Abstract

A Buffon-Laplace type problems for an irregular lattice and with maximum probability

Highlights

  • In some previous papers [1], [2], [3], [4], [5], [6], [7], [8], [9] and [10] the authors studies same Laplace problems with different fundamental cells

  • We want to compute the probability that a segment s with random position and of constant length l < min intersects a side of lattice, i.e. the probability Pint that the segment s intersects a side of the fundamental cell C0

  • The position of the segment s is determinated by middle point and by the angle φ that s forms with line BC (o AD)

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Summary

Introduction

In some previous papers [1], [2], [3], [4], [5], [6], [7], [8], [9] and [10] the authors studies same Laplace problems with different fundamental cells. We want to compute the probability that a segment s with random position and of constant length l < min (atgα, b − 2atgα) intersects a side of lattice , i.e. the probability Pint that the segment s intersects a side of the fundamental cell C0. To compute the probability Pint we consider the limit positions of segment s, for a fixed value of φ, in the cells C0i, (i = 1, 2, 3).

Results
Conclusion

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