Abstract
This paper gives an overview of statistical inference for disordered sphere packing processes. These processes are used extensively in physics and engineering in order to represent the internal structure of composite materials, packed bed reactors, and powders at rest, and are used as initial arrangements of grains in the study of avalanches and other problems involving powders in motion. Packing processes are spatial processes which are neither stationary nor ergodic. Classical spatial statistical models and procedures cannot be applied to these processes, but alternative models and procedures can be developed based on ideas from statistical physics. Most of the development of models and statistics for sphere packings has been undertaken by scientists and engineers. This review summarizes their results from an inferential perspective.
Highlights
Disordered sphere packing processes are a widely-used class of spatial stochastic processes for which few effective inferential methods are available
Standard methods from spatial statistical inference are of no use in these assessments, but strategies for model assessment can be constructed from statistical tools developed in the fields of application
There appeared to be a well-defined limit to the density achievable by these methods, which resulted in the proposal that there was a well-defined and stable physical state termed a random close packing of spheres
Summary
Disordered sphere packing processes are a widely-used class of spatial stochastic processes for which few effective inferential methods are available. Realizations of these processes are used to model many composite and granular materials in physics and engineering, but rarely is any assessment of model fit undertaken. Almost all models and descriptive statistics for packings have arisen from applications of packings to problems in science and engineering This review gathers these achievements and organizes them into a coherent inferential program. It begins with a presentation of the major uses of sphere packings in science and engineering. The review ends with a discussion of how model assessment can be undertaken, given the nature of the models and the descriptive statistics available
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