Pub Date : 2025-12-17DOI: 10.1134/S0021894425700026
A. A. Emelyanov, M. Yu. Plotnikov, N. I. Timoshenko, I. B. Yudin, V. Yu. Ul’yanitskii, I. S. Batraev
We present the results of an investigation on the erosive wear of polycrystalline diamond coatings grown on molybdenum substrates. Prior to diamond deposition, the molybdenum substrate surface was treated with a flow of alundum or silicon carbide microparticles. Diamond coatings were grown on the substrates via gas-jet deposition from a H2–CH4–Ar mixture activated in a microwave discharge. Substrate surface pretreatment has been shown to ensure an increase in the wear resistance of the diamond coatings.
{"title":"Effect of Substrate Surface Treatment on the Erosive Wear of Polycrystalline Diamond Coatings Produced by Gas-Jet Deposition","authors":"A. A. Emelyanov, M. Yu. Plotnikov, N. I. Timoshenko, I. B. Yudin, V. Yu. Ul’yanitskii, I. S. Batraev","doi":"10.1134/S0021894425700026","DOIUrl":"10.1134/S0021894425700026","url":null,"abstract":"<p>We present the results of an investigation on the erosive wear of polycrystalline diamond coatings grown on molybdenum substrates. Prior to diamond deposition, the molybdenum substrate surface was treated with a flow of alundum or silicon carbide microparticles. Diamond coatings were grown on the substrates via gas-jet deposition from a H<sub>2</sub>–CH<sub>4</sub>–Ar mixture activated in a microwave discharge. Substrate surface pretreatment has been shown to ensure an increase in the wear resistance of the diamond coatings.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":"66 3","pages":"440 - 445"},"PeriodicalIF":0.6,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145766264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-17DOI: 10.1134/S002189442570018X
Murilo Oliveira Alves Ferreira, Kaue Ribeiro dos Santos, Rogério Valentim Gelamo, Natália Bueno Leite Slade, Carlos Antônio Reis Baptista, Tiago José Pires de Oliveira, Haroldo Cavalcanti Pinto, Jéferson Aparecido Moreto
This research investigates the influence of Nb2O5 coatings, produced by using reactive sputtering technique, on the surface of middle-tension specimens M(T), regarding fatigue crack growth curves (da/dN versus ΔK) under exposure to a 0.6 mol L–1 NaCl saline solution. Results demonstrated the corrosion process occurred in the vicinity of the crack tip, where stresses are elevated, and significant plastic deformation prevails, notably influenced by slip bands that induce microcracks, exposing fresh material layers to the corrosive surroundings. The Nb2O5 coatings enhanced the fatigue-corrosion resistance of the 2198-T851 aluminium alloy. This study marks an initial step towards more comprehensive investigations into the impact of Nb2O5 coating on improving the mechanical properties of the 2198-T851 aluminium alloy.
本文研究了反应溅射法制备的Nb2O5涂层对中拉伸试样M(T)表面在0.6 mol L-1 NaCl盐溶液下疲劳裂纹扩展曲线(da/dN vs ΔK)的影响。结果表明,腐蚀过程发生在裂纹尖端附近,应力升高,明显的塑性变形盛行,特别是受诱发微裂纹的滑移带的影响,将新的材料层暴露在腐蚀环境中。Nb2O5涂层增强了2198-T851铝合金的抗疲劳腐蚀性能。本研究为更全面地研究Nb2O5涂层对改善2198-T851铝合金力学性能的影响迈出了第一步。
{"title":"Fatigue-Corrosion Studies on the 2198-T851 (Al–Cu–Li) Alloy Containing Nb2O5 Sputtered Coating","authors":"Murilo Oliveira Alves Ferreira, Kaue Ribeiro dos Santos, Rogério Valentim Gelamo, Natália Bueno Leite Slade, Carlos Antônio Reis Baptista, Tiago José Pires de Oliveira, Haroldo Cavalcanti Pinto, Jéferson Aparecido Moreto","doi":"10.1134/S002189442570018X","DOIUrl":"10.1134/S002189442570018X","url":null,"abstract":"<p>This research investigates the influence of Nb<sub>2</sub>O<sub>5</sub> coatings, produced by using reactive sputtering technique, on the surface of middle-tension specimens <i>M</i>(<i>T</i>), regarding fatigue crack growth curves (<i>da</i>/<i>dN</i> versus Δ<i>K</i>) under exposure to a 0.6 mol L<sup>–1</sup> NaCl saline solution. Results demonstrated the corrosion process occurred in the vicinity of the crack tip, where stresses are elevated, and significant plastic deformation prevails, notably influenced by slip bands that induce microcracks, exposing fresh material layers to the corrosive surroundings. The Nb<sub>2</sub>O<sub>5</sub> coatings enhanced the fatigue-corrosion resistance of the 2198-T851 aluminium alloy. This study marks an initial step towards more comprehensive investigations into the impact of Nb<sub>2</sub>O<sub>5</sub> coating on improving the mechanical properties of the 2198-T851 aluminium alloy.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":"66 3","pages":"620 - 632"},"PeriodicalIF":0.6,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145766260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-17DOI: 10.1134/S0021894425700038
G. S. Ganchenko, V. S. Shelistov, V. A. Popov, E. A. Demekhin
The paper presents the results of numerical simulation of the electrophoresis of a single spherical ion-selective granule in a viscoelastic electrolyte within the Oldroyd-B and FENE-CR fluid models. The study is limited to weak and moderate electric fields, which corresponds to electrophoresis of the first kind. The dependence of the granule’s electrophoretic velocity on the polymer concentration and relaxation time is obtained.
{"title":"Electrophoresis of an Ion-Selective Granule in Non-Newtonian Fluids in Moderate Electric Fields","authors":"G. S. Ganchenko, V. S. Shelistov, V. A. Popov, E. A. Demekhin","doi":"10.1134/S0021894425700038","DOIUrl":"10.1134/S0021894425700038","url":null,"abstract":"<p>The paper presents the results of numerical simulation of the electrophoresis of a single spherical ion-selective granule in a viscoelastic electrolyte within the Oldroyd-B and FENE-CR fluid models. The study is limited to weak and moderate electric fields, which corresponds to electrophoresis of the first kind. The dependence of the granule’s electrophoretic velocity on the polymer concentration and relaxation time is obtained.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":"66 3","pages":"446 - 456"},"PeriodicalIF":0.6,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145766308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-17DOI: 10.1134/S0021894425700063
B. S. Zlobin, V. V. Kiselev, A. A. Shtertser, I. S. Batraev
For 30KhGSA grade steel with different hardness, two methods of creating a weld by explosive welding of low-plastic materials without cracking have been experimentally investigated: 1) the use of welding modes that lead to the formation of a flat, waveless contact zone; 2) the use of a ductile intermediate layer, so that the welding modes corresponding to the strength properties of the material of this layer can be applyed. A scale of characteristic sizes has been constructed that marks the bounderies between the flow zones of the material with different strain rates and makes it possible to estimate the thickness of the plastic deformation localization band and the zone of intense plastic deformation. It is shown that the minimum thickness of the intermediate layer, at which it is not fragmented during joint plastic deformation of the welded plates, is determined by the thickness of the plastic deformation localization band. The principal possibility of explosive welding of plates with an intermediate layer produced by detonation spraying is shown for the first time.
{"title":"Explosive Welding of Low-Plastic Steels","authors":"B. S. Zlobin, V. V. Kiselev, A. A. Shtertser, I. S. Batraev","doi":"10.1134/S0021894425700063","DOIUrl":"10.1134/S0021894425700063","url":null,"abstract":"<p>For 30KhGSA grade steel with different hardness, two methods of creating a weld by explosive welding of low-plastic materials without cracking have been experimentally investigated: 1) the use of welding modes that lead to the formation of a flat, waveless contact zone; 2) the use of a ductile intermediate layer, so that the welding modes corresponding to the strength properties of the material of this layer can be applyed. A scale of characteristic sizes has been constructed that marks the bounderies between the flow zones of the material with different strain rates and makes it possible to estimate the thickness of the plastic deformation localization band and the zone of intense plastic deformation. It is shown that the minimum thickness of the intermediate layer, at which it is not fragmented during joint plastic deformation of the welded plates, is determined by the thickness of the plastic deformation localization band. The principal possibility of explosive welding of plates with an intermediate layer produced by detonation spraying is shown for the first time.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":"66 3","pages":"471 - 481"},"PeriodicalIF":0.6,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145766311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-17DOI: 10.1134/S0021894425700099
T. A. Ishmuratov, A. Ya. Davletbaev
An approach is presented for estimating the average acoustic velocity in the annulus of a mechanized well, which is subsequently used to determine the gas–liquid interface (dynamic level). This approach accounts for the distribution and variation of gas component analysis, thermobaric conditions, and the presence of phase transitions. The main step in solving the problem is to determine the gas composition distribution in the region from the wellhead to the gas–liquid interface. The approach is based on the laws of thermodynamics of equilibrium processes. The approach is tested in more than 100 wells at several fields in Western Siberia. The convergence of the testing results is verified by comparing them with field experimental measurements of acoustic velocity via acoustic well sounding.
{"title":"Calculating the Average Acoustic Velocity in the Annulus of a Mechanized Well","authors":"T. A. Ishmuratov, A. Ya. Davletbaev","doi":"10.1134/S0021894425700099","DOIUrl":"10.1134/S0021894425700099","url":null,"abstract":"<p>An approach is presented for estimating the average acoustic velocity in the annulus of a mechanized well, which is subsequently used to determine the gas–liquid interface (dynamic level). This approach accounts for the distribution and variation of gas component analysis, thermobaric conditions, and the presence of phase transitions. The main step in solving the problem is to determine the gas composition distribution in the region from the wellhead to the gas–liquid interface. The approach is based on the laws of thermodynamics of equilibrium processes. The approach is tested in more than 100 wells at several fields in Western Siberia. The convergence of the testing results is verified by comparing them with field experimental measurements of acoustic velocity via acoustic well sounding.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":"66 3","pages":"500 - 510"},"PeriodicalIF":0.6,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145766312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-17DOI: 10.1134/S0021894425700075
I. S. Gertsel, A. A. Golyshev
The study investigates the possibility of controlling the structural and phase state of the titanium matrix composite Ti–6Al–4V–B4C during direct laser deposition. A correlation has been established between the laser processing modes and the microstructure of the composite: variations in energy parameters lead to changes in the concentration of secondary phases (TiB, TiB2, TiC). In this work, synchrotron radiation was utilized for phase analysis, allowing for the determination of the phase composition of the composite through diffraction patterns. It was demonstrated that increasing the laser energy input affects the microhardness of the material, resulting in a 25% increase. The study also evaluates the efficacy of employing additional substrate heating to regulate the extent of dissolution of the initial ceramic particles within the metallic matrix by varying the laser radiation modes. Phase transformation analysis in the titanium matrix composite was performed using X-ray phase analysis with a synchrotron radiation source.
{"title":"Control of the Structural-Phase Composition of Titanium Matrix Composites during Direct Laser Deposition","authors":"I. S. Gertsel, A. A. Golyshev","doi":"10.1134/S0021894425700075","DOIUrl":"10.1134/S0021894425700075","url":null,"abstract":"<p>The study investigates the possibility of controlling the structural and phase state of the titanium matrix composite Ti–6Al–4V–B<sub>4</sub>C during direct laser deposition. A correlation has been established between the laser processing modes and the microstructure of the composite: variations in energy parameters lead to changes in the concentration of secondary phases (TiB, TiB<sub>2</sub>, TiC). In this work, synchrotron radiation was utilized for phase analysis, allowing for the determination of the phase composition of the composite through diffraction patterns. It was demonstrated that increasing the laser energy input affects the microhardness of the material, resulting in a 25% increase. The study also evaluates the efficacy of employing additional substrate heating to regulate the extent of dissolution of the initial ceramic particles within the metallic matrix by varying the laser radiation modes. Phase transformation analysis in the titanium matrix composite was performed using X-ray phase analysis with a synchrotron radiation source.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":"66 3","pages":"482 - 486"},"PeriodicalIF":0.6,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145766266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-17DOI: 10.1134/S0021894425700129
K. B. Sabitov, A. G. Khakimov
The frequency spectrum and modes of bending vibrations of rectangular plates in contact with a liquid or gas are determined. An expression is obtained for the distributed transverse load on a plate hinged along the contour. The surfaces of the plate are in contact with a medium of different density and pressure. The medium can be both compressible and incompressible. The effects of the average pressure, the curvature of the middle surface, and the added mass of the gas medium on the bending are determined.
{"title":"Effect of Ambient Pressure and Density on the Spectrum of Vibration Frequencies of Rectangular Plates Hinged along the Contour","authors":"K. B. Sabitov, A. G. Khakimov","doi":"10.1134/S0021894425700129","DOIUrl":"10.1134/S0021894425700129","url":null,"abstract":"<p>The frequency spectrum and modes of bending vibrations of rectangular plates in contact with a liquid or gas are determined. An expression is obtained for the distributed transverse load on a plate hinged along the contour. The surfaces of the plate are in contact with a medium of different density and pressure. The medium can be both compressible and incompressible. The effects of the average pressure, the curvature of the middle surface, and the added mass of the gas medium on the bending are determined.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":"66 3","pages":"546 - 559"},"PeriodicalIF":0.6,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145766310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-07DOI: 10.1134/S0021894425020166
K. A. Mushankova, L. V. Stepanova
This paper presents an overdeterministic algorithm for constructing the asymptotics of the stress field near the tip of a nanocrack in an anisotropic linear elastic body with cubic symmetry. A molecular dynamics solution of the problem of mixed loading (mode I fracture and transverse shear) of single-crystal copper and aluminum nanoplates with a central cut is described. Based on this solution, an asymptotic representation for the stress tensor components was derived. The atomistic stresses in the vicinity of the crack tip were calculated, and the coefficients of the series representing the stress field were determined using the values of the atomistic stress tensor components. The molecular dynamics calculations were performed for a temperature of 10 K to exclude the occurrence of nonlinear elastic deformation near the crack tip. The stress fields in the atomistic and analytical solutions were compared. The stresses at different distances from the nanocrack tip are in good agreement with the solutions of problems of classical macroscopic theory of anisotropic elasticity and can be described using a series that extends the Williams series to anisotropic media. In the series extended to anisotropic materials, the regular (nonsingular) terms are taken into account and the series coefficients of these terms are determined. It is shown that the developed algorithm can be used to effectively determine the coefficients of the higher-order terms of the series.
{"title":"Molecular Dynamics Calculations of Asymptotic Series Coefficients for Stress Fields","authors":"K. A. Mushankova, L. V. Stepanova","doi":"10.1134/S0021894425020166","DOIUrl":"10.1134/S0021894425020166","url":null,"abstract":"<p>This paper presents an overdeterministic algorithm for constructing the asymptotics of the stress field near the tip of a nanocrack in an anisotropic linear elastic body with cubic symmetry. A molecular dynamics solution of the problem of mixed loading (mode I fracture and transverse shear) of single-crystal copper and aluminum nanoplates with a central cut is described. Based on this solution, an asymptotic representation for the stress tensor components was derived. The atomistic stresses in the vicinity of the crack tip were calculated, and the coefficients of the series representing the stress field were determined using the values of the atomistic stress tensor components. The molecular dynamics calculations were performed for a temperature of 10 K to exclude the occurrence of nonlinear elastic deformation near the crack tip. The stress fields in the atomistic and analytical solutions were compared. The stresses at different distances from the nanocrack tip are in good agreement with the solutions of problems of classical macroscopic theory of anisotropic elasticity and can be described using a series that extends the Williams series to anisotropic media. In the series extended to anisotropic materials, the regular (nonsingular) terms are taken into account and the series coefficients of these terms are determined. It is shown that the developed algorithm can be used to effectively determine the coefficients of the higher-order terms of the series.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":"66 2","pages":"350 - 364"},"PeriodicalIF":0.6,"publicationDate":"2025-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145456212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-07DOI: 10.1134/S0021894425020178
E. I. Palchikov
Erosion of electrodes in a three-electrode pulsed X-ray tube with a rechargeable insulated electrode operating in the explosive emission mode at a voltage of 600 kV and pulsed current up to 1000 A was investigated. Erosion was produced by the action of high pulsed electric fields and pulsed flows of electrons and plasma during vacuum breakdown in X-ray tubes. X-ray fluorescence microanalysis using a scanning microscope revealed the presence of numerous metal balls of size 10–40 (mu )m formed from both the tungsten anode material and the material of the third insulated Kovar electrode. Several stages of detachment of the balls by the electric field were detected on the insulated electrode. The critical values of the Coulomb forces at which droplets arise in accordance with a dynamic model (taking into account the kinetic energy accumulated by the mass during the time of exposure to the electric field and surface energy) and the electric field pressures during the operation of the tube were estimated, allowing an explanation of the observed phenomena.
{"title":"Erosion of Electrodes in a Three-Electrode Pulsed X-Ray Tube with Explosive Emission","authors":"E. I. Palchikov","doi":"10.1134/S0021894425020178","DOIUrl":"10.1134/S0021894425020178","url":null,"abstract":"<p>Erosion of electrodes in a three-electrode pulsed X-ray tube with a rechargeable insulated electrode operating in the explosive emission mode at a voltage of 600 kV and pulsed current up to 1000 A was investigated. Erosion was produced by the action of high pulsed electric fields and pulsed flows of electrons and plasma during vacuum breakdown in X-ray tubes. X-ray fluorescence microanalysis using a scanning microscope revealed the presence of numerous metal balls of size 10–40 <span>(mu )</span>m formed from both the tungsten anode material and the material of the third insulated Kovar electrode. Several stages of detachment of the balls by the electric field were detected on the insulated electrode. The critical values of the Coulomb forces at which droplets arise in accordance with a dynamic model (taking into account the kinetic energy accumulated by the mass during the time of exposure to the electric field and surface energy) and the electric field pressures during the operation of the tube were estimated, allowing an explanation of the observed phenomena.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":"66 2","pages":"183 - 190"},"PeriodicalIF":0.6,"publicationDate":"2025-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145456543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-07DOI: 10.1134/S0021894425020014
R. Abazari, K. Yildirim
In this paper, we have approximated the solutions of the Cahn–Hilliard equation (CH) with the logarithmic potential function which arises in the modeling of phase separation of binary alloys. The CH equation is a high-order nonlinear equation, consequently, utilizing a common difference scheme on the CH equation causes long stencil schemes. To resolve the faults of long stencil schemes, we split the CH equation to second-order system under the Neumann boundary condition and we applied second-order scheme based on the 2D Crank–Nicolson method to discrete it. The uniqueness and error estimation of the approximated solution is proved. Also, preserving the conservation of mass and decreasing the total energy are investigated. Finally, to confirm the theoretical results, three examples with various initial conditions are presented.
{"title":"Numerical Study of the 2D Cahn–Hilliard Model of Phase Separation with Logarithmic Potential","authors":"R. Abazari, K. Yildirim","doi":"10.1134/S0021894425020014","DOIUrl":"10.1134/S0021894425020014","url":null,"abstract":"<p>In this paper, we have approximated the solutions of the Cahn–Hilliard equation (CH) with the logarithmic potential function which arises in the modeling of phase separation of binary alloys. The CH equation is a high-order nonlinear equation, consequently, utilizing a common difference scheme on the CH equation causes long stencil schemes. To resolve the faults of long stencil schemes, we split the CH equation to second-order system under the Neumann boundary condition and we applied second-order scheme based on the 2D Crank–Nicolson method to discrete it. The uniqueness and error estimation of the approximated solution is proved. Also, preserving the conservation of mass and decreasing the total energy are investigated. Finally, to confirm the theoretical results, three examples with various initial conditions are presented.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":"66 2","pages":"242 - 263"},"PeriodicalIF":0.6,"publicationDate":"2025-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145456604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}