Auluck, F. C. ; Kothari, D. S.
(1954)
*Random fragmentation*
Nature, 174
.
pp. 565-566.
ISSN 0028-0836

Full text not available from this repository.

Official URL: http://www.nature.com/nature/journal/v174/n4429/ab...

Related URL: http://dx.doi.org/10.1038/174565a0

## Abstract

The problem of random fragmentation of a line into a finite number of N parts has received considerable attention, partly because of its application in assessing the randomness of radioactive disintegrations and cosmic ray events. For a line of length l the average number of fragments equal to or greater than x is^{1}: N(x) = N(1-x/l)^{N-1}.(1) This equation is readily applied to discuss^{2} an idealized case of random fragmentation of area. Consider a rectangle of sides l_{1} and l_{2} (area ∑= l _{1} l_{2}) and imagine it to be divided into subrectangles by drawing at random N_{1} and N _{2} lines respectively parallel to the two sides of the rectangle. If N(S) be the average number of elements of area equal to or exceeding S, we have, using equation (1): N(S) = N_{1}N_{2}(N_{1}-1)(N_{2}-1)/l_{1}l_{2}∫∫
_{xy>S}(1-x/I_{1})N^{-1}_{1} dxdy ˜ −2N_{0}(S/S_{0})^{1/2}K_{1}[2_{0}(S/S_{0})^{1/2}] where K _{1}(z) is the usual Bessel function of imaginary argument, N _{0}= N _{1} N _{2} is the total number of elements and S _{0} the average area of an element, S_{0} = ∑/N_{0} For S»S _{0} we obtain the approximate relation: N(S) ˜ π^{1/2} N_{0}(S/S_{0})^{1/4} exp{ −2 (S/S_{0})^{1/2}}.

Item Type: | Article |
---|---|

Source: | Copyright of this article belongs to Nature Publishing Group. |

ID Code: | 32333 |

Deposited On: | 30 Mar 2011 11:21 |

Last Modified: | 09 Jun 2011 08:23 |

Repository Staff Only: item control page