Diagnostics of the medium structure by long wave of finite amplitude

Vakhnenko, Vyacheslav O.; Danylenko, V.A.; Michtchenko, A.

doi:10.1016/s0020-7462(99)00082-7

Cited by 7 publications

(5 citation statements)

References 8 publications

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“…The numerical scheme for system (28) is based on the integro-interpolating method [22] in which the approximation of the integral conservation laws is used. Note that, instead of the second equation of system (1), it is more convenient to use the following equation describing the volume element changing [22]:…”

Section: Numerical Simulations Of Dynamical Behavior Of the Soliton-l...mentioning

confidence: 99%

“…As it is shown in a number of papers (see e.g. [26][27][28] and references therein), the balance equations for mass and momentum in the long wave approximation retain their classical form, and the information about the presence of structure is manifested in the dynamical equation of state (DES), relating the pressure field to the field of density. In this study, we consider a model of a nonlinear elastic medium containing multiple evenly distributed inclusions (these can be cracks, cavities, or inclusions of a substance that differs significantly from the carrier material in its physical properties).…”

Section: Introductionmentioning

confidence: 99%

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Soliton-like solutions supported by refined hydrodynamic-type model of an elastic medium with soft inclusions

Vladimirov,

Skurativskyi

2024

NAMC

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A nonlinear elastic medium containing sharp inhomogeneities is considered. The properties of a modified model of such a medium are investigated. The modification consists in including in the asymptotic equation of state those terms that were discarded in the previously considered models. The main purpose of the ongoing research is to analyze the existence, stability, and dynamic properties of soliton-like solutions within the modified model, as well as to compare these solutions with analogous solutions obtained in the previously considered models.

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Section: Numerical Simulations Of Dynamical Behavior Of the Soliton-l...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Soliton-like solutions supported by refined hydrodynamic-type model of an elastic medium with soft inclusions

Vladimirov,

Skurativskyi

2024

NAMC

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“…We describe the wave processes in nonequilibrium heterogeneous media in terms of an asymptotic averaged model [18][19][20][21][22]. The obtained integral differential system of equations cannot be reduced to the average terms (pressure, mass velocity, specific volume) and contains the terms with characteristic sizes of individual components.…”

Section: Asymptotic Averaged Model For Structured Mediummentioning

confidence: 99%

“…The immediate employment of a method of the asymptotic averaging in Eulerian variables is impossible because of the variability of the microstructure sizes. However, from the zero approximation in the equations of motion (11), which are presented by the averaged values p, u, and V hi , the equations can be rewritten in the Eulerian system of coordinates r, t E ðÞ utilizing a transformation from the Lagrangian system s, t ðÞ [18][19][20][21][22]:…”

Section: System Of Equations In Eulerian Coordinatesmentioning

confidence: 99%

Mathematical Fundamentals of a Diagnostic Method by Long Nonlinear Waves for the Structured Media

Vakhnenko¹,

Vengrovich²,

Michtchenko³

2020

Advances in Complex Analysis and Applications

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We have proven that the long wave with finite amplitude responds to the structure of the medium. The heterogeneity in a medium structure always introduces additional nonlinearity in comparison with the homogeneous medium. At the same time, a question appears on the inverse problem, namely, is there sufficient information in the wave field to reconstruct the structure of the medium? It turns out that the knowledge on the evolution of nonlinear waves enables us to form the theoretical fundamentals of the diagnostic method to define the characteristics of a heterogeneous medium using the long waves of finite amplitudes (inverse problem). The mass contents of the particular components can be denoted with specified accuracy by this diagnostic method.

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“…Thus, it is proved that, in the general case, the heterogeneities in a medium introduce the additional nonlinearity. This effect provides the basis for a new method of diagnostics to define the properties of multicomponent media using the propagation [20].…”

Section: ≤ a B A A B Bmentioning

confidence: 99%

Blast Waves in Multi-Component Medium with Thermal Relaxation

Vakhnenko¹

2014

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The mathematical models of relaxing media with a structure for describing nonlinear long-wave processes are explored. The wave processes in non-equilibrium heterogeneous media are studied in terms of the suggested asymptotic averaged model. On the microstructure level of the medium, the dynamical behavior is governed only by the laws of thermodynamics, while, on the macrolevel, the motion of the medium can be described by the wave-dynamical laws. It is proved rigorously that on the acoustic level, the propagation of long waves can be properly described only in terms of dispersive dissipative properties of the medium, and in this case, the dynamical behavior of the medium can be modeled by a homogeneous relaxing medium. At the same time, the dynamical behavior of the medium cannot be modeled by a homogeneous medium even for long waves, if they are nonlinear. For a finite-amplitude wave, the structure of medium produces nonlinear effects even if the individual components of the medium are described by a linear law. The heterogeneity of the structure of medium always introduces additional nonlinearity. It is shown that the solution of many problems for multi-component media with incompressible phases can be obtained through the known solution of a similar problem for a homogeneous compressible medium by means of the suggested transformation. It is not necessary to solve directly the problem for the medium with incompressible component, and it is sufficient just to transform the known solution of the similar problem for a homogeneous medium. The scope for the suggested transformation is demonstrated by the reference to the strong explosion state in a two-phase medium. The special attention is focused on the research of blast waves in multi-component media with thermal relaxation. The dependence of the shock damping parameters on the thermal relaxation time is analyzed in order to provide a deeper understanding of the damping of shock waves in such media and to determine their effectiveness as localizing media. This problem attracts the interest also in view of the practical possibility to estimate the efficiency of medium for damping the shock wave action. To find the nature of the relaxation interaction between the components of medium and to estimate the attenuation of shock waves generated by solid explosives, we have studied experimentally both the velocity field of shock waves and the pressure at front in an air foam. The comparison of experimental and theoretical investigations of the relaxation phenomena which accompany the propagation of shock waves in foam indicates that within the scope of relaxation hy-V. O. Vakhnenko 1056 drodynamics it is possible to explain the observed phenomena and estimate the efficiency of medium as localizer of the shock wave action.

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Diagnostics of the medium structure by long wave of finite amplitude

Cited by 7 publications

References 8 publications

Soliton-like solutions supported by refined hydrodynamic-type model of an elastic medium with soft inclusions

Soliton-like solutions supported by refined hydrodynamic-type model of an elastic medium with soft inclusions

Mathematical Fundamentals of a Diagnostic Method by Long Nonlinear Waves for the Structured Media

Blast Waves in Multi-Component Medium with Thermal Relaxation

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