles suspended in the region of consideration. The effect of environmental fluctuations has been studied with the help of Lyapunov functionals. The model is analyzed in the presence of white noise and proved that if rain persists, the pollutants can be totally washed out. It has been observed that the environmental disturbances are not much favorable in such experiments as the presence of environmental disturbance may destabilize the system. It is found that to remove pollutants completely, it is necessary to prevent the formation of pollutants. The simulation is performed to support the analytical findings.

摘要

为了减少大气污染或印度首都德里等污染城市，使用人工降雨是一种解决方案。在本文中，我们提出并分析了一个非线性数学模型，以降低降雨造成的污染水平。在所提出的模型中，考虑了五个变量，即；(i) 水汽的数密度，(ii) 云滴的数密度，(iii) 雨滴的数密度，(iv) 气溶胶的累积浓度，和 (v) 考虑区域内悬浮的污染物颗粒浓度。在 Lyapunov 泛函的帮助下研究了环境波动的影响。该模型在存在白噪声的情况下进行分析，证明如果持续下雨，污染物可以被完全冲刷掉。已经观察到，环境干扰在此类实验中不太有利，因为环境干扰的存在可能会破坏系统的稳定性。发现要彻底去除污染物，就必须防止污染物的形成。执行模拟以支持分析结果。