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

Anatoly Ivanovich Kupchishin, Evgeniy Vladimirovich Shmygalev, Tatyana Alexandrovna Shmygaleva, Almaz Binuruli Jorabayev

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)59-70
Number of pages12
JournalModern Applied Science
Volume9
Issue number3
DOIs
Publication statusPublished - 1 Jan 2015
Externally publishedYes

Fingerprint

Markov chains
ion irradiation
cascades
defects
radiation
penetration
flow velocity
Markov processes
collisions
ions
energy dissipation
interactions

Keywords

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

ASJC Scopus subject areas

  • General

Cite this

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

In: Modern Applied Science, Vol. 9, No. 3, 01.01.2015, p. 59-70.

Research output: Contribution to journalArticle

Kupchishin, Anatoly Ivanovich ; Shmygalev, Evgeniy Vladimirovich ; Shmygaleva, Tatyana Alexandrovna ; Jorabayev, Almaz Binuruli. / Relationship between markov chains and radiation defect formation processes by ion irradiation. In: Modern Applied Science. 2015 ; Vol. 9, No. 3. pp. 59-70.
@article{f2224b8d03f04201a711edeb868e5040,
title = "Relationship between markov chains and radiation defect formation processes by ion irradiation",
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.",
keywords = "Cascade-probabilistic, Defect formation, Ion, Markov chain, Markov processes",
author = "Kupchishin, {Anatoly Ivanovich} and Shmygalev, {Evgeniy Vladimirovich} and Shmygaleva, {Tatyana Alexandrovna} and Jorabayev, {Almaz Binuruli}",
year = "2015",
month = "1",
day = "1",
doi = "10.5539/mas.v9n3p59",
language = "English",
volume = "9",
pages = "59--70",
journal = "Modern Applied Science",
issn = "1913-1844",
publisher = "Canadian Center of Science and Education",
number = "3",

}

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

VL - 9

SP - 59

EP - 70

JO - Modern Applied Science

JF - Modern Applied Science

SN - 1913-1844

IS - 3

ER -