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Volumn 56, Issue 3, 1997, Pages 2858-2868

Chaotic particle dynamics in viscous flows: The three-particle Stokeslet problem

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0001122578     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.56.2858     Document Type: Article
Times cited : (107)

References (60)
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    • E.g., J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Prentice Hall, Englewood Cliffs, NJ, 1965)
    • E.g., J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Prentice Hall, Englewood Cliffs, NJ, 1965);
  • 4
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    • American Society of Mechanical Engineers, New York, edited by T. C. Crowe
    • Numerical Methods in Multiphase Flows, edited by T. C. Crowe (American Society of Mechanical Engineers, New York, 1994).
    • (1994) Numerical Methods in Multiphase Flows
  • 6
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    • P. Venema, 282, 45 (1995);
    • (1995) , vol.282 , pp. 45
    • Venema, P.1
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    • J. Chem. Phys. 96, 3137 (1992).JCPSA6
    • (1992) J. Chem. Phys. , vol.96 , pp. 3137
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    • A. J. C. Ladd, J. Fluid Mech. 271, 1994
    • A. J. C. Ladd, J. Fluid Mech. 271, 1994.
  • 39
    • 0004128127 scopus 로고
    • Cambridge University Press, Cambridge, England
    • P. G. Saffman, Vortex Dynamics (Cambridge University Press, Cambridge, England, 1992).
    • (1992) Vortex Dynamics
    • Saffman, P.G.1
  • 43
    • 85037223591 scopus 로고    scopus 로고
    • The solutions to Eq. (6) possess a homogeneity property: rescaling all variables by the same factor (Formula presented): (Formula presented) is equivalent to rescaling the time by (Formula presented): (Formula presented)
    • The solutions to Eq. (6) possess a homogeneity property: rescaling all variables by the same factor (Formula presented): (Formula presented) is equivalent to rescaling the time by (Formula presented): (Formula presented).
  • 45
    • 85037250777 scopus 로고    scopus 로고
    • defines a direction in the phase space (the set of geometrically similar configurations) along which no local divergence takes place. Thus, besides the translations along the trajectories, there is a second direction in which the local Lyapunov exponent is zero. Because of the conservation of phase-space volume, the sum of Lyapunov exponents must be zero and hence the last exponent must be (Formula presented)
    • defines a direction in the phase space (the set of geometrically similar configurations) along which no local divergence takes place. Thus, besides the translations along the trajectories, there is a second direction in which the local Lyapunov exponent is zero. Because of the conservation of phase-space volume, the sum of Lyapunov exponents must be zero and hence the last exponent must be (Formula presented).
  • 46
    • 85037204458 scopus 로고    scopus 로고
    • T. Tél, in Directions in Chaos, edited by Hao Bai-Lin (World Scientific, Singapore, 1990), Vol. 3, pp. 149–221; in STATPHYS’19, edited by Hao Bai-lin (World Scientific, Singapore, 1996), pp. 346–362
    • T. Tél, in Directions in Chaos, edited by Hao Bai-Lin (World Scientific, Singapore, 1990), Vol. 3, pp. 149–221;in STATPHYS’19, edited by Hao Bai-lin (World Scientific, Singapore, 1996), pp. 346–362.
  • 47
    • 5544275518 scopus 로고
    • CHAOEH special issue on chaotic scattering, CHAOS 3(4) (1993)
    • E. Ott and T. Tél, CHAOS 3, 317 (1993); CHAOEHspecial issue on chaotic scattering, CHAOS 3(4) (1993).
    • (1993) CHAOS , vol.3 , pp. 317
    • Ott, E.1    Tél, T.2
  • 51
    • 85037195636 scopus 로고    scopus 로고
    • Due to the reversibility property of Eq. (6), it is true that the time reversed dynamics of a starting configuration (Formula presented), (Formula presented), (Formula presented) is the same as the direct dynamics of the mirror configuration (Formula presented), (Formula presented), (Formula presented). Therefore, if a point (Formula presented) in the relative coordinate representation [see Eq. (6)] is on the stable manifold of the chaotic saddle at a fixed (Formula presented) and (Formula presented), then the point (Formula presented) belonging to (Formula presented), (Formula presented) is on the unstable manifold. Thus, the unstable manifold on the (Formula presented) plane is obtained, in general, by rotating the plot of the stable manifold by 180(Formula presented) and interchanging the positions of particles 1 and 2. Due to the specific choice (Formula presented) used in Figs. 44 and 55(a), the unstable manifold is just the mirror image of the stable one with respect to the axis (Formula presented)
    • Due to the reversibility property of Eq. (6), it is true that the time reversed dynamics of a starting configuration (Formula presented), (Formula presented), (Formula presented) is the same as the direct dynamics of the mirror configuration (Formula presented), (Formula presented), (Formula presented). Therefore, if a point (Formula presented) in the relative coordinate representation [see Eq. (6)] is on the stable manifold of the chaotic saddle at a fixed (Formula presented) and (Formula presented), then the point (Formula presented) belonging to (Formula presented), (Formula presented) is on the unstable manifold. Thus, the unstable manifold on the (Formula presented) plane is obtained, in general, by rotating the plot of the stable manifold by 180(Formula presented) and interchanging the positions of particles 1 and 2. Due to the specific choice (Formula presented) used in Figs. 44 and 55(a), the unstable manifold is just the mirror image of the stable one with respect to the axis (Formula presented).
  • 57
    • 85037203700 scopus 로고    scopus 로고
    • (private communication)
    • R.J. Phillips (private communication).
    • Phillips, R.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.