Diffusion by amplitude modulation in Hamiltonian systems

Jukka Heikkinen, Rainer Salomaa

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)

Abstract

Diffusion in Hamiltonian systems with a modulation in the force amplitude is analyzed. The modulation of the force expands the spectrum and, hence, the diffusion region, provided that the Chirikov overlap parameter exceeds the threshold for stochasticity in the expanded domain. Analytical formulas for the diffusion coefficient are derived as a function of modulation parameters, and the results are compared with the numerical solutions of the dynamical equations. For periodic modulation there is no diffusion in the nonresonant region, while for an irregular modulation involving random changes in the particle phase space coordinates, the diffusion extends into the nonresonant region. The nonresonant diffusion coefficient is found to decrease at least as |υυp|-4, the detailed behavior being strongly dependent on the modulation parameters. Here, υ is the particle velocity and υp denotes the average phase velocity of the force spectrum.

Original languageEnglish
Pages (from-to)365 - 378
Number of pages14
JournalPhysica D: Nonlinear Phenomena
Volume64
Issue number4
DOIs
Publication statusPublished - 1993
MoE publication typeA1 Journal article-refereed

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Heikkinen, Jukka ; Salomaa, Rainer. / Diffusion by amplitude modulation in Hamiltonian systems. In: Physica D: Nonlinear Phenomena. 1993 ; Vol. 64, No. 4. pp. 365 - 378.
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abstract = "Diffusion in Hamiltonian systems with a modulation in the force amplitude is analyzed. The modulation of the force expands the spectrum and, hence, the diffusion region, provided that the Chirikov overlap parameter exceeds the threshold for stochasticity in the expanded domain. Analytical formulas for the diffusion coefficient are derived as a function of modulation parameters, and the results are compared with the numerical solutions of the dynamical equations. For periodic modulation there is no diffusion in the nonresonant region, while for an irregular modulation involving random changes in the particle phase space coordinates, the diffusion extends into the nonresonant region. The nonresonant diffusion coefficient is found to decrease at least as |υ−υp|-4, the detailed behavior being strongly dependent on the modulation parameters. Here, υ is the particle velocity and υp denotes the average phase velocity of the force spectrum.",
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Diffusion by amplitude modulation in Hamiltonian systems. / Heikkinen, Jukka; Salomaa, Rainer.

In: Physica D: Nonlinear Phenomena, Vol. 64, No. 4, 1993, p. 365 - 378.

Research output: Contribution to journalArticleScientificpeer-review

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T1 - Diffusion by amplitude modulation in Hamiltonian systems

AU - Heikkinen, Jukka

AU - Salomaa, Rainer

N1 - Project code: YDI0030

PY - 1993

Y1 - 1993

N2 - Diffusion in Hamiltonian systems with a modulation in the force amplitude is analyzed. The modulation of the force expands the spectrum and, hence, the diffusion region, provided that the Chirikov overlap parameter exceeds the threshold for stochasticity in the expanded domain. Analytical formulas for the diffusion coefficient are derived as a function of modulation parameters, and the results are compared with the numerical solutions of the dynamical equations. For periodic modulation there is no diffusion in the nonresonant region, while for an irregular modulation involving random changes in the particle phase space coordinates, the diffusion extends into the nonresonant region. The nonresonant diffusion coefficient is found to decrease at least as |υ−υp|-4, the detailed behavior being strongly dependent on the modulation parameters. Here, υ is the particle velocity and υp denotes the average phase velocity of the force spectrum.

AB - Diffusion in Hamiltonian systems with a modulation in the force amplitude is analyzed. The modulation of the force expands the spectrum and, hence, the diffusion region, provided that the Chirikov overlap parameter exceeds the threshold for stochasticity in the expanded domain. Analytical formulas for the diffusion coefficient are derived as a function of modulation parameters, and the results are compared with the numerical solutions of the dynamical equations. For periodic modulation there is no diffusion in the nonresonant region, while for an irregular modulation involving random changes in the particle phase space coordinates, the diffusion extends into the nonresonant region. The nonresonant diffusion coefficient is found to decrease at least as |υ−υp|-4, the detailed behavior being strongly dependent on the modulation parameters. Here, υ is the particle velocity and υp denotes the average phase velocity of the force spectrum.

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