Open Access
Math. Model. Nat. Phenom.
Volume 18, 2023
Article Number 1
Number of page(s) 16
Section Physics
Published online 06 January 2023
  1. O.M. Alifanov, Inverse Heat Transfer Problems. Springer-Verlag, Berlin (1994). [Google Scholar]
  2. N. Anento, A. Serra and Y. Osetsky, Effect of nickel on point defects diffusion in Fe-Ni alloys. Acta Mater. 132 (2017) 367-373. [CrossRef] [Google Scholar]
  3. I. Apyhtina, K. Kovaleva, A. Novikov, D. Orelkina, A. Petelin and E. Yakushko, Diffusion controlled grain boundary and triple junction wetting in polycrystalline solid metal. Defect Diffus. Forum 363 (2015) 127-129. [CrossRef] [Google Scholar]
  4. T. Beierling, R. Gorny and G. Sadowski, Modeling growth rates in static layer melt crystallization. Cryst. Growth Des. 13 (2013) 5229-5240. [CrossRef] [Google Scholar]
  5. A.C. Briozzo and M.F. Natale, Ona two-phase Stefan problem with convective boundary condition including a density jump at the free boundary. Math. Methods Appi. Sci. 43 (2020) 3744-3753. [CrossRef] [Google Scholar]
  6. J. Cheng, S. Lu and M. Yamamoto, Reconstruction of the Stefan-Boltzmann coefficients in a heat-transfer process. Inverse Prob. 28 (2012) 045007. [CrossRef] [MathSciNet] [Google Scholar]
  7. J. Cheng, Y. Xing, E. Dong, L. Zhao, H. Liu, T. Chang, M. Chen, J. Wang, J. Lu and J. Wan, An overview of laser metal deposition for cladding: defect formation mechanisms, defect suppression methods and performance improvements of laser-cladded layers. Materials (Basel, Switzerland) 15 (2022) 5522. [CrossRef] [PubMed] [Google Scholar]
  8. M.V. Chepak-Gizbrekht, Modeling of grain-boundary diffusion taking into account the grain shape. AIP Conf. Proc. 2167 (2019) 020050. [CrossRef] [Google Scholar]
  9. C. Evans, D. Indjin, Z. Ikonic, P. Harrison, M. Vitiello, V. Spagnolo and G. Scamarcio, Thermal modeling of terahertz quantum-cascade lasers: comparison of optical waveguides. IEEE J. Quantum Electr. 44. (2008) 680-685. [CrossRef] [Google Scholar]
  10. J. Fuller and E. Marotta, Thermal contact conductance of metal/polymer joints: an analytical and experimental investigation. J. Thermophys. Heat Transfer 15 (2001) 228-238. [CrossRef] [Google Scholar]
  11. R. Ghai, K. Chen and N. Baddour, Modeling thermal conductivity of porous thermal barrier coatings. Coatings 9 (2019) 101. [CrossRef] [Google Scholar]
  12. M.A. Gonik and F. Baltaretu, Problem of attaining constant impurity concentration over ingot height. Modern Electr. Mater. 4 (2018) 41-51. [CrossRef] [Google Scholar]
  13. A. Gupta, V. Kulitcki, B.T. Kavakbasi, Y. Buranova, J. Neugebauer, G. Wilde, T. Hickel and S.V. Divinski, Precipitate-induced nonlinearities of diffusion along grain boundaries in Al-based alloy. Phys. Rev. Mater. 2 (2018) 073801. [CrossRef] [Google Scholar]
  14. G.P. Grabovetskaya, I.P. Mishin, I.V. Ratochka, S.G. Psakhie and Yu. R. Kolobov, Grain boundary diffusion of nickel in submicrocrystalline molybdenum processed by severe plastic deformation. Tech. Phys. Lett. 34 (2008) 136-138. [CrossRef] [Google Scholar]
  15. S. Herth, T. Michel, H. Tanimoto, M. Egersmann, R. Dittmar, H.-E. Schaefer, W. Frank and R. Wurschum, Self-diffusion in nanocrystalline Fe and Fe-rich alloys. Defect Diffus. Forum 194-199 (2001) 1199-1204. [CrossRef] [Google Scholar]
  16. R. Jendrzejewski, I. Kreja and G. Sliwinski, Temperature distribution in laser-clad multi-layers. Mater. Sci. Eng. A 379 (2004) 313-320. [CrossRef] [Google Scholar]
  17. E.M. Kartashov and G.S. Krotov, Analytical solution of the single-phase Stefan problem. Math. Models Comput. Simul. 1 (2009) 180-188. [CrossRef] [MathSciNet] [Google Scholar]
  18. I. Kaur, Y. Mishin and W. Gust, Fundamentals of grain and interphase boundary diffusion. Wiley, Chichester (1995). [Google Scholar]
  19. A.G. Kesarev, V.V. Kondrat’ev and I.L. Lomaev, Description of grain-boundary diffusion in nanostructured materials for thin-fìlm diffusion source. Phys. Metals Metallogr. 116 (2015) 225-234. [CrossRef] [Google Scholar]
  20. Y.R. Kolobov, G.P. Grabovetskaya, M.B. Ivanov, A.P. Zhilyaev and R.Z. Valiev, Grain boundary diffusion characteristics of nanostructured nickel. Scr. Mater. 44 (2001) 873-878. [CrossRef] [Google Scholar]
  21. Yu.R. Kolobov, G.P. Grabovetskaya, K.V. Ivanov and M.B. Ivanov, Grain boundary diffusion and mechanisms of creep of nanostructured metals. Interface Science 10 (2002) 31-36. [CrossRef] [Google Scholar]
  22. Y.R. Kolobov, R.Z. Valiev, G.P. Grabovetskaya et al., Grain boundary diffusion and properties of nanostructured materials. Cambridge International Science Publishing, Cambridge, UK (2007), 250 p. [Google Scholar]
  23. V.V. Krasil’nikov and S.E. Savotchenko, Grain boundary diffusion patterns under nonequilibrium and migration of grain boundaries in nanoctructure materials. Bull. Russ. Acad. Sci.: Phys. 73 (2009) 1277-1283. [CrossRef] [Google Scholar]
  24. Z. Li, G. Yu, X. He, S. Li, H. Li and Q. Li, Study of thermal behavior and solidifìcation characteristics during laser welding of dissimilar metals. Res. Phys. 12 (2019) 1062-1072. [Google Scholar]
  25. K. Marquardt (nee Hartmann), E. Petrishcheva, E. Gardés et al., Grain boundary and volume diffusion experiments in yttrium aluminium garnet bicrystals at 1,723 K: a miniaturized study. Contrib. Mineral Petrol. 162 (2011) 739-749. [CrossRef] [Google Scholar]
  26. H. Mehrer, Diffusion in Solids. Fundamentals, Methods, Materials, Diffusion-Controlled Processes, Springer-Verlag, Berlin, Heidelberg (2007), p. 645. [Google Scholar]
  27. A.M. Meirmanov, The Stefan Problem, Walter de Gruyter, Berlin, Germany (1992). [Google Scholar]
  28. M.F. Natale and D.A. Tarzia, Explicit solutions to the one-phase Stefan problem with temperature-dependent thermal conductivity and a convective term. Int. J. Eng. Sci. 41 (2003) 1685-1689. [CrossRef] [Google Scholar]
  29. V. Niziev, F. Mirzade, V. Panchenko, M. Khomenko, R. Grishaev, S. Pityana and C. Rooyen, Numerical study to represent non-isothermal melt-crystallization kinetics at laser-powder cladding. Model. Numer. Simul. Mater. Sci. 3 (2013) 61-69. [Google Scholar]
  30. D. Prokoshkina, V. Esin, G. Wilde and S.V. Divinski, Grain boundary width, energy and self-diffusion in nickel: effect of material purity. Acta Mater. 61 (2013) 5188-5197. [CrossRef] [Google Scholar]
  31. A.O. Rodin and A. Khairullin, Ni grain boundary diffusion in Cu-Co alloys. Defect Diffus. Forum 363, (2015) 130-132. [CrossRef] [Google Scholar]
  32. S.E. Savotchenko, Peculiarities of recrystallization activated by a diffusion flow of an impurity from a thin-fìlm coating. Eur. Phys. J. B 94 (2021) 190. [CrossRef] [Google Scholar]
  33. S.E. Savotchenko, The nonlinear wave and diffusion processes in media with a jump change in characteristics depending on the amplitude of the fìeld distribution. Commun. Nonlinear Sci. Numer. Simul. 99 (2021) 105785. [CrossRef] [Google Scholar]
  34. S.E. Savotchenko, Models of activated recrystallization on isolated grain boundaries in polycrystals. Modern Phys. Lett. B 36 (2022) 2150536. [CrossRef] [Google Scholar]
  35. S.E. Savotchenko and A.N. Cherniakov, Diffusion from a constant source along nonequilibrium dislocation pipes. Int. J. Heat Mass Transfer 188 (2022) 122655. [CrossRef] [Google Scholar]
  36. S.E. Savotchenko and A.N. Cherniakov The nonlinear diffusion model of recrystallization. J. Heat Transfer 144 (2022) 064501. [CrossRef] [Google Scholar]
  37. S.E. Savotchenko, M.B. Ivanov and O.V. Yurova, Single-phase model of recrystallization of molybdenum activated by diffusion of nickel impurities. Russ. Phys. J. 50 (2007) 1118-1123. [CrossRef] [Google Scholar]
  38. L. Shumylyak, V. Zhykharevych and S. Ostapov, Modeling of impurities segregation phenomenon in the melt crystallization process by continuous cellular automata method. Prikladnaya diskretnaya matematika 31 (2016) 104-118. [CrossRef] [Google Scholar]
  39. L.N. Tao, The Stefan problem with an imperfect thermal contact at the interface. J. Appl. Mech. 49 (1982) 715-720. [CrossRef] [MathSciNet] [Google Scholar]
  40. D.A. Tarzia, Exact solution for a Stefan problem with convective boundary condition and density jump. PAMM Proc. Appl. Math. Mech. 7 (2007) 1040307-1040308. [CrossRef] [Google Scholar]
  41. W.A. Tiller, K. Jackson, J.W. Rutter and B. Chalmers, The redistribution of solute atoms during the solidifìcation of metals. Acta Metall. 1 (1953) 428-437. [CrossRef] [Google Scholar]
  42. C. Wang, M. He, X. Liua and J.A. Malen, Modeling the tunable thermal conductivity of intercalated layered materials with three-directional anisotropic phonon dispersion and relaxation time. J. Mater. Chem. C 10 (2022) 11686-11696. [CrossRef] [Google Scholar]
  43. T. Wei, Uniqueness of moving boundary for a heat conduction problem with nonlinear interface conditions. Appl. Math. Lett. 23 (2010) 600-604. [CrossRef] [MathSciNet] [Google Scholar]
  44. Y. Xian, P. Zhang, S. Zhai, P. Yang and Z. Zheng, Re-estimation of thermal contact resistance considering near-fìeld thermal radiation effect. Appl. Therm. Eng. 157 (2019) 113601. [CrossRef] [Google Scholar]
  45. G. Yang, M. Yamamoto and J. Cheng, Heat transfer in composite materials with Stefan-Boltzmann interface conditions. Math. Methods Appl. Sci. 31 (2008) 1297-1314. [CrossRef] [MathSciNet] [Google Scholar]
  46. L. Zhuo, D. Lesnic and S. Meng, Reconstruction of the heat transfer coefficient at the interface of a bi-material. Inverse Prob. Sci. Eng. 28 (2020) 374-401. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.