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Nucleation Rate Identification in Binary Phase Transition

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The Impact of Applications on Mathematics

Part of the book series: Mathematics for Industry ((MFI,volume 1))

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Abstract

In this chapter, we study a PDE-ODE system arising from binary phase transition coupled with an energy balance to account for recalescence effects. The phase transition is described by classic arguments on nucleation and growth process. The main novelty of our work is the identification of temperature dependent nucleation rates from measurements in a subdomain. We prove the uniqueness of the parameter identification problem and numerical results support the theoretical results.

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Author information

Authors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117, Berlin, Germany

    Dietmar Hömberg

  2. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Shuai Lu

  3. Mathematical Science and Technology Research Laboratory, Advanced Technology Research Laboratories, Technical Development Bureau, Nippon Steel & Sumitomo Metal Corporation, 20-1 Shintomi, Futtsu, Chiba, 293-8511, Japan

    Kenichi Sakamoto

  4. Department of Mathematical Sciences, The University of Tokyo, Komaba Meguro, Tokyo, 153-8914, Japan

    Masahiro Yamamoto

Authors
  1. Dietmar Hömberg
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  2. Shuai Lu
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  3. Kenichi Sakamoto
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  4. Masahiro Yamamoto
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Corresponding author

Correspondence to Shuai Lu .

Editor information

Editors and Affiliations

  1. Institute for Mathematics and Industry, Kyushu University, Fukuoka, Japan

    Masato Wakayama

  2. CSIRO (Commonwealth Scientific and Industrial Research Organisation), Canberra, Aust Capital Terr, Australia

    Robert S. Anderssen

  3. School of Mathematical Sciences, Fudan University, Shanghai, China

    Jin Cheng

  4. Kyushu University, Fukuoka, Japan

    Yasuhide Fukumoto

  5. Institute of Natural and Mathematical Sciences, Massey University, Palmerston North, Auckland, New Zealand

    Robert McKibbin

  6. Institute of Mathematics, Free University of Berlin, Berlin, Germany

    Konrad Polthier

  7. Kyushu University, Fukuoka, Japan

    Tsuyoshi Takagi

  8. Department of Mathematics, National University of Singapore, Singapore, Singapur, Singapore

    Kim-Chuan Toh

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Hömberg, D., Lu, S., Sakamoto, K., Yamamoto, M. (2014). Nucleation Rate Identification in Binary Phase Transition. In: Wakayama, M., et al. The Impact of Applications on Mathematics. Mathematics for Industry, vol 1. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54907-9_17

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  • DOI: https://doi.org/10.1007/978-4-431-54907-9_17

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  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-54906-2

  • Online ISBN: 978-4-431-54907-9

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