Elena Shchepakina

Samara National Research University

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Vladimir Sobolev

Samara National Research University

Olga Korotkova

University of Miami

СС

С.С. Сажин

University of Brighton

ДА

Д.В. Антонов

Tomsk Polytechnic University

ПА

П. А. Стрижак

National Research Tomsk State University

E. S. Golodova

N. M. Firstova

Samara National Research University

SŞ

Serkan Şahin

TED University

ми

математики и электроники

Michael P. Mortell

University College Cork

Cooperative Institutions

Weierstrass Institute for Applied Analysis and Stochastics

Russian Academy of Sciences

Samara National Research University

Technische Universität Berlin

Forschungsverbund Berlin

Humboldt-Universität zu Berlin

Technical University of Munich

Institute of Thermophysics

National Research Tomsk State University

Politecnico di Milano

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Rectangular Multi-Gaussian Schell-Model beams in atmospheric turbulence

Journal of Optics (2014)

Olga Korotkova Elena Shchepakina

Optical beams radiated by a recently introduced class of Rectangular Multi-Gaussian Schell-Model (RMGSM) source are examined on propagation in free space and in atmospheric turbulence, with both classic and non-classic power spectra of the refractive-index fluctuations. The expression for the cross-spectral density function of such beams has been derived and used for the analysis of their spectral density (average intensity). The RMGSM beams are shown to preserve the square/rectangular shape of the transverse intensity distribution and the maximum intensity level in the flat part for relatively large distances from the source on propagation in classic turbulence. This makes the novel beams attractive for free-space optical communications and surface processing in the presence of the atmosphere.

Atmospheric optics

10.1088/2040-8978/16/4/045704

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Citations (45)

Multi-Gaussian Schell-model beams

Journal of the Optical Society of America A (2012)

Olga Korotkova Serkan Şahin Elena Shchepakina

In a recent publication [Opt. Lett.37, 2970 (2012)10.1364/OL.37.002970], a novel class of planar stochastic sources, generating far fields with flat intensity profiles, was introduced. In this paper we examine the behavior of the spectral density and the state of coherence of beamlike fields generated by such sources on propagation in free space and linear isotropic random media. In particular, we find that at sufficiently large distances from the source, the medium destroys the flat intensity profile, even if it remains such for intermediate distances from the source.

Intensity

Radiant intensity

Spatial coherence

Free space

10.1364/josaa.29.002159

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Citations (208)

ESTIMATION OF DELAYED LOSS OF STABILITY IN DIFFERENTIAL EQUATIONS WITH CANARDS

Vestnik of Samara University Natural Science Series (2013)

E. S. Golodova Elena Shchepakina

The paper is devoted to the investigation of phenomenon of delayed loss of stability in singularly perturbed systems of ordinary differential equations. The estimation for delayed loss of stability is obtained for the differential system with a canard. The problem of maximal temperature of safe combustion determination is considered as an illustration for the obtained mathematical result.

10.18287/2541-7525-2013-19-3-12-24

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Citations (1)

Representations of Slow Integral Manifolds

Lecture notes in mathematics (2014)

Elena Shchepakina Vladimir Sobolev Michael P. Mortell

Manifold (fluid mechanics)

Center manifold

10.1007/978-3-319-09570-7_4

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Spectral Gaussian Schell-model beams

Optics Letters (2013)

Elena Shchepakina Olga Korotkova

A generalization of the classic Gaussian Schell-model source is considered for which the rms width of the beam σ and the rms width of the spectral degree of coherence δ are assumed to depend on wavelength. It is shown that the functional form σ(λ) and δ(λ) of such a source can affect the behavior of the spectral density, the degree of coherence, and the degree of polarization of the propagating beam.

Degree of polarization

Degree of coherence

Coherence theory

Coherence time

10.1364/ol.38.002233

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Citations (10)

Stable/unstable slow integral manifolds in critical cases

Journal of Physics Conference Series (2017)

Elena Shchepakina

The paper deals with the problem of a construction of global stable/unstable slow integral manifolds of the singularly perturbed systems in critical cases. In addition to the well-known critical cases a novel scenario of the stability change of the slow integral manifold is considered. All three critical cases leading to the change of the stability are discussed via the Hindmarsh-Rose dynamic model. It is shown that the suitable choice of the additional parameters of the system yields the slow integral manifold with multiple change of its stability.

Manifold (fluid mechanics)

Stable manifold

Center manifold

10.1088/1742-6596/811/1/012016

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Unstable Invariant Manifolds in a Control Problem of the Combustion Process of a Gas Mixture

Elena Shchepakina

We consider a control problem of the combustion process of a gas mixture with taking into account the consumption of the reagent and oxidizer. In the system, depending on the values of the control parameter, either slow burnout regime or thermal explosion can be observed. It is shown that there is a critical regime separating these two regimes. The value of the control parameter corresponding to the critical regime is found. The analysis is based on the technique of the continuation of unstable invariant manifolds.

Continuation

10.1109/stab54858.2022.9807573

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Calculation of critical conditions for the filtration combustion model

Olga Vidilina Elena Shchepakina

The paper is devoted to the study of the dynamic model of the autocatalytic combustion reaction in an inert medium with partial heat removal from the reaction phase to the environment. We pay particular attention to modelling of the critical regime, which is a kind of a watershed between the slow burning regimes and explosion modes. New algorithm for computing a critical value of the control parameter is presented.

Filtration (mathematics)

Inert

Autocatalysis

10.18287/1613-0073-2017-1904-151-157

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Conditions for the loss of stability of eqiulibrium manifold in satellite model

Elena Shchepakina Vladimir Sobolev

The problem of stabilizing a spin satellite by means of passive dampers is considered. The application of the method of integral manifolds allows us to find conditions for the loss of stability in the analytical form.

Manifold (fluid mechanics)

10.18287/1613-0073-2017-1904-49-51

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STUDY OF OSCILLATORY PROCESSES IN THE ONE MODEL OF ELECTROCHEMICAL REACTOR

N. M. Firstova Elena Shchepakina

The paper deals with the study of the features of oscillatory processes in the electrocatalytic reaction mechanism underlying the electrochemical reactor. The conditions for the existence of several types of oscillations (small amplitude harmonic oscillations, relaxation oscillations and oscillations of transitional type) is obtained.

Harmonic

Oscillation (cell signaling)

Harmonic Analysis

10.18287/1613-0073-2016-1638-731-741

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Citations (7)