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On the distribution of free path lengths . . .
, 2003
"... For r ∈ (0, 1), let Zr = {x ∈ R 2  dist(x,Z 2)> r/2} and τr(x, v) = inf{t> 0  x + tv ∈ ∂Zr}. Let Φr(t) be the probability that τr(x, v) ≥ t for x and v uniformly distributed in Zr and S1 respectively. We prove in this paper that limsup ǫ→0 + ..."
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For r ∈ (0, 1), let Zr = {x ∈ R 2  dist(x,Z 2)> r/2} and τr(x, v) = inf{t> 0  x + tv ∈ ∂Zr}. Let Φr(t) be the probability that τr(x, v) ≥ t for x and v uniformly distributed in Zr and S1 respectively. We prove in this paper that limsup ǫ→0 +
Free path lengths in quasi crystals
 J. Stat. Phys
, 2012
"... ABSTRACT. The Lorentz gas is a model for a cloud of point particles (electrons) in a distribution of scatterers in space. The scatterers are often assumed to be spherical with a fixed diameter d, and the point particles move with constant velocity between the scatterers, and are specularly reflected ..."
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Cited by 6 (0 self)
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reflected when hitting a scatterer. There is no interaction between point particles. An interesting question concerns the distribution of free path lengths, i.e. the distance a point particle moves between the scattering events, and how this distribution scales with scatterer diameter, scatterer density
On the Distribution of Free Path Lengths for the Periodic Lorentz Gas
"... Consider the domain Z " = fx 2 Rn j dist(x; "Zn) ? "flg; and let the free path length be defined as ..."
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Cited by 51 (9 self)
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Consider the domain Z " = fx 2 Rn j dist(x; "Zn) ? "flg; and let the free path length be defined as
On the distribution of the free path length of the linear flow in a honeycomb. Ann
 Inst. Fourier 59 (2009), 1043–1075. MR2543662, Zbl 1173.37036
"... Abstract. Letℓ�2 be an integer. For eachε∈(0, 1 2) remove fromR2 the union of discs of radiusε centered at the integer lattice points (m, n), with m�n(modℓ). Consider a pointlike particle moving linearly at unit speed, with velocityω, along a trajectory starting at the origin, and its free path len ..."
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Cited by 6 (3 self)
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Abstract. Letℓ�2 be an integer. For eachε∈(0, 1 2) remove fromR2 the union of discs of radiusε centered at the integer lattice points (m, n), with m�n(modℓ). Consider a pointlike particle moving linearly at unit speed, with velocityω, along a trajectory starting at the origin, and its free path
The distribution of the free path lengths in the periodic twodimensional Lorentz gas in the smallscatterer limit
, 2003
"... We study the free path length and the geometric free path length in the model of the periodic twodimensional Lorentz gas (Sinai billiard). We give a complete and rigorous proof for the existence of their distributions in the smallscatterer limit and explicitly compute them. As a corollary one get ..."
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Cited by 27 (6 self)
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We study the free path length and the geometric free path length in the model of the periodic twodimensional Lorentz gas (Sinai billiard). We give a complete and rigorous proof for the existence of their distributions in the smallscatterer limit and explicitly compute them. As a corollary one
The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems
, 2008
"... The periodic Lorentz gas describes the dynamics of a point particle in a periodic array of spherical scatterers, and is one of the fundamental models for chaotic diffusion. In the present paper we investigate the BoltzmannGrad limit, where the radius of each scatterer tends to zero, and prove the ..."
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Cited by 45 (19 self)
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the existence of a limiting distribution for the free path length. We also discuss related problems, such as the statistical distribution of directions of lattice points that are visible from a fixed position.
Mathematical Physics c © SpringerVerlag 1998 On the Distribution of Free Path Lengths for the Periodic Lorentz Gas
, 1996
"... Abstract: Consider the domain Z " = fx 2 Rn j dist(x; "Zn)> "γg; and let the free path length be defined as "(x;!) = infft> 0 j x − t! 2 Z"g: The distribution of values of " is studied in the limit as " ! 0 for all γ 1. It is shown that the value γc = nn− ..."
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Abstract: Consider the domain Z " = fx 2 Rn j dist(x; "Zn)> "γg; and let the free path length be defined as "(x;!) = infft> 0 j x − t! 2 Z"g: The distribution of values of " is studied in the limit as " ! 0 for all γ 1. It is shown that the value γc = nn
A HighThroughput Path Metric for MultiHop Wireless Routing
, 2003
"... This paper presents the expected transmission count metric (ETX), which finds highthroughput paths on multihop wireless networks. ETX minimizes the expected total number of packet transmissions (including retransmissions) required to successfully deliver a packet to the ultimate destination. The E ..."
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Cited by 1108 (5 self)
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. The ETX metric incorporates the effects of link loss ratios, asymmetry in the loss ratios between the two directions of each link, and interference among the successive links of a path. In contrast, the minimum hopcount metric chooses arbitrarily among the different paths of the same minimum length
Results 1  10
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