{"title":"Electromagnetic force acting on the particles in conducting media","authors":"V. Ozernykh, I. Kolesnichenko","doi":"10.1063/5.0059558","DOIUrl":"https://doi.org/10.1063/5.0059558","url":null,"abstract":"This paper presents a numerical study of the electromagnetic field in a two-phase conductive medium composed of particles and liquid with different electrical conductivity. Different configurations are considered, in which the size of the region and the location and number of particles inside the cell with an electrically conductive liquid vary. Analysis of the results of the numerical experiments gives the characteristic ratios between the cell and particle sizes, at which the boundaries of the region have no impact on the force. It has been found that the force of interaction between two particles depends on the distance between them, and that the electromagnetic force acting on the particles is related to the electrical conductivity of the particles and liquid. The simulation results can be used as a basis for derivation of the constitutive relations needed to study the process of electromagnetic separation.","PeriodicalId":177478,"journal":{"name":"29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122989965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Numerical study of the influence of acoustic vibrations on the interaction in the ensemble of gas bubbles and solid particles in a liquid","authors":"V. Konovalov, T. Lyubimova","doi":"10.1063/5.0060293","DOIUrl":"https://doi.org/10.1063/5.0060293","url":null,"abstract":"In this work, we numerically investigate the capture of deposited solid particles by an ensemble of floating gas bubbles in a liquid that is subjected to the action of low-amplitude acoustic vibrations. The calculations were carried out for millimeter air bubbles in water with particle characteristics corresponding to the flotation process. It is shown that the pulsating field is significantly weakened inside the bubble ensemble as a result of the \"screening\" effect, which is fully manifested in the limit of a very high vibration frequency. However, pulsations of a high but finite frequency, taking into account the compressibility of the gas in the bubbles and with a sufficient intensity of their excitation, are able to penetrate deep into the volume of the liquid and thereby increase the area of particle capture.","PeriodicalId":177478,"journal":{"name":"29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES","volume":"16 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114059721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Mathematical modeling of the growth of an ellipsoidal particle in a supersaturated solution","authors":"M. Nikishina, D. Alexandrov","doi":"10.1063/5.0059601","DOIUrl":"https://doi.org/10.1063/5.0059601","url":null,"abstract":"Based on experimental data showing that crystal shapes are often far from spherical, it becomes important to find another more accurate way of constructing a theory of crystal growth in supersaturated solutions. Very often, during the study of the evolution of crystals, one can notice that their shape in most cases is close to ellipsoidal. That is why, in this article, this case is considered when the crystals have an ellipsoidal shape. The growth of an individual ellipsoidal crystal in a supersaturated solution at the stage of phase transition was studied. The growth rate of the volume of an ellipsoidal crystal, as a function of the current volume of the particle and supersaturation, is found explicitly. A mathematical model describing the growth of an ensemble of ellipsoidal particles in a supersaturated liquid is formulated. The graph demonstrating the relationship between the growth rate of a particle and its volume is plotted and analyzed. It is shown that the amount of impurity essentially affects the growth rate of ellipsoidal crystals. This rate increases with increasing the impurity concentration in the supersaturated mixture.","PeriodicalId":177478,"journal":{"name":"29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128424823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modeling surface growth of bone tissue","authors":"Yanina Izmaylova, A. Freidin","doi":"10.1063/5.0059595","DOIUrl":"https://doi.org/10.1063/5.0059595","url":null,"abstract":"","PeriodicalId":177478,"journal":{"name":"29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116354357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Transitional processes in linear stochastic parabolic and hyperbolic systems with constant delays","authors":"I. Poloskov","doi":"10.1063/5.0059644","DOIUrl":"https://doi.org/10.1063/5.0059644","url":null,"abstract":"","PeriodicalId":177478,"journal":{"name":"29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124191293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Propagation and stability of chemical reaction fronts in coupled problems of mechanochemistry","authors":"A. Freidin, A. Morozov, W. Müller","doi":"10.1063/5.0059711","DOIUrl":"https://doi.org/10.1063/5.0059711","url":null,"abstract":"","PeriodicalId":177478,"journal":{"name":"29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123912635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the formulation of the constitutive relations of a two-phase elastic-deformable saturated porous bilogical material","authors":"P. Trusov, N. Zaitseva, M. Tsinker","doi":"10.1063/5.0059556","DOIUrl":"https://doi.org/10.1063/5.0059556","url":null,"abstract":"","PeriodicalId":177478,"journal":{"name":"29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES","volume":"7 10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115311904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Validation of the Planar3D ELSA module for hydraulic fracturing simulation","authors":"E. Starobinskii, S. S. Barsukov, E. Shel","doi":"10.1063/5.0059571","DOIUrl":"https://doi.org/10.1063/5.0059571","url":null,"abstract":"","PeriodicalId":177478,"journal":{"name":"29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115321424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Theoretical limitations for aggregation methods of analysis based on affine interactions","authors":"D. Sotnikov, A. Berlina, A. Zherdev, B. Dzantiev","doi":"10.1063/5.0060806","DOIUrl":"https://doi.org/10.1063/5.0060806","url":null,"abstract":"","PeriodicalId":177478,"journal":{"name":"29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129672719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quasilinearization technique for solving nonlinear problems of solid mechanics","authors":"L. Stepanova, R. M. Zhabbarov","doi":"10.1063/5.0059706","DOIUrl":"https://doi.org/10.1063/5.0059706","url":null,"abstract":"","PeriodicalId":177478,"journal":{"name":"29TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES","volume":"254 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121287573","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}