Relaxation dynamics of a polymer network modeled by a multihierarchical structure

Jurjiu, Aurel; Volta, A.; Beu, Titus A.

doi:10.1103/physreve.84.011801

Cited by 32 publications

(37 citation statements)

References 41 publications

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“…IV, SD; scaling behavior is, on the other hand, the rule for linear chains and for fractals. [28][29][30][31] In fact, for FD the corresponding curves in the region of intermediate frequencies can be approximated through logarithmic forms. 8 The broadening of the spectra with growing q, as discussed above, manifests itself through a broadening of the [G (ω)]-shapes.…”

Section: Discussionmentioning

confidence: 99%

Analytical model for the dynamics of semiflexible dendritic polymers

Fürstenberg

Dolgushev

Blumen

2012

The Journal of Chemical Physics

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We study the dynamics of semiflexible dendritic polymers following the method of Dolgushev and Blumen [J. Chem. Phys. 131, 044905 (2009)]. The scheme allows to formulate in analytical form the corresponding Langevin equations. We determine the eigenvalues by first block-diagonalizing the problem, which allows to treat even very large dendritic objects. A basic ingredient of the procedure is the observation that a set of eigenmodes in the semiflexible case is similar to that chosen by Cai and Chen [Macromolecules 30, 5104 (1997)] for fully flexible dendritic structures. Varying the flexibility of the macromolecules allows us to better understand their mechanical loss moduli G"(ω) based on their eigenvalue spectra. We present the G"(ω) for a series of stiffness parameters and for different functionalities of the branching points.

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Section: Discussionmentioning

confidence: 99%

Analytical model for the dynamics of semiflexible dendritic polymers

Fürstenberg

Dolgushev

Blumen

2012

The Journal of Chemical Physics

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“…Since the network under consideration displays self-similar architecture, we can solve the eigenvalues of P g by using the decimation approach [50,51], which is a general technique applicable to self-similar networks and has been utilized to compute the eigenvalues of Laplacian matrices for Vicsek fractals [52][53][54] as well as their extensions [55]. Next, we use the decimation method to evaluate all the eigenvalues of P g .…”

Section: A Recursive Solution To Eigenvaluesmentioning

confidence: 99%

Eigenvalues for the transition matrix of a small-world scale-free network: Explicit expressions and applications

2015

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The eigenvalues of the transition matrix for random walks on a network play a significant role in the structural and dynamical aspects of the network. Nevertheless, it is still not well understood how the eigenvalues behave in small-world and scale-free networks, which describe a large variety of real systems. In this paper, we study the eigenvalues for the transition matrix of a network that is simultaneously scale-free, small-world, and clustered. We derive explicit simple expressions for all eigenvalues and their multiplicities, with the spectral density exhibiting a power-law form. We then apply the obtained eigenvalues to determine the mixing time and random target access time for random walks, both of which exhibit unusual behaviors compared with those for other networks, signaling discernible effects of topologies on spectral features. Finally, we use the eigenvalues to count spanning trees in the network.

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“…Next, we apply the decimation method [31,32] to determine the eigenvalues and their multiplicities of P n . The decimation approach is universal and has been used to compute the Laplacian spectra of Vicsek fractals [36][37][38] and their extensions [39]. We now address the eigenvalue problem for matrix P n+1 .…”

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confidence: 99%

Exact eigenvalue spectrum of a class of fractal scale-free networks

Zhang¹,

Hu²,

Sheng³

et al. 2012

EPL

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-The eigenvalue spectrum of the transition matrix of a network encodes important information about its structural and dynamical properties. We study the transition matrix of a family of fractal scale-free networks and analytically determine all the eigenvalues and their degeneracies. We then use these eigenvalues to evaluate the closed-form solution to the eigentime for random walks on the networks under consideration. Through the connection between the spectrum of transition matrix and the number of spanning trees, we corroborate the obtained eigenvalues and their multiplicities.

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Relaxation dynamics of a polymer network modeled by a multihierarchical structure

Cited by 32 publications

References 41 publications

Analytical model for the dynamics of semiflexible dendritic polymers

Analytical model for the dynamics of semiflexible dendritic polymers

Eigenvalues for the transition matrix of a small-world scale-free network: Explicit expressions and applications

Exact eigenvalue spectrum of a class of fractal scale-free networks

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