Yunakovsky Alexey Dmitrievich
key scientist
D.Sc., Prof.
Education:
Gorky State University, 1963, “mathematics computational mathematic”, D.Sc., Prof.
Scientific interests:
mathematical physics, numerical mathematics, numerical simulation (plasma physics, HF-electronics, electrodynamics)
Specialized scientific interests:
Spectral methods for the nonlinear Schroedinger equation, method of discrete sources in application to the Helmholtz type equation, analytical and numerical methods of research corrugated and helical waveguides.
Professional career:
Scientifically researchn radiophysical institute (since 1966 till 1977), Institute of Applied Physics, Russian Academy of Sciences (since 1977 till nowadays), laboratory of computational physics
Award bonus grant:
Grant RFBR
01-01-00577-а
Simulation of the electrodynamical systems of energy accumulation and its optimization
09-01-00705
Mathematical modeling of broad-band waveguide systems with mode converters of millimeter and terahertz frequency bands.
Educational activity:
Management of scientific work of students and job seekers (PhD thesis defended - 4)
Reading special courses for masters and specialists:
Computer geometry (NNSUniv., Dep. Mat.Soft.)
Fast and parallelized algorithms (NNSUniv., Dep. Mat.Soft.)
Modern methods of signal processing (wavelet theory), ((NNSUniv., Masters Comp.Math. and Mech-Mat.)
Mathematical modeling of control systems (NSTU Univ. Applied Mathematics, MSc)
Computed tomography (UNN IUD Univ. Dep. Mo.)
Number of publications:
732 (48 in reviewed journals, 18 in scientific proceedings, 3 monograph 4 teaching aids)
The most significant papers and results:
Монографии:
A.D.Yunakovsky. Simulation of the Nonlinear Schrodinger Equation.
Abstract
The monograph is dedicated to the problem of mathematical simulation of nonlinear Shrodinger equation which is highly universal and is used in many fields of physics for description of the wave processes/ The basic principles of construction of the approximate solutions are stated. The examples of these algorithms bases on the splitting-up in physical processes are presented and validated by spectral and grid methods. For reading the proofs of properties of the used algorithms ,it is sufficient to know the elements of the functional analysis. The necessary knowledge about Discrete Fourier Transform is given in appendix. This book is intended for specialists in the field of physical processes, advanced students and postgraduates.
A.D.Yunakovsky. Basics of Numerical Methods for Physicists
ABOUT THE BOOK. Problems of great importance for scientists engaged in computations are discussed in the book. The present book successfully combines the most settled elements of the theory of numerical methods (approved themselves effective) with description of new directions of their development. In every case an attempt has been made in the book to show problems really actual for professionals in appropriate fields and to point out possible ''underwater reefs'' The main goal of the book is to provide a deep knowledge of quantitative properties of solutions in construction of effective algorithms.
Today a new trend of thinking by moduli, systems or transforms reflecting entry and exit of the subprogram, which realizes a chosen method according to precisely determined rules, is developed. The book helps the reader to elaborate understanding of the fact that obtaining a good result it is not enough for considering even well-known subprograms as some "black box". It must become grey or even perfectly transparent for a user.
The book contains interesting and necessary materials attractive not only for students and postgraduates, but also for specialists in numerical methods. It will contribute to the development of constructive numerical methods for study of applied problems.
1The most cited paper on numerical methods in plasma physics
Litvak A.G., Vironov V.A.,Fraiman G.M., Yunakovskii A.D. “Termal Self-Effect of Wave Beamsin Plasma with a Nonlocal Nonlinearity” Plasma Physics Reports.1975.Vol. 1, P. 31
2 The most cited paper on microwave electronics
Ya.L.Bogomolov, V.L.Bratman, N.S.Ginzburg, M.I.Petelin, A.D.Yunakovsky “Nonstationary generation in free electron lasers”, Opt.Commun., 1981, Vol. 36, No. 3, p. 209
Abstract
Evolution of the alternating field structure in the high-Q multimode cavity excited by the beam of relativistic electron oscillators is described by a self-consistent set of equations. Stationary and pulse injection regimes are investigated. The injection current increasing over the threshold, three consecutive stages take place: a) stationary single-mode generation (or, correspondingly, generation of identical pulses), b) periodic and c) stochastic self-modulation.
3 Satellite to 1 paper
Ya.L.Bogomolov, A.D.Yunakovsky “Numerical simulation of nonstationary processes in free electron lasers”, J. Comput. Phys., 1985, Vol. 58, No. 1, p. 80
Abstract
A computational scheme is developed to integrate a set of self-consistent equations describing the evolution of the field structure in free electron lasers. The proposed scheme is fourth-order accurate in space and third-order accurate in time. The boundedness of solution is provided by a number of integrals in the scheme. Stationary and pulse electron injection regimes are investigated. In both cases the scheme permits effective calculation of the following regimes: (a) stationary single-mode generation (or, correspondingly, generation of identical pulses), (b) periodic self-modulation, (c) stochastic self-modulation.
4 Pioneer paper on the operator exponential numerical scheme for the nonlinear Schroedinger equation
Ya.L.Bogomolov, A.D.Yunakovsky “Split-step Fourier Method for Nonlinear Schroedinger Equation” Proceedings of the int. conf. “Days on diffraction”, S-Petersburg, Universitas Petrpolitana, p. 34 (DOI: 10.1109/DD.2006.348170)
Abstract
Various versions of the split-step Fourier method (SSFM) for the nonlinear Schroedinger equation (NLSE) are presented. New versions are introduced, namely: the operator exponential scheme (OES) and the simplified one (SOES). Comparison between these schemes is made. The approach for comparison is to (a) fix the accuracy; (b) leave mesh parameters free and compare the computing time required to attain such accuracy for various choices of the parameters. The results of our study suggest OES and SOES as effective numerical schemes for NLSE.
5 Llast papers concerning on the method of discrete sources
Ya.L.Bogomolov, E.S.Semenov, A.D.Yunakovsky “Optimization of the Paraxial Region Profile for a Quasy-Optical Electron Accelerator” Technical Physics, 2007, Vol. 52, No. 5, p. 668 (both in Russian and in English)
Богомолов Я.Л., Семенов Е.С., Юнаковский А.Д. «Синтезирование ускорительной секции электрон-позитронного коллайдера» Математическое моделирование, 2008, Т. 20, № 7, стр. 45 (in Russian)
Ya.L.Bogomolov, E.S.Semenov, A.D.Yunakovsky “Selection a paraxial region profile for the accelerating structure of an electron-positron collider” Technical Physics Letters, 2009, Vol. 35, No. 7, p. 13 (DOI 10.1134/s 1063785009070049) (both in Russian and in English)
Богомолов Я.Л., Семенов Е.С., Юнаковский А.Д. «Численное моделирование резонансных режимов в приосевом объеме квазиоптического ускорителя электронов» Математическое моделирование, 2010, Т. 22, № 12, стр. 13 (in Russian)
Additional important information:
Nowadays there is a working team inside the laboratory in research of the method of discrete sources in application to the problems of electromagnetic wave propagation in the regions with the edges.
