1
|
Hegedűs F, Krähling P, Aron M, Lauterborn W, Mettin R, Parlitz U. Feedforward attractor targeting for non-linear oscillators using a dual-frequency driving technique. CHAOS (WOODBURY, N.Y.) 2020; 30:073123. [PMID: 32752633 DOI: 10.1063/5.0005424] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2020] [Accepted: 06/15/2020] [Indexed: 06/11/2023]
Abstract
A feedforward control technique is presented to steer a harmonically driven, non-linear system between attractors in the frequency-amplitude parameter plane of the excitation. The basis of the technique is the temporary addition of a second harmonic component to the driving. To illustrate this approach, it is applied to the Keller-Miksis equation describing the radial dynamics of a single spherical gas bubble placed in an infinite domain of liquid. This model is a second-order, non-linear ordinary differential equation, a non-linear oscillator. With a proper selection of the frequency ratio of the temporary dual-frequency driving and with the appropriate tuning of the excitation amplitudes, the trajectory of the system can be smoothly transformed between specific attractors; for instance, between period-3 and period-5 orbits. The transformation possibilities are discussed and summarized for attractors originating from the subharmonic resonances and the equilibrium state (absence of external driving) of the system.
Collapse
Affiliation(s)
- F Hegedűs
- Department of Hydrodynamic Systems, Faculty of Mechanical Engineering, Budapest University of Technology and Economics, Műegyetem rakpart 3, H-1111 Budapest, Hungary
| | - P Krähling
- Department of Hydrodynamic Systems, Faculty of Mechanical Engineering, Budapest University of Technology and Economics, Műegyetem rakpart 3, H-1111 Budapest, Hungary
| | - M Aron
- Research Group Biomedical Physics, Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077 Göttingen, Germany and Institut für Dynamik komplexer Systeme, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany
| | - W Lauterborn
- Drittes Physikalisches Institut, Georg-August-Universität Göttingen, Friedrich-Hund Platz 1, D-37077 Göttingen, Germany
| | - R Mettin
- Drittes Physikalisches Institut, Georg-August-Universität Göttingen, Friedrich-Hund Platz 1, D-37077 Göttingen, Germany
| | - U Parlitz
- Research Group Biomedical Physics, Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077 Göttingen, Germany and Institut für Dynamik komplexer Systeme, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany
| |
Collapse
|
2
|
de Lima EF, de Carvalho RE, Forlevesi MD. Nonchaotic laser pulse dissociation through deformed tori. Phys Rev E 2020; 101:022207. [PMID: 32168701 DOI: 10.1103/physreve.101.022207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2019] [Accepted: 01/29/2020] [Indexed: 06/10/2023]
Abstract
We consider the nonlinear classical dynamics of a diatomic molecule under the action of a laser field in the framework of the driven Morse oscillator model. We investigate the influence of the dipole function and the laser field on the deformations of the surviving, invariant tori. For intense and high-frequency fields, some invariant tori traverse the separatrix of motion, visiting both the bound and unbound regions of the interatomic potential. Based on this fact, we propose the use of appropriately designed laser pulses to induce dissociation of trajectories on such invariant tori. This mechanism constitutes a controlled nonchaotic route for dissociation, which is an alternative to chaotic multiphoton dissociation and to chirped pulse dissociation.
Collapse
Affiliation(s)
- Emanuel F de Lima
- Departamento de Física, Universidade Federal de São Carlos São Carlos SP 13565-905, Brazil
| | - R Egydio de Carvalho
- Universidade Estadual Paulista (UNESP) Instituto de Geociências e Ciências Exatas-IGCE Rio Claro SP 13506-900, Brazil
| | - M D Forlevesi
- Universidade Estadual Paulista (UNESP) Instituto de Geociências e Ciências Exatas-IGCE Rio Claro SP 13506-900, Brazil
| |
Collapse
|
3
|
de Lima EF, Ramos TN, de Carvalho RE. Role of the range of the dipole function in the classical dynamics of molecular dissociation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:014901. [PMID: 23410476 DOI: 10.1103/physreve.87.014901] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2012] [Revised: 12/08/2012] [Indexed: 06/01/2023]
Abstract
The dissociation dynamics of heteronuclear diatomic molecules induced by infrared laser pulses is investigated within the framework of the classical driven Morse oscillator. The interaction between the molecule and the laser field described in the dipole formulation is given by the product of a time-dependent external field with a position-dependent permanent dipole function. The effects of changing the spatial range of the dipole function in the classical dissociation dynamics of large ensembles of trajectories are studied. Numerical calculations have been performed for distinct amplitudes and carrier frequencies of the external pulses and also for ensembles with different initial energies. It is found that there exist a set of values of the dipole range for which the dissociation probability can be completely suppressed. The dependence of the dissociation on the dipole range is explained through the examination of the Fourier series coefficients of the dipole function in the angle variable of the free system. In particular, the suppression of dissociation corresponds to dipole ranges for which the Fourier coefficients associated with nonlinear resonances are null and the chaotic region in the phase space is reduced to thin layers. In this context, it is shown that the suppression of dissociation of heteronuclear molecules for certain frequencies of the external field is a consequence of the finite range of the corresponding permanent dipole.
Collapse
Affiliation(s)
- Emanuel F de Lima
- Instituto de Geociências e Ciências Exatas, UNESP-Univ Estadual Paulista, Rio Claro, São Paulo 13506-900, Brazil.
| | | | | |
Collapse
|
4
|
Farantos SC, Schinke R, Guo H, Joyeux M. Energy Localization in Molecules, Bifurcation Phenomena, and Their Spectroscopic Signatures: The Global View. Chem Rev 2009; 109:4248-71. [DOI: 10.1021/cr900069m] [Citation(s) in RCA: 64] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Stavros C. Farantos
- Institute of Electronic Structure and Laser, Foundation for Research and Technology—Hellas, and Department of Chemistry, University of Crete, Iraklion 711 10, Crete, Greece, Max-Planck-Institut für Dynamik und Selbstorganisation, D-37073 Göttingen, Germany, Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, and Laboratoire de Spectrométrie Physique, Université Joseph Fourier—Grenoble I, BP 87, F-38402, St. Martin d’Heres Cedex, France
| | - Reinhard Schinke
- Institute of Electronic Structure and Laser, Foundation for Research and Technology—Hellas, and Department of Chemistry, University of Crete, Iraklion 711 10, Crete, Greece, Max-Planck-Institut für Dynamik und Selbstorganisation, D-37073 Göttingen, Germany, Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, and Laboratoire de Spectrométrie Physique, Université Joseph Fourier—Grenoble I, BP 87, F-38402, St. Martin d’Heres Cedex, France
| | - Hua Guo
- Institute of Electronic Structure and Laser, Foundation for Research and Technology—Hellas, and Department of Chemistry, University of Crete, Iraklion 711 10, Crete, Greece, Max-Planck-Institut für Dynamik und Selbstorganisation, D-37073 Göttingen, Germany, Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, and Laboratoire de Spectrométrie Physique, Université Joseph Fourier—Grenoble I, BP 87, F-38402, St. Martin d’Heres Cedex, France
| | - Marc Joyeux
- Institute of Electronic Structure and Laser, Foundation for Research and Technology—Hellas, and Department of Chemistry, University of Crete, Iraklion 711 10, Crete, Greece, Max-Planck-Institut für Dynamik und Selbstorganisation, D-37073 Göttingen, Germany, Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, and Laboratoire de Spectrométrie Physique, Université Joseph Fourier—Grenoble I, BP 87, F-38402, St. Martin d’Heres Cedex, France
| |
Collapse
|