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Related Experiment Videos

Moving average fields, macro-scale response measures, and homogenizing micro-scale variation.

John J McCoy1

  • 1The Catholic University of America, Washington, DC 20064, USA. mccoy@cua.edu

The Journal of the Acoustical Society of America
|July 16, 2005
PubMed
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Deriving macro-scale models faces challenges in field relationships and closure problems. Multiresolution wavelet analysis offers a framework for precise macro-scale fields and exact closure problem solutions.

Area of Science:

  • Multiscale modeling
  • Wavelet analysis
  • Scientific computing

Background:

  • Deriving macro-scale prediction models from detailed underlying models presents significant challenges.
  • Key issues include defining the precise relationship between macro and micro-scale fields and solving the closure problem.
  • Current methods like moving averages and common assumptions for closure problems have limitations.

Purpose of the Study:

  • To challenge the conventional understanding of moving averages for macro-scale field representation.
  • To critique the validity of common assumptions used to solve closure problems in model derivation.
  • To introduce multiresolution analysis using orthogonal wavelets as a robust framework for these challenges.

Main Methods:

  • Challenging the efficacy of moving averages in eliminating micro-scale variations.

Related Experiment Videos

  • Demonstrating the invalidity of typical assumptions in solving closure problems.
  • Applying orthogonal wavelet systems for multiresolution analysis.

    • Main Results:

    • Moving averages do not fully eliminate micro-scale variation, only appearing to do so in specific representations.
    • Common assumptions for closure problems are often demonstrably invalid, despite sometimes yielding reasonable results.
    • Multiresolution analysis provides a framework for precisely defining macro-scale fields free of micro-scale variation.

    Conclusions:

    • Orthogonal wavelet systems offer a formally exact solution to closure problems.
    • This approach precisely defines macro-scale response fields by eliminating all micro-scale variation.
    • Multiresolution analysis provides a superior framework for deriving accurate macro-scale prediction models.