• Research

    • Point processes, hyperuniformity, numerical integration, gravitational allocation.
  • Programming language

    • Python


  • Preprint, 2022

    On estimating the structure factor of a point process, with applications to hyperuniformity

  • Python Package, 2022

    Hyperuniformity structure_factor:

    CI-tests codecov docs-build docs-page PyPi version Python >=3.7.1,<3.10 Open In Colab

    • Hyperuniformity is the study of stationary point processes with a sub-Poisson variance of the number of points in a large window. For the homogeneous Poisson point process, the variance of the number of points that fall in a large window is of the order of the window volume. In contrast, for hyperuniform (HU) point processes, the corresponding variance is much lower than the volume of that window, with a ratio going to zero.

      In the context of amorphous structures, hyperuniformity implies a hidden form of order, in which the system remains macroscopically uniform, despite not being crystalline. The concept of hyperuniformity sheds light on a variety of seemingly unrelated fields, including density fluctuations in the early universe, biological tissue, statistical physics, colloidal or granular packings, micro fluids, driven nonequilibrium systems…

      There are many candidate HU processes in the physics literature, but rigorously proving that a point process is HU is usually difficult. It is thus desirable to have standardized numerical tests of hyperuniformity. A common practice in statistical physics is to estimate a spectral measure called the structure factor, the behavior of which around zero is a sign of hyperuniformity.

      We survey existing estimators of the structure factor and gather them all in the Python toolbox structure_factor. Moreover, structure_factor contains a method for testing the effective hyperunifomity of a given point process and the possible class of hyperuniformity. The documentation of the Package is published via the GitHub workflow file (here). Furthermore, a tutorial notebook containing a detailed example of the methods of structure_factor applied on a realization from the Ginibre ensemble is available.