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Rudenko, Oleg
Publications (10 of 67) Show all publications
Nefedov, N. N. & Rudenko, O. (2018). On Front Motion in a Burgers-Type Equation with Quadratic and Modular Nonlinearity and Nonlinear Amplification. Doklady. Mathematics, 97(1), 99-103
Open this publication in new window or tab >>On Front Motion in a Burgers-Type Equation with Quadratic and Modular Nonlinearity and Nonlinear Amplification
2018 (English)In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 97, no 1, p. 99-103Article in journal (Refereed) Published
Abstract [en]

A singularly perturbed initial-boundary value problem for a parabolic equation known in applications as a Burgers-type or reaction-diffusion-advection equation is considered. An asymptotic approximation of solutions with a moving front is constructed in the case of modular and quadratic nonlinearity and nonlinear amplification. The influence exerted by nonlinear amplification on front propagation and blowing- up is determined. The front localization and the blowing-up time are estimated.

Place, publisher, year, edition, pages
MAIK NAUKA/INTERPERIODICA/SPRINGER, 2018
National Category
Other Mathematics Other Mechanical Engineering
Identifiers
urn:nbn:se:bth-16079 (URN)10.1134/S1064562418010143 (DOI)000427590400026 ()
Available from: 2018-04-06 Created: 2018-04-06 Last updated: 2018-04-06Bibliographically approved
Rudenko, O. & Gurbatov, S. N. (2018). Statistical Problems for the Generalized Burgers Equation: High-Intensity Noise in Waveguide Systems. Doklady. Mathematics, 97(1), 95-98
Open this publication in new window or tab >>Statistical Problems for the Generalized Burgers Equation: High-Intensity Noise in Waveguide Systems
2018 (English)In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 97, no 1, p. 95-98Article in journal (Refereed) Published
Abstract [en]

A one-dimensional equation is presented that generalizes the Burgers equation known in the theory of waves and in turbulence models. It describes the nonlinear evolution of waves in pipes of variable cross section filled with a dissipative medium, as well as in ray tubes, if the approximation of geometric acoustics of an inhomogeneous medium is used. The generalized equation is reduced to the common Burgers equation with a dissipative parameter-the "Reynolds-Goldberg number," depending on the coordinate. The method for solving statistical problems corresponding to specified characteristics of a noise signal at the input of the system is described. Integral expressions for exact solutions are given for the correlation function and the noise intensity spectrum experiencing nonlinear distortions during propagation in a waveguide. For waves in a dissipative medium, an approximate method of calculating statistical characteristics is given, consisting in finding an auxiliary correlation function and the subsequent nonlinear functional transformation. Solutions have a complicated form, so physical analysis of phenomena requires the numerical methods. For some correlation functions of stationary noise with initial Gaussian statistics and some waveguide systems, it is possible to obtain simple results.

Place, publisher, year, edition, pages
MAIK NAUKA/INTERPERIODICA/SPRINGER, 2018
National Category
Other Mathematics Other Mechanical Engineering
Identifiers
urn:nbn:se:bth-16078 (URN)10.1134/S1064562418010040 (DOI)000427590400025 ()
Available from: 2018-04-06 Created: 2018-04-06 Last updated: 2018-04-06Bibliographically approved
Rudenko, O. & Hedberg, C. (2017). A new equation and exact solutions describing focal fields in media with modular nonlinearity. Nonlinear dynamics, 89(3), 1905-1913
Open this publication in new window or tab >>A new equation and exact solutions describing focal fields in media with modular nonlinearity
2017 (English)In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 89, no 3, p. 1905-1913Article in journal (Refereed) Published
Abstract [en]

Brand-new equations which can be regarded as modifications of Khokhlov–Zabolotskaya–Kuznetsov or Ostrovsky–Vakhnenko equations are suggested. These equations are quite general in that they describe the nonlinear wave dynamics in media with modular nonlinearity. Such media exist among composites, meta-materials, inhomogeneous and multiphase systems. These new models are interesting because of two reasons: (1) the equations admit exact analytic solutions and (2) the solutions describe real physical phenomena. The equations model nonlinear focusing of wave beams. It is shown that inside the focal zone a stationary waveform exists. Steady-state profiles are constructed by the matching of functions describing the positive and negative branches of exact solutions of an equation of Klein–Gordon type. Such profiles have been observed many times during experiments and numerical studies. The non-stationary waves can contain singularities of two types: discontinuity of the wave and of its derivative. These singularities are eliminated by introducing dissipative terms into the equations—thereby increasing their order. © 2017 The Author(s)

Place, publisher, year, edition, pages
Springer Netherlands, 2017
Keyword
Bimodular media, Exact solution, Focusing, HIFU, High-intensity focused ultrasound, Modified KZ–OV, Modular nonlinearity, Nonlinear partial differential equation, Control nonlinearities, Partial differential equations, High intensity focused ultrasound, Nonlinear partial differential equations, Nonlinear equations
National Category
Other Materials Engineering
Identifiers
urn:nbn:se:bth-14471 (URN)10.1007/s11071-017-3560-8 (DOI)000405962800025 ()2-s2.0-85019632379 (Scopus ID)
Available from: 2017-06-13 Created: 2017-06-13 Last updated: 2017-08-22Bibliographically approved
Mikhailov, S. G. & Rudenko, O. (2017). A simple nonlinear element model. Acoustical Physics, 63(3), 270-274
Open this publication in new window or tab >>A simple nonlinear element model
2017 (English)In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 63, no 3, p. 270-274Article in journal (Refereed) Published
Abstract [en]

We study experimentally the behavior of a nonlinear element, a light plate pressed to the opening in the cavity of an acoustic resonator. Measurements of field oscillations inside and outside the cavity have shown that for large amplitudes, they become essentially anharmonic. The time dependences of displacement of the plate with increasing amplitude of the exciting voltage demonstrates a gradual change in the shape of vibrations from harmonic to half-period oscillation. A constant component appears in the cavity: rarefaction or outflow of the medium through the orifice. We construct a theory for nonlinear oscillations of a plate taking into account its different elastic reactions to compression and rarefaction with allowance for monopole radiation by the small-wave-size plate or radiation of a plane wave by the plate. We calculate the amplitudes of the harmonics and solve the problem of low-frequency stationary noise acting on the plate. We obtain expressions for the correlation function and mean power at the output given a normal random process at the input.

Place, publisher, year, edition, pages
MAIK NAUKA/INTERPERIODICA/SPRINGER, 2017
Keyword
artificial nonlinear element, acoustic diode, harmonic generation, flow of the medium, modular nonlinearity
National Category
Mechanical Engineering Other Physics Topics
Identifiers
urn:nbn:se:bth-14842 (URN)10.1134/S1063771017030101 (DOI)000402993600003 ()
Available from: 2017-07-03 Created: 2017-07-03 Last updated: 2017-08-23Bibliographically approved
Hedberg, C. & Rudenko, O. (2017). Collisions, mutual losses and annihilation of pulses in a modular nonlinear medium. Nonlinear dynamics, 90(3), 2083-2091
Open this publication in new window or tab >>Collisions, mutual losses and annihilation of pulses in a modular nonlinear medium
2017 (English)In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 90, no 3, p. 2083-2091Article in journal (Refereed) Published
Abstract [en]

One of the most important sections of nonlinear wave theory is related to the collisions of single pulses. These often exhibit corpuscular properties. For example, it is well known that solitons described by the Korteweg–de Vries equation and a few other conservative model equations exhibit properties of elastic particles, while shock waves described by dissipative models like Burgers’ equation stick together as absolutely inelastic particles when colliding. The interactions of single pulses in media with modular nonlinearity considered here reveal new physical features that are still poorly understood. There is an analogy between the single pulses collision and the interaction of clots of chemical reactants, such as fuel and oxidant, where the smaller component disappears and the larger one decreases after a reaction. At equal “masses” both clots can be annihilated. In this work various interactions of two and three pulses are considered. The conditions for which a complete annihilation of the pulses occurs are indicated. © 2017 The Author(s)

Place, publisher, year, edition, pages
Springer Netherlands, 2017
Keyword
Annihilation, Bimodular media, Modular nonlinearity, Mutual loss, Nonlinear partial differential equation, Pulse interaction, Control nonlinearities, Partial differential equations, Shock waves, Nonlinear partial differential equations, Nonlinear equations
National Category
Other Mechanical Engineering Other Physics Topics
Identifiers
urn:nbn:se:bth-15214 (URN)10.1007/s11071-017-3785-6 (DOI)000413286700038 ()2-s2.0-85028966269 (Scopus ID)
Available from: 2017-09-29 Created: 2017-09-29 Last updated: 2017-11-02Bibliographically approved
Rudenko, O. (2017). One-dimensional model of KZ-type equations for waves in the focal region of cubic and quadratically-cubic nonlinear media. Doklady. Mathematics, 96(1), 399-402
Open this publication in new window or tab >>One-dimensional model of KZ-type equations for waves in the focal region of cubic and quadratically-cubic nonlinear media
2017 (English)In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 96, no 1, p. 399-402Article in journal (Refereed) Published
Abstract [en]

Solutions of the equation describing the high-intensity wave profile within the focal region are derived. This equation is similar to the previously studied models with quadratic and modular nonlinearities, but it is adapted for cubic and quadratically-cubic (QC) nonlinear media, where other physical processes are realized. This simplified one-dimensional equation can be regarded as a "projection" of a three-dimensional equation of Khokhlov-Zabolotskaya type (KZ) onto the axis of the wave beam. Stationary profiles at high intensities of focused waves turn out to be periodic sequences of half-periods of triangular shape with singularities of the derivative at extremum points. Such profiles are typical for nonlinear systems with low-frequency dispersion. There is shown to exist a saturation effect-the amplitude of the wave in the focus cannot exceed a certain maximum value, which does not depend on the initial amplitude.

Place, publisher, year, edition, pages
MAIK NAUKA/INTERPERIODICA/SPRINGER, 2017
Keyword
BURGERS-EQUATION; DYNAMICS
National Category
Mathematics
Identifiers
urn:nbn:se:bth-15160 (URN)10.1134/S1064562417040238 (DOI)000409365100025 ()
Available from: 2017-09-21 Created: 2017-09-21 Last updated: 2017-09-29Bibliographically approved
Vasiljeva, O. A., Lapshin, E. A. & Rudenko, O. (2017). Projection of the Khokhlov-Zabolotskaya Equation on the Axis of Wave Beam As a Model of Nonlinear Diffraction. Doklady. Mathematics, 96(3), 646-649
Open this publication in new window or tab >>Projection of the Khokhlov-Zabolotskaya Equation on the Axis of Wave Beam As a Model of Nonlinear Diffraction
2017 (English)In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 96, no 3, p. 646-649Article in journal (Refereed) Published
Abstract [en]

An equation is obtained that describes the nonlinear diffraction of a focused wave in a half-space starting from the wave source, then through the focus region up to the far zone, where the wave becomes spherically divergent. In contrast to the Khokhlov-Zabolotskaya equation (KZ), which contains two spatial variables, the calculation of the field on the beam axis is reduced to a simpler one-dimensional problem. Integral relations that are useful for numerical calculation are indicated. The profiles of a periodic wave harmonic at the input to the medium are constructed. A comparison with the results of a numerical solution of problems based on KZ is made, which revealed a good accuracy of the approximate model. The passage of a wave through the focus region, accompanied by the formation of shock fronts, diffraction phase shifts and asymmetric distortion of regions of different polarity, is traced.

Place, publisher, year, edition, pages
MAIK NAUKA/INTERPERIODICA/SPRINGER, 2017
National Category
Mathematics
Identifiers
urn:nbn:se:bth-15782 (URN)10.1134/S1064562417060151 (DOI)000419258300026 ()
Available from: 2018-01-18 Created: 2018-01-18 Last updated: 2018-01-18Bibliographically approved
Rudenko, O. (2016). A nonlinear screen as an element for sound absorption and frequency conversion systems. Acoustical Physics, 62(1), 46-50
Open this publication in new window or tab >>A nonlinear screen as an element for sound absorption and frequency conversion systems
2016 (English)In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 62, no 1, p. 46-50Article in journal (Refereed) Published
Abstract [en]

The paper discusses a model for a screen with dissipative and nonlinear elastic properties that can be used in acoustic sound absorption and frequency conversion systems. Calculation and estimation schemes are explained that are necessary for understanding the functional capabilities of the device. Examples of the nonlinear elements in the screen and promising applications are described.

Place, publisher, year, edition, pages
Maik Nauka/Interperiodica, 2016
Keyword
nonlinear screen, absorption, frequency conversion, parametric loudspeaker
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:bth-11663 (URN)10.1134/S106377101601005X (DOI)000368685200006 ()
External cooperation:
Available from: 2016-03-02 Created: 2016-02-29 Last updated: 2017-11-30Bibliographically approved
Rudenko, O. (2016). Equation admitting linearization and describing waves in dissipative media with modular, quadratic, and quadratically cubic nonlinearities. Doklady Mathematics, 94(3), 703-707
Open this publication in new window or tab >>Equation admitting linearization and describing waves in dissipative media with modular, quadratic, and quadratically cubic nonlinearities
2016 (English)In: Doklady Mathematics, ISSN 1064-5624, Vol. 94, no 3, p. 703-707Article in journal (Refereed) Published
Abstract [en]

A second-order partial differential equation admitting exact linearization is discussed. It contains terms with nonlinearities of three types—modular, quadratic, and quadratically cubic—which can be present jointly or separately. The model describes nonlinear phenomena, some of which have been studied, while others call for further consideration. As an example, individual manifestations of modular nonlinearity are discussed. They lead to the formation of singularities of two types, namely, discontinuities in a function and discontinuities in its derivative, which are eliminated by dissipative smoothing. The dynamics of shock fronts is studied. The collision of two single pulses of different polarity is described. The process reveals new properties other than those of elastic collisions of conservative solitons and inelastic collisions of dissipative shock waves.

Place, publisher, year, edition, pages
Maik Nauka/Interperiodica, 2016
Keyword
BURGERS-EQUATION; MODEL
National Category
Other Physics Topics
Identifiers
urn:nbn:se:bth-13795 (URN)10.1134/S1064562416060053 (DOI)000392142200024 ()2-s2.0-85008700671 (Scopus ID)
Note

Open access

Available from: 2017-01-20 Created: 2017-01-20 Last updated: 2017-09-12Bibliographically approved
Rudenko, O. (2016). Exact solutions of an integro-differential equation with quadratically cubic nonlinearity. Doklady. Mathematics, 94(1), 468-471
Open this publication in new window or tab >>Exact solutions of an integro-differential equation with quadratically cubic nonlinearity
2016 (English)In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 94, no 1, p. 468-471Article in journal (Refereed) Published
Abstract [en]

Exact solutions of a nonlinear integro-differential equation with quadratically cubic nonlinear term are found. The equation governs, in particular, stationary shock wave propagation in relaxing media. For the exponential kernel the shapes of both compression and rarefaction shocks having a finite width of the front are calculated. For media with limited "memorizing time" the difference relation permitting the construction of wave profile by the mapping method is derived. The initial equation is rather general. It governs the evolution of nonlinear waves in real distributed systems, for example, in biological tissues, structurally inhomogeneous media and in some meta-materials.

Place, publisher, year, edition, pages
Maik Nauka/Interperiodica, 2016
National Category
Other Mathematics
Identifiers
urn:nbn:se:bth-13053 (URN)10.1134/S1064562416040050 (DOI)000382860900027 ()
Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2017-11-30Bibliographically approved
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