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RESEARCH PRODUCT

A Langevin Approach to the Diffusion Equation

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We propose a generalized Langevin equation as a model for the diffusion equation of air pollution in the atmosphere. We write down a partial stochastic differential equation for the pollutant concentration, which we solve exactly obtaining the first and the second moment of the pollutant concentration. We obtain a linear multiplicative stochastic differential equation for the Fourier components of the concentration, which can be used to calculate higher moments of the concentration. We obtain the exact steady state solution in the case of neutral atmosphere and a general expression of the mean concentration as a function of the fluctuation intensity of the wind speed, the diffusion coefficients and their derivatives. We also obtain the asymptotic expression of the mean concentration along the x axis and functional forms of the mean concentration for different laws of the diffusion coefficient.