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(b) Ground tilt distribution.
(a) Ground displacements, (b) ground tilt distribution, (c) magnified version of (a), and (d) Magnified version of (b).
The finite size contribution is always inversely proportional to the width of the NWs, while the broadening due to tilt distribution increases linearly with Q.
For the 120 min radial overgrowth time shown in Figure 3, the broadening due to tilt distribution is larger than that due to finite NW width.
The position of possible detector streak is marked with white (I), broadening due to tilt distribution with red (II) and broadening due to finite radius of the nanowires as black (III).
Tilt distribution is a general feature in NW samples and is a limiting factor when performing high resolution XRD on such samples.
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To show this, let o N be the observed samples coming from the main channel, e.g., driven from the tilted distribution Q Y ∣ X N ( s ~ 0, v N ∣ x N ).
Equivalently, when observed samples come from the opponent channel, e.g., drawn from the tilted distribution Q Z ∣ X N ( s ~ 1, v N ∣ x N ), we have ∑ i ∈ N B ℓ ( o i, 0 ) + ∑ i ∈ N W ℓ ( o i, 1 ) → P N 2 μ ′ ( s ~ 1 ; H 1 ).
be tilted distributions over the set, and μ x (s; H j ) the semi-invariant moment generating function of ℓ v, x) distributed under hypothesis H j. The mean of the log-likelihood function ℓ v, x) governed by the tilted distributions QY∣X s,v∣x) is μ x′(s; H0).
When choosing s = s ~ 0 for QY∣X s,v∣x) and s = s ~ 1 for QZ∣X s,v∣x), the mean of the log-likelihood function ℓ v, x) governed by these tilted distributions will be equal to the threshold λ of the test 30.
These color maps suggest a possible dependency with specific random arrangements of the scales and ridges such as the relative tilt angle distribution in the wing membranes [1, 7].
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