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Using convex quadratic programming to model random media with Gaussian random fields.

John A Quintanilla1, W Max Jones

  • 1Department of Mathematics, P.O. Box 311430, University of North Texas, Denton, Texas 76203, USA. jquintanilla@unt.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 16, 2007
PubMed
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Gaussian random fields (GRFs) model two-phase media. This study introduces convex quadratic programming to find optimal autocorrelation functions, enhancing GRF model versatility for materials science applications.

Area of Science:

  • Materials Science
  • Statistical Physics
  • Computational Mathematics

Background:

  • Gaussian random fields (GRFs) are established models for two-phase random media.
  • Accurate modeling requires optimizing field autocorrelation functions to match phase autocorrelation functions.
  • Existing methods often rely on limited, pre-defined parameter families.

Purpose of the Study:

  • To develop and present a novel technique for optimizing field autocorrelation functions in GRF models.
  • To improve the accuracy and versatility of GRF models for random media.
  • To apply the optimized GRF model to a real-world materials science problem.

Main Methods:

  • Utilized convex quadratic programming for optimization.
  • Focused on finding the best admissible field autocorrelation function under discretization.

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  • Optimized over all admissible functions, not restricted to parametrized families.

    • Main Results:

    • The convex quadratic programming approach efficiently identifies optimal autocorrelation functions.
    • Demonstrated significantly enhanced versatility of the GRF model compared to previous studies.
    • Successfully applied the technique to model a tetraethoxysilane aerogel system using scattering data.

    Conclusions:

    • The proposed optimization technique offers a more powerful and flexible approach to GRF modeling.
    • This method advances the ability to accurately represent complex random media.
    • The findings have implications for materials characterization and design.