ISSN:
1572-9613
Keywords:
Rigid spheres
;
Rigid disks
;
Rigid rods
;
Elasticity
;
High pressure
;
Polytopes
;
Convexity
;
Crystal anharmonicity
;
Pair correlation functions
;
Multidimensional geometry
;
Crystalline order
;
Crystal defects
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract The available configuration space for finite systems of rigid particles separates into equivalent disconnected regions if those systems are highly compressed. This paper presents a study of the geometric properties of the limiting high-compression regions (polytopes) for rods, disks, and spheres. The molecular distribution functions represent cross sections through the convex polytopes, and for that reason they are obliged to exhibit single-peak behavior by the Brünn-Minkowski inequality. We demonstrate that increasing system dimensionality implies tendency toward nearest-neighbor particle-pair localization away from contact. The relation between the generalized Euler theorem for the limiting polytopes and cooperative “jamming” of groups of particles is explored. A connection is obtained between the moments of inertia of the polytopes (regarded as solid homogeneous bodies) and crystal elastic properties. Finally, we provide a list of unsolved problems in this geometrical many-body theory.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01007250
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