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Title: Kinetics of Aggregation with Choice

Abstract

Here we generalize the ordinary aggregation process to allow for choice. In ordinary aggregation, two random clusters merge and form a larger aggregate. In our implementation of choice, a target cluster and two candidate clusters are randomly selected and the target cluster merges with the larger of the two candidate clusters.We study the long-time asymptotic behavior and find that as in ordinary aggregation, the size density adheres to the standard scaling form. However, aggregation with choice exhibits a number of different features. First, the density of the smallest clusters exhibits anomalous scaling. Second, both the small-size and the large-size tails of the density are overpopulated, at the expense of the density of moderate-size clusters. Finally, we also study the complementary case where the smaller candidate cluster participates in the aggregation process and find an abundance of moderate clusters at the expense of small and large clusters. Additionally, we investigate aggregation processes with choice among multiple candidate clusters and a symmetric implementation where the choice is between two pairs of clusters.

Authors:
ORCiD logo [1];  [2]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division and Center for Nonlinear Studies
  2. Boston Univ., MA (United States). Dept. of Physics
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1337116
Alternate Identifier(s):
OSTI ID: 1335729
Report Number(s):
LA-UR-16-27687
Journal ID: ISSN 2470-0045
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 94; Journal Issue: 6; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Mathematics

Citation Formats

Ben-Naim, Eli, and Krapivsky, Paul. Kinetics of Aggregation with Choice. United States: N. p., 2016. Web. doi:10.1103/PhysRevE.94.062119.
Ben-Naim, Eli, & Krapivsky, Paul. Kinetics of Aggregation with Choice. United States. doi:10.1103/PhysRevE.94.062119.
Ben-Naim, Eli, and Krapivsky, Paul. Thu . "Kinetics of Aggregation with Choice". United States. doi:10.1103/PhysRevE.94.062119. https://www.osti.gov/servlets/purl/1337116.
@article{osti_1337116,
title = {Kinetics of Aggregation with Choice},
author = {Ben-Naim, Eli and Krapivsky, Paul},
abstractNote = {Here we generalize the ordinary aggregation process to allow for choice. In ordinary aggregation, two random clusters merge and form a larger aggregate. In our implementation of choice, a target cluster and two candidate clusters are randomly selected and the target cluster merges with the larger of the two candidate clusters.We study the long-time asymptotic behavior and find that as in ordinary aggregation, the size density adheres to the standard scaling form. However, aggregation with choice exhibits a number of different features. First, the density of the smallest clusters exhibits anomalous scaling. Second, both the small-size and the large-size tails of the density are overpopulated, at the expense of the density of moderate-size clusters. Finally, we also study the complementary case where the smaller candidate cluster participates in the aggregation process and find an abundance of moderate clusters at the expense of small and large clusters. Additionally, we investigate aggregation processes with choice among multiple candidate clusters and a symmetric implementation where the choice is between two pairs of clusters.},
doi = {10.1103/PhysRevE.94.062119},
journal = {Physical Review E},
number = 6,
volume = 94,
place = {United States},
year = {2016},
month = {12}
}

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