Mathematical Models for Studying Environment Pollution Risks

The problem of longterm ecological prediction by means of mathematical modeling with available factual data on climate dynamics is discussed. The technique of quantitative estimates of risk/vulnerability on the basis of forward and inverse modeling and methods of the sensitivity theory is described. Examples of the calculated risk domains for Lake Baikal are given.     

Optimal forecasting of natural processes with uncertainty assessment

The problem of optimal forecasting of environmental changes induced by various factors is discussed. The proposed technique is based on variational principles and methods of the sensitivity theory with allowance for uncertainties in mathematical models and input data. Optimal forecasting is understood as forecasting where the estimates of cost functionals are independent of variations of the sought state functions. In addition to state functions, the forecasted characteristics include risk and vulnerability functions for receptor areas and quantification of uncertainties. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 156–166, March–April, 2009.     

Mathematical modeling of the motion of a portion of helium under pulsed injection over a fixed bed of cenospheres

A mathematical model is constructed and an analytical solution is obtained for the problem of a one-dimensional steady flow of a mixture of different gases with hollow permeable particles. The case of a one-dimensional unsteady flow of such a mixture is analyzed numerically. The numerical solutions are compared with experimental data on the motion of the peak concentration of helium in a fixed bed filled with cenospheres (solid hollow permeable spherical particles). The permeability of cenosphere walls and the drag coeficient of cenospheres in the gas flow are determined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 92–102, May–June, 2007.