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Petrov, Alexander Georgievich
Professor
Doctor of physico-mathematical sciences (1989)
Speciality: 01.02.05 (Mechanics of fluids, gases and plasmas)
Birth date: 08.07.1944
E-mail: ,
Keywords: fluid mechanics; gamiltonian mechanics; chaotic dynamics; mixing; nonlinear waves; Boussinesq–type equations.

Subject:

The total integral of the Boussinesq–type equations for surface gravity long waves in the form Kulikovsky–Drozdova form is found. The equations of Kulikovsky–Drozdova published in 1996 describes waves in channel. Nonstationary flow of a viscoplastic medium between two parallel plates was considered for the case of varying pressure gradient. The problem is reduced to the Stephan problem. Four multiparameter family of exact solutions are found. The new modification of a method of an average of a Hamilton systems is offered. The method is based on analytical expression of the Poincare maps in parametrical form. The developed method gives an asymptotic solution of a problem about a spherical pendulum with arbitrary vibration of a suspension point. The motion of particles of an incompressible viscous and visco-plastic mediums in thin layer whose boundary varies in a periodic way was investigated. Transition to the globally dynamical chaos is described.

Biography

Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1966 (department of highdrodymics). Ph.D. thesis was defended in 1971. D.Sci. thesis was defended in 1989. A list of my works contains more than 100 titles and 3 monographs.
   
Main publications:
  • Klimov D. M., Petrov A. G. Analytical solutions of the boundary-value problem of nonstationary flow of viscoplasic medium between two plates // Archive of Applied Mechanics. V. 70. 2000. p. 3–16.

https://www.mathnet.ru/eng/person17977
https://ru.wikipedia.org/wiki/Petrov,_Aleksandr_Georgievich
List of publications on Google Scholar
https://mathscinet.ams.org/mathscinet/MRAuthorID/205081
https://elibrary.ru/author_items.asp?authorid=14501
https://orcid.org/0000-0002-0618-2285

Publications in Math-Net.Ru Citations
2024
1. A. G. Petrov, “On tautochronic motions”, Dokl. RAN. Math. Inf. Proc. Upr., 518 (2024),  22–28  mathnet  elib; Dokl. Math., 110:4 (2024), 312–317
2. A. G. Petrov, V. A. Rumyantseva, “Method of normal coordinates for studying forced oscillations of dissipative systems in mechanics and electrical engineering”, Prikl. Mekh. Tekh. Fiz., 65:5 (2024),  141–156  mathnet
3. A. G. Petrov, “Exponentially convergent numerical scheme for the stream function of potential flow over axisymmetric bodies”, Zh. Vychisl. Mat. Mat. Fiz., 64:3 (2024),  392–402  mathnet  elib; Comput. Math. Math. Phys., 64:3 (2024), 370–380
2023
4. V. V. Vedenyapin, A. A. Bay, A. G. Petrov, “On derivation of equations of gravitation from the principle of least action, relativistic Milne-Mccree solutions and Lagrange points”, Dokl. RAN. Math. Inf. Proc. Upr., 514:1 (2023),  69–73  mathnet  elib; Dokl. Math., 108:3 (2023), 481–485
5. D. V. Maklakov, A. G. Petrov, “Potential flow around two circular cylinders”, Prikl. Mekh. Tekh. Fiz., 64:3 (2023),  95–109  mathnet  elib; J. Appl. Mech. Tech. Phys., 64:3 (2023), 442–454
6. N. D. Baikov, A. G. Petrov, “On a flow around a cylinder over uneven bottom”, Zh. Vychisl. Mat. Mat. Fiz., 63:3 (2023),  424–435  mathnet  mathscinet  elib; Comput. Math. Math. Phys., 63:3 (2023), 401–412 1
2022
7. V. V. Vedenyapin, V. I. Parenkina, A. G. Petrov, Zhang Haochen, “Vlasov-Einstein equation and Lagrange points”, Keldysh Institute preprints, 2022, 023, 23 pp.  mathnet 2
2021
8. A. G. Petrov, “Algorithm for construction of quadrature formulas with exponential convergence for linear operators acting on periodic functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 2,  86–92  mathnet; Russian Math. (Iz. VUZ), 65:2 (2021), 75–80  isi  scopus 4
9. A. G. Petrov, “Areas of attraction of the pendulum under the influence of oblique vibration of the suspension point”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 8:3 (2021),  511–522  mathnet; Vestn. St. Petersbg. Univ., Math., 8:4 (2021), 273–281
10. A. G. Petrov, “The inverse problem of stabilization of a spherical pendulum in a given position under oblique vibration.”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 8:2 (2021),  255–269  mathnet; Vestn. St. Petersbg. Univ., Math., 8:3 (2021), 151–161 1
2020
11. A. G. Petrov, “On parametric representations of orthogonal and symplectic matrices”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 6,  93–98  mathnet; Russian Math. (Iz. VUZ), 64:6 (2020), 80–85  isi  scopus 1
12. S. V. Sanduleanu, A. G. Petrov, “Interaction of two nearly contacting gas bubbles pulsating in a liquid in an alternating pressure field”, Pis'ma v Zh. Èksper. Teoret. Fiz., 112:3 (2020),  165–171  mathnet  elib; JETP Letters, 112:3 (2020), 150–156  isi  scopus
2019
13. A. O. Zakhar'in, A. V. Andrianov, A. G. Petrov, “Stimulated terahertz emission in a system of excitons in photoexcited silicon”, Pis'ma v Zh. Èksper. Teoret. Fiz., 109:12 (2019),  821–825  mathnet  elib; JETP Letters, 109:12 (2019), 781–785  isi  scopus 2
14. A. G. Petrov, “Saturation-Free Numerical Scheme for Computing the Flow Past a Lattice of Airfoils with a Sharp Edge”, Rus. J. Nonlin. Dyn., 15:2 (2019),  135–143  mathnet  elib
15. A. O. Kazakova, A. G. Petrov, “Computation of viscous flow between two arbitrarily moving cylinders of arbitrary cross section”, Zh. Vychisl. Mat. Mat. Fiz., 59:6 (2019),  1063–1082  mathnet  elib; Comput. Math. Math. Phys., 59:6 (2019), 1030–1048  isi  scopus 4
2018
16. A. V. Andrianov, A. O. Zakhar'in, A. G. Petrov, “Intraexciton and intracenter terahertz radiation from doped silicon under interband photoexcitation”, Pis'ma v Zh. Èksper. Teoret. Fiz., 107:9 (2018),  564–568  mathnet  elib; JETP Letters, 107:9 (2018), 540–543  isi  elib  scopus 2
17. Alexander Petrov, Mariana Lopushanski, Vladimir Vanovskiy, “Stability of capillary waves of finite amplitude”, Lect. Notes Electr. Eng., 428 (2018),  51–57  mathnet  scopus
18. Alexander Petrov, Mariana Lopushanski, “Ellipsoid movement in ideal or viscous fluid”, MATEC Web Conf., 211 (2018),  15004–7  mathnet  isi  scopus
19. Alexander Petrov, Mariana Lopushanski, “Study of finite amplitude capillary waves stability”, MATEC Web Conf., 211 (2018),  4008–7  mathnet  isi  scopus
20. A. G. Petrov, “Problems of hydrodynamics for a triaxial ellipsoid”, Prikl. Mekh. Tekh. Fiz., 59:4 (2018),  50–63  mathnet  elib; J. Appl. Mech. Tech. Phys., 59:4 (2018), 618–630
21. A. G. Petrov, V. V. Vanovskiy, “Nonlinear oscillations of a spring pendulum at the 1 : 1 : 2 resonance: theory, experiment, and physical analogies”, Trudy Mat. Inst. Steklova, 300 (2018),  168–175  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 300 (2018), 159–167  isi  scopus 3
22. N. D. Baikov, A. G. Petrov, “Deformation of cylindrical cavities in plane-parallel potential flows with circulation and under the action of mass forces”, Num. Meth. Prog., 19:3 (2018),  207–214  mathnet
2017
23. N. D. Baikov, A. G. Petrov, “Formation of a cumulative jet in the plane-parallel flow of a perfect fluid”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2017, no. 5,  42–47  mathnet; Moscow University Mechanics Bulletin, 72:5 (2017), 119–123  isi  scopus 2
2016
24. A. G. Petrov, Sh. V. Sanduleanu, “Simulation of electrochemical machining using the boundary element method with no saturation”, Zh. Vychisl. Mat. Mat. Fiz., 56:10 (2016),  1810–1820  mathnet  elib; Comput. Math. Math. Phys., 56:10 (2016), 1793–1802  isi  scopus 3
25. A. G. Petrov, I. I. Potapov, “Computation of forces acting on bodies in plane and axisymmetric cavitation flow problems”, Zh. Vychisl. Mat. Mat. Fiz., 56:2 (2016),  318–331  mathnet  elib; Comput. Math. Math. Phys., 56:2 (2016), 320–333  isi  scopus 2
2015
26. K. A. Ivanov, A. G. Petrov, M. A. Kaliteevski, A. J. Gallant, “Anharmonic Bloch oscillation of electrons in biased superlattices”, Pis'ma v Zh. Èksper. Teoret. Fiz., 102:12 (2015),  911–918  mathnet  elib; JETP Letters, 102:12 (2015), 796–802  isi  scopus 5
2014
27. A. G. Petrov, I. I. Potapov, “Causes of bed instability”, Prikl. Mekh. Tekh. Fiz., 55:6 (2014),  114–119  mathnet  elib; J. Appl. Mech. Tech. Phys., 55:6 (2014), 1005–1009 1
28. A. G. Petrov, I. I. Potapov, “Sediment transport under normal and tangential bottom stresses with the bottom slope taken into account”, Prikl. Mekh. Tekh. Fiz., 55:5 (2014),  100–105  mathnet  elib; J. Appl. Mech. Tech. Phys., 55:5 (2014), 812–817 6
2013
29. A. G. Petrov, I. I. Potapov, “Effect of turbulent viscosity on the formation and motion of bottom waves”, Prikl. Mekh. Tekh. Fiz., 54:1 (2013),  57–68  mathnet  elib; J. Appl. Mech. Tech. Phys., 54:1 (2013), 49–58
30. A. G. Petrov, “Constructing solutions of the Navier–Stokes equations for a fluid layer between moving parallel plates at low and moderate Reynolds numbers”, Prikl. Mekh. Tekh. Fiz., 54:1 (2013),  51–56  mathnet  elib; J. Appl. Mech. Tech. Phys., 54:1 (2013), 44–48 1
2012
31. A. G. Petrov, “Exact solution of the Navier–Stokes equations in a fluid layer between the moving parallel plates”, Prikl. Mekh. Tekh. Fiz., 53:5 (2012),  13–18  mathnet  elib; J. Appl. Mech. Tech. Phys., 53:5 (2012), 642–646 6
2011
32. V. I. Sankin, A. V. Andrianov, A. O. Zahar'in, A. G. Petrov, “Terahertz radiation induced by the Wannier-Stark localization of electrons in a natural silicon carbide superlattice”, Pis'ma v Zh. Èksper. Teoret. Fiz., 94:5 (2011),  393–396  mathnet; JETP Letters, 94:5 (2011), 362–365  isi  scopus 10
33. A. G. Petrov, I. I. Potapov, “Generation mechanism of bed wave in a sand-bed channel”, Prikl. Mekh. Tekh. Fiz., 52:2 (2011),  81–91  mathnet  elib; J. Appl. Mech. Tech. Phys., 52:2 (2011), 224–233
34. A. G. Petrov, “Saturation-free numerical scheme for computing the flow past a lattice of airfoils and the determination of separation points in a viscous fluid”, Zh. Vychisl. Mat. Mat. Fiz., 51:7 (2011),  1326–1338  mathnet  mathscinet; Comput. Math. Math. Phys., 51:7 (2011), 1239–1250  isi  scopus 8
2010
35. A. G. Petrov, I. I. Potapov, “Formulation and solution of the problem of the stability of a cohesionless channel bottom”, Prikl. Mekh. Tekh. Fiz., 51:1 (2010),  62–74  mathnet  elib; J. Appl. Mech. Tech. Phys., 51:1 (2010), 51–61 3
2009
36. V. P. Varin, A. G. Petrov, “A hydrodynamic model of human cochlea”, Zh. Vychisl. Mat. Mat. Fiz., 49:9 (2009),  1708–1723  mathnet  zmath; Comput. Math. Math. Phys., 49:9 (2009), 1632–1647  isi  scopus 5
2008
37. V. P. Varin, A. G. Petrov, “A mathematical model of human cochlea”, Keldysh Institute preprints, 2008, 096, 26 pp.  mathnet
38. A. G. Petrov, “Quadrature formulas for periodic functions and their application to the boundary element method”, Zh. Vychisl. Mat. Mat. Fiz., 48:8 (2008),  1344–1361  mathnet  mathscinet  zmath  elib; Comput. Math. Math. Phys., 48:8 (2008), 1266–1283  isi  elib  scopus 18
2006
39. A. G. Petrov, S. V. Rotkin, “Energy relaxation of hot carriers in single-wall carbon nanotubes by surface optical phonons of the substrate”, Pis'ma v Zh. Èksper. Teoret. Fiz., 84:3 (2006),  185–189  mathnet; JETP Letters, 84:3 (2006), 156–160  isi  scopus 20
2004
40. A. G. Petrov, “Asymptotic Methods for Solving the Hamilton Equations with the Use of a Parametrization of Canonical Transformations”, Differ. Uravn., 40:5 (2004),  626–638  mathnet  mathscinet; Differ. Equ., 40:5 (2004), 672–685 9
2003
41. A. G. Petrov, “Poincaré mapping method for hydrodynamic systems. Dynamic chaos in a fluid layer between eccentrically rotating cylinders”, Prikl. Mekh. Tekh. Fiz., 44:1 (2003),  3–21  mathnet  elib; J. Appl. Mech. Tech. Phys., 44:1 (2003), 1–16
2002
42. D. V. Georgievskii, D. M. Klimov, A. G. Petrov, “Inertialess deformation of weakly inhomogeneous viscous media”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2002, no. 2,  37–41  mathnet
2000
43. A. G. Petrov, P. G. Petrov, “Sediment-discharge vector in a turbulent flow above an eroded bottom”, Prikl. Mekh. Tekh. Fiz., 41:2 (2000),  102–112  mathnet  elib; J. Appl. Mech. Tech. Phys., 41:2 (2000), 298–308 4
1998
44. A. G. Petrov, L. V. Fishkis, “Wind turbulent flow in a basin of constant depth bounded by a vertical rectangular wall”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1998, no. 4,  55–58  mathnet  zmath
1995
45. A. G. Petrov, V. G. Smolyanin, “On the equation for the curvature of a curve changing in time and having a given distribution of distinguished points on it”, Uspekhi Mat. Nauk, 50:5(305) (1995),  249–250  mathnet  mathscinet  zmath; Russian Math. Surveys, 50:5 (1995), 1092–1094  isi 1
46. A. G. Petrov, V. G. Smolyanin, “An equation for the curvature and interpolation of a line that changes over time”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1995, no. 6,  69–71  mathnet  mathscinet  zmath 1
47. O. S. Alferov, A. G. Petrov, “Turbulent flow over rotating rough surface”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1995, no. 3,  60–65  mathnet  zmath
1992
48. A. G. Petrov, P. G. Petrov, “Sediment transport by turbulent flow above a bottom subject to erosion”, Prikl. Mekh. Tekh. Fiz., 33:4 (1992),  61–69  mathnet; J. Appl. Mech. Tech. Phys., 33:4 (1992), 531–538
1991
49. A. G. Petrov, V. G. Smolyanin, “Calculation of a capillary-gravity wave profile on a surface of a heavy liquid of a finite depth”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1991, no. 3,  92–96  mathnet  zmath 3
1989
50. A. G. Petrov, “The energy dissipation rate of a viscous fluid with a condition for shear stress on a boundary streamline”, Dokl. Akad. Nauk SSSR, 304:5 (1989),  1082–1086  mathnet  mathscinet  zmath; Dokl. Math., 34:2 (1989), 101–103
51. A. G. Petrov, “Circulation within viscous deformed drops moving at a constant velocity in a gas”, Prikl. Mekh. Tekh. Fiz., 30:6 (1989),  127–134  mathnet; J. Appl. Mech. Tech. Phys., 30:6 (1989), 957–964 6
1988
52. A. G. Petrov, “Internal circulation and deformation of viscous drops”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1988, no. 3,  85–88  mathnet  zmath
1986
53. A. G. Petrov, “Asymptotic expansions of thin axisymmetric cavities”, Prikl. Mekh. Tekh. Fiz., 27:5 (1986),  45–49  mathnet; J. Appl. Mech. Tech. Phys., 27:5 (1986), 667–672 4
1985
54. A. G. Petrov, “The resistance force acting on an axisymmetric nonthin body for small cavitation numbers”, Dokl. Akad. Nauk SSSR, 282:6 (1985),  1320–1323  mathnet  mathscinet  zmath
1984
55. A. G. Petrov, N. B. Sotina, “Universal, cavity-shape-independent relations for cavitation flow with small cavitation numbers”, Prikl. Mekh. Tekh. Fiz., 25:5 (1984),  110–117  mathnet; J. Appl. Mech. Tech. Phys., 25:5 (1984), 758–766
1982
56. O. V. Voinov, A. G. Petrov, “Stability of relative motion of phases in two-phase flows”, Prikl. Mekh. Tekh. Fiz., 23:1 (1982),  83–90  mathnet; J. Appl. Mech. Tech. Phys., 23:1 (1982), 76–82 1
1981
57. A. G. Petrov, “A direct variational method of calculating plane and axisymmetric cavitation flows”, Dokl. Akad. Nauk SSSR, 257:6 (1981),  1323–1327  mathnet  zmath 1
58. O. V. Voinov, A. G. Petrov, “Physical model and equation of motion for a two-phase medium taking into account random particle (bubbles) motion”, Prikl. Mekh. Tekh. Fiz., 22:6 (1981),  78–87  mathnet; J. Appl. Mech. Tech. Phys., 22:6 (1981), 803–811 1
1978
59. A. G. Petrov, “Reactions acting on a small solid in plane-parallel vortex flow”, Dokl. Akad. Nauk SSSR, 238:1 (1978),  33–35  mathnet  zmath
1977
60. O. V. Voinov, A. G. Petrov, “The stability of a small body in a nonuniform flow”, Dokl. Akad. Nauk SSSR, 237:6 (1977),  1303–1306  mathnet  mathscinet  zmath
1974
61. A. G. Petrov, “Stability of gas-bubble equilibrium shape in uniform flow of an ideal fluid”, Prikl. Mekh. Tekh. Fiz., 15:5 (1974),  49–54  mathnet; J. Appl. Mech. Tech. Phys., 15:5 (1974), 623–627
62. V. V. Voinov, O. V. Voinov, A. G. Petrov, “A method of calculating the potential flow of an incompressible fluid around a solid revolution”, Zh. Vychisl. Mat. Mat. Fiz., 14:3 (1974),  797–802  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 14:3 (1974), 263–268 6
1973
63. O. V. Voinov, A. G. Petrov, “Motion of a deforming body in an ideal liquid from a state of rest”, Dokl. Akad. Nauk SSSR, 212:5 (1973),  1086–1088  mathnet  zmath
64. O. V. Voinov, A. G. Petrov, “Lagrangian of a gas bubble in a nonuniform flow”, Dokl. Akad. Nauk SSSR, 210:5 (1973),  1036–1039  mathnet  zmath
65. O. V. Voinov, A. G. Petrov, “Motion of a small sphere in a nonhomogeneous flow of an incompressible liquid”, Prikl. Mekh. Tekh. Fiz., 14:5 (1973),  57–61  mathnet; J. Appl. Mech. Tech. Phys., 14:5 (1973), 650–653
1972
66. O. V. Voinov, A. M. Golovin, A. G. Petrov, “Transfer of energy from an evaporating drop in a vapor medium”, Prikl. Mekh. Tekh. Fiz., 13:1 (1972),  74–78  mathnet; J. Appl. Mech. Tech. Phys., 13:1 (1972), 63–67
1971
67. A. G. Petrov, “Curvilinear motion of an ellipsoidal bubble”, Prikl. Mekh. Tekh. Fiz., 12:3 (1971),  90–93  mathnet; J. Appl. Mech. Tech. Phys., 12:3 (1971), 422–424
1970
68. O. V. Voinov, A. M. Golovin, A. G. Petrov, “Motion of ellipsoidal bubble in low-viscosity liquid”, Prikl. Mekh. Tekh. Fiz., 11:3 (1970),  76–81  mathnet; J. Appl. Mech. Tech. Phys., 11:3 (1970), 427–431 1
1968
69. A. M. Golovin, A. G. Petrov, “Motion of a pair of bubbles in a liquid of low viscosity”, Prikl. Mekh. Tekh. Fiz., 9:3 (1968),  29–36  mathnet; J. Appl. Mech. Tech. Phys., 9:3 (1968), 256–259

Presentations in Math-Net.Ru
1. Нелинейные вынужденные колебания газового пузырька в жидкости с большой амплитудой
A. G. Petrov
International Conference "Mathematical Methods of Mechanics" dedicated to the anniversary of academician A. G. Kulikovskii
March 21, 2023 15:40   
2. Уравнение Власова-Эйнштейна и точки Лагранжа
V. V. Vedenyapin, N. N. Fimin, V. M. Chechetkin, A. G. Petrov
Hamiltonian systems and statistical mechanics
November 28, 2022 16:30   
3. Управление маятником с помощью косой вибрации
A. G. Petrov
Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS (Novikov Seminar)
April 13, 2022 18:30   
4. Управление маятником с помощью косой вибрации
A. G. Petrov
Differential equations, analysis and control: theory and applications
March 21, 2022 18:25
5. Параметрическое представление симмплектических матриц
A. G. Petrov
Research Seminar of the Department of Higher Algebra MSU
February 17, 2020
6. Нелинейные колебания маятника на пружине при резонансе 1:1:2. Течения, эксперимент и физические аналогии
A. G. Petrov
All-Russian conference "Modern Problems of Continuum Mechanics" devoted to 110 anniversary of L. I. Sedov
November 15, 2017 17:40
7. Численный расчет течения вязкой жидкости между двумя движущимися цилиндрами
A. G. Petrov, A. O. Kazakova
All-Russian conference "Modern Problems of Continuum Mechanics" devoted to 110 anniversary of L. I. Sedov
November 14, 2017 16:00
8. О вычислении гамильтоновой нормальной формы
A. G. Petrov
Seminar "Optimal Control and Dynamical Systems"
April 23, 2008 12:00
9. Квазистационаpное движение слабонеодноpодной вязкой жидкости в тонком слое
A. G. Petrov, D. V. Georgievskii
Scientic seminar «Actual problems of geometry and mechanics » named after Prof. V.V. Trofimov
October 27, 2000 18:30

Organisations
 
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