Analysis of the Efficiency PETSc and PETIGA Libraries in Solving the Problem of Crystal Growth

We present an analysis of high performance computational method for solving the problem of crystal grows. The method uses PETSc and PETIGA C-language based libraries and supports parallel computing. The evolution of calculation process was studied in series of special computations are obtained on innovative mobile cluster platform, which provides exclusive system tuning abilities. The results of research confirm the high efficiency of the proposed algorithm on multi-core computer systems and allow us to recommend the use of PETSc and PETIGA for solving high order differential equations

Numerical scheme for solution of an approximation of Saint-Venant equation

In the work [4] the Saint-Venant's one-dimensional differential model and kinematic approximation describing the free movement of water in an open channel is under consideration. This model is widely used for the calculation of the flow of rivers in the various fields of engineering. Quality of engineering projects depends on the accuracy and speed of the mathematical calculations. This paper presents a promising method for the numerical solution of one approximation of the Saint-Venant's model. © 2014 Ilya Starodumov

Modeling and simulation of heat/mass transport, nucleation and growth kinetics in phase transformations

The present theme issue is devoted to recent trends and research directions in the phase transformation phenomena occurring in metastable and heterogeneous materials. All papers are concerned with modern theories, experiments, and computer simulations in the wide area of phase transformations. Particular attention is paid to traditional research domains representing the theoretical background for recent simulations and experiments that are as well specifically highlighted herein. Such rapidly developing research directions as phase-field modeling, laser treatment of surfaces, nanostructures, and influence of external fields on the microstructure formation are specially covered in this issue. © 2020, EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature

Simulation of electromagnetic parameters in a laboratory installation

The paper devoted to the numerical simulation of electromagnetic and heat transfer processes in laboratory installation with two concentric cylindrical electrodes and liquid metal. The electromagnetic and temperature fields of laboratory installation are presented. The results obtained for the laboratory installation can be used in the metallurgical industry for the simulation and optimization of electrometallurgical furnaces. © Published under licence by IOP Publishing Ltd.The authors acknowledge the support of the Russian Science Foundation under the project no. 19-79-00118

Simulation of the electromagnetic processes in a metallurgical furnace with two bottom electrodes

The paper presented electromagnetic processes occurring in an ore reduction furnace with two bottom electrodes. The physical and mathematical formulations of the problem are given, as well as the methodology and algorithm for the numerical simulation of the problem. © Published under licence by IOP Publishing Ltd.The authors acknowledge the support of the Russian Science Foundation under the project no. 19-79-00118

Distillation optimization: Parameterized relationship between feed flow rate of a steady-state distillation column and heat duties of reboiler and condenser

The paper considers the problem of maximum efficiency for the system of distillation columns. Columns in such systems are connected in parallel or sequential way. The mixture being separated is assumed to be close to ideal one. Authors parameterize the relationship between feed flow rate and heat duties of a steady-state binary distillation column using two parameters: the reversible efficiency and the irreversibility coefficient. This relationship is later being used to solve the problems of optimal distribution of heat and feed flows within the system. The results obtained allow one to estimate minimum heat energy demand for distillation of the given feed flow, maximum performance, and efficiency of the system. © 2022 John Wiley & Sons, Ltd.Robert Sterling Clark Foundation, RSCF: 20-61-46013This work is supported by RSCF Grant 20-61-46013

Influence of joule heat and heat of electric arc on the vortex flow in DC arc furnace

The paper devoted to the numerical simulation of processes in DC electric arc furnaces with the bottom electrode. These furnaces have shown higher efficiency, low heat loss, lower components wear and higher quality of steel production. The biggest disadvantage of such furnaces is a high rate of fettle wear near the bottom electrode that connected with electrovortex flow. Electrovortex flows appearing under electromagnetic forces as a result of non-homogeneous distribution of the current density through the liquid conductor. This effect can be observed in many technological processes: Electro slag remelting process (including DC and AC metallurgical furnaces, electrolysis cells and submerged-resistor induction furnaces), arc welding, processes of semiconductor crystals growing, electro vortex engines etc. © Published under licence by IOP Publishing Ltd.Russian Science Foundation, RSF: 19-79-00118The research was supported by Russian Science Foundation (project No. 19-79-00118)

Stochastic Model of Virus–Endosome Fusion and Endosomal Escape of pH-Responsive Nanoparticles

In this paper, we set up a stochastic model for the dynamics of active Rab5 and Rab7 proteins on the surface of endosomes and the acidification process that govern the virus–endosome fusion and endosomal escape of pH-responsive nanoparticles. We employ a well-known cut-off switch model for Rab5 to Rab7 conversion dynamics and consider two random terms: white Gaussian and Poisson noises with zero mean. We derive the governing equations for the joint probability density function for the endosomal pH, Rab5 and Rab7 proteins. We obtain numerically the marginal density describing random fluctuations of endosomal pH. We calculate the probability of having a pH level inside the endosome below a critical threshold and therefore the percentage of viruses and pH-responsive nanoparticles escaping endosomes. Our results are in good qualitative agreement with experimental data on viral escape. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.Funding: S.F. and N.K. were funded by EPSRC Grant No. EP/V008641/1. D.A. and I.S. were funded by the Ministry of Science and Higher Education of the Russian Federation (Project No. 075-15-2021-1002)

On the Theory of Directional Solidification in the Presence of a Mushy Zone

Abstract: A model is developed for the directional solidification of a binary melt with a two-phase zone (mushy zone), where the fraction of the liquid phase is described by a space–time scaling relation. Self-similar variables are introduced and the interphase boundary growth is inversely proportional to the square root of time. The mathematical model of the process is reformulated using self-similar variables. Exact self-similar solutions of heat-and-mass transfer equations are determined in the presence of two mobile phase-transition boundaries, namely, solid–mushy zone and mushy zone–liquid ones. The temperature and impurity concentration distributions in the solid phase, the mushy zone, and the melt are found as integral expressions. A decrease in the dimensionless cooled-boundary temperature leads to an increase in the solidification rate and the fraction of the liquid phase. The solidification rate, the parabolic growth constants, and the fraction of the liquid phase at the solid–mushy zone boundary are determined depending on the scaling parameter and the thermophysical constants of the solidifying melt. The positions of the solid–mushy zone and mushy zone–binary melt phase transition boundaries are found. The dependences of the solidification rate (inversely proportional to the square root of time) are analyzed. The scaling parameter significantly is shown to substantially affect the solidification rate and the fraction of the liquid phase in the phase transformation region. The developed model and the method of its solution can be generalized to the case of directional solidification of multicomponent melts in the presence of several phase transformation regions (e.g., main and cotectic two-phase zones during the solidification of three-component melts). © 2021, Pleiades Publishing, Ltd.This work was supported by the Russian Foundation for Basic Research (project no. 18-58-00034 Bel_a) and the Belarussian Foundation for Basic Research (project no. F18R-195)