| Slow passage through resonance. | |
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MedLine Citation:
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PMID: 22181533 Owner: NLM Status: Publisher |
Abstract/OtherAbstract:
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The slow passage problem through a resonance is considered. As a model problem, we consider a damped harmonically forced oscillator whose forcing frequency is slowly ramped linearly in time. The setup is similar to the familiar slow passage through a Hopf bifurcation problem, where for slow variations of the control parameter, oscillations are delayed until the parameter has exceeded the critical value of the static-parameter problem by an amount that is the difference between the Hopf value and the initial value of the parameter. In sharp contrast, in the resonance problem there is an early onset of resonance, setting in when the ramped forcing frequency is midway between its initial value and the natural frequency for resonance in the unforced problem; we term this value the jump frequency. Numerically, we find that the jump frequency is independent of the system's damping coefficient, and so we also consider the undamped problem, which is analytically tractable. The analysis of the undamped problem confirms the numerical results found in the damped problem that the maximal amplitude obtained at the jump frequency scales as A∼ε^{-1/2}, ε being the ramp rate, and that the jump frequency is midway between the initial frequency at the start of the ramp and the natural frequency of the unforced problem. |
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Authors:
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Youngyong Park; Younghae Do; Juan M Lopez |
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Publication Detail:
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Type: JOURNAL ARTICLE Date: 2011-11-11 |
Journal Detail:
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Title: Physical review. E, Statistical, nonlinear, and soft matter physics Volume: 84 ISSN: 1550-2376 ISO Abbreviation: - Publication Date: 2011 Nov |
Date Detail:
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Created Date: 2011-12-20 Completed Date: - Revised Date: - |
Medline Journal Info:
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Nlm Unique ID: 101136452 Medline TA: Phys Rev E Stat Nonlin Soft Matter Phys Country: - |
Other Details:
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Languages: ENG Pagination: 056604 Citation Subset: - |
Affiliation:
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Department of Mathematics, Kyungpook National University, Daegu 702-701, South Korea. |
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From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine
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