From statistics of regular tree-like graphs to distribution function and gyration radius of branched polymers

Alexander Y. Grosberg, Sergei K. Nechaev

    Research output: Contribution to journalArticle

    Abstract

    We consider flexible branched polymer, with quenched branch structure, and show that its conformational entropy as a function of its gyration radius R, at large R, obeys, in the scaling sense, ΔS ∼ R2/(a2L), with a bond length (or Kuhn segment) and L defined as an average spanning distance. We show that this estimate is valid up to at most the logarithmic correction for any tree. We do so by explicitly computing the largest eigenvalues of Kramers matrices for both regular and 'sparse' three-branched trees, uncovering on the way their peculiar mathematical properties.

    Original languageEnglish (US)
    Article number345003
    JournalJournal of Physics A: Mathematical and Theoretical
    Volume48
    Issue number34
    DOIs
    StatePublished - Aug 6 2015

    Fingerprint

    Trees (mathematics)
    gyration
    Bond length
    Distribution functions
    Distribution Function
    Entropy
    Polymers
    distribution functions
    Radius
    Statistics
    statistics
    radii
    Largest Eigenvalue
    polymers
    Graph in graph theory
    Logarithmic
    Branch
    eigenvalues
    Scaling
    Valid

    Keywords

    • branched polymers
    • eigenvalue analysis
    • Kramers theorem

    ASJC Scopus subject areas

    • Mathematical Physics
    • Physics and Astronomy(all)
    • Statistical and Nonlinear Physics
    • Modeling and Simulation
    • Statistics and Probability

    Cite this

    From statistics of regular tree-like graphs to distribution function and gyration radius of branched polymers. / Grosberg, Alexander Y.; Nechaev, Sergei K.

    In: Journal of Physics A: Mathematical and Theoretical, Vol. 48, No. 34, 345003, 06.08.2015.

    Research output: Contribution to journalArticle

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