### Abstract

It is shown that self-ion collisional cascades exhibit multifractality. The structure of the cascades was studied by analyzing the length distribution n(l,L) of the free flight path l traveled by particles during the cascade evolution. It was found that the collisional cascade can be partitioned into an infinity of subsets, each one characterized by a fixed value of x=lnl/lnL (where L is the system size) and a distinct value of the fractal dimension (x). The mechanism for multifractality based on an underlying multiplicative process is illustrated on a simple geometrical model. The multiscaling structure of the function n(l,L) is discussed.

Original language | English |
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Pages (from-to) | 2639-2645 |

Number of pages | 7 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 50 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1994 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*50*(4), 2639-2645. https://doi.org/10.1103/PhysRevE.50.2639

**Multifractality and multiscaling in collision cascades.** / Kun, F.; Bardos, G.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 50, no. 4, pp. 2639-2645. https://doi.org/10.1103/PhysRevE.50.2639

}

TY - JOUR

T1 - Multifractality and multiscaling in collision cascades

AU - Kun, F.

AU - Bardos, G.

PY - 1994

Y1 - 1994

N2 - It is shown that self-ion collisional cascades exhibit multifractality. The structure of the cascades was studied by analyzing the length distribution n(l,L) of the free flight path l traveled by particles during the cascade evolution. It was found that the collisional cascade can be partitioned into an infinity of subsets, each one characterized by a fixed value of x=lnl/lnL (where L is the system size) and a distinct value of the fractal dimension (x). The mechanism for multifractality based on an underlying multiplicative process is illustrated on a simple geometrical model. The multiscaling structure of the function n(l,L) is discussed.

AB - It is shown that self-ion collisional cascades exhibit multifractality. The structure of the cascades was studied by analyzing the length distribution n(l,L) of the free flight path l traveled by particles during the cascade evolution. It was found that the collisional cascade can be partitioned into an infinity of subsets, each one characterized by a fixed value of x=lnl/lnL (where L is the system size) and a distinct value of the fractal dimension (x). The mechanism for multifractality based on an underlying multiplicative process is illustrated on a simple geometrical model. The multiscaling structure of the function n(l,L) is discussed.

UR - http://www.scopus.com/inward/record.url?scp=4243143595&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4243143595&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.50.2639

DO - 10.1103/PhysRevE.50.2639

M3 - Article

VL - 50

SP - 2639

EP - 2645

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 4

ER -