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A stochastic model for making artificial rain using aerosols

Author

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  • Misra, A.K.
  • Tripathi, Amita

Abstract

In this paper, a nonlinear deterministic mathematical model along with its stochastic version for artificial rain is proposed and analyzed. We have considered three dynamical variables in the modeling process; namely (i) density of cloud droplets, (ii) density of raindrops, and (iii) concentration of mixture of conducive aerosols. It is assumed that the cloud droplets are continuously formed in the atmosphere at a constant rate but its conversion into raindrops does not take place in the same proportion. The artificially introduced aerosols increase the rate of formation of raindrops from cloud droplets. These aerosols are introduced in the regional atmosphere at a rate proportional to the density of cloud droplets. The proposed model is analyzed using stability theory of differential equations in deterministic as well as stochastic environment. Numerical simulation is performed to see the effect of important parameters on the process leading to rainfall.

Suggested Citation

  • Misra, A.K. & Tripathi, Amita, 2018. "A stochastic model for making artificial rain using aerosols," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 1113-1126.
    • Handle: RePEc:eee:phsmap:v:505:y:2018:i:c:p:1113-1126
    DOI: 10.1016/j.physa.2018.04.054
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    References listed on IDEAS

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    1. Zhang, Xinhong & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Dynamics of a stochastic SIS model with double epidemic diseases driven by Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 767-777.
    2. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
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