3,421 research outputs found
Random Sequential Addition of Hard Spheres in High Euclidean Dimensions
Employing numerical and theoretical methods, we investigate the structural
characteristics of random sequential addition (RSA) of congruent spheres in
-dimensional Euclidean space in the infinite-time or
saturation limit for the first six space dimensions ().
Specifically, we determine the saturation density, pair correlation function,
cumulative coordination number and the structure factor in each =of these
dimensions. We find that for , the saturation density
scales with dimension as , where and
. We also show analytically that the same density scaling
persists in the high-dimensional limit, albeit with different coefficients. A
byproduct of this high-dimensional analysis is a relatively sharp lower bound
on the saturation density for any given by , where is the structure factor at
(i.e., infinite-wavelength number variance) in the high-dimensional limit.
Consistent with the recent "decorrelation principle," we find that pair
correlations markedly diminish as the space dimension increases up to six. Our
work has implications for the possible existence of disordered classical ground
states for some continuous potentials in sufficiently high dimensions.Comment: 38 pages, 9 figures, 4 table
Dagstuhl Reports : Volume 1, Issue 2, February 2011
Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn
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