Inclusive (almost!) application of numerical techniques in Materials Science

An overview of combined application of mathematical topics lectured in ENGN2020 @ Brown University Spring '19

Posted by Sayan Samanta on May 27, 2020 · 2 mins read

This post in based on the syllabus of ENGN 2020 - Mathematical Methods in Engineering and Physics II offered during the Spring semester at Brown University, RI, USA.

ENGN 2020 is an extensive course on the application of a wide spectrum of numerical techniques that can be used to solve real-life engineering problems. Unfortunately, due the large syllabus, the utility of the lessons learnt in this course can often be underestimated or forgotten. In this post we shall look at a Materials science phenomena known as Spinodal Decomposition, which can be mathematically modeled by the Cahn-Hilliard Equation. The algorithm demonstrated below is borrowed from the work done by Dr. Saswata Bhattacharya and colleagues at the Indian Institute of Science, Bangalore (IISC).

However, the details of the particular computer experiment is not the primary take-away here, rather, the application of apparently disconnected mathematical topics in tandem that leads to the physically comparable results is what's important and shall be stressed upon.

Here is the presentation.

References

  1. J. W. Cahn and J. E. Hilliard, "Free Energy of a Nonuniform System. I. Interfacial Free Energy", J. Chem. Phys. 28, 258 (1958); https://doi.org/10.1063/1.1744102
  2. E. Schrödinger, "An Undulatory Theory of the Mechanics of Atoms and Molecules",Phys. Rev. 28, 1049 (1926); https://doi.org/10.1103/PhysRev.28.1049
  3. P. Hohenberg and W. Kohn, "Inhomogeneous Electron Gas", Phys. Rev. 136, B864 (1964); https://doi.org/10.1103/PhysRev.136.B864
  4. A. Fick, "Uber Diffusion",Annalen der Physik und Chemie von J. C. Pogendorff, 94, 59 (1855); https://doi.org/10.1002/andp.18551700105
  5. L.Q.Chen and J.Shen, "Applications of semi-implicit Fourier-spectral method to phase field equations", Comput. Phys. Commun. 108, 147 (1998); https://doi.org/10.1016/S0010-4655(97)00115-X
  6. S.Bhattacharya and T.A. Abhinandanan, "A study of phase separation in ternary alloys", Bull. Mater. Sci. 26, 193 (2003); https://doi.org/10.1007/BF02712812

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