Using this approach, in [Hut03b] it has been shown that convergence holds for a subclass of Bernoulli distributions if the class is dense, but fails if the class is gappy, showing that a denseness characterization of M could be promising in general.
Universal Convergence of Semimeasures on Individual Random Sequences
Using this approach, in [Hut03b] it has been shown that convergence holds for a subclass of Bernoulli distributions if the class is dense, but fails if the class is gappy, showing that a denseness characterization of M could be promising in general.
On Semimeasures Predicting Martin-Loef Random Sequences
We now introduce a straightforward approach for applying this methodology to L2 (Ω), where the gappy data is given by function evaluations on a discrete subset of Ω.
Efficient response surface methods based on generic surrogate models
So the effort for the solution of a nonlinear least squares gappy POD problem is justiﬁed.
Efficient response surface methods based on generic surrogate models
The Field-free gap model (hereafter referred to as gappy penumbra) was possibly ﬁrst proposed by Choudhuri (1986,) to explain the connection between umbral dots and penumbral bright grains.
Models and Observations of Sunspot Penumbrae
The gappy penumbral model, as initially proposed (,), does not clearly identify the origin of Evershed effect.
Models and Observations of Sunspot Penumbrae
Both the ﬂux-tube and gappy-penumbra models feature one of t he key ingredients to explain the polarization pro ﬁles observed in the penumbra at ≃ 1 arcsec resolution: the uncombed structure of the magnetic ﬁeld (see Sect. 1).
Models and Observations of Sunspot Penumbrae
So far, the gappy penumbral model has not be used to explain the polarization signals in the sunspot penumbra.
Models and Observations of Sunspot Penumbrae
Contrary to the problems faced by the horizontal ﬂux-tube mo del, the gappy penumbral model allows for a very efﬁcient heating mechanism.
Models and Observations of Sunspot Penumbrae
The gappy penumbral model does not suffer from this shortcoming in the inner penumbra, since the vertical component of the magnetic ﬁeld does not totally vanish on top of the gap.
Models and Observations of Sunspot Penumbrae
However, this peculiarity of the gappy penumbral model poses problems in the outer penumbra, where inclinations of ∼ 110◦ with respect to the vertical are also observed over radially extended regions.
Models and Observations of Sunspot Penumbrae
These results share common points with both the ﬂux-tube model and the gappy penumbral model.
Models and Observations of Sunspot Penumbrae
These convective motions in the deep layers are in agreement with the predictions of the gappy penumbral model ().
Models and Observations of Sunspot Penumbrae
This is in better agreement with the gappy penumbral model.
Models and Observations of Sunspot Penumbrae
Keeping these simulations in mind, we could bring together the gappy and embedded-ﬂux tube model if on the one hand we consider a ﬂux-tube (where the magn etic ﬁeld is horizontal) that is highly squeezed vertically and that harbors a convective ﬂow pattern (besides the horizontal Evershed ﬂow along its axis).
Models and Observations of Sunspot Penumbrae
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