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The content of organic carbon is one of the essential factors that define soil quality. It is also notoriously challenging to model due to a multitude of biological and abiotic factors influencing the process. In this study, we investigate how decomposition of soil organic matter is affected by soil moisture and temperature. Soil organic carbon turnover is simulated by the CENTURY model. The accuracy of soil moisture data used is ensured by data assimilation approach, combing mathematical model and satellite retrievals. Numerical experiments demonstrate the influence of soil moisture regimes and climate on the quantity of soil humus stocks.

Purpose is to analyze distribution of granulometric composition of tuff as well as ultimate composition and identify dependence of its softening in the process of water saturation based upon a set of experiments to assess raw materials importance of the mineral. Methods. Laboratory experiments were carried out to determine ultimate composition of tuff extracted from different open pits of the region. Methods of mathematical statistics were applied to derive analytical dependences describing the tuff softening in the process of water saturation. The dependences denote logarithmic nature of the saturation increase along with the increase in the sample weight. Findings. It has been determined that tuff is a valuable mineral rather than basalt extraction waste. Thus, tuff needs both mining and complex approaches for processing and extracting of useful metals and silicates. Analytical dependences of tuff softening during water saturation have been defined. The dependences denote logarithmic nature of the saturation increase based upon a sample weight increment. Magnetic susceptibility of tuff, turned on magnetic field induction, has been identified. Dependences of distribution of technological indices (i.e. product yield, copper content and yield) in terms of granulometric-size class have been identified; the basic factors for crushing process have been determined; and regression dependences of grinder efficiency upon the input factors have been derived. Regression model of a crushing process of a general technological scheme of ore processing has been obtained involving the initial fragmentation using a jaw crusher, and additional fragmentation (i.e. reduction) using a sizer. Originality.It has been determined that magnetic susceptible tuff share is 49% of the sample weight; the remaining part is a silicate share. Logarithmic nature of the analytical softening dependences while water saturating has been identified. The above-mentioned denotes the increased saturation along with the increase in a sample weight. Practical implications. The definition of tuff ultimate composition as well as analytical softening dependences in the process of water saturation makes it possible to calculate the required water consumption. Keywords: tuff, basalt, softening, water saturation, silicate, magnetic susceptibility, ultimate composition, crushing

This paper deals with a nonlinear soil moisture transport problem, solved with addition of satellite observed soil moisture. The satellite data are assimilated into the model using Newtonian nudging method. Evaluation is done by the triple collocation method, which involves three independent data sources: model results, ground stations and ERA5 climatic data. The results testify that model results are nearly as accurate as the ground station measurements.

In this paper we study a mathematical model of soil moisture transport with variable porosity. The problem is set for the case of highly concentrated solute spilled onto soil surface. We investigate the way solute transfer, adsorption of contaminant by soil particles and variable porosity influence infiltration of solute into the soil profile. For that purpose, two models are used: a classical one and the one with consideration of mentioned factors. By comparing the results of both models, we established that high concentration of solute causes moisture transport to transpire more slowly, and the pollutant to remain on the soil surface for longer time. Numerical results indicate that porosity can vary considerably under the conditions of intensive contamination with salts.

The mathematical model of filtering with regard to colmatation and suffusion in the system bioplato-filter 2. This saturated porous medium is considered in terms of a complex heterogeneous system "fill"-"concentration of pollutants in porous liquid-concentration of colmatating particles. Vzaêmovplivi system parameters are taken into account through: 1) the dynamic change of the porosity of the backfill in the process of filtering; 2) nonlinear dependence coefficient filter porosity of backfill; 3) dependence of velocity of filtration coefficient of filtering and gradient heads, and hence – and porosity. Taking into account the following interplays allowed to increase the adequacy of mathematical models for the study of physical processes, however, led to the necessity of the study of nonlinear boundary value problems for systems of differential equations in partial derivatives. Nonlinearity of the boundary value problem does not allow to speak about her analytical solutions. Numerical solutions of the problems found by the method of finite elements with a software implementation of the relevant algorithms in FreeFem ++. Computer modeling showed that when taking into account nonlinear dependence coefficient of filtration from the concentration of colmatating particles and dynamic changes of porosity in the process of filtering, predictive performance bioplato for six months reduced by 25 % . Therefore, it is necessary to develop engineering solutions for reducing the influence of the colmatation-suffusion processes on the processes of filtering. The forecasting work bioplato relevant conduct on the design stage in order to implement predictive calculations. It is done by means of mathematical and computer modeling

The problem of pollution transfer by water flow in open channel was considered. The mathematical model of the problem was constructed. The numerical solution of the onedimensional boundary problem was obtained. The computational algorithm for solving the problem was programmed to implement. A series of numerical experiments with their further analysis was conducted.