Monitoring energy transfer in hyperbranched macromolecules through fluorescence depolarization

Blumen, A.; Volta, A.; Jurjiu, Aurel; Koslowski, Th.

doi:10.1016/j.jlumin.2004.10.012

Cited by 27 publications

(52 citation statements)

References 32 publications

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“…Moreover, the four curves saturate to a constant value later than those of Fig. 5, while the plateau values 〈 P (∞)〉 are exactly the same for both figures and equal to 1/ N g 67. This indicates that the equipartition of the energy over all beads is reached faster for the networks than for the dual Sierpinski gaskets with the same number of nodes and edges.…”

Section: Resultsmentioning

confidence: 59%

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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: 59%

“…5 a waviness superimposed at early times can be observed immediately. Such waviness has been predicted in the regular hyperbranched fractals6 and it is related to high symmetry (regularity) of the network, i.e. the averaging due to possible disorder will smooth out the curves.…”

Section: Resultsmentioning

confidence: 82%

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

Liu

Dolgushev

et al. 2015

Sci Rep

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“…Thus, in this way each eigenvalue λ g−1 i in g−1 gives rise to two new eigenvalues in (2) g . Inserting each Laplacian eigenvalue of U g − 1 into Eqs.…”

Section: A Eigenvaluesmentioning

confidence: 96%

“…(1) g contains all eigenvalues equal to 1, while (2) g includes the remaining eigenvalues. Thus, (1) …”

Section: A Eigenvaluesmentioning

confidence: 99%

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Laplacian spectra of recursive treelike small-world polymer networks: Analytical solutions and applications

Liu

Zhang²

2013

The Journal of Chemical Physics

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A central issue in the study of polymer physics is to understand the relation between the geometrical properties of macromolecules and various dynamics, most of which are encoded in the Laplacian spectra of a related graph describing the macrostructural structure. In this paper, we introduce a family of treelike polymer networks with a parameter, which has the same size as the Vicsek fractals modeling regular hyperbranched polymers. We study some relevant properties of the networks and show that they have an exponentially decaying degree distribution and exhibit the small-world behavior. We then study the Laplacian eigenvalues and their corresponding eigenvectors of the networks under consideration, with both quantities being determined through the recursive relations deduced from the network structure. Using the obtained recursive relations we can find all the eigenvalues and eigenvectors for the networks with any size. Finally, as some applications, we use the eigenvalues to study analytically or semi-analytically three dynamical processes occurring in the networks, including random walks, relaxation dynamics in the framework of generalized Gaussian structure, as well as the fluorescence depolarization under quasiresonant energy transfer. Moreover, we compare the results with those corresponding to Vicsek fractals, and show that the dynamics differ greatly for the two network families, which thus enables us to distinguish between them.

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