Bogomolov Yakov Leonidovich
senior scientist, Ph.D
Education:
Gorky State University, 1977, “mathematics”
Ph.D. thesis “Mathematical simulation of nonstationary interaction between ensembles of charged particles and electromagnetic fields”, 1990
scientific supervisors are A.G.Litvak and A.D.Yunakovsky
Scientific interests:
mathematical physics, numerical mathematics, numerical simulation (plasma physics, HF-electronics, electrodynamics)
Specialized scientific interests
Spectral methods for the nonlinear Schroedinger equation, operator compact-implicit methods for the parabolic equation, method of discrete sources in application to the Helmholtz type equation, special stable numerical methods for ordinary differential equations of the second order
Professional career:
Institute of Applied Physics, Russian Academy of Sciences (since 1977 till nowadays), laboratory of computational physics
Short-dated scientific visits:
Sofia university (Bulgaria) – 1989
Nagoya university (Japan) – 2007
Educational activity:
Instructor in mathematics in Gorky Polytechnical Institute (the 1980s)
Lecturer in informatics in N.Novgorod State University (the 1990s)
Frequent invited speaker in summer physical-mathematical schools and the organizer of mathematical Olympiads for high class pupils
Number of publications:
42 (24 in reviewed journals, 9 in scientific proceedings, 9 in conference proceedings)
The most significant papers and results:
The most cited pape:
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.
Satellite to 9.1 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.
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.
Last 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.
