Abstract
A notorious problem in mathematics and physics is to create a solvable model for random sequential adsorption of non-overlapping congruent spheres in the d-dimensional Euclidean space with (Formula presented.). Spheres arrive sequentially at uniformly chosen locations in space and are accepted only when there is no overlap with previously deposited spheres. Due to spatial correlations, characterizing the fraction of accepted spheres remains largely intractable. We study this fraction by taking a novel approach that compares random sequential adsorption in Euclidean space to the nearest-neighbor blocking on a sequence of clustered random graphs. This random network model can be thought of as a corrected mean-field model for the interaction graph between the attempted spheres. Using functional limit theorems, we characterize the fraction of accepted spheres and its fluctuations.
| Original language | English |
|---|---|
| Pages (from-to) | 872-894 |
| Number of pages | 23 |
| Journal | Journal of Statistical Physics |
| Volume | 173 |
| Issue number | 3-4 |
| DOIs | |
| Publication status | Published - 1 Nov 2018 |
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Keywords
- Functional limit theorems
- Jamming fraction
- Mean-field analysis
- Random geometric graph
- Random sequential adsorption
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Corrected mean-field model for random sequential adsorption on random geometric graphs. / Dhara, S.; van Leeuwaarden, J.S.H.; Mukherjee, D.
In: Journal of Statistical Physics, Vol. 173, No. 3-4, 01.11.2018, p. 872-894.Research output: Contribution to journal › Article › Academic › peer-review
TY - JOUR
T1 - Corrected mean-field model for random sequential adsorption on random geometric graphs
AU - Dhara, S.
AU - van Leeuwaarden, J.S.H.
AU - Mukherjee, D.
PY - 2018/11/1
Y1 - 2018/11/1
N2 - A notorious problem in mathematics and physics is to create a solvable model for random sequential adsorption of non-overlapping congruent spheres in the d-dimensional Euclidean space with (Formula presented.). Spheres arrive sequentially at uniformly chosen locations in space and are accepted only when there is no overlap with previously deposited spheres. Due to spatial correlations, characterizing the fraction of accepted spheres remains largely intractable. We study this fraction by taking a novel approach that compares random sequential adsorption in Euclidean space to the nearest-neighbor blocking on a sequence of clustered random graphs. This random network model can be thought of as a corrected mean-field model for the interaction graph between the attempted spheres. Using functional limit theorems, we characterize the fraction of accepted spheres and its fluctuations.
AB - A notorious problem in mathematics and physics is to create a solvable model for random sequential adsorption of non-overlapping congruent spheres in the d-dimensional Euclidean space with (Formula presented.). Spheres arrive sequentially at uniformly chosen locations in space and are accepted only when there is no overlap with previously deposited spheres. Due to spatial correlations, characterizing the fraction of accepted spheres remains largely intractable. We study this fraction by taking a novel approach that compares random sequential adsorption in Euclidean space to the nearest-neighbor blocking on a sequence of clustered random graphs. This random network model can be thought of as a corrected mean-field model for the interaction graph between the attempted spheres. Using functional limit theorems, we characterize the fraction of accepted spheres and its fluctuations.
KW - Functional limit theorems
KW - Jamming fraction
KW - Mean-field analysis
KW - Random geometric graph
KW - Random sequential adsorption
UR - http://www.scopus.com/inward/record.url?scp=85044391878&partnerID=8YFLogxK
U2 - 10.1007/s10955-018-2019-8
DO - 10.1007/s10955-018-2019-8
M3 - Article
AN - SCOPUS:85044391878
VL - 173
SP - 872
EP - 894
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
SN - 0022-4715
IS - 3-4
ER -