Length scales in granular matter

by Song-Chuan Zhao
Doctoral thesis
Date of Examination:2013-02-28
Date of issue:2013-04-24
Advisor:Prof. Dr. Stephan Herminghaus
Referee:Prof. Dr. Stephan Herminghaus
Referee:Prof. Dr. Annette Zippelius
Persistent Address: http://dx.doi.org/10.53846/goediss-3812

 

 

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Abstract

English

Jammed packings of granular materials differ from thermal systems normally described by statistical mechanics. In recent years a statistical mechanics of static granular media has emerged by using the volume of the system as the macroscopic variable. Voronoi volume is a popular building block of the system volume. We measure the two-point correlation of free Voronoi volumes in binary disc packings. Both positive correlation and negative correlation are observed. We extract three lengths to describe the spatial extension of the correlations, and show how the lengths develop with packing fractions. The influence of the correlations on the statistical mechanics are studied by measuring the configurational temperature replacing the thermodynamic temperature by three methods. The configurational temperature becomes intensive for sample size larger than the characteristic length of the correlation between Voronoi volumes. In the second part, we perform the same analysis on 3D sphere packings.
Keywords: granular matter; statistical theory; disc packings; granular matter; statistical theory; disc packings; sphere packings
 
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