Browsing by Author "Ram Naresh"

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A nonlinear mathematical model to study the interactions of hot gases with cloud droplets and raindrops
(2009) Shyam Sundar; Ram Naresh; A.K. Misra; J.B. Shukla
In this paper, a nonlinear mathematical model is proposed and analyzed to study the interactions of hot gases with cloud droplets as well as with raindrops and their removal by rain from the stable atmosphere. The atmosphere, during rain, is assumed to consist of five nonlinearly interacting phases i.e. the vapour phase, the phase of cloud droplets, the phase of raindrops, the phase of hot gaseous pollutants and the absorbed phase of hot gases in the raindrops (if it exists). It is further assumed that these phases undergo ecological type growth and nonlinear interactions. The proposed model is analyzed using stability theory of differential equations and by numerical simulation. It is shown that the cumulative concentration of gaseous pollutants decreases due to rain and its equilibrium level depends upon the density of cloud droplets, the rate of formation of raindrops, emission rate of pollutants, the rate of falling absorbed phase on the ground, etc. It is noted here that if gases are very hot, cloud droplets are not formed and rain may not take place. In such a case gaseous pollutants may not be removed from the atmosphere due to non-occurrence of rain. © 2008 Elsevier Inc. All rights reserved.
How artificial rain can be produced? A mathematical model
(2010) J.B. Shukla; A.K. Misra; Ram Naresh; Peeyush Chandra
A non-linear mathematical model for rain making from water vapor in the atmosphere is proposed and analyzed. The model considers the process of artificial rain by introducing two kinds of aerosol particles conducive to nucleation of cloud droplets and formation of rain drops. The model analysis shows that, for uninterrupted rain, the water vapor in the atmosphere must be formed continuously with the required rate of rainfall. It is shown further that the intensity of rainfall increases as the concentrations of externally introduced aerosols, as well as the density of water vapor in the atmosphere, increase. Numerical simulation is also performed to see the effect of various parameters on the process of artificial rain making leading to rainfall. © 2009 Elsevier Ltd. All rights reserved.
Modeling the effect of time delay in controlling the carrier dependent infectious disease - Cholera
(2012) A.K. Misra; S.N. Mishra; A.L. Pathak; Peeyush Misra; Ram Naresh
A delay mathematical model for the control of cholera epidemic is proposed and analyzed. It is assumed that the disease spreads through carriers, which makes the human food contaminated by transporting bacteria from the environment. It is also assumed that insecticides are used to control the carriers with the rate proportional to the density of carriers. The analysis of model shows that the disease may be controlled by spraying insecticides but a longer delay in spraying insecticides may destabilize the system. Simulation is also carried out to support the analytical results. © 2012 Elsevier Inc. All rights reserved.
Modeling the effects of aerosols to increase rainfall in regions with shortage
(Springer-Verlag Wien, 2013) J.B. Shukla; Shyam Sundar; A.K. Misra; Ram Naresh
It is well known that the emissions of hot gases from various power stations and other industrial sources in the regional atmosphere cause decrease in rainfall around these complexes. To overcome this shortage, one method is to introduce artificially conducive aerosol particles in the atmosphere using aeroplane to increase rainfall. To prove the feasibility of this idea, in this paper, a nonlinear mathematical model is proposed involving five dependent variables, namely, the volume density of water vapour, number densities of cloud droplets and raindrops, and the concentrations of small and large size conducive aerosol particles. It is assumed that two types of aerosol particles are introduced in the regional atmosphere, one of them is of small size CCN type which is conducive to increase cloud droplets from vapour phase, while the other is of large size and is conducive to transform the cloud droplets to raindrops. The model is analyzed using stability theory of differential equations and computer simulation. The model analysis shows that due to the introduction of conducive aerosol particles in the regional atmosphere, the rainfall increases as compared to the case when no aerosols are introduced in the atmosphere of the region under consideration. The computer simulation confirms the analytical results. © 2013 Springer-Verlag Wien.
Modelling and analysis of the effects of aerosols in making artificial rain
(Springer Science and Business Media Deutschland GmbH, 2016) A.K. Misra; Amita Tripathi; Ram Naresh; J.B. Shukla
To overcome the water crisis for irrigation and other purposes, in this paper, we propose a non-linear mathematical model for artificial rain making by considering five dependent variables namely, water vapor density, densities of cloud droplets of small and large sizes, density of rain drops and cumulative concentration of mixture of aerosols of different sizes. It is assumed that these aerosols are conducive to the process of rain making, i.e. (a) the formation of small size cloud droplets from water vapors through the processes of nucleation and condensation, (b) changing them into large size cloud droplets through the processes of condensation, agglomeration, etc., and (c) changing these large cloud droplets into rain drops. The proposed model is analyzed using stability theory of differential equations. It is found that only one equilibrium is feasible and sufficient conditions for stability of such equilibrium are obtained. It is shown that the intensity of rainfall increases as the cumulative concentration of externally introduced aerosols in the atmosphere increases. Analysis reveals that for the continuous rainfall, it is necessary that water vapors must be continuously formed in the atmosphere. The numerical simulation of the model supports the analytical results. © 2016, Springer International Publishing Switzerland.
Modelling the Effect of Washout of Hot Pollutants for Increasing Rain in an Industrial Area
(Springer Science and Business Media Deutschland GmbH, 2023) Shyam Sundar; A.K. Misra; Ram Naresh; J.B. Shukla
In areas where hot gases and nanoparticulate materials are released uncontrollably from pollutants generating sources which are human population density dependent, the rainfall is significantly affected. When these hot gases and nanoparticulate materials mix with clouds, the cloud droplets evaporate, causing no rain or less intense rain. For increasing rain, the abatement of these pollutants is necessary and the washout of these pollutants by water drops is one of the effective removal mechanisms. Taking this into account, in this paper, a nonlinear mathematical model is proposed to analyse the effect of hot pollutants on rainfall and its control by washout of hot pollutants at sources of emission using spraying water droplets. To model the phenomenon, five nonlinearly interacting variables are considered namely densities of water vapours, clouds droplets, raindrops, the cumulative concentration of hot pollutants and the density of water drops introduced in the atmosphere to washout the hot pollutants. On analysing the model, using the stability theory of differential equations, it is found that the rain fall decreases as the cumulative concentration of hot pollutants increases. The spraying of water drops at the sources of emissions in the industrial area reduces the cumulative concentration of hot pollutants, which ultimately stimulates an increase in the density of raindrops in the atmosphere. Numerical simulation is also done to validate analytical results. © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.