### 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 ∼ R^{2}/(a^{2}L), 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 language | English (US) |
---|---|

Article number | 345003 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 48 |

Issue number | 34 |

DOIs | |

State | Published - Aug 6 2015 |

### Fingerprint

### 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

*Journal of Physics A: Mathematical and Theoretical*,

*48*(34), [345003]. https://doi.org/10.1088/1751-8113/48/34/345003

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

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 48, no. 34, 345003. https://doi.org/10.1088/1751-8113/48/34/345003

}

TY - JOUR

T1 - From statistics of regular tree-like graphs to distribution function and gyration radius of branched polymers

AU - Grosberg, Alexander Y.

AU - Nechaev, Sergei K.

PY - 2015/8/6

Y1 - 2015/8/6

N2 - 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.

AB - 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.

KW - branched polymers

KW - eigenvalue analysis

KW - Kramers theorem

UR - http://www.scopus.com/inward/record.url?scp=84947610102&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84947610102&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/48/34/345003

DO - 10.1088/1751-8113/48/34/345003

M3 - Article

VL - 48

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 34

M1 - 345003

ER -