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Dissipative solitons in binary fluid convection
1. | Departament de Física Aplicada, Universitat Politècnica de Catalunya, Campus Nord, 08034 Barcelona, Spain, Spain, Spain |
2. | Department of Physics, University of California, California, Berkeley, CA 94720, United States |
References:
[1] |
N. Akhmediev and A. Ankiewicz (eds), "Dissipative Solitons," Lect. Notes in Physics, 661, Springer, Berlin, 2005. |
[2] |
P. Assemat, A. Bergeon and E. Knobloch, Spatially localized states in Marangoni convection in binary mixtures, Fluid Dyn. Res., 40 (2008), 852-876.
doi: 10.1016/j.fluiddyn.2007.11.002. |
[3] |
W. Barten, M. Lücke, M. Kamps and R. Schmitz, Convection in binary fluid mixtures. I. Extended traveling-wave and stationary states, Phys. Rev. E, 51 (1995), 5636-5661.
doi: 10.1103/PhysRevE.51.5636. |
[4] |
O. Batiste and E. Knobloch, Simulations of localized states of stationary convection in 3He-4He mixtures, Phys. Rev. Lett., 95 (2005), 244501. |
[5] |
O. Batiste, E. Knobloch, A. Alonso and I. Mercader, Spatially localized binary-fluid convection, J. Fluid Mech., 560 (2006), 149-158.
doi: 10.1017/S0022112006000759. |
[6] |
M. Beck, J. Knobloch, D. J. B. Lloyd, B. Sandstede and T. Wagenknecht, Snakes, ladders, and isolas of localized patterns, SIAM J. Math. Anal., 41 (2009), 936-972.
doi: 10.1137/080713306. |
[7] |
A. Bergeon and E. Knobloch, Spatially localized states in natural doubly diffusive convection, Phys. Fluids, 20 (2008), 034102.
doi: 10.1063/1.2837177. |
[8] |
A. Bergeon, J. Burke, E. Knobloch and I. Mercader, Eckhaus instability and homoclinic snaking, Phys. Rev. E, 78 (2008), 046201.
doi: 10.1103/PhysRevE.78.046201. |
[9] |
S. Blanchflower, Magnetohydrodynamic convectons, Phys. Lett. A, 261 (1999), 74-81.
doi: 10.1016/S0375-9601(99)00573-3. |
[10] |
S. Blanchflower and N. O. Weiss, Three-dimensional magnetohydrodynamic convectons, Phys. Lett. A, 294 (2002), 297-303.
doi: 10.1016/S0375-9601(02)00076-2. |
[11] |
C. S. Bretherton and E. A. Spiegel, Intermittency through modulational instability, Phys. Lett. A, 96 (1983), 152-156.
doi: 10.1016/0375-9601(83)90491-7. |
[12] |
J. Burke and E. Knobloch, Snakes and ladders: Localized states in the Swift-Hohenberg equation, Phys. Lett. A, 360 (2007), 681-688.
doi: 10.1016/j.physleta.2006.08.072. |
[13] |
P. Coullet, C. Riera and C. Tresser, Stable static localized structures in one dimension, Phys. Rev. Lett., 84 (2000), 3069-3072.
doi: 10.1103/PhysRevLett.84.3069. |
[14] |
J. H. P. Dawes, Localized convection cells in the presence of a vertical magnetic field, J. Fluid Mech., 570 (2007), 385-406.
doi: 10.1017/S0022112006002795. |
[15] |
Q. Feng, J. V. Moloney and A. C. Newell, Transverse patterns in lasers, Phys. Rev. A, 50 (1994), 3601-3604.
doi: 10.1103/PhysRevA.50.R3601. |
[16] |
K. Ghorayeb and A. Mojtabi, Double diffusive convection in a vertical rectangular cavity, Phys. Fluids, 9 (1997), 2339-2348.
doi: 10.1063/1.869354. |
[17] |
D. Jung and M. Lücke, Bistability of moving and self-pinned fronts of supercritical localized convection structures, Europhys. Lett., 80 (2007), 14002, 1-6. |
[18] |
E. Knobloch, A. E. Deane, J. Toomre and D. R. Moore, Doubly diffusive waves, in "Multiparameter Bifurcation Theory" (eds. M. Golubitsky and J. Guckenheimer), Contemp. Math., 56 (1986), American Mathematical Society, Providence, R.I., 203-216. |
[19] |
P. Kolodner, Observations of the Eckhaus instability in one-dimensional traveling-wave convection, Phys. Rev. A, 46 (1992), 1739-1742.
doi: 10.1103/PhysRevA.46.R1739. |
[20] |
P. Kolodner, Coexisting traveling waves and steady rolls in binary-fluid convection, Phys. Rev. E, 48 (1993), R665-668.
doi: 10.1103/PhysRevE.48.R665. |
[21] |
P. Kolodner, J. A. Glazier and H. L. Williams, Dispersive chaos in one-dimensional traveling-wave convection, Phys. Rev. Lett., 65 (1990), 1579-1582.
doi: 10.1103/PhysRevLett.65.1579. |
[22] |
I. Mercader, A. Alonso and O. Batiste, Numerical analysis of the Eckhaus instability in travelling-wave convection in binary mixtures, Eur. Phys. J. E, 15 (2004), 311-318.
doi: 10.1140/epje/i2004-10071-7. |
[23] |
I. Mercader, A. Alonso and O. Batiste, Spatiotemporal dynamics near the onset of convection for binary mixtures in cylindrical containers, Phys. Rev. E, 77 (2008), 036313.
doi: 10.1103/PhysRevE.77.036313. |
[24] |
I. Mercader, O. Batiste and A. Alonso, Continuation of travelling-wave solutions of the Navier-Stokes equations, Int. J. Num. Methods in Fluids, 52 (2006), 707-721.
doi: 10.1002/fld.1196. |
[25] |
I. Mercader, O. Batiste, A. Alonso and E. Knobloch, Localized pinning states in closed containers: Homoclinic snaking without bistability, Phys. Rev. E, 80 (2009), 025201(R).
doi: 10.1103/PhysRevE.80.025201. |
[26] |
I. Mercader, O. Batiste, A. Alonso and E. Knobloch, Convectons in periodic and bounded domains, Fluid Dyn. Res., 42 (2010), 025505.
doi: 10.1088/0169-5983/42/2/025505. |
[27] |
D. R. Ohlsen, S. Y. Yamamoto, C. M. Surko and P. Kolodner, Transition from traveling-wave to stationary convection in fluid mixtures, Phys. Rev. Lett., 65 (1990), 1431-1434.
doi: 10.1103/PhysRevLett.65.1431. |
[28] |
Y. Pomeau, Front motion, metastability and subcritical bifurcations in hydrodynamics, Physica D, 23 (1986), 3-11.
doi: 10.1016/0167-2789(86)90104-1. |
[29] |
P. D. Woods and A. R. Champneys, Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian Hopf bifurcation, Physica D, 129 (1999), 147-170.
doi: 10.1016/S0167-2789(98)00309-1. |
show all references
References:
[1] |
N. Akhmediev and A. Ankiewicz (eds), "Dissipative Solitons," Lect. Notes in Physics, 661, Springer, Berlin, 2005. |
[2] |
P. Assemat, A. Bergeon and E. Knobloch, Spatially localized states in Marangoni convection in binary mixtures, Fluid Dyn. Res., 40 (2008), 852-876.
doi: 10.1016/j.fluiddyn.2007.11.002. |
[3] |
W. Barten, M. Lücke, M. Kamps and R. Schmitz, Convection in binary fluid mixtures. I. Extended traveling-wave and stationary states, Phys. Rev. E, 51 (1995), 5636-5661.
doi: 10.1103/PhysRevE.51.5636. |
[4] |
O. Batiste and E. Knobloch, Simulations of localized states of stationary convection in 3He-4He mixtures, Phys. Rev. Lett., 95 (2005), 244501. |
[5] |
O. Batiste, E. Knobloch, A. Alonso and I. Mercader, Spatially localized binary-fluid convection, J. Fluid Mech., 560 (2006), 149-158.
doi: 10.1017/S0022112006000759. |
[6] |
M. Beck, J. Knobloch, D. J. B. Lloyd, B. Sandstede and T. Wagenknecht, Snakes, ladders, and isolas of localized patterns, SIAM J. Math. Anal., 41 (2009), 936-972.
doi: 10.1137/080713306. |
[7] |
A. Bergeon and E. Knobloch, Spatially localized states in natural doubly diffusive convection, Phys. Fluids, 20 (2008), 034102.
doi: 10.1063/1.2837177. |
[8] |
A. Bergeon, J. Burke, E. Knobloch and I. Mercader, Eckhaus instability and homoclinic snaking, Phys. Rev. E, 78 (2008), 046201.
doi: 10.1103/PhysRevE.78.046201. |
[9] |
S. Blanchflower, Magnetohydrodynamic convectons, Phys. Lett. A, 261 (1999), 74-81.
doi: 10.1016/S0375-9601(99)00573-3. |
[10] |
S. Blanchflower and N. O. Weiss, Three-dimensional magnetohydrodynamic convectons, Phys. Lett. A, 294 (2002), 297-303.
doi: 10.1016/S0375-9601(02)00076-2. |
[11] |
C. S. Bretherton and E. A. Spiegel, Intermittency through modulational instability, Phys. Lett. A, 96 (1983), 152-156.
doi: 10.1016/0375-9601(83)90491-7. |
[12] |
J. Burke and E. Knobloch, Snakes and ladders: Localized states in the Swift-Hohenberg equation, Phys. Lett. A, 360 (2007), 681-688.
doi: 10.1016/j.physleta.2006.08.072. |
[13] |
P. Coullet, C. Riera and C. Tresser, Stable static localized structures in one dimension, Phys. Rev. Lett., 84 (2000), 3069-3072.
doi: 10.1103/PhysRevLett.84.3069. |
[14] |
J. H. P. Dawes, Localized convection cells in the presence of a vertical magnetic field, J. Fluid Mech., 570 (2007), 385-406.
doi: 10.1017/S0022112006002795. |
[15] |
Q. Feng, J. V. Moloney and A. C. Newell, Transverse patterns in lasers, Phys. Rev. A, 50 (1994), 3601-3604.
doi: 10.1103/PhysRevA.50.R3601. |
[16] |
K. Ghorayeb and A. Mojtabi, Double diffusive convection in a vertical rectangular cavity, Phys. Fluids, 9 (1997), 2339-2348.
doi: 10.1063/1.869354. |
[17] |
D. Jung and M. Lücke, Bistability of moving and self-pinned fronts of supercritical localized convection structures, Europhys. Lett., 80 (2007), 14002, 1-6. |
[18] |
E. Knobloch, A. E. Deane, J. Toomre and D. R. Moore, Doubly diffusive waves, in "Multiparameter Bifurcation Theory" (eds. M. Golubitsky and J. Guckenheimer), Contemp. Math., 56 (1986), American Mathematical Society, Providence, R.I., 203-216. |
[19] |
P. Kolodner, Observations of the Eckhaus instability in one-dimensional traveling-wave convection, Phys. Rev. A, 46 (1992), 1739-1742.
doi: 10.1103/PhysRevA.46.R1739. |
[20] |
P. Kolodner, Coexisting traveling waves and steady rolls in binary-fluid convection, Phys. Rev. E, 48 (1993), R665-668.
doi: 10.1103/PhysRevE.48.R665. |
[21] |
P. Kolodner, J. A. Glazier and H. L. Williams, Dispersive chaos in one-dimensional traveling-wave convection, Phys. Rev. Lett., 65 (1990), 1579-1582.
doi: 10.1103/PhysRevLett.65.1579. |
[22] |
I. Mercader, A. Alonso and O. Batiste, Numerical analysis of the Eckhaus instability in travelling-wave convection in binary mixtures, Eur. Phys. J. E, 15 (2004), 311-318.
doi: 10.1140/epje/i2004-10071-7. |
[23] |
I. Mercader, A. Alonso and O. Batiste, Spatiotemporal dynamics near the onset of convection for binary mixtures in cylindrical containers, Phys. Rev. E, 77 (2008), 036313.
doi: 10.1103/PhysRevE.77.036313. |
[24] |
I. Mercader, O. Batiste and A. Alonso, Continuation of travelling-wave solutions of the Navier-Stokes equations, Int. J. Num. Methods in Fluids, 52 (2006), 707-721.
doi: 10.1002/fld.1196. |
[25] |
I. Mercader, O. Batiste, A. Alonso and E. Knobloch, Localized pinning states in closed containers: Homoclinic snaking without bistability, Phys. Rev. E, 80 (2009), 025201(R).
doi: 10.1103/PhysRevE.80.025201. |
[26] |
I. Mercader, O. Batiste, A. Alonso and E. Knobloch, Convectons in periodic and bounded domains, Fluid Dyn. Res., 42 (2010), 025505.
doi: 10.1088/0169-5983/42/2/025505. |
[27] |
D. R. Ohlsen, S. Y. Yamamoto, C. M. Surko and P. Kolodner, Transition from traveling-wave to stationary convection in fluid mixtures, Phys. Rev. Lett., 65 (1990), 1431-1434.
doi: 10.1103/PhysRevLett.65.1431. |
[28] |
Y. Pomeau, Front motion, metastability and subcritical bifurcations in hydrodynamics, Physica D, 23 (1986), 3-11.
doi: 10.1016/0167-2789(86)90104-1. |
[29] |
P. D. Woods and A. R. Champneys, Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian Hopf bifurcation, Physica D, 129 (1999), 147-170.
doi: 10.1016/S0167-2789(98)00309-1. |
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