Geometric attractor of an electron beam passing through a crystal
The Lemmlein algorithm assigns a cyclic interaction of a mathematical point with other (n+1) points of the n - dimensional Euclidean space. In this paper generalization A of the Lemmlein algorithm for an arbitrary number of points m situated in the n - dimensional Riemann space is proposed. Algorith...
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| Published in: | Вопросы атомной науки и техники |
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| Date: | 2001 |
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| Format: | Article |
| Language: | English |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2001
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/79473 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Geometric attractor of an electron beam passing through a crystal / A.M. Gurin // Вопросы атомной науки и техники. — 2001. — № 6. — С. 147-148. — Бібліогр.: 8 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859962375199784960 |
|---|---|
| author | Gurin, A.M. |
| author_facet | Gurin, A.M. |
| citation_txt | Geometric attractor of an electron beam passing through a crystal / A.M. Gurin // Вопросы атомной науки и техники. — 2001. — № 6. — С. 147-148. — Бібліогр.: 8 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | The Lemmlein algorithm assigns a cyclic interaction of a mathematical point with other (n+1) points of the n - dimensional Euclidean space. In this paper generalization A of the Lemmlein algorithm for an arbitrary number of points m situated in the n - dimensional Riemann space is proposed. Algorithm A generates a Markovian chain consisting of the finite number of combinatorially different strongly convergent attractors. Algorithm A is generalized to describe the interaction of mass points, e.g., the motion of electrons in the real crystal medium. The strong convergence of the attractors provides stability of the electron trajectories in the vicinity of an attractor in the unit cell of the crystal after electron scattering at the crystal defects.
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| first_indexed | 2025-12-07T16:20:37Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-79473 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T16:20:37Z |
| publishDate | 2001 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Gurin, A.M. 2015-04-02T15:07:34Z 2015-04-02T15:07:34Z 2001 Geometric attractor of an electron beam passing through a crystal / A.M. Gurin // Вопросы атомной науки и техники. — 2001. — № 6. — С. 147-148. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 12.20.-m, 13.40.-f, 13.60-Hb, 13.88.+e https://nasplib.isofts.kiev.ua/handle/123456789/79473 The Lemmlein algorithm assigns a cyclic interaction of a mathematical point with other (n+1) points of the n - dimensional Euclidean space. In this paper generalization A of the Lemmlein algorithm for an arbitrary number of points m situated in the n - dimensional Riemann space is proposed. Algorithm A generates a Markovian chain consisting of the finite number of combinatorially different strongly convergent attractors. Algorithm A is generalized to describe the interaction of mass points, e.g., the motion of electrons in the real crystal medium. The strong convergence of the attractors provides stability of the electron trajectories in the vicinity of an attractor in the unit cell of the crystal after electron scattering at the crystal defects. The research described in this publication was made possible in part by Grant № U22000 from the International Science Foundation. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Electrodynamics of high energies in matter and strong fields Geometric attractor of an electron beam passing through a crystal Геометрический аттрактор пучка электронов, прошедших через кристалл Article published earlier |
| spellingShingle | Geometric attractor of an electron beam passing through a crystal Gurin, A.M. Electrodynamics of high energies in matter and strong fields |
| title | Geometric attractor of an electron beam passing through a crystal |
| title_alt | Геометрический аттрактор пучка электронов, прошедших через кристалл |
| title_full | Geometric attractor of an electron beam passing through a crystal |
| title_fullStr | Geometric attractor of an electron beam passing through a crystal |
| title_full_unstemmed | Geometric attractor of an electron beam passing through a crystal |
| title_short | Geometric attractor of an electron beam passing through a crystal |
| title_sort | geometric attractor of an electron beam passing through a crystal |
| topic | Electrodynamics of high energies in matter and strong fields |
| topic_facet | Electrodynamics of high energies in matter and strong fields |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79473 |
| work_keys_str_mv | AT gurinam geometricattractorofanelectronbeampassingthroughacrystal AT gurinam geometričeskiiattraktorpučkaélektronovprošedšihčerezkristall |