Servicios Personalizados
Revista
Articulo
Indicadores
-
Citado por SciELO
-
Accesos
Links relacionados
-
Similares en SciELO
Compartir
Revista mexicana de física
versión impresa ISSN 0035-001X
Rev. mex. fis. vol.58 no.5 México oct. 2012
Investigación
A density oscillator model
A. Hubardª, C. Málagab, H. Arceb, and H. Gonzálezb
ª Benjamin Levich Institute, City College of CUNY, 140th Street and Convent Avenue, New York, N.Y. 10031, USA.
b Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico City 04510, D.F. Mexico.
Recibido el 12 de junio de 2012;
Aceptado el 9 de agosto de 2012
Abstract
We present a model equation describing the behavior of a density oscillator and a set of experiments to test the model. The system consists of a cup containing salty water with an orifice in its base, partially submerged in an outer vessel filled with fresh water. Such a setup produces an oscillatory flow of water through the orifice. The density oscillator is an oscillatory system that shares common features with more complex systems with a stable limit cycle. Although a Rayleigh equation has been used as a model equation for these systems, we propose a different approach based on the integration of the hydrodynamic equations on a streamline. The model reproduces the experimental oscillation and predicts the period as a function of the physical parameters. Phase resetting curves observed in experiments under external biphasic excitation can be reproduced by the model.
Keywords: Density oscillator; saline oscillator; non linear oscillators.
PACS: 47.20.Bp; 82.40.Bj
DESCARGAR ARTÍCULO EN FORMATO PDF
Acknowledgements
We want to thank Michel Guevara for his revision and valuable comments. Jaime Garcia for his support with the experimental setup; Alicia Falcon and Araceli Torres for their help with data acquisition. This work was partially funded by PAPIIT-UNAM IN118611.
References
1. S. Nakata, K. Miyazaki, S. Izuhara, H. Yamaoka, and D. Tanaka, J. Phys. Chem. 113 (2009) 6876. [ Links ]
2. A. Ijspeert, J. Nakanishi and S. Schaal, Learning rhythmic movements by demonstration using nonlinear oscillators, in: (Proceedings of the 2002 IEEE/RSJ Intl. Conference on Intelligent Robots and Systems). [ Links ]
3. N. Loeuille and M. Ghil, BMC Ecology 4 (2004) 217. [ Links ]
4. A. Ijspeert, Neural Networks 21 (2008) 642. [ Links ]
5. J. Hallinan and J. Wiles, Evolving genetic regulatory networks using an artificial genome., in: 2nd Asia-Pacfic Bioinformatics Conference (APBC2004). [ Links ]
6. M. Takinoue, New Generation Computing 27 (2009) 107. [ Links ]
7. M. R. Guevara and L. Glass, J. Math. Biol. 14 (1982) 1. [ Links ]
8. L. Glass, Nonlinear Dynamics in Physiology and Medicine (Springer- Verlag, New York, 2003) Chapter: Resetting and entraining biological rhythms. [ Links ]
9. H. Gonzalez, H. Arce and M. R. Guevara, Phys. Review E 78 (2008) 036217. [ Links ]
10. S. Martin, Geophysical Fluid Dynamics (Gordon and Breach Science Publishers, 1970) Chapter: A Hydrodynamic Curiosity: the Salt Oscillator. [ Links ]
11. K. Yoshikawa, N. Oyama, M. Shoji and S. Nakata, Am. J. Phys. 59 (1991) 137. [ Links ]
12. K. Yoshikawa, S. Nakata, M. Yamanaka and T. Waki, J. of Chemical Education 66 (1989) 205. [ Links ]
13. S. Nakata, T. Miyata, N. Ojima and K. Yoshikawa, Physica D 115 (1998) 313. [ Links ]
14. K. Yoshikawa, K. Fukunaga, and M. Kawakami, Chem. Phys. Lett. 174 (1990) 203. [ Links ]
15. K. Miyakawa and K. Yamada, Physica D 151 (2001) 217. [ Links ]
16. K. Miyakawa and K. Yamada, Physica D 127 (1999) 177. [ Links ]
17. M. Okamura and K. Yoshikawa, Phys. Review E 61 (2000) 2445. [ Links ]
18. S. Upadhyay, A. K. Das, V. Agarwala and R. C. Srivastava, Langmuir 8 (1992) 2567. [ Links ]
19. R. P. Rastogi, R. C. Srivastava, and S. Kumar, J. Colloid Interface Sci. 283 (2005) 139. [ Links ]
20. J. Dempster, Computer Analysis of Electrophysical Signals (Academic Press, San Diego, 1993) [ Links ]
21. M. R. Guevara and A. Shrier, Ann. N. Y. Acad. Sci. 591 (1990) 11. [ Links ]
22. P. Alfredsson and T. Lagerstedt, Physics of fluids 24 (1981) 10. [ Links ]