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14
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84926857434
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The notational distinction of Ref. 8 between the applied superfluid field upsilon vecs,a and v vecn is here dropped, upsilon vecs,a being replaced by v vecs and interpreted as a local average of the superfluid velocity field. The assumption is that random fluctuations in v vecs due to other nearby parts of the vortex tangle are either unimportant or average to zero over time scales short compared to other significant time scales.
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15
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84926791605
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The friction parameters are related to the conventional Hall-Vinen parameters B and B prime by α = ρn B/2 rho and α prime = ρn B prime /2 rho. A table of α , α prime versus temperature is given in Ref. 8.
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18
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84926835573
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From the theoretical point of view, L depends on alpha and α prime, which in turn are functions of T and P.
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20
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84926813561
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See, however, Fig. 18 in Sec. III, which implies that some nonuniformity corrections may arise when L becomes small.
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22
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84926813560
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Critical angles arise when considering the interaction of the vortex tangle with rough channel walls.
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23
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84926853408
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As happens, the dependence of the vortex-tangle properties on alpha and α prime turns out to be relatively weak. This is fortunate since, strictly speaking, alpha and α prime are not constants in Eq. (3). Because of the complex interactions between the excitation gas and the vortex core, alpha and α prime exhibit a residual dependence on the relative velocity between the normal fluid and the co, generally, they can also depend on the history of this relative velocity, leading for example to a frequency dependence in oscillating fl, such effects can affect the absolute values of the scaling coefficients, they are not large enough to significantly distort the scaling arguments. The subject has most recently been discussed by
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(1987)
J. Low. Temp. Phys.
, vol.66
, pp. 263
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More1
While2
Swanson, C.E.3
Wagner, W.T.4
Donnelly, R.J.5
Barenghi, C.F.6
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27
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84926813559
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C. E. Swanson, Ph.D. thesis, University of Oregon, 1985.
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30
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84926791604
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It is interesting to note that if the real-wall results are averaged over the whole channel rather than just the center portion, the agreement with the values calculated using periodic boundary conditions is improved considerably. See Fig. 18.
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31
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84926835572
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The effects of the logarithmic correction to DELTA should not be confused with the issues raised by the logarithmic variation of beta. As will be discussed in Sec. IV, the latter leads to small but quantifiable effects which are clearly observed experimentally. Of course, the assumption throughout is that {| s vec {prime prime} |} ¯ a0 << 1.
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32
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84926857433
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The differences in the converged value of L ¯ ^1/2 in Figs. 9, 13, and 14 arise from the fact that these calculations were carried out using somewhat different values of DELTA.
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36
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84926813558
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K. Mimura and K. Lusczcynski, Proceedings of the 18th International Conference on Low Temperature Physics, Kyoto, 1987
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(1987)
Jpn. J. Appl. Phys.
, vol.26
, pp. 93
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38
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84926835571
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The notation of Ref. 21 differs from ours. I ¯para L ¯ and I ¯ppd L ¯ are called LA and LT, respectively. ( I ¯para - cL I ¯l ) is denoted by G.
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