A NUMERICAL APPROACH STUDYING THE EFFECTS OF PRECIPITATION SCAVENGING ON STEADY-STATE DISPERSION OF AIR POLLUTANTS

The present paper demonstrates the applicability of finite element method of weighted residuals to study the effects of precipitation scavenging through raindrops on the steady-state dispersion of air pollutants in the atmosphere under realistic variable wind and diffusivity profiles.Here,the washout of pollutants by rain droplets is considered and the whole analysis for the pollutant concentration is carried out in two phases viz.gaseous phase and droplet phase.The model solutions are obtained by using local basis and asymmetric quadratic weighting functions which can provide a promising alternative to the standard Galerkin formulation for problems with advective and diffusive terms.The results of the model reveal that the precipitation scavenging by rain is quite effective in cleaning the polluted atmosphere.Anticipating the need of pollutant concentration in rain drops regarding acid precipitation(or acid rain),the concentration of the absorbed pollutant in the droplet phase are also analyzed.So,the present study provides an understanding on the concentration distribution of pollutant in gaseous and droplet phases,under the effects of variable wind and diffusivity profiles.

A New Approach on Mixed-Type Nondifferentiable Higher-Order Symmetric Duality

In this paper,a new mixed-type higher-order symmetric duality in scalar-objective programming is formulated.In the literature we have results either Wolfe or Mond–Weir-type dual or separately,while in this we have combined those results over one model.The weak,strong and converse duality theorems are proved for these programs underη-invexity/η-pseudoinvexity assumptions.Self-duality is also discussed.Our results generalize some existing dual formulations which were discussed by Agarwal et al.(Generalized second-order mixed symmetric duality in nondifferentiable mathematical programming.Abstr.Appl.Anal.2011.https://doi.org/10.1155/2011/103597),Chen(Higher-order symmetric duality in nonlinear nondifferentiable programs),Gulati and Gupta(Wolfe type second order symmetric duality in nondifferentiable programming.J.Math.Anal.Appl.310,247–253,2005,Higher order nondifferentiable symmetric duality with generalized F-convexity.J.Math.Anal.Appl.329,229–237,2007),Gulati and Verma(Nondifferentiable higher order symmetric duality under invexity/generalized invexity.Filomat 28(8),1661–1674,2014),Hou andYang(On second-order symmetric duality in nondifferentiable programming.J Math Anal Appl.255,488–491,2001),Verma and Gulati(Higher order symmetric duality using generalized invexity.In:Proceeding of 3rd International Conference on Operations Research and Statistics(ORS).2013.https://doi.org/10.5176/2251-1938_ORS13.16,Wolfe type higher order symmetric duality under invexity.J Appl Math Inform.32,153–159,2014).