Spectra of Husimi cacti: Exact results and applications

Galiceanu, Mircea; Blumen, A.

doi:10.1063/1.2787005

Cited by 36 publications

(48 citation statements)

References 28 publications

(28 reference statements)

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“…We are now embarking on the dynamics of energy transfer over a system of chromophores678. As a usual way, we assume that the nodes (beads) only transfer their energy with their nearest neighbors.…”

Section: Resultsmentioning

confidence: 99%

“…For instance, in the framework of generalized Gaussian structures (GGSs)2345, the dynamics of polymer networks is fully described through the Laplacian eigenvectors and eigenvalues. In the field of GGSs and dynamical processes, the investigation of Laplacian eigenmodes has a paramount importance for the relaxation dynamics, the fluorescence depolarization by quasiresonant energy transfer678, the mean first-passage time problems91011, and so on. Laplacian eigenvalues and eigenvectors play an irreplaceable role and they are also relevant to multi-aspects of complex network structures, like spanning trees12, resistance distance13 and community structure14.…”

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confidence: 99%

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Laplacian spectra of a class of small-world networks and their applications

Liu

Dolgushev

et al. 2015

Sci Rep

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One of the most crucial domains of interdisciplinary research is the relationship between the dynamics and structural characteristics. In this paper, we introduce a family of small-world networks, parameterized through a variable d controlling the scale of graph completeness or of network clustering. We study the Laplacian eigenvalues of these networks, which are determined through analytic recursive equations. This allows us to analyze the spectra in depth and to determine the corresponding spectral dimension. Based on these results, we consider the networks in the framework of generalized Gaussian structures, whose physical behavior is exemplified on the relaxation dynamics and on the fluorescence depolarization under quasiresonant energy transfer. Although the networks have the same number of nodes (beads) and edges (springs) as the dual Sierpinski gaskets, they display rather different dynamic behavior.

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Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

Laplacian spectra of a class of small-world networks and their applications

Liu

Dolgushev

et al. 2015

Sci Rep

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“…It is then a simple matter to verify that for a " b the equilibrium bond-bond correlations hd a Á d b i GGS , evaluated with respect to the Boltzmann distribution, expðÀV GGS =k B TÞ, vanish. The generalization of Equation 15 to STP consists now in taking as generalized potential the expression…”

Section: Simulation Proceduresmentioning

confidence: 99%

Branched Semiflexible Polymers: Theoretical and Simulation Aspects

Dolgushev

Berezovska

Blumen

2011

Macro Theory & Simulations

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Recent approaches for taking stiffness effects into account when modeling multifunctional polymer structures are reported. The theoretical part is focused on arbitrary tree‐like polymers, modeled through extensions of the GGS scheme that allows the inclusion of local constraints. The theoretical findings are compared to the results of numerical simulations in which stiffness is included into the bond fluctuation model with the help of additional bending potentials. The procedure is illustrated by evaluating the static properties of semiflexible linear chains, stars, cospectral polymers and rings. The dynamical properties are exemplified by the mechanical relaxation of semiflexible polymers, including situations in which the local conditions at different sites are the same or different.magnified image

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“…In recent years, extensive attention has been focused on the study of spectra for various matrices of complex networks [14][15][16], such as the adjacency matrix [17][18][19], the Laplacian matrix [20][21][22][23][24], the modularity matrix [25,26], and the nonback-tracking matrix [27]. In the context of the transition matrix, a conscientious effort has been devoted to determine the eigenvalues for some classic fractals [28][29][30][31] and treelike networks [32][33][34][35].…”

Section: Introductionmentioning

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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Spectra of Husimi cacti: Exact results and applications

Cited by 36 publications

References 28 publications

Laplacian spectra of a class of small-world networks and their applications

Laplacian spectra of a class of small-world networks and their applications

Branched Semiflexible Polymers: Theoretical and Simulation Aspects

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

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