Analysis of aerosol pollution processes in the vicinity of the Irkutsk aluminum plant

The issues of assessing the pollution fields in the vicinity of industrial enterprises are discussed according to the monitoring studies of the snow cover. The formulations of problems of low-parameter reconstruction of concentration fields are considered on the basis of model descriptions of the processes of transport of impurities in the surface layer of the atmosphere. With regard to the Irkutsk aluminum plant, the results of studies of the pollution of its surroundings with aluminum are presented. Using the data of route observations, a numerical reconstruction of the fluoride content in the snow cover was carried out. The quality control of the results obtained is carried out by comparing the measured and calculated concentrations of impurities at the control points of observation.

Inverse Problem for an Equation of the Reaction-Diffusion-Advection Type with Data on the Position of a Reaction Front: Features of the Solution in the Case of a Nonlinear Integral Equation in a Reduced Statement

The paper considers the features of numerical reconstruction of the advection coefficient when solving the coefficient inverse problem for a nonlinear singularly perturbed equation of the reaction-diffusion-advection type. Information on the position of a reaction front is used as data of the inverse problem. An important question arises: is it possible to obtain a mathematical connection between the unknown coefficient and the data of the inverse problem? The methods of asymptotic analysis of the direct problem help to solve this question. But the reduced statement of the inverse problem obtained by the methods of asymptotic analysis contains a nonlinear integral equation for the unknown coefficient. The features of its solution are discussed. Numerical experiments demonstrate the possibility of solving problems of such class using the proposed methods.

Numerical Reconstruction of Porous Architecture for Suspension Plasma Sprayed Coatings

The porous architecture of coatings has a significant influence on the coating performances and thus should be properly designed for the intended applications. For simulating the coating properties, it is necessary to determine the numerical representation of the coating microstructure. In this study, YSZ coatings were manufactured by suspension plasma spray (SPS). Afterwards, the porous architecture of as-prepared coatings was investigated by the combination of three techniques, imaging analysis, Ultra Small Angle X-ray Scattering (USAXS), and X-ray transmission. A microstructural model for reconstructing the porous architecture of the SPS coating was subsequently computed according to the collected experimental results. Finally, the coating thermal properties were simulated based on the model and were compared with the experimental results.

Pore Space Reconstruction of Shale Using Improved Variational Autoencoders

Pore space reconstruction is of great significance to some fields such as the study of seepage mechanisms in porous media and reservoir engineering. Shale oil and shale gas, as unconventional petroleum resources with abundant reserves in the whole world, attract extensive attention and have a rapid increase in production. Shale is a type of complex porous medium with evident fluctuations in various mineral compositions, dense structure, and low hardness, leading to a big challenge for the characterization and acquisition of the internal shale structure. Numerical reconstruction technology can achieve the purpose of studying the engineering problems and physical problems through numerical calculation and image display methods, which also can be used to reconstruct a pore structure similar to the real pore spaces through numerical simulation and have the advantages of low cost and good reusability, casting light on the characterization of the internal structure of shale. The recent branch of deep learning, variational auto-encoders (VAEs), has good capabilities of extracting characteristics for reconstructing similar images with the training image (TI). The theory of Fisher information can help to balance the encoder and decoder of VAE in information control. Therefore, this paper proposes an improved VAE to reconstruct shale based on VAE and Fisher information, using a real 3D shale image as a TI, and saves the parameters of neural networks to describe the probability distribution. Compared to some traditional methods, although this proposed method is slower in the first reconstruction, it is much faster in the subsequent reconstructions due to the reuse of the parameters. The proposed method also has advantages in terms of reconstruction quality over the original VAE. The findings of this study can help for better understanding of the seepage mechanisms in shale and the exploration of the shale gas industry.

Uniqueness and numerical reconstruction for inverse problems dealing with interval size search

<p style='text-indent:20px;'>We consider a heat equation and a wave equation in one spatial dimension. This article deals with the inverse problem of determining the size of the spatial interval from some extra boundary information on the solution. Under several different circumstances, we prove uniqueness, non-uniqueness and some size estimates. Moreover, we numerically solve the inverse problems and compute accurate approximations of the size. This is illustrated with several satisfactory numerical experiments.</p>