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Grain Growth and the Effect of Different Time Scales

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Research in Mathematics of Materials Science

Part of the book series: Association for Women in Mathematics Series ((AWMS,volume 31))

Abstract

Many technologically useful materials are polycrystals composed of a myriad of small monocrystalline grains separated by grain boundaries. Dynamics of grain boundaries play a crucial role in determining the grain structure and defining the materials properties across multiple scales. In this work, we consider two models for the motion of grain boundaries with the dynamic lattice misorientations and the triple junctions drag, and we conduct extensive numerical study of the models, as well as present relevant experimental results of grain growth in thin films.

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Acknowledgements

The authors are grateful to David Kinderlehrer for the fruitful discussions, inspiration, and motivation of the work. Matthew Patrick and Amirali Zangiabadi are thanked for assistance with the experimental work. Katayun Barmak acknowledges partial support of NSF DMS-1905492, Yekaterina Epshteyn acknowledges partial support of NSF DMS-1905463, Chun Liu acknowledges partial support of NSF DMS-1950868, and Masashi Mizuno acknowledges partial support of JSPS KAKENHI Grant No. 18K13446, 22K03376.

Author information

Authors and Affiliations

  1. Columbia University, New York, NY, USA

    Katayun Barmak

  2. West High School, Salt Lake City, UT, USA

    Anastasia Dunca

  3. University of Utah, Salt Lake City, UT, USA

    Yekaterina Epshteyn

  4. Illinois Institute of Technology, Chicago, IL, USA

    Chun Liu

  5. Nihon University, Tokyo, Japan

    Masashi Mizuno

Authors
  1. Katayun Barmak
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  2. Anastasia Dunca
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  3. Yekaterina Epshteyn
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  4. Chun Liu
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  5. Masashi Mizuno
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Corresponding author

Correspondence to Yekaterina Epshteyn .

Editor information

Editors and Affiliations

  1. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, USA

    Malena I. Español

  2. Mathematics Department, University of Pittsburgh, Pittsburgh, PA, USA

    Marta Lewicka

  3. Department of Mathematics, Heriot-Watt University, Edinburgh, UK

    Lucia Scardia

  4. Institute of Mathematics, Universität Würzburg, Würzburg, Germany

    Anja Schlömerkemper

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Barmak, K., Dunca, A., Epshteyn, Y., Liu, C., Mizuno, M. (2022). Grain Growth and the Effect of Different Time Scales. In: Español, M.I., Lewicka, M., Scardia, L., Schlömerkemper, A. (eds) Research in Mathematics of Materials Science. Association for Women in Mathematics Series, vol 31. Springer, Cham. https://doi.org/10.1007/978-3-031-04496-0_2

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