### Abstract

The work was performed within in the context of cascade-probabilistic method, the essence of which is to obtain and further application of cascade-probability functions (CPF) for different particles. CPF make sense probability of that a particle generated at some depth h' reaches a certain depth h after the n-th number of collisions. We consider the interaction of ions with solids and relationship between radiation defect formation processes and Markov processes and Markov chains. It shows how to get the recurrence relations for the simplest CPF from the Chapman-Kolmogorov equations. In this case the particle does not change its direction of movement after the collision, the flow rate does not depend on time, and consequently, on the depth of penetration. We also obtained recurrence relations for the CPF with the energy loss of ions from the Kolmogorov-Chapman equations, the flow rate depends on the depth of penetration.

Original language | English |
---|---|

Pages (from-to) | 59-70 |

Number of pages | 12 |

Journal | Modern Applied Science |

Volume | 9 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Jan 2015 |

Externally published | Yes |

### Fingerprint

### Keywords

- Cascade-probabilistic
- Defect formation
- Ion
- Markov chain
- Markov processes

### ASJC Scopus subject areas

- General

### Cite this

*Modern Applied Science*,

*9*(3), 59-70. https://doi.org/10.5539/mas.v9n3p59

**Relationship between markov chains and radiation defect formation processes by ion irradiation.** / Kupchishin, Anatoly Ivanovich; Shmygalev, Evgeniy Vladimirovich; Shmygaleva, Tatyana Alexandrovna; Jorabayev, Almaz Binuruli.

Research output: Contribution to journal › Article

*Modern Applied Science*, vol. 9, no. 3, pp. 59-70. https://doi.org/10.5539/mas.v9n3p59

}

TY - JOUR

T1 - Relationship between markov chains and radiation defect formation processes by ion irradiation

AU - Kupchishin, Anatoly Ivanovich

AU - Shmygalev, Evgeniy Vladimirovich

AU - Shmygaleva, Tatyana Alexandrovna

AU - Jorabayev, Almaz Binuruli

PY - 2015/1/1

Y1 - 2015/1/1

N2 - The work was performed within in the context of cascade-probabilistic method, the essence of which is to obtain and further application of cascade-probability functions (CPF) for different particles. CPF make sense probability of that a particle generated at some depth h' reaches a certain depth h after the n-th number of collisions. We consider the interaction of ions with solids and relationship between radiation defect formation processes and Markov processes and Markov chains. It shows how to get the recurrence relations for the simplest CPF from the Chapman-Kolmogorov equations. In this case the particle does not change its direction of movement after the collision, the flow rate does not depend on time, and consequently, on the depth of penetration. We also obtained recurrence relations for the CPF with the energy loss of ions from the Kolmogorov-Chapman equations, the flow rate depends on the depth of penetration.

AB - The work was performed within in the context of cascade-probabilistic method, the essence of which is to obtain and further application of cascade-probability functions (CPF) for different particles. CPF make sense probability of that a particle generated at some depth h' reaches a certain depth h after the n-th number of collisions. We consider the interaction of ions with solids and relationship between radiation defect formation processes and Markov processes and Markov chains. It shows how to get the recurrence relations for the simplest CPF from the Chapman-Kolmogorov equations. In this case the particle does not change its direction of movement after the collision, the flow rate does not depend on time, and consequently, on the depth of penetration. We also obtained recurrence relations for the CPF with the energy loss of ions from the Kolmogorov-Chapman equations, the flow rate depends on the depth of penetration.

KW - Cascade-probabilistic

KW - Defect formation

KW - Ion

KW - Markov chain

KW - Markov processes

UR - http://www.scopus.com/inward/record.url?scp=84920115868&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84920115868&partnerID=8YFLogxK

U2 - 10.5539/mas.v9n3p59

DO - 10.5539/mas.v9n3p59

M3 - Article

AN - SCOPUS:84920115868

VL - 9

SP - 59

EP - 70

JO - Modern Applied Science

JF - Modern Applied Science

SN - 1913-1844

IS - 3

ER -