Ergodic properties of crystallization processes

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Ergodic properties of crystallization processes. / Davydov, Yu; Illig, A.

In: Journal of Mathematical Sciences , Vol. 163, No. 4, 11.2009, p. 375-381.

Research output: Contribution to journal › Article › peer-review

Author

Davydov, Yu ; Illig, A. / Ergodic properties of crystallization processes. In: Journal of Mathematical Sciences . 2009 ; Vol. 163, No. 4. pp. 375-381.

BibTeX

@article{f3ecfaf6e22d42fd9716c497a3444aaf,

title = "Ergodic properties of crystallization processes",

abstract = "We consider a birth and growth process with germs which are born according to a Poisson point process whose intensity measure is invariant under translations of the space. The germs can be born in the unoccupied space; then they grow until they occupy the available space. In this general framework, the crystallization process can be characterized by a random field, which assigns to any point of the state space the first time at which this point is reached by a crystal. Under general conditions on the growth speed and geometric shape of free crystals, we prove that the random field is mixing in the sense of ergodic theory. This result is illustrated by applications to the problem of parameter estimation. Bibliography: 7 titles.",

author = "Yu Davydov and A. Illig",

year = "2009",

month = nov,

doi = "10.1007/s10958-009-9680-z",

language = "English",

volume = "163",

pages = "375--381",

journal = "Journal of Mathematical Sciences (Switzerland)",

issn = "1072-3374",

publisher = "Springer Nature",

number = "4",

}

RIS

TY - JOUR

T1 - Ergodic properties of crystallization processes

AU - Davydov, Yu

AU - Illig, A.

PY - 2009/11

Y1 - 2009/11

N2 - We consider a birth and growth process with germs which are born according to a Poisson point process whose intensity measure is invariant under translations of the space. The germs can be born in the unoccupied space; then they grow until they occupy the available space. In this general framework, the crystallization process can be characterized by a random field, which assigns to any point of the state space the first time at which this point is reached by a crystal. Under general conditions on the growth speed and geometric shape of free crystals, we prove that the random field is mixing in the sense of ergodic theory. This result is illustrated by applications to the problem of parameter estimation. Bibliography: 7 titles.

AB - We consider a birth and growth process with germs which are born according to a Poisson point process whose intensity measure is invariant under translations of the space. The germs can be born in the unoccupied space; then they grow until they occupy the available space. In this general framework, the crystallization process can be characterized by a random field, which assigns to any point of the state space the first time at which this point is reached by a crystal. Under general conditions on the growth speed and geometric shape of free crystals, we prove that the random field is mixing in the sense of ergodic theory. This result is illustrated by applications to the problem of parameter estimation. Bibliography: 7 titles.

UR - http://www.scopus.com/inward/record.url?scp=70549103374&partnerID=8YFLogxK

U2 - 10.1007/s10958-009-9680-z

DO - 10.1007/s10958-009-9680-z

M3 - Article

AN - SCOPUS:70549103374

VL - 163

SP - 375

EP - 381

JO - Journal of Mathematical Sciences (Switzerland)

JF - Journal of Mathematical Sciences (Switzerland)

SN - 1072-3374

IS - 4

ER -

ID: 73460815