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2 results

  • 3 - Direct Numerical Simulation of Materials Using Computational Grains

  • Leiting Dong, Beihang University, China, Satya N. Atluri, University of California, Irvine
  • Book:
    Computational Grains
    Published online:
    05 October 2023
    Print publication:
    19 October 2023, pp 27-44

  • Summary

    This chapter discusses some general algorithms which are useful in the computational homogenization using the Computational Grains (CGs) method. First, an algorithm for generating a statistically equivalent representative volume element (SERVE) is presented. Then, an algorithm to divide the SERVE in to Voronoi cells (polygons in 2D and polyhedrons in 3D), and using a CG in each Voronoi cell is discussed. The role of parallel computation is also discussed.

  • 9 - Spectrogram Geometry 1

  • from Part II - Geometry and Statistics
  • Patrick Flandrin
  • Book:
    Explorations in Time-Frequency Analysis
    Published online:
    22 August 2018
    Print publication:
    06 September 2018, pp 69-76

  • Summary

    Elaborating on spectrograms viewed as smoothed Wigner distributions, their fine geometrical structure can be explained in cases of increasing complexity. This is detailed by resorting to the interference geometry of Wigner distributions. This allows in particular to make a connection between the zeros of the transforms and the Voronoi cells attached to local maxima.