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The accurate characterization of particle size and morphology is crucial across numerous scientific and industrial fields. While microscopy is a powerful tool for visualizing particle geometry, traditional image analysis often relies on basic parameters like area and equivalent circular diameter, which are insufficient for describing non-spherical or complex particles. This paper presents a novel methodology for the analysis of particles from micrographs, combining deep learningbased segmentation with parametric polygon approximation. Optical microscopy images were obtained for model systems of increasing complexity: monodisperse polystyrene spheres, SAPO-34 cubes, ZSM-5 hexagonal prisms, and a multi-component mixture of all three. Neural network segmentation was performed using the DLgram01 cloud service, trained on manually annotated images. A custom Python program was developed to process the resulting segmentation polygons. The core of the method involves fitting a parameterized polygon to each segmented particle’s contour. The optimal value of geometric parameters for each particle is determined by minimizing a “dissimilarity” function that measures the discrepancy between the segmentation and the parametric shape. This approach was validated on the simple spherical system, yielding a size distribution consistent with conventional projected diameter methods. For more complex cubic SAPO-34 particles, the rectangle fit revealed deviations from the ideal shape, providing a more complete morphological description than using a single size parameter. In the mixture of particles, the method successfully classified and extracted distinct parameter distributions for each particle type. The results for each class in the mixture were statistically consistent with those obtained from the single-component systems, demonstrating the method’s robustness and accuracy. The proposed methodology provides a powerful and universal tool for automated, high-throughput particle analysis, enabling the extraction of detailed shape parameters and the construction of comprehensive size and morphology distributions for complex particulate systems.

This article is devoted to the problem of mathematical modeling of nonferrous metal casting and investigation of the influence of main technological parameters on the cooling process of continuously casted copper under down-draw and up-draw.

Numerical calculations of structures and vibrational spectra of small water clusters are performed by solution of the molecular Schrodinger equation in the density functional theory framework using B3LYP and X3LYP hybrid functionals. Spectral features and evolution of hydrogen bond properties in clusters with their size increasing are discussed. The vibrotational Hamiltonian parameters and Fermi and Darling-Dennison anharmonic resonances in small water oligomers are determined. Obtained results may be used in quantum mechanics/molecular dynamics simulations of water and processes in active site of enzyme.

The paper describes the results of computer simulation of time-dependent temperature fields arising in polar dielectrics irradiated by focused electron bunches with average electron energy when analyzing with electron microscopy techniques. The mathematical model was based on solving several-dimensional nonstationary heat conduction equation with use of numerical finite element method. The approximation of thermal source was performed taking into account the estimation of initial electron distribution determined by Monte-Carlo simulation of electron trajectories. The simulation program was designed in Matlab. The geometrical modeling and calculation results demonstrated the main features of model sample heating by electron beam were presented at the given experimental parameters as well as source approximation.

The article is dedicated to mathematic modeling of natural water desalination process by method of thermal distillation. The article gives the equations which allow describing the processes of film flowing and boiling of water, steam condensation and vacuum maintenance. The article presents the algorithm of calculation, implemented in MatLab computer mathematic system and Excel electronic tables, and the initial data required for the calculation. The model has been checked for adequacy. The calculation of ten-effect distillation system is given. The results of work can be used in design and optimization of process conditions for distillation systems.

The problem of accumulation and the statistical analysis of computer experiment results are solved. The main experiment program is considered as the data source. The results of main experiment are collected on specially prepared sheet Excel with pre-organized structure for the accumulation, statistical processing and visualization of the data. The created method and the program are used at efficiency research of the scientific researches which are carried out by authors.

An algorithm of applied problem solving was described to calculate electrical characteristics of electrical field effects in ferroelectrics electron-beam charged. The algorithm was based on implementation of the deterministic model using finite element method as well as taking into account Monte-Carlo simulation results of electron transport. The program application was developed to perform computing experiments.

WS-BPEL is a widely accepted standard for specification of business distributed and parallel processes. This standard is a mismatch of algebraic and Petri net paradigms. Following that, it is easy to specify WS-BPEL business process with unwanted features. That is why the verification of WS-BPEL business processes is very important. The intent of this paper is to show some possibilities for conversion of a WS-BPEL processes into more formal specifications that can be verified. CSP and Z-notation are used as formal models. Z-notation is useful for specification of abstract data types. Web services can be viewed as a kind of abstract data types.

The article describes the state of the art computer simulation in the field of metal forming processes, the main problem points of traditional methods were identified. The method, that allows to predict the deformation distribution in the volume of deformable metal with taking into account of microstructure behavioral characteristics in deformation load conditions, was described. The method for optimizing computational resources of multiscale models by using statistical similar representative volume elements (SSRVE) was presented. The modeling methods were tested on the process of single pass drawing of round rod from steel grade 20. In a comparative analysis of macro and micro levels models differences in quantitative terms of the stress-strain state and their local distribution have been identified. Microlevel model also allowed to detect the compressive stresses and strains, which were absent at the macro level model. Applying the SSRVE concept repeatedly lowered the calculation time of the model while maintaining the overall accuracy.

In this article the model of strong replicas agreement was analyzed. The process of preparing and conducting the nature experiment in the cloud in order to proof the model adequacy was described. Specifications of the program for implementation of database access to the NoSQL system and the program for handling journals were presented. One part of obtained experiments results was used for model adaptation, another part — for adequacy evaluating. The adequacy analysis is presented.