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Statistical inference for disordered sphere packings. (English) Zbl 1302.62205

Summary: 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.

MSC:

62M30 Inference from spatial processes
62-02 Research exposition (monographs, survey articles) pertaining to statistics
52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry)
60D05 Geometric probability and stochastic geometry
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
74E15 Crystalline structure
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Full Text: DOI arXiv Euclid

References:

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