2018
DOI: 10.1088/1751-8121/aae5ee
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On the free path length distribution for linear motion in an n-dimensional box

Abstract: We consider the distribution of free path lengths, or the distance between consecutive bounces of random particles, in an n-dimensional rectangular box. If each particle travels a distance R, then, as R → ∞ the free path lengths coincides with the distribution of the length of the intersection of a random line with the box (for a natural ensemble of random lines) and we give an explicit formula (piecewise real analytic) for the probability density function in dimension two and three.In dimension two we also co… Show more

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Cited by 1 publication
(3 citation statements)
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References 20 publications
(36 reference statements)
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“…This coincides with Knudsen's λ g = 2hw/(h + w); for an infinite channel, L → ∞, and that for infinite parallel planes (w → ∞), λ g = 2h. In this latter case, the geometric path distribution p g ∞ (l) can be found when w, L → ∞ in the geometric path distribution of Holmin et al 30 (Supporting Information (eqs S1 and S2)):…”
Section: Resultsmentioning
confidence: 92%
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“…This coincides with Knudsen's λ g = 2hw/(h + w); for an infinite channel, L → ∞, and that for infinite parallel planes (w → ∞), λ g = 2h. In this latter case, the geometric path distribution p g ∞ (l) can be found when w, L → ∞ in the geometric path distribution of Holmin et al 30 (Supporting Information (eqs S1 and S2)):…”
Section: Resultsmentioning
confidence: 92%
“…The calculations of the effective mean free path λ 0 in an infinite channel with rectangular cross section or in the parallel planes geometry 27 are not trivial. From eq 2, λ 0 can be obtained through integrations: p T (l) can be found in Paik 31 or assumed to be exponential, while p g (l) can be found in Holmin et al 30 and in Supporting Information (eqs S1 and S2)). The resulting λ 0 is shown in Figure 3 (red solid line) for a gas with thermal mean free path λ T = 44.5 nm in a box of dimensions w = 3 μm, L = 1 μm.…”
Section: Resultsmentioning
confidence: 99%
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