Corrected mean-field model for random sequential adsorption on random geometric graphs

S. Dhara, J.S.H. van Leeuwaarden, D. Mukherjee

Research output: Contribution to journalArticleAcademicpeer-review

22 Downloads (Pure)

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 languageEnglish
Pages (from-to)872-894
Number of pages23
JournalJournal of Statistical Physics
Volume173
Issue number3-4
DOIs
Publication statusPublished - 1 Nov 2018

Fingerprint

Random Geometric Graph
Random Sequential Adsorption
Mean-field Model
adsorption
Euclidean geometry
Euclidean space
Functional Limit Theorem
Solvable Models
Random Networks
Congruent
Spatial Correlation
mathematics
Random Graphs
Network Model
Overlap
Nearest Neighbor
theorems
Physics
Fluctuations
physics

Keywords

  • Functional limit theorems
  • Jamming fraction
  • Mean-field analysis
  • Random geometric graph
  • Random sequential adsorption

Cite this

@article{a90d511d64724a378598b2a194f8a11f,
title = "Corrected mean-field model for random sequential adsorption on random geometric graphs",
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.",
keywords = "Functional limit theorems, Jamming fraction, Mean-field analysis, Random geometric graph, Random sequential adsorption",
author = "S. Dhara and {van Leeuwaarden}, J.S.H. and D. Mukherjee",
year = "2018",
month = "11",
day = "1",
doi = "10.1007/s10955-018-2019-8",
language = "English",
volume = "173",
pages = "872--894",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer",
number = "3-4",

}

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 journalArticleAcademicpeer-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 -