Moving finite-size particles in a flow: A physical example of pitchfork bifurcations of tori

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 77, Issue 2, 2008, Pages

  Zahnow, Jens C ^a   Feudel, Ulrike ^a  

^a UNIVERSITY OF OLDENBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

PARTICLE SIZE; REYNOLDS NUMBER;

MASS RATIO; PARAMETER SPACE; PARTICLE MOTION; STOKES DRAG;

BIFURCATION (MATHEMATICS);

EID: 40549097784     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.77.026215     Document Type: Article

References (43)

1. H. Aref, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112084001233 143, 1 (1984).
2. J. Ottino, The Kinematics of Mixing: Stretching, Chaos and Transport (Cambridge University Press, Cambridge, U.K., 1989).
3. T. Tél, A. DeMoura, C. Grebogi, and Károlyi, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2005.01.005 413, 91 (2005).
4. A. Basset, A Treatise on Hydrodynamics (Deighton Bell, London, 1888), Vol. 2.
5. J. Boussinesq, Theorie Analytique de la Chaleur, (L'Icole Polytechnique, Paris, 1903), Vol. 2.
6. C. Oseen, Hydrodynamik (Akademische Verlagsgesellschaft, Leipzig, 1927).
7. M. R. Maxey and J. J. Riley, Phys. Fluids PFLDAS 0031-9171 10.1063/1.864230 26, 883 (1983).
8. M. Maxey, Phys. Fluids PFLDAS 0031-9171 10.1063/1.866206 30, 1915 (1987).
9. I. J. Benczik, Z. Toroczkai, and T. Tél, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.164501 89, 164501 (2002).
10. L. Wang, M. Maxey, T. Burton, and D. Stock, Phys. Fluids A PFADEB 0899-8213 10.1063/1.858401 4, 1789 (1992).
11. C. López, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.027202 66, 027202 (2002).
12. I. J. Benczik, Z. Toroczkai, and T. Tél, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.036303 67, 036303 (2003).
13. Y. Do and Y.-C. Lai, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70. 036203 70, 036203 (2004).
14. G. A. Jackson, Deep-Sea Res., Part A DRPPD5 0198-0149 37, 1197 (1990).
15. J. Ruiz and A. Izquierdo, Oceanol. Acta 20, 597 (1997). 0399-1784
16. S. Melis, M. Verduyn, G. Storti, M. Morbidelli, and J. Baldyga, AIChE J. AICEAC 0001-1541 10.1002/aic.690450703 45, 1383 (1999).
17. D. Thomas, S. Judd, and N. Fawcett, Water Res. WATRAG 0043-1354 10.1016/S0043-1354(98)00392-3 33, 1579 (1999).
18. J. Flesch, P. Spicer, and S. Pratsinis, AIChE J. AICEAC 0001-1541 10.1002/aic.690450518 45, 1114 (1999).
19. B. Han, S. Akeprathumchai, S. Wickramasinghe, and X. Qian, AIChE J. AICEAC 0001-1541 10.1002/aic.690490709 49, 1687 (2003).
20. T. Nishikawa, Z. Toroczkai, and C. Grebogi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.038301 87, 038301 (2001).
21. T. Nishikawa, Z. Toroczkai, C. Grebogi, and T. Tél, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.026216 65, 026216 (2002).
22. L. Yu, C. Grebogi, and E. Ott, in Nonlinear Structure in Physical Systems, edited by, L. Lam, and, H. Morris, (Springer, New York, 1990), pp. 223-231.
23. H. Broer, G. Huitema, F. Takens, and B. Braaksma, Unfoldings and Bifurcations of Quasi-Periodic Tori, Memoirs of the American Methematical Society Vol. 83 (American Mathematical Society, Providence, RI, 1994).
24. S. Newhouse, D. Ruelle, and F. Takens, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01940759 64, 35 (1978).
25. V. Afraimovich and L. Shilnikov, Methods of Qualitative Theory of Differential Equations (Gorkii University Press, Gorky, Russia, 1983), pp. 3-26.
26. S. Ostlund, D. Rand, J. Sethna, and E. Siggia, Physica D PDNPDT 0167-2789 10.1016/0167-2789(95)00034-2 8, 303 (1983).
27. V. S. Anishchenko and M. A. Safonova, Radiotekh. Elektron. (Moscow) RAELA4 0033-8494 32, 1207 (1987).
28. C. Baesens, J. Guckenheimer, S. Kim, and R. MacKay, Physica D PDNPDT 0167-2789 10.1016/0167-2789(91)90155-3 49, 387 (1991).
29. G. A. Held and C. Jeffries, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.56.1183 56, 1183 (1986).
30. T. Schneider, H. Heng, and W. Martienssen, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/22/7/004 22, 499 (1993).
31. C. Giberti and R. Zansai, Physica D PDNPDT 0167-2789 10.1016/0167- 2789(93)90165-W 65, 300 (1993).
32. V. Anishchenko, M. Safonova, U. Feudel, and J. Kurths, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 10.1142/S0218127494000423 4, 595 (1994).
33. U. Feudel, M. Safonova, J. Kurths, and V. Anishchenko, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 10.1142/S0218127496000746 6, 1319 (1996).
34. V. Franceschini and R. Zanasi, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/5/1/008 5, 189 (1992).
35. A. B. Belogortsev, D. M. Vavriv, and O. A. Tretyakov, Appl. Mech. Rev. 46, 374 (1993). 0003-6900
36. F. Feudel and N. Seehafer, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.52.3506 52, 3506 (1995).
37. J. H. Sun, Acta Math. Sin. English Ser. ZZZZZZ 1000-9574 19, 159 (2003).
38. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Oxford University Press, London, 1961).
39. S. Wiggins, Global Bifurcations and Chaos: Analytical Methods (Springer, New York, 1988).
40. M. Manton, Boundary-Layer Meteorol. BLMEBR 0006-8314 10.1007/BF02137681 6, 487 (1974).
41. H. Nusse and J. Yorke, Physica D PDNPDT 0167-2789 10.1016/0167-2789(89) 90253-4 36, 137 (1989).
42. I. Shimada and T. Nagashima, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.61.1605 61, 1605 (1979).
43. H. Osinga, J. Wiersing, P. Glendinning, and U. Feudel, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 10.1142/S0218127401004029 11, 3085 (2001).