Skip to main content

A Reduced Model for Simulating Grain Growth

  • Conference paper
Book cover Free Boundary Problems

Abstract

We introduce a reduced model to study normal grain growth in two dimensions, which is based on the gradient flow structure of the mean curvature flow. In the simplified model, we restrict this gradient flow to grain boundaries which are straight lines. We present simulations for a large number of grains and we also study the effect of anisotropies.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L. Bronsard and F. Reitich, On three-phase boundary motion and the sin-gular limit of a vector-valued Ginzburg-Landau equation, Arch. Rat. Mech. Anal. 124, 4 (1993), 355–379.

    Article  MathSciNet  MATH  Google Scholar 

  2. V. E. Fradkov, A theoretical investigation of two-dimensional grain growth in the `gas` approximation, Phil. Mag. Letters 58, 6 (1988), 271–275.

    Google Scholar 

  3. V. E. Fradkov and D. Udler, 2d normal grain growth: topological aspects, Advances in Physics 43 (1994), 739–789.

    Article  Google Scholar 

  4. V. E. Fradkov, D. Udler, and R. E. Kris, Computer simulation of two-dimensional normal grain growth (the ‘gas’ approximation), Phil. Mag. Letters 58, 6 (1988), 277–283.

    Google Scholar 

  5. D. Kinderlehrer, private communication.

    Google Scholar 

  6. D. Kinderlehrer and C. Liu, Evolution of grain boundaries, Math. Mod.Meth. Appl. Sc. 4, 11 (2001), 713–729.

    Article  MathSciNet  Google Scholar 

  7. K. Kawasaki, T. Nagai, and K. Nakashima, Vertex models for two-dimensional grain growth, Philosophical Magazine B 60 (1989), 399–421.

    Article  Google Scholar 

  8. T. Nagai, K. Fuchizaki, and K. Kawasaki, Orientation effect on grain growth, Physica A 204 (1994), 450–463.

    Article  Google Scholar 

  9. J. E. Taylor and J. W. Cahn, Linking anisotropic sharp and diffuse surface motion laws via gradient flows, J. Stat. Phys. 77 (1994), 183–197.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer Basel AG

About this paper

Cite this paper

Henseler, R., Niethammer, B., Otto, F. (2003). A Reduced Model for Simulating Grain Growth. In: Colli, P., Verdi, C., Visintin, A. (eds) Free Boundary Problems. ISNM International Series of Numerical Mathematics, vol 147. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7893-7_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-7893-7_14

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9613-9

  • Online ISBN: 978-3-0348-7893-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics