Персона: Шаргатов, Владимир Анатольевич
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Институт лазерных и плазменных технологий
Стратегическая цель Института ЛаПлаз – стать ведущей научной школой и ядром развития инноваций по лазерным, плазменным, радиационным и ускорительным технологиям, с уникальными образовательными программами, востребованными на российском и мировом рынке образовательных услуг.
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Руководитель научной группы "Математические модели физических процессов изделий в экстремальных условиях эксплуатации"
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Шаргатов
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Владимир Анатольевич
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17 results
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- ПубликацияТолько метаданныеDynamics of front-like water evaporation phase transition interfaces(2019) Il'ichev, A. T.; Shargatov, V. A.; Gorkunov, S. V.; Шаргатов, Владимир Анатольевич; Горкунов, Сергей Владимирович© 2018 We study global dynamics of phase transition evaporation interfaces in the form of traveling fronts in horizontally extended domains of porous layers where a water located over a vapor. These interfaces appear, for example, as asymptotics of shapes of localized perturbations of the unstable plane water evaporation surface caused by long-wave instability of vertical flows in the non-wettable porous domains. Properties of traveling fronts are analyzed analytically and numerically. The asymptotic behavior of perturbations are described analytically using propagation features of traveling fronts obeying a model diffusion equation derived recently for a weakly nonlinear narrow waveband near the threshold of instability. In context of this problem the fronts are unstable though nonlinear interplay makes possible formation of stable wave configurations. The paper is devoted to comparison of the known results of front dynamics for the model diffusion equation, when two phase transition interfaces are close, and their dynamics in general situation when both interfaces are sufficiently far from each other.
- ПубликацияТолько метаданныеAnalytical description of the structure of special discontinuities described by a generalized KdV–Burgers equation(2019) Chugainova, A. P.; Shargatov, V. A.; Шаргатов, Владимир Анатольевич© 2018 Elsevier B.V. Traveling wave solutions of a generalized KdV–Burgers equation are studied. The nonlinearity is specified as a piecewise linear flux function consisting of four parts. A boundary value shock-structure problem is solved. An analytical solution describing the structures of special discontinuities (undercompressive shocks) is obtained, and the behavior of these solutions is examined for various parameters of the problem.
- ПубликацияТолько метаданныеStability of finite perturbations of the phase transition interface for one problem of water evaporation in a porous medium(2020) Il'ichev, A. T.; Shargatov, V. A.; Gorkunov, S. V.; Шаргатов, Владимир Анатольевич; Горкунов, Сергей Владимирович© 2020 Elsevier Inc.We study global dynamics of phase transition evaporation interfaces in horizontally extended domains of porous layers where a water located over a vapor. The derivation of the model equation describing the secondary structures, which bifurcate from the ground state in a small neighborhood of the instability threshold in the case of a quasi-stationary approach to the description of the diffusion process, is presented. The resulting equation is reduced to the equation in the form of Kolmogorov-Petrovsky-Piskounov. The obtained approximate equation predicts the existence of stationary solutions in the full problem. To verify the obtained results, the numerical solution of the problem of the motion of the phase transition interface is performed using the original program code developed by the authors. The results of numerical simulation are used to verify the possibility of using stationary solutions obtained in the weakly nonlinear approximation to determine the scenario for the development of the initial localized finite amplitude perturbation. It is shown that the obtained approximate stationary solutions accurately predict the behavior of the perturbation in the vicinity of the turning point of the bifurcation diagram. A modification of the formulas describing an approximate stationary soliton-like solution is proposed in the case when the perturbation amplitude is comparable with the height of a low-permeable layer of a porous medium in which the phase transition interface is located. By numerical simulation it is shown that this modified approximate solution is in good agreement with the results of numerical calculation for the full problem.
- ПубликацияТолько метаданныеCritical Evolution of Finite Perturbations of a Water Evaporation Surface in Porous Media(2020) Il'ichev, A. T.; Gorkunov, S. V.; Shargatov, V. A.; Горкунов, Сергей Владимирович; Шаргатов, Владимир Анатольевич© 2020, Pleiades Publishing, Ltd.Abstract—: It is shown that the approximate steady-state solutions, which satisfy the model dissipative equation that describes the process of water evaporation in the neighborhood of the instability threshold of a phase transition interface, determine localized damped finite-amplitude perturbations when a certain condition is fulfilled. These steady-state solutions can be used for forecasting the scenario of the development of a perturbation with sufficient accuracy if this perturbation has no common points with any steady-state solution. If the initial position of the phase transition front is located between the spectrally stable solution and any of the steady-state solutions, this front damps. If the initial position of the front is located above at least one of the spectrally unstable steady-state solutions, then the solution is catastrophically restructured.
- ПубликацияТолько метаданныеTraveling waves and undercompressive shocks in solutions of the generalized Korteweg–de Vries–Burgers equation with a time-dependent dissipation coefficient distribution(2020) Chugainova, A. P.; Shargatov, V. A.; Шаргатов, Владимир Анатольевич© 2020, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.Solutions of the generalized KdV–Burgers equation are analyzed in the case when the dissipation coefficient depends on the spatial coordinate and time. Solutions in the form of traveling waves describing the structure of discontinuities, including special discontinuities, are studied. In the frame of this problem, nonstationary solutions of the generalized KdV–Burgers equation including the special discontinuity are numerically found.
- ПубликацияТолько метаданныеDynamics of Perturbations under Diffusion in a Porous Medium(2020) Il'ichev, A. T.; Shargatov, V. A.; Шаргатов, Владимир Анатольевич© 2020, Pleiades Publishing, Ltd.Abstract: We consider the dynamics of finite perturbations of a plane phase transition surface in the problem of evaporation of a fluid inside a low-permeability layer of a porous medium. In the case of a nonwettable porous medium, the problem has two stationary solutions, each containing a discontinuity. These discontinuities correspond to plane stationary phase transition surfaces located inside the low-permeability porous layer. One of these surfaces is unstable with respect to long-wavelength perturbations, while the other is stable. We study the evolution of perturbations of the stable plane phase transition surface. It is known that when two phase transition surfaces are located close enough to each other, the dynamics of a weakly nonlinear and weakly unstable wave packet is described by the Kolmogorov–Petrovskii–Piskunov (KPP) diffusion equation. As traveling wave solutions, this equation has heteroclinic solutions with either oscillating or monotonic structure of the front. The boundary value problem in the full statement, which should be considered if the distance between the stable and unstable plane phase transition surfaces is not small, also has similar solutions. We formulate a sufficient condition for the decrease of finite perturbations of the stable plane phase transition surface. This condition depends on their position with respect to the standing wave type and traveling front type solutions of the model equations in the model description when the KPP equation holds.
- ПубликацияТолько метаданныеOn the Structure Stability of a Neutrally Stable Shock Wave in a Gas and on Spontaneous Emission of Perturbations(2020) Kulikovskii, A. G.; Il'ichev, A. T.; Chugainova, A. P.; Shargatov, V. A.; Шаргатов, Владимир Анатольевич© 2020, Pleiades Publishing, Inc.Abstract: We analyze the stability of the structure of a neutrally stable shock wave, which is also referred to as a spontaneously emitting shock wave. We have obtained solutions describing linear sinusoidal perturbations emerging in the structure and downflow which depend on the coordinate along the emitting structure. It is shown that these perturbations decay with time. We have also considered the limit transition for the dimensionless width of the structure, which tends to zero. The results obtained in the limit coincide with classical results when the shock wave is treated as the discontinuity surface.
- ПубликацияТолько метаданныеStability of shock wave structures in nonlinear elastic media(2019) Chugainova, A. P.; Il'ichev, A. T.; Shargatov, V. A.; Шаргатов, Владимир Анатольевич© The Author(s) 2019.The stationary structure stability of discontinuous solutions to nonlinear hyperbolic equations describing the propagation of quasi-transverse waves with velocities close to characteristic ones are studied. A procedure to analyze spectral (linear) stability of these solutions is described. The main focus is the stability analysis of special discontinuities, the stationary structure of which is represented by the integral curve connecting two saddle points corresponding to the states in front of and behind the discontinuity. This analysis is done using the properties of the Evans function, an analytic function on the right complex half-plane, which has zeros in this domain if and only if there exist unstable modes of linearization around a solution representing a special discontinuity with the structure.
- ПубликацияТолько метаданныеSpontaneously Radiating Shock Waves(2019) Kulikovskiy, A. G.; Il'ichev, A. T.; Chugainova, A. P.; Shargatov, V. A.; Шаргатов, Владимир Анатольевич© 2019, Pleiades Publishing, Ltd.Abstract: In this paper, we built a solution representing the structure of a spontaneously radiating shock wave and studied its stability in the linear approximation. We found waves of linear disturbances that can propagate through a structure and waves radiating into the flow region behind the structure, i.e., waves corresponding to the spontaneous radiation of disturbances by a shock wave considered as a discontinuity surface.
- ПубликацияТолько метаданныеStudy of nonstationary solutions of a generalized Korteweg-de Vries-Burgers equation(2019) Chugainova, A. P.; Shargatov, V. A.; Шаргатов, Владимир Анатольевич© 2019 Author(s).The evolution of structures of special discontinuities representing solutions of the Cauchy problem for a generalized Korteweg-de Vries-Burgers equation is numerically investigated with allowance for complex nonlinearity, dispersion, and dissipation. Various perturbations of these solutions are considered, and a decay scenario for a solution representing a special discontinuity structure is analyzed.