Uniform Line Filling of Space: Bertrand’s Paradox Revisited

Evangelos  Marakis; Ravitej  Uppu; Pepijn W.H. Pinkse; Matthias Christiaan Velsink

Uniform Line Filling of Space: Bertrand’s Paradox Revisited

Evangelos Marakis, Ravitej Uppu, Pepijn W.H. Pinkse, Matthias Christiaan Velsink

Complex Photonic Systems

Research output: Contribution to conference › Poster › Other research output

Abstract

We are interested in finding templates for direct laser writing of deterministic uncorrelated multiple scattering media. To this end, we want to fill space in a homogeneous way with random lines. It turns out that this is a remarkably difficult problem, which is related to a paradox found by J. Bertrand in 1889. Following insights from Jaynes [1], we solve this problem in 2D and find an analytic expression for the distribution of line lengths. We discuss progress towards solving the 3D case.

Original language	English
Publication status	Published - 10 Oct 2017
Event	41st Annual Meeting NNV AMO Lunteren 2017 - Lunteren, Netherlands Duration: 10 Oct 2017 → 11 Oct 2017 Conference number: 41 http://www.ru.nl/amolunteren/

Conference

Conference	41st Annual Meeting NNV AMO Lunteren 2017
Country/Territory	Netherlands
City	Lunteren
Period	10/10/17 → 11/10/17
Internet address	http://www.ru.nl/amolunteren/

Cite this

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title = "Uniform Line Filling of Space: Bertrand{\textquoteright}s Paradox Revisited",

abstract = "We are interested in finding templates for direct laser writing of deterministic uncorrelated multiple scattering media. To this end, we want to fill space in a homogeneous way with random lines. It turns out that this is a remarkably difficult problem, which is related to a paradox found by J. Bertrand in 1889. Following insights from Jaynes [1], we solve this problem in 2D and find an analytic expression for the distribution of line lengths. We discuss progress towards solving the 3D case.",

author = "Evangelos Marakis and Ravitej Uppu and Pinkse, {Pepijn W.H.} and Velsink, {Matthias Christiaan}",

year = "2017",

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T1 - Uniform Line Filling of Space: Bertrand’s Paradox Revisited

AU - Marakis, Evangelos

AU - Uppu, Ravitej

AU - Pinkse, Pepijn W.H.

AU - Velsink, Matthias Christiaan

N1 - Conference code: 41

PY - 2017/10/10

Y1 - 2017/10/10

N2 - We are interested in finding templates for direct laser writing of deterministic uncorrelated multiple scattering media. To this end, we want to fill space in a homogeneous way with random lines. It turns out that this is a remarkably difficult problem, which is related to a paradox found by J. Bertrand in 1889. Following insights from Jaynes [1], we solve this problem in 2D and find an analytic expression for the distribution of line lengths. We discuss progress towards solving the 3D case.

AB - We are interested in finding templates for direct laser writing of deterministic uncorrelated multiple scattering media. To this end, we want to fill space in a homogeneous way with random lines. It turns out that this is a remarkably difficult problem, which is related to a paradox found by J. Bertrand in 1889. Following insights from Jaynes [1], we solve this problem in 2D and find an analytic expression for the distribution of line lengths. We discuss progress towards solving the 3D case.

M3 - Poster

T2 - 41st Annual Meeting NNV AMO Lunteren 2017

Y2 - 10 October 2017 through 11 October 2017

ER -

Uniform Line Filling of Space: Bertrand’s Paradox Revisited

Abstract

Conference

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