Vladimir Danilov
- Laboratory Head:Centre for Fundamental Studies / Laboratory of Mathematical Methods in Natural Science
- Research Professor, Leading Research Fellow:HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE) / School of Applied Mathematics
- Vladimir Danilov has been at HSE University since 2012.
Education, Degrees and Academic Titles
- 1990Professor
- 1990
Doctor of Sciences* in Mathematical Modelling, Numerical Methods and Software Complexes
Lomonosov Moscow State University
Thesis Title: Mathematical Modelling of Heat and Mass Transfer - 1972
Degree
Moscow Institute of Electronic Engineering
* Doctor of Sciences
A post-doctoral degree called Doctor of Sciences is given to reflect second advanced research qualifications or higher doctorates in ISCED 2011.
A post-doctoral degree called Doctor of Sciences is given to reflect second advanced research qualifications or higher doctorates in ISCED 2011.
Courses (2023/2024)
- Mathematical models of nonlinear processes (Optional course (faculty); HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 1 module)Rus
- Past Courses
Courses (2022/2023)
- Analysis of nonlinear and multiphase processes (Master’s programme; HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 1 year, 3, 4 module)Rus
- Mathematical models of nonlinear processes (Optional course (faculty); 1, 2 module)Rus
Courses (2021/2022)
- Analysis of nonlinear and multiphase processes (Master’s programme; HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 1 year, 3, 4 module)Rus
- Mathematical models of nonlinear processes (Optional course (faculty); HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 1, 2 module)Rus
Courses (2020/2021)
- Contemporary Methods for Data Analysis: Analysis of Nonlinear and Multiphase Processes (Master’s programme; HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 1 year, 3, 4 module)Rus
- Mathematical models of nonlinear processes (Bachelor’s programme; HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 4 year, 1, 2 module)Rus
Courses (2019/2020)
- Asymptotic Methods Non-linear Processes Research (Bachelor’s programme; HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 4 year, 1, 2 module)Rus
- Contemporary Methods for Data Analysis: Analysis of Nonlinear and Multiphase Processes (Master’s programme; HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 1 year, 3, 4 module)Rus
- Research Seminar (Master’s programme; HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 2 year, 1-3 module)Rus
Courses (2018/2019)
- Asymptotic Methods Non-linear Processes Research (Bachelor’s programme; HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 4 year, 1, 2 module)Rus
- Calculus (Bachelor’s programme; HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 1 year, 1-4 module)Rus
- Contemporary Methods for Data Analysis: Analysis of Nonlinear and Multiphase Processes (Master’s programme; HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 1 year, 3, 4 module)Rus
- Research Seminar (Master’s programme; HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 1 year, 1-4 module)Rus
Courses (2017/2018)
- Asymptotic Methods Non-linear Processes Research (Bachelor’s programme; HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 4 year, 1, 2 module)Rus
- Calculus (Bachelor’s programme; HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 1 year, 1-4 module)Rus
- Contemporary Methods for Data Analysis: Analysis of Nonlinear and Multiphase Processes (Master’s programme; HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 1 year, 3, 4 module)Rus
- Research Seminar (Master’s programme; HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 1 year, 1-4 module)Rus
- Research Seminar (4th year) (Bachelor’s programme; HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE); 4 year, 1, 2 module)Rus
20232
- Article Danilov V., Gaydukov R. Ice-water phase transition on a substrate // Russian Journal of Mathematical Physics. 2023. Vol. 30. No. 2. P. 165-175. doi
- Article Гайдуков Р. К., Данилов В. Г., Фонарева А. В. Моделирование таяния-намерзания льда в задаче обтекания жидкостью малой неровности // Известия РАН. Механика жидкости и газа. 2023. № 5. С. 82-94. doi
20223
- Article V. G. Danilov, R. K. Gaydukov. Asymptotic multiscale solutions to Navier–Stokes equations with fast oscillating perturbations in boundary layers // Russian Journal of Mathematical Physics. 2022. Vol. 29. No. 4. P. 431-455. doi
- Article Р. К. Гайдуков, В. Г. Данилов Асимптотические решения задач обтекания с двухпалубными структурами пограничного слоя // Математические заметки. 2022. Т. 112. № 4. С. 521-533. doi
- Chapter Гайдуков Р. К., Данилов В. Г., Фонарева А. В. Моделирование фазовых переходов при обтекании малой неровности // В кн.: Волны и вихри в сложных средах: 13-ая международная конференция – школа молодых ученых; 30 ноября – 02 декабря 2022 г. М. : ООО «ИСПО-принт», 2022. С. 68-71.
20211
Article Danilov V., Rakhel M. Development of Maslov’s Approach to the Construction of Nonoscillating WKB-Type Solutions // Russian Journal of Mathematical Physics. 2021. Vol. 28. No. 2. P. 179-187. doi
20202
- Book Danilov V., Gaydukov R., Vadim Kretov. Mathematical Modeling of Emission in Small-Size Cathode. Springer, 2020. doi
- Article Danilov V. Weak Asymptotics Method Approach to the Problem of δ-Shock Wave Interactions // Mathematical notes. 2020. Vol. 108. No. 1. P. 29-38. doi
20194
- Article Danilov V. Averaging under Rayleigh-Taylor instability and density mushy region generation // European Journal of Mechanics - B/Fluids. 2019. Vol. 74. P. 152-158. doi
- Article Danilov V. G. Interaction of δ-Shock Waves in a System of Pressureless Gas Dynamics Equations // Russian Journal of Mathematical Physics. 2019. Vol. 26. No. 3. P. 306-319. doi
- Chapter Gaydukov R., Danilov V. Multideck structures of boundary layers in compressible flows, in: Proceedings of the International Conference DAYS on DIFFRACTION 2019. IEEE, 2019. P. 51-56. doi
- Chapter Гайдуков Р. К., Данилов В. Г. Многопалубные структуры в задачах обтекания поверхностей с малыми периодическими возмущениями // В кн.: XII Всероссийский съезд по фундаментальным проблемам теоретической и прикладной механики: сборник трудов в 4 томах. Т. 2: Механика жидкости и газа. Уфа : РИЦ БашГУ, 2019. doi С. 92-94.
20182
- Chapter Gaydukov R., Danilov V. Equations for velocity oscillations in problems of a fluid flow along a plate with small periodic irregularities on the surface for large Reynolds numbers, in: Proceedings of the International Conference DAYS on DIFFRACTION 2018. IEEE, 2018. P. 118-123. doi
- Article V.G. Danilov. Stepwise Approximations and Limiting Generalized Solution to Hyperbolic Conservation Law // Russian Journal of Mathematical Physics. 2018. Vol. 25. No. 4. P. 434-458. doi
20172
- Article Danilov V. G., Gaydukov R. K. Double-deck structure of the boundary layer in the problem of flow in an axially symmetric pipe with small irregularities on the wall for large Reynolds numbers // Russian Journal of Mathematical Physics. 2017. Vol. 24. No. 1. P. 1-18. doi
- Article Danilov V. G. Nonsmooth Nonoscillating Exponential-type Asymptotics for Linear Parabolic PDE // SIAM Journal on Mathematical Analysis. 2017. Vol. 49. No. 5. P. 3550-3572. doi
20165
- Chapter Gaidukov R.K., Danilov V.G. Double-deck structures of boundary layers in flows, in: Abstracts: Russian-French Workshop “Mathematical Hydrodynamics”, August 22–27, 2016. Novosibirsk : , 2016. P. 20-22.
- Article Danilov V. G. Forward and backward in time Cauchy problems for systems of parabolic-type PDE with a small parameter // Mathematische Nachrichten. 2016. Vol. 289. No. 7. P. 802-819. doi
- Chapter Danilov V., Turuntaev I. S. Interactive Educational System Based on Generative Approach, and the Problem of Answer Checking, in: Smart Education and e-Learning 2016 Issue 59. Switzerland : Springer, 2016. P. 527-537. doi
- Article Danilov V.G. Nonsmooth nonoscillating WKB–Maslov-type asymptotics for linear parabolic PDE // Russian Journal of Mathematical Physics. 2016. Vol. 23. No. 2. P. 185-199. doi
- Article Гайдуков Р. К., Данилов В. Г. Асимптотики решений задач обтекания несжимаемой жидкостью поверхностей c малыми неровностями при больших числах Рейнольдса // Наноструктуры. Математическая физика и моделирование. 2016. Т. 15. № 1. С. 5-102.
20152
- Article Danilov V., Gaydukov R. Double-Deck Structure of the Boundary Layer in Problems of Flow around Localized Perturbations on a Plate // Mathematical notes. 2015. Vol. 98. No. 4. P. 561-571. doi
- Article Danilov V., Gaydukov R. Vortices in the Prandtl boundary layer induced by irregularities on a plate // Russian Journal of Mathematical Physics. 2015. Vol. 22. No. 2. P. 161-173. doi
20143
- Article Danilov V., Gaydukov R., Vadim Kretov, Rudnev V. Modelling of Liquid Nuclei Generation for Field-Emission Silicon Nanocathode // IEEE Transactions on Electron Devices. 2014. Vol. 61. No. 12. P. 4232-4239.
- Chapter Данилов В. Г., Гайдуков Р. К. Вихревые течения в пограничных слоях вдоль поверхностей с малыми неровностями // В кн.: Волны и вихри в сложных средах: 5-ая Международная научная школа молодых ученых. М. : МАКС Пресс, 2014. С. 154-157.
- Book Данилов В. Г., Руднев В. Ю., Гайдуков Р. К., Кретов В. И. Математическое моделирование эмиссии из катодов малых размеров. М. : Научно-техническое издательство «Горячая линия – Телеком», 2014.
20133
- Article Danilov V. Global-in-Time Asymptotic Solutions to Kolmogorov-Feller-Type Parabolic Pseudodifferential Equations with Small Parameter—Forward- and Backward-in-Time Motion // Abstract and Applied Analysis. 2013. P. 1-11. doi
- Chapter Danilov V., Gaydukov R. Oscillations in classical boundary layer for flow with double-deck boundary layers structure, in: Proceedings of International Conference DAYS on DIFFRACTION 2013.. , 2013. P. 28-31.
- Article Данилов В.Г., Руднев В.Ю., Гайдуков Р.К., Кретов В.И. Математическое описание режима "плавление-затвердевание" в автоэмиссионном катоде при учете эффекта Ноттингама // Наноструктуры. Математическая физика и моделирование. 2013. Т. 9. № 1. С. 39-84.
20124
- Article Albeverio S., Danilov V. Construction of global-in-time solutions to Kolmogorov-Feller pseudodifferential equations with a small parameter using characteristics // Mathematische Nachrichten. 2012. Vol. 285. No. 4. P. 426-439. doi
- Article Danilov V., Rudnev V. Numerical and analytical investigation of a free boundaries confluence for the pfase field system // Russian Journal of Mathematical Physics. 2012. Vol. 19. No. 2. P. 146-158.
- Article Rudnev V., Danilov V., Kretov V. I. Simulation of the heat transfer in the nanocathode // Open Journal of Applied Sciences. 2012. Vol. 2. P. 78-81.
- Article Данилов В. Г., Руднев В. Ю. Численное исследование локализованного возмущения температуры в модели фазового поля в случае слияния свободных границ // Журнал вычислительной математики и математической физики. 2012. Т. 52. № 11. С. 2080-2092.
20112
- Article Danilov V., Albeverio S. Global in Time Solutions to Kolmogorov–Feller Pseudodifferential Equations with Small Parameter / Пер. с рус. // Russian Journal of Mathematical Physics. 2011. Vol. 18. No. 1. P. 10-25.
- Article Danilov V., Mitrovic D. Shock wave formation process for a multidimension scalar conservation law // Quarterly of Applied Mathematics. 2011. Vol. LXIX. No. 4. P. 613-634.
20102
- Article Danilov V., Mitrovic D., Bojkovic V. Linearization of the Riemann problem for a triangular system of conservation laws and delta shock wave formation process // Mathematical Methods in Applied Sciences. 2010. Vol. 33. P. 904-921.
- Chapter Danilov V. On the relation between the Maslov-Whitham method and the weak asymptotics method, in: Linear and non-linear theory of generalized functions and its applications / Ed. by A. Kaminski, M. Oberguggenberger, S. Pilipović. Vol. 88. Warsz. : PWN, 2010. P. 55-65.
Conferences
- 2019Международная конференция "Актуальные проблемы математической физики" (Москва). Presentation: Construction of the Fundamental Solution Asymptotics via Creation-Annihilation Operators to Parabolic PDE with a Small Parameter
- Quasilinear Equations, Inverse Problems and Their Applications (Долгопрудный). Presentation: Construction of fundamental solution to degenerate parabolic equation
- 2016International Conference on Generalised Functions (Дубровник). Presentation: Weak asymptotics and solutions of cauchy problem for hyperbolic conservation laws with piecewise smooth initial conditions
- 2014International Conference on Generalized Functions 2014 (Саутхемптон). Presentation: On the Maslov-Whitham and Colombeau approaches in comparison with the weak asymptotics method