Sevastyanov Leonid Antonovich
Sevastyanov Leonid Antonovich
Doctor en Ciencias Físicas y Matemáticas

¡Ves la tarea - resuélvela, por esa razón se te da el intelecto!

1971

Es graduado del Departamento de Física Teórica, la Facultad de Ciencias Físicas y Matemáticas y Ciencias Naturales de la Universidad de la Amistad de los Pueblos “P. Lumumba”. La especialidad de “Física”.

En 1971

Ingresó en el doctorantado en la dirección de “Métodos del análisis funcional para la física”. El tutor científico: Doctor en Ciencias Físicas y Matemáticas, Profesor Titular Zhelobenko D. P.. Al mismo tiempo, trabajó a tiempo parcial en el Instituto de Investigaciones Nucleares en el grupo del Profesor Titular Kazarnovskiy Yu.M. Los resultados de las investigaciones se utilizaron en el diseño de los trajes espaciales para los vuelos espaciales.

1980 ‒ 1985

Jefe del equipo de investigadores en el marco de un proyecto sobre la óptica adaptativa para las comunicaciones espaciales. El modelo matemático desarrollado para la calibración de las superficies ópticas y los métodos para la calibración de las ópticas de gran tamaño se introdujeron en el Instituto de Óptica Estatal “S.I. Vavilov”.

1984

Defendió su tesis de candidato a doctor sobre la modelación del proceso de deposición al vacío de los elementos ópticos integrados de un perfil complejo.

1999

Defendió su tesis doctoral sobre el “Modelo matemático de la deposición de pantalla: un experimento computacional usando los resultados de los experimentos in situ”, la especialidad de 05.13.16 – “El uso de las computadoras, la modelación matemática y los métodos matemáticos en las investigaciones científicas”.

De 1999 hasta el presente

Profesor Titular del Departamento de Sistemas de Telecomunicaciones, renombrado en el Departamento de la Informática Aplicada y la Teoría de la Probabilidad de la RUDN.

Es redactor principal adjunto de la revista científica de “Vestnik RUDN, la serie de Matemáticas, Informática y Física”, Presidente del Consejo de Disertación D 212.203.28 adjunto a la RUDN. Durante los últimos 30 años, Leonid Sevastyanov viene siendo el miembro de los comités de programas de varias conferencias internacionales sobre la modelación matemática y la física computacional.

Docencia

A lo largo de los años, impartió los siguientes cursos de conferencias:

  • Los métodos numéricos.
  • Las matemáticas discretas.
  • La modelación matemática.
  • La programación científica.
  • La modelación matemática de las nanoestructuras ópticas.
  • Los métodos variacionales en la modelación matemática.
     

Ciencia

Bajo la dirección de Leonid Sevastyanov, se llevan a cabo las investigaciones sobre la modelación matemática de una amplia gama de procesos y sistemas, tanto de origen natural como artificial, la solución analítica y numérica de una amplia clase de tareas aplicadas de la física computacional, se dedica a la modelación de los recubrimientos ópticos con tamaños característicos de subonda (nanométricos) y el desarrollo de los métodos del diagnóstico computacional de los tejidos rígidos y blandos en el rango óptico de la radiación electromagnética. Según los resultados de las investigaciones, el Profesor Titular recibió 8 certificados de derechos de autor para las invenciones, publicó más de 150 artículos científicos y 5 monografías.

Intereses Científicos

  • La solución numérica de los problemas de la óptica de guías de onda,     la modelación de las estructuras ópticas integradas.
  • La modelación computacional de las mediciones mecánicas cuánticas.
  • La modelación computacional de las propiedades físicas de las películas de grafeno.
The generalization of the incomplete Galerkin method to the description of the transitions of the “horn” type between open planar waveguides is discussed. The obtained result is characterized by a high degree of analyticity of the derived equations and this is expected to enhance the efficiency of the eigenwave modeling in open irregular waveguides.
To implement the method of adiabatic waveguide modes for modeling the propagation of polarized monochromatic electromagnetic radiation in irregular integrated optics structures it is necessary to expand the desired solution in basic adiabatic waveguide modes. This expansion requires the use of the scalar product in the space of waveguide vector fields of integrated optics waveguide. This work solves the first stage of this problem – the construction of the scalar product in the space of vector solutions of the eigenmode problem (classical and generalized) waveguide modes of an open planar waveguide. In constructing the mentioned sesquilinear form, we used the Lorentz reciprocity principle of waveguide modes and tensor form of the Ostrogradsky-Gauss theorem.
Presentation of the probability as an intrinsic property of the nature leads researchers to switch from deterministic to stochastic description of the phenomena. The procedure of stochastization of one-step process was formulated. It allows to write down the master equation based on the type of of the kinetic equations and assumptions about the nature of the process. The kinetics of the interaction has recently attracted attention because it often occurs in the physical, chemical, technical, biological, environmental, economic, and sociological systems. However, there are no general methods for the direct study of this equation. Leaving in the expansion terms up to the second order we can get the Fokker-Planck equation, and thus the Langevin equation. It should be clearly understood that these equations are approximate recording of the master equation. However, this does not eliminate the need for the study of the master equation. Moreover, the power series produced during the master equation decomposition may be divergent (for example, in spatial models). This makes it impossible to apply the classical perturbation theory. It is proposed to use quantum field perturbation theory for the statistical systems (the so-called Doi method). This work is a methodological material that describes the principles of master equation solution based on quantum field perturbation theory methods. The characteristic property of the work is that it is intelligible for non-specialists in quantum field theory. As an example the Verhulst model is used because of its simplicity and clarity (the first order equation is independent of the spatial variables, however, contains non-linearity). We show the full equivalence of the operator and combinatorial methods of obtaining and study of the one-step process master equation.
As a result of the application of a technique of multistep processes stochastic models construction the range of models, implemented as a self-consistent differential equations, was obtained. These are partial differential equations (master equation, the Fokker--Planck equation) and stochastic differential equations (Langevin equation). However, analytical methods do not always allow to research these equations adequately. It is proposed to use the combined analytical and numerical approach studying these equations. For this purpose the numerical part is realized within the framework of symbolic computation. It is recommended to apply stochastic Runge--Kutta methods for numerical study of stochastic differential equations in the form of the Langevin. Under this approach, a program complex on the basis of analytical calculations metasystem Sage is developed. For model verification logarithmic walks and Black--Scholes two-dimensional model are used. To illustrate the stochastic "predator--prey" type model is used. The utility of the combined numerical-analytical approach is demonstrated.
The paper describes the relationship between the solutions of Maxwell’s equations which can be considered at least locally as plane waves and the curvilinear coordinates of geometrical optics; it generalizes the results achieved by Lüneburg, concerning the evolution of surfaces of electromagnetic fields discontinuities. If vectors  and  are orthogonal to each other and their directions do not change with time t, but may vary from point to point in the domain G, then under some conditions there is an orthogonal coordinate system  in which -lines represent rays of geometrical optics, -lines point out -direction and, -lines point out -direction. This coordinate system will be called phase-ray coordinate system. In the article, it will be proved that field under study can be represented by two scalar functions. The article will also specify the necessary and sufficient conditions for the existence of a coordinate system, generated by the solution of Maxwell’s equations with the holonomic field of the Poynting vector. It is shown that the class of solutions of Maxwell’s equations, as described in this work, includes monochromatic polarized waves, and the Hilbert–Courant solutions and their generalizations.
The mathematical model of light propagation in a planar gradient optical waveguide consists of the Maxwell’s equations supplemented by the matter equations and boundary conditions. In the coordinates adapted to the waveguide geometry, the Maxwell’s equations are separated into two independent sets for the TE and TM polarizations. For each there are three types of waveguide modes in a regular planar optical waveguide: guided modes, substrate radiation modes, and cover radiation modes. We implemented in our work the numerical-analytical calculation of typical representatives of all the classes of waveguide modes. In this paper we consider the case of a linear profile of planar gradient waveguide, which allows for the most complete analytical description of the solution for the electromagnetic field of the waveguide modes. Namely, in each layer we are looking for a solution by expansion in the fundamental system of solutions of the reduced equations for the particular polarizations and subsequent matching them at the boundaries of the waveguide layer. The problem on eigenvalues (discrete spectrum) and eigenvectors is solved in the way that first we numerically calculate (approximately, with double precision) eigenvalues, then numerically and analytically—eigenvectors. Our modelling method for the radiation modes consists in reducing the initial potential scattering problem (in the case of the continuous spectrum) to the equivalent ones for the Jost functions: the Jost solution from the left for the substrate radiation modes and the Jost solution from the right for the cover radiation modes.
Background. By the means of the method of stochastization of one-step processes we get the simplified mathematical model of the original stochastic system. We can explore these models by standard methods, as opposed to the original system. The process of stochastization depends on the type of the system under study. Purpose. We want to get a unified abstract formalism for stochastization of one-step processes. This formalism should be equivalent to the previously introduced. Methods. To unify the methods of construction of the master equation, we propose to use the diagram technique. Results. We get a diagram technique, which allows to unify getting master equation for the system under study. We demonstrate the equivalence of the occupation number representation and the state vectors representation by using a Verhulst model. Conclusions. We have suggested a convenient diagram formalism for unified construction of stochastic systems.
This paper studies program implementation problem of pseudo-random number generators in OpenModelica. We give an overview of generators of pseudo-random uniform distributed numbers. They are used as a basis for construction of generators of normal and Poisson distributions. The last step is the creation of Wiener and Poisson stochastic processes generators. We also describe the algorithm to call external C-functions from programs written in Modelica. This allows us to use random number generators implemented in the C language.
This paper studies program implementation problem of pseudo-random number generators in OpenModelica. We give an overview of generators of pseudo-random uniform distributed numbers. They are used as a basis for construction of generators of normal and Poisson distributions. The last step is the creation of Wiener and Poisson stochastic processes generators. We also describe the algorithm to call external C-functions from programs written in Modelica. This allows us to use random number generators implemented in the C language.
Representing a probability density function (PDF) and other quantities describing a solution of stochastic differential equations by a functional integral is considered in this paper. Methods for the approximate evaluation of the arising functional integrals are presented. Onsager–Machlup functionals are used to represent PDF by a functional integral. Using these functionals the expression for PDF on a small time interval Δt can be written. This expression is true up to terms having an order higher than one relative to Δt. A method for the approximate evaluation of the arising functional integrals is considered. This method is based on expanding the action along the classical path. As an example the application of the proposed method to evaluate some quantities to solve the equation for the Cox–Ingersol–Ross type model is considered.
В работе рассматривается задача дифракции электромагнитного TE-поляризованного монохроматического излучения на трёхмерном утолщении волноводного слоя регулярного планарного трёхслойного диэлектрического волновода, формирующем тонкоплёночную волноводную линзу. Предлагается приближенная математическая модель, в которой открытый волновод рассматривается внутри вспомогательного закрытого волновода, приводящая к корректной математической постановке задачи дифракции. В работе показано, что параметры направляемых мод открытого волновода устойчивы к сдвигам границ объемлющего закрытого волновода. Следовательно, предлагаемый подход адекватно описывает распространение поляризованного света в открытом плавнонерегулярном волноводе. За счёт локального утолщения волноводного слоя возникает эффект деполяризации излучения, который требует рассмотрения векторного характера распространяющегося электромагнитного излучения. В работе задача дифракции решается в адиабатическом приближении по малому параметру, соответствующему нерегулярности. Проведение численных экспериментов позволило показать, что с уменьшением малого параметра матрица коэффициентов отражения стремится к нулю, а матрица коэффициентов прохождения стремится к единичной матрице. Причём обменные вклады, которым соответствуют недиагональные элементы матриц, стремятся к нулю на порядок быстрее, чем диагональные члены. Так что, эффектами деполяризации в рассматриваемой конфигурации можно пренебречь.
The paper deals with a numerical solution of the problem of waveguide propagation of polarized light in smoothly-irregular transition between closed regular waveguides using the incomplete Galerkin method. This method consists in replacement of variables in the problem of reduction of the Helmholtz equation to the system of differential equations by the Kantorovich method and in formulation of the boundary conditions for the resulting system. The formulation of the boundary problem for the ODE system is realized in computer algebra system Maple. The stated boundary problem is solved using Maples libraries of numerical methods.
Dmitriy Divakov, Mikhail Malykh, Leonid Sevastianov, Anton Sevastianov and Anastasia Tiutiunnik 2017 The numerical-analytical implementation of the cross-sections method to the open waveguide transition of the "horn" type [10337-23] Proceedings of SPIE Vol. 10337
Multilayered integrated-optical waveguides consisting of homogeneous dielectric layers of constant or variable thickness are studied by the cross-sections method. The method is based on the cross-sections of the expansion in a complete set of waveguide modes of comparison waveguides. Used in the implementation of the method table of scalar products of the modes is calculated analytically using computer algebra system. The resulting system of integro-differential equations for the expansion coefficients is solved numerically.
Migran Gevorkyan, Dmitriy Kulyabov, Konstantin Lovetskiy, Leonid Sevastianov and Anton Sevastianov 2017 Field calculation for the horn waveguide transition in the single-mode approximation of the cross-sections method [10337-25] Proceedings of SPIE Vol. 10337
We investigate the waveguide propagation of polarized monochromatic light in a smoothly irregular transition between two regular planar dielectric waveguides. The single-mode approximation of the cross-sections method is used. The smooth evolution of the electromagnetic field of a propagating mode is calculated. The calculation is performed by the regularized stable numerical metod.
Edik Ayryan, Genin Dashitsyrenov, Evgeniy Laneev, Konstantin Lovetskiy, Leonid Sevastianov and Anton Sevastianov 2017 Mathematical synthesis of the thickness profile of the waveguide Lüneburg lens using the adiabatic waveguide modes method [10337-27] Proceedings of SPIE Vol. 10337
In the work the classical and generalized Luneburg lens in bulk and waveguide implementation are described. The link between the focusing inhomogeneity of the effective refractive index of waveguide Luneburg lens and the irregularity of the waveguide layer thickness generating this inhomogeneity is demonstrated. For the dispersion relation of irregular thin-film waveguide in the model of adiabatic waveguide modes the problem of mathematical synthesis and computer-aided design of the waveguide layer thickness profile for the Luneburg thin-film generalized waveguide lens with a given focal length is being solved. The calculations are carried out in normalized (in a special way) coordinates in order to adapt the used relations to computer calculations. The obtained solution is compared with the same solution within the cross-sections method.