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 |
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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 journal › Article
}
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 -