Persons: Petrov, Alexander Georgievich

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Petrov, Alexander Georgievich

Total publications:	72 (72)
in MathSciNet:	11 (11)
in zbMATH:	16 (16)
in Web of Science:	19 (19)
in Scopus:	20 (20)
Cited articles:	39
Citations:	158
Presentations:	11

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

List of publications:

scientific publications

by years

by types

by times cited

common list

		Citations (Crossref Cited-By Service + Math-Net.Ru)


2025
1.	A. G. Petrov, I. I. Potapov, “On the erosion of the bottom caused by a suspended turbulent jet”, Proceedings of ISP RAS, 37:2 (2025), 181–194

2024
2.	A. G. Petrov, “Approximate gyroscope theory and its applications to the motion of space objects”, Dokl. Math., 110:3 (2024), 497–499
3.	A. G. Petrov, “On tautochronic motions”, Dokl. Math., 110:1 (2024), 312–317
4.	A. G. Petrov, V. A. Rumyantseva, “Method of normal coordinates for studying forced oscillations of dissipative systems in mechanics and electrical engineering”, J. Appl. Mech. Tech. Phys., 65:5 (2024), 917–932
5.	A. G. Petrov, “Exponentially convergent numerical scheme for the stream function of potential flow over axisymmetric bodies”, Comput. Math. Math. Phys., 64:3 (2024), 370–380

2023
6.	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. Math., 108:3 (2023), 481–485
7.	D. V. Maklakov, A. G. Petrov, “Potential flow around two circular cylinders”, J. Appl. Mech. Tech. Phys., 64:3 (2023), 442–454
8.	N. D. Baikov, A. G. Petrov, “On a flow around a cylinder over uneven bottom”, Comput. Math. Math. Phys., 63:3 (2023), 401–412

2022
9.	V. V. Vedenyapin, V. I. Parenkina, A. G. Petrov, Zhang Haochen, “Vlasov-Einstein equation and Lagrange points”, Keldysh Institute preprints, 2022

2021
10.	A. G. Petrov, “Algorithm for construction of quadrature formulas with exponential convergence for linear operators acting on periodic functions”, Russian Math. (Iz. VUZ), 65:2 (2021), 75–80
11.	A. G. Petrov, “Areas of attraction of the pendulum under the influence of oblique vibration of the suspension point”, Vestn. St. Petersbg. Univ., Math., 8:4 (2021), 273–281
12.	A. G. Petrov, “The inverse problem of stabilization of a spherical pendulum in a given position under oblique vibration.”, Vestn. St. Petersbg. Univ., Math., 8:3 (2021), 151–161

2020
13.	A. G. Petrov, “On parametric representations of orthogonal and symplectic matrices”, Russian Math. (Iz. VUZ), 64:6 (2020), 80–85
14.	S. V. Sanduleanu, A. G. Petrov, “Interaction of two nearly contacting gas bubbles pulsating in a liquid in an alternating pressure field”, JETP Letters, 112:3 (2020), 150–156

2019
15.	A. O. Zakhar'in, A. V. Andrianov, A. G. Petrov, “Stimulated terahertz emission in a system of excitons in photoexcited silicon”, JETP Letters, 109:12 (2019), 781–785
16.	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
17.	A. O. Kazakova, A. G. Petrov, “Computation of viscous flow between two arbitrarily moving cylinders of arbitrary cross section”, Comput. Math. Math. Phys., 59:6 (2019), 1030–1048

2018
18.	A. V. Andrianov, A. O. Zakhar'in, A. G. Petrov, “Intraexciton and intracenter terahertz radiation from doped silicon under interband photoexcitation”, JETP Letters, 107:9 (2018), 540–543
19.	Alexander Petrov, Mariana Lopushanski, Vladimir Vanovskiy, “Stability of capillary waves of finite amplitude”, Applied Physics, System Science and Computers, APSAC 2017: International Conference on Applied Physics, System Science and Computers, Lect. Notes Electr. Eng., 428, Springer, Cham, 2018, 51–57
20.	Alexander Petrov, Mariana Lopushanski, “Ellipsoid movement in ideal or viscous fluid”, MATEC Web Conf., 211 (2018), 15004, 7 pp.
21.	Alexander Petrov, Mariana Lopushanski, “Study of finite amplitude capillary waves stability”, MATEC Web Conf., 211 (2018), 4008, 7 pp.
22.	A. G. Petrov, “Problems of hydrodynamics for a triaxial ellipsoid”, J. Appl. Mech. Tech. Phys., 59:4 (2018), 618–630
23.	A. G. Petrov, V. V. Vanovskiy, “Nonlinear oscillations of a spring pendulum at the 1 : 1 : 2 resonance: theory, experiment, and physical analogies”, Proc. Steklov Inst. Math., 300 (2018), 159–167
24.	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

2017
25.	N. D. Baikov, A. G. Petrov, “Formation of a cumulative jet in the plane-parallel flow of a perfect fluid”, Moscow University Mechanics Bulletin, 72:5 (2017), 119–123

2016
26.	A. G. Petrov, Sh. V. Sanduleanu, “Simulation of electrochemical machining using the boundary element method with no saturation”, Comput. Math. Math. Phys., 56:10 (2016), 1793–1802
27.	A. G. Petrov, I. I. Potapov, “Computation of forces acting on bodies in plane and axisymmetric cavitation flow problems”, Comput. Math. Math. Phys., 56:2 (2016), 320–333

2015
28.	JETP Letters, 102:12 (2015), 796–802

2014
29.	A. G. Petrov, I. I. Potapov, “Causes of bed instability”, J. Appl. Mech. Tech. Phys., 55:6 (2014), 1005–1009
30.	A. G. Petrov, I. I. Potapov, “Sediment transport under normal and tangential bottom stresses with the bottom slope taken into account”, J. Appl. Mech. Tech. Phys., 55:5 (2014), 812–817

2013
31.	A. G. Petrov, I. I. Potapov, “Effect of turbulent viscosity on the formation and motion of bottom waves”, J. Appl. Mech. Tech. Phys., 54:1 (2013), 49–58
32.	A. G. Petrov, “Constructing solutions of the Navier–Stokes equations for a fluid layer between moving parallel plates at low and moderate Reynolds numbers”, J. Appl. Mech. Tech. Phys., 54:1 (2013), 44–48

2012
33.	A. G. Petrov, “Exact solution of the Navier–Stokes equations in a fluid layer between the moving parallel plates”, J. Appl. Mech. Tech. Phys., 53:5 (2012), 642–646

2011
34.	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”, JETP Letters, 94:5 (2011), 362–365
35.	A. G. Petrov, I. I. Potapov, “Generation mechanism of bed wave in a sand-bed channel”, J. Appl. Mech. Tech. Phys., 52:2 (2011), 224–233
36.	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”, Comput. Math. Math. Phys., 51:7 (2011), 1239–1250

2010
37.	A. G. Petrov, I. I. Potapov, “Formulation and solution of the problem of the stability of a cohesionless channel bottom”, J. Appl. Mech. Tech. Phys., 51:1 (2010), 51–61

2009
38.	V. P. Varin, A. G. Petrov, “A hydrodynamic model of human cochlea”, Comput. Math. Math. Phys., 49:9 (2009), 1632–1647

2008
39.	V. P. Varin, A. G. Petrov, “A mathematical model of human cochlea”, Keldysh Institute preprints, 2008
40.	A. G. Petrov, “Quadrature formulas for periodic functions and their application to the boundary element method”, Comput. Math. Math. Phys., 48:8 (2008), 1266–1283

2006
41.	A. G. Petrov, S. V. Rotkin, “Energy relaxation of hot carriers in single-wall carbon nanotubes by surface optical phonons of the substrate”, JETP Letters, 84:3 (2006), 156–160

2004
42.	A. G. Petrov, “Asymptotic Methods for Solving the Hamilton Equations with the Use of a Parametrization of Canonical Transformations”, Differ. Equ., 40:5 (2004), 672–685

2003
43.	A. G. Petrov, “Poincaré mapping method for hydrodynamic systems. Dynamic chaos in a fluid layer between eccentrically rotating cylinders”, J. Appl. Mech. Tech. Phys., 44:1 (2003), 1–16

2002
44.	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

2000
45.	A. G. Petrov, P. G. Petrov, “Sediment-discharge vector in a turbulent flow above an eroded bottom”, J. Appl. Mech. Tech. Phys., 41:2 (2000), 298–308

1998
46.	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

1995
47.	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”, Russian Math. Surveys, 50:5 (1995), 1092–1094
48.	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
49.	O. S. Alferov, A. G. Petrov, “Turbulent flow over rotating rough surface”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1995, no. 3, 60–65

1992
50.	A. G. Petrov, P. G. Petrov, “Sediment transport by turbulent flow above a bottom subject to erosion”, J. Appl. Mech. Tech. Phys., 33:4 (1992), 531–538

1991
51.	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

1989
52.	A. G. Petrov, “The energy dissipation rate of a viscous fluid with a condition for shear stress on a boundary streamline”, Dokl. Math., 34:2 (1989), 101–103
53.	A. G. Petrov, “Circulation within viscous deformed drops moving at a constant velocity in a gas”, J. Appl. Mech. Tech. Phys., 30:6 (1989), 957–964

1988
54.	A. G. Petrov, “Internal circulation and deformation of viscous drops”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1988, no. 3, 85–88

1986
55.	A. G. Petrov, “Asymptotic expansions of thin axisymmetric cavities”, J. Appl. Mech. Tech. Phys., 27:5 (1986), 667–672

1985
56.	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

1984
57.	A. G. Petrov, N. B. Sotina, “Universal, cavity-shape-independent relations for cavitation flow with small cavitation numbers”, J. Appl. Mech. Tech. Phys., 25:5 (1984), 758–766

1982
58.	O. V. Voinov, A. G. Petrov, “Stability of relative motion of phases in two-phase flows”, J. Appl. Mech. Tech. Phys., 23:1 (1982), 76–82

1981
59.	A. G. Petrov, “A direct variational method of calculating plane and axisymmetric cavitation flows”, Dokl. Akad. Nauk SSSR, 257:6 (1981), 1323–1327
60.	O. V. Voinov, A. G. Petrov, “Physical model and equation of motion for a two-phase medium taking into account random particle (bubbles) motion”, J. Appl. Mech. Tech. Phys., 22:6 (1981), 803–811

1978
61.	A. G. Petrov, “Reactions acting on a small solid in plane-parallel vortex flow”, Dokl. Akad. Nauk SSSR, 238:1 (1978), 33–35

1977
62.	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

1974
63.	A. G. Petrov, “Stability of gas-bubble equilibrium shape in uniform flow of an ideal fluid”, J. Appl. Mech. Tech. Phys., 15:5 (1974), 623–627
64.	V. V. Voinov, O. V. Voinov, A. G. Petrov, “A method of calculating the potential flow of an incompressible fluid around a solid revolution”, U.S.S.R. Comput. Math. Math. Phys., 14:3 (1974), 263–268

1973
65.	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
66.	O. V. Voinov, A. G. Petrov, “Lagrangian of a gas bubble in a nonuniform flow”, Dokl. Akad. Nauk SSSR, 210:5 (1973), 1036–1039
67.	O. V. Voinov, A. G. Petrov, “Motion of a small sphere in a nonhomogeneous flow of an incompressible liquid”, J. Appl. Mech. Tech. Phys., 14:5 (1973), 650–653

1972
68.	O. V. Voinov, A. M. Golovin, A. G. Petrov, “Transfer of energy from an evaporating drop in a vapor medium”, J. Appl. Mech. Tech. Phys., 13:1 (1972), 63–67

1971
69.	A. G. Petrov, “Curvilinear motion of an ellipsoidal bubble”, J. Appl. Mech. Tech. Phys., 12:3 (1971), 422–424

1970
70.	O. V. Voinov, A. M. Golovin, A. G. Petrov, “Motion of ellipsoidal bubble in low-viscosity liquid”, J. Appl. Mech. Tech. Phys., 11:3 (1970), 427–431

1968
71.	O. V. Voinov, A. M. Golovin, A. G. Petrov, “Perenos energii ot izluchayuschei sfery s molekulyarnoi teploprovodnostyu.”, Zh. prikl. mat. i mekh., 32:5 (1968), 882–893
72.	A. M. Golovin, A. G. Petrov, “Motion of a pair of bubbles in a liquid of low viscosity”, J. Appl. Mech. Tech. Phys., 9:3 (1968), 256–259

Presentations in Math-Net.Ru

1.	Параметризация ортогональных, симплектических и ортогонально-симплектических матриц. A. G. Petrov Hamiltonian systems and statistical mechanics October 20, 2025 16:30
2.	Об аналитических методах в механике A. G. Petrov Scientic seminar «Actual problems of geometry and mechanics » named after Prof. V.V. Trofimov May 23, 2025 18:30
3.	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
4.	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
5.	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
6.	Управление маятником с помощью косой вибрации A. G. Petrov Differential equations, analysis and control: theory and applications March 21, 2022 18:25
7.	Параметрическое представление симмплектических матриц A. G. Petrov Research Seminar of the Department of Higher Algebra MSU February 17, 2020
8.	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
9.	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
10.	О вычислении гамильтоновой нормальной формы A. G. Petrov Seminar "Optimal Control and Dynamical Systems" April 23, 2008 12:00
11.	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

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