2007/11/19 by Jeffrey D. Picka, Jeffrey Picka, Picka, Jeffrey
Engineering · Materials Science · Mathematics · #Applications (stat.AP) #Crystallization and Solubility Studies #FOS: Computer and information sciences #Granular flow and fluidized beds #Material Dynamics and Properties #Methodology (stat.ME) #stat.AP #stat.ME
paper · pdf · doi:10.48550/arxiv.0711.3035
54 pages, no figures; revised
openalex publication_date 2007/11/19 · arxiv created 2009/10/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Sphere packings are essential to the development of physical models for powders, composite materials, and the atomic structure of the liquid state. There is a strong scientific need to be able to assess the fit of packing models to data, but this is complicated by the lack of formal probabilistic models for packings. Without formal models, simulation algorithms and collections of physical objects must be used as models. Identification of common aspects of different realizations of the same packing process requires the use of new descriptive statistics, many of which have yet to be developed. Model assessment will require the use of large samples of independent and identically distributed realizations, rather than the large single stationary realizations found in conventional spatial statistics. The development of procedures for model assessment will resemble the development of thermodynamic models, and will be based on much exploration and experimentation rather than on extensions of established statistical methods.