Homogenization of highly oscillatory Hamiltonian systems:
Abstract: "The paper studies Hamiltonian systems with a strong potential forcing the solutions to oscillate on a very small time scale. In particular, we are interested in the limit situation where the size [epsilon] of this small time scale tends to zero but the velocity components remain osci...
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin-Wilmersdorf
1995
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| Series: | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC
1995,39 |
| Subjects: | |
| Summary: | Abstract: "The paper studies Hamiltonian systems with a strong potential forcing the solutions to oscillate on a very small time scale. In particular, we are interested in the limit situation where the size [epsilon] of this small time scale tends to zero but the velocity components remain oscillating with an amplitude variation of order O(1). The process of establishing an effective initial value problem for the limit positions will be called homogenization of the Hamiltonian system. This problem occurs in mechanics as the problem of realization of holonomic constraints, in plasma physics as the problem of guiding center motion, in the simulation of biomolecules as the so called smoothing problem. We suggest the systematic use of the notion of weak convergence in order to approach this problem. This methodology helps to establish unified and short proofs of the known results which throw light on the inherent structure of the problem. Moreover, we give a careful and critical review of the literature." |
| Physical Description: | 30 S. |
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| 245 | 1 | 0 | |a Homogenization of highly oscillatory Hamiltonian systems |c Folkmar A. Bornemann ; Christof Schütte |
| 264 | 1 | |a Berlin-Wilmersdorf |c 1995 | |
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| 490 | 1 | |a Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |v 1995,39 | |
| 520 | 3 | |a Abstract: "The paper studies Hamiltonian systems with a strong potential forcing the solutions to oscillate on a very small time scale. In particular, we are interested in the limit situation where the size [epsilon] of this small time scale tends to zero but the velocity components remain oscillating with an amplitude variation of order O(1). The process of establishing an effective initial value problem for the limit positions will be called homogenization of the Hamiltonian system. This problem occurs in mechanics as the problem of realization of holonomic constraints, in plasma physics as the problem of guiding center motion, in the simulation of biomolecules as the so called smoothing problem. We suggest the systematic use of the notion of weak convergence in order to approach this problem. This methodology helps to establish unified and short proofs of the known results which throw light on the inherent structure of the problem. Moreover, we give a careful and critical review of the literature." | |
| 650 | 4 | |a Degree of freedom | |
| 650 | 4 | |a Hamiltonian systems | |
| 700 | 1 | |a Schütte, Christof |d 1966- |e Verfasser |0 (DE-588)1049564030 |4 aut | |
| 830 | 0 | |a Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |v 1995,39 |w (DE-604)BV004801715 |9 1995,39 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-007142474 | |
Record in the Search Index
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| author | Bornemann, Folkmar 1967- Schütte, Christof 1966- |
| author_GND | (DE-588)120096269 (DE-588)1049564030 |
| author_facet | Bornemann, Folkmar 1967- Schütte, Christof 1966- |
| author_role | aut aut |
| author_sort | Bornemann, Folkmar 1967- |
| author_variant | f b fb c s cs |
| building | Verbundindex |
| bvnumber | BV010700827 |
| classification_rvk | SS 4777 |
| ctrlnum | (OCoLC)35423798 (DE-599)BVBBV010700827 |
| discipline | Informatik |
| format | Book |
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| id | DE-604.BV010700827 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-10T17:07:56Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007142474 |
| oclc_num | 35423798 |
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| owner | DE-12 DE-703 |
| owner_facet | DE-12 DE-703 |
| physical | 30 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| record_format | marc |
| series | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |
| series2 | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |
| spelling | Bornemann, Folkmar 1967- Verfasser (DE-588)120096269 aut Homogenization of highly oscillatory Hamiltonian systems Folkmar A. Bornemann ; Christof Schütte Berlin-Wilmersdorf 1995 30 S. txt rdacontent n rdamedia nc rdacarrier Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC 1995,39 Abstract: "The paper studies Hamiltonian systems with a strong potential forcing the solutions to oscillate on a very small time scale. In particular, we are interested in the limit situation where the size [epsilon] of this small time scale tends to zero but the velocity components remain oscillating with an amplitude variation of order O(1). The process of establishing an effective initial value problem for the limit positions will be called homogenization of the Hamiltonian system. This problem occurs in mechanics as the problem of realization of holonomic constraints, in plasma physics as the problem of guiding center motion, in the simulation of biomolecules as the so called smoothing problem. We suggest the systematic use of the notion of weak convergence in order to approach this problem. This methodology helps to establish unified and short proofs of the known results which throw light on the inherent structure of the problem. Moreover, we give a careful and critical review of the literature." Degree of freedom Hamiltonian systems Schütte, Christof 1966- Verfasser (DE-588)1049564030 aut Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC 1995,39 (DE-604)BV004801715 1995,39 |
| spellingShingle | Bornemann, Folkmar 1967- Schütte, Christof 1966- Homogenization of highly oscillatory Hamiltonian systems Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC Degree of freedom Hamiltonian systems |
| title | Homogenization of highly oscillatory Hamiltonian systems |
| title_auth | Homogenization of highly oscillatory Hamiltonian systems |
| title_exact_search | Homogenization of highly oscillatory Hamiltonian systems |
| title_full | Homogenization of highly oscillatory Hamiltonian systems Folkmar A. Bornemann ; Christof Schütte |
| title_fullStr | Homogenization of highly oscillatory Hamiltonian systems Folkmar A. Bornemann ; Christof Schütte |
| title_full_unstemmed | Homogenization of highly oscillatory Hamiltonian systems Folkmar A. Bornemann ; Christof Schütte |
| title_short | Homogenization of highly oscillatory Hamiltonian systems |
| title_sort | homogenization of highly oscillatory hamiltonian systems |
| topic | Degree of freedom Hamiltonian systems |
| topic_facet | Degree of freedom Hamiltonian systems |
| volume_link | (DE-604)BV004801715 |
| work_keys_str_mv | AT bornemannfolkmar homogenizationofhighlyoscillatoryhamiltoniansystems AT schuttechristof homogenizationofhighlyoscillatoryhamiltoniansystems |