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4
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4243173373
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C.W. Meyer, G. Ahlers, and D.S. Cannell, Phys. Rev. Lett. 59, 1577 (1987); G. Ahlers, C.W. Meyer, and D.S. Cannell, J. Stat. Phys. 54, 1121 (1989).
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Meyer, C.W.1
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0001665957
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C.W. Meyer, G. Ahlers, and D.S. Cannell, Phys. Rev. Lett. 59, 1577 (1987); G. Ahlers, C.W. Meyer, and D.S. Cannell, J. Stat. Phys. 54, 1121 (1989).
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I. Rehberg, S. Rasenat, M. de la Torre-Juarez, W. Schöpf, F. Hörner, G. Ahlers, and H.R. Brand, Phys. Rev. Lett. 67, 596 (1991).
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Rehberg, I.1
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De La Torre-Juarez, M.3
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Hörner, F.5
Ahlers, G.6
Brand, H.R.7
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7
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0034592313
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For a review, see E. Bodenschatz, W. Pesch, and G. Ahlers, Annu. Rev. Fluid Mech. 32, 709 (2000).
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Bodenschatz, E.1
Pesch, W.2
Ahlers, G.3
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8
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33646988542
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private communication
-
By linear theory (LT) we mean that the nonlinear terms in the equations of motion (e.g., in the Boussinesq equations for RBC, see Ref. [6]) are neglected. As pointed out by J.V. Sengers (private communication), even in LT the stochastic terms in fluctuating hydrodynamics lead to mode coupling; but they do not lead to nonlinear saturation as the onset is approached from below.
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-
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Sengers, J.V.1
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10
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0000311695
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V.M. Zaitsev and M.I. Shliomis, Zh. Éksp. Teor. Fiz. 59, 1583 (1970) [Sov. Phys. JETP 32, 866 (1971)].
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Sov. Phys. JETP
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, pp. 866
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-
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12
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33646976812
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Fluctuations, Instabilities, and Phase Transitions, edited by T. Riste (Plenum, New York), Sec. 4.2
-
See R. Graham, in Fluctuations, Instabilities, and Phase Transitions, Vol. 11 of NATO Advanced Study Institute, Series B: Physics, edited by T. Riste (Plenum, New York, 1975), Sec. 4.2.
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NATO Advanced Study Institute, Series B: Physics
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Graham, R.1
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20
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33646988046
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For a discussion of these results, see also Ref. [6]
-
For a discussion of these results, see also Ref. [6].
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-
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21
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0001516741
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The effective noise intensity F, and thus the critical region, becomes large for RBC of a fluid near a liquid-gas critical point because small cell spacings can be used and because the thermal diffusivity (which enters into F) becomes small [see Eqs. (2.17) and (3.12c) of Ref. [12]]. This was noted also by M. Assenheimer and V. Steinberg, Europhys. News 27, 143 (1996).
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Europhys. News
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Assenheimer, M.1
Steinberg, V.2
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22
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5544291532
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For a review of pattern formation in liquid crystals, see L. Kramer and W. Pesch, Annu. Rev. Fluid Mech. 27, 515 (1995); W. Pesch and U. Behn, in Evolution of Spontaneous Structures in Dissipative Continuous Systems, Lecture Notes in Physics Vol. M55, edited by F.H. Busse and S.C. Müller (Springer, New York, 1998).
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Annu. Rev. Fluid Mech.
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Kramer, L.1
Pesch, W.2
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23
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0003939213
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Evolution of Spontaneous Structures in Dissipative Continuous Systems, edited by F.H. Busse and S.C. Müller (Springer, New York)
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For a review of pattern formation in liquid crystals, see L. Kramer and W. Pesch, Annu. Rev. Fluid Mech. 27, 515 (1995); W. Pesch and U. Behn, in Evolution of Spontaneous Structures in Dissipative Continuous Systems, Lecture Notes in Physics Vol. M55, edited by F.H. Busse and S.C. Müller (Springer, New York, 1998).
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Lecture Notes in Physics
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Pesch, W.1
Behn, U.2
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24
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84860921536
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Ph.D. thesis, Universität Bayreuth, Bayreuth, Germany
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F.-D. Hörner, Ph.D. thesis, Universität Bayreuth, Bayreuth, Germany, 1996.
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(1996)
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Hörner, F.-D.1
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27
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M.A. Scherer, G. Ahlers, F. Hörner, and I. Rehberg, Phys. Rev. Lett. 85, 3754 (2000).
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Phys. Rev. Lett.
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Scherer, M.A.1
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Hörner, F.3
Rehberg, I.4
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32
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33646970441
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note
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For wave vectors very different from the critical wave vectors and for large ε, corrections are expected which will remove the ultraviolet divergence of the integral of Eq. (2) (for the RBC analog, see, for instance, Ref. [15]). For our work Eq. (2) is expected to be an excellent approximation.
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-
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37
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0000083494
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I. Rehberg, S. Rasenat, M. de la Torre Juárez, and V. Steinberg, Phys. Rev. Lett. 61, 2449 (1988).
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Phys. Rev. Lett.
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Rehberg, I.1
Rasenat, S.2
De La Torre Juárez, M.3
Steinberg, V.4
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38
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0005874071
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edited by P.E. Cladis and P. Muhoray (Addison-Wesley, Reading, MA)
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M. Dennin, G. Ahlers, and D.S. Cannell, in Spatio-Temporal Patterns, edited by P.E. Cladis and P. Muhoray (Addison-Wesley, Reading, MA, 1994), p. 353.
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(1994)
Spatio-temporal Patterns
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Dennin, M.1
Ahlers, G.2
Cannell, D.S.3
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39
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0005879820
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M. Dennin, D.S. Cannell, and G. Ahlers, Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 261, 377 (1995).
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Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A
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Dennin, M.1
Cannell, D.S.2
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3743110039
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M. Dennin, M. Treiber, L. Kramer, G. Ahlers, and D.S. Cannell, Phys. Rev. Lett. 76, 319 (1996).
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Phys. Rev. Lett.
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Dennin, M.1
Treiber, M.2
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0031118650
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M. Treiber, N. Éber, Á. Buka, and L. Kramer, J. Phys. II 7, 649 (1997).
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Treiber, M.1
Éber, N.2
Buka, Á.3
Kramer, L.4
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43
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33646968571
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note
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The light source (model LS-1-LL) was provided by Ocean Optics, Inc., 380 Main Street, Dunedin, FL 34698.
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44
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33646985278
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note
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A second cell, which was filled with the same material about 9 months after the doping of the NLC showed the same patterns at onset and the same values of conductivities.
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-
-
-
45
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33646967920
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note
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As a filter we used a single glass slide (Coming Micro Slides Plain) as provided by Corning Glass Works, Corning, NY 14830.
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46
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0024867696
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S. Rasenat, G. Hartung, B.L. Winkler, and I. Rehberg, Exp. Fluids 7, 412 (1989).
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(1989)
Exp. Fluids
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Rasenat, S.1
Hartung, G.2
Winkler, B.L.3
Rehberg, I.4
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48
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0005828822
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B.L. Winkler, W. Decker, H. Richter, and I. Rehberg, Physica D 61, 284 (1992).
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(1992)
Physica D
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Winkler, B.L.1
Decker, W.2
Richter, H.3
Rehberg, I.4
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