Kinetics of Aggregation with Choice

doi:10.1103/PhysRevE.94.062119

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:

^[1]; Krapivsky, Paul ^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division and Center for Nonlinear Studies
Boston Univ., MA (United States). Dept. of Physics

Publication Date:: 2016-12-01

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.

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                    Ben-Naim, Eli, & Krapivsky, Paul. Kinetics of Aggregation with Choice.  United States.  doi:10.1103/PhysRevE.94.062119.

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                    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.

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@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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DOI: 10.1103/PhysRevE.94.062119

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Works referenced in this record:

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Similar Records

Title: Kinetics of Aggregation with Choice

Abstract

Citation Formats

Explosive Percolation Transition is Actually Continuous journal, December 2010

Glassy dynamics in the asymmetrically constrained kinetic Ising chain journal, September 2003

Phase transition with nonthermodynamic states in reversible polymerization journal, June 2008

Kinetics of rouleau formation. I. A mass action approach with geometric features journal, February 1982

Explosive Percolation in Random Networks journal, March 2009

Front propagation into unstable states journal, November 2003

Scaling theory and exactly solved models in the kinetics of irreversible aggregation journal, August 2003

Explosive Percolation Is Continuous journal, July 2011

Explosive Percolation Transition is Actually Continuous
journal, December 2010

Glassy dynamics in the asymmetrically constrained kinetic Ising chain
journal, September 2003

Phase transition with nonthermodynamic states in reversible polymerization
journal, June 2008

Kinetics of rouleau formation. I. A mass action approach with geometric features
journal, February 1982

Explosive Percolation in Random Networks
journal, March 2009

Front propagation into unstable states
journal, November 2003

Scaling theory and exactly solved models in the kinetics of irreversible aggregation
journal, August 2003

Explosive Percolation Is Continuous
journal, July 2011