Energy transfer and trapping in regular hyperbranched macromolecules

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

doi:10.1016/j.physa.2005.05.005

Cited by 25 publications

(40 citation statements)

References 14 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%

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%

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

Liu

Dolgushev

et al. 2015

Sci Rep

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“…We note that similar phenomenon is also observed for Vicsek fractals. 2,3 However, at intermediate times, the curves for different g behave quite different, but no scaling is observed, meaning that no curves follow a linear behavior. This phenomenon is as opposed to that for Vicsek fratals, the corresponding curves of which show an obvious algebraic behavior.…”

Section: Fluorescence Depolarizationmentioning

confidence: 97%

“…This phenomenon is as opposed to that for Vicsek fratals, the corresponding curves of which show an obvious algebraic behavior. 2,3 The disparity in P(t) makes it easy to differentiate between Vicsek fractals and the polymer networks studied here.…”

Section: Fluorescence Depolarizationmentioning

confidence: 99%

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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“…Often, simplifying assumptions are invoked -for example, in work by Blumen et al [78], an exact solution has been derived for fractal polymers for which all chromophores have the same absorption cross-section, all rates of transfer between nearest neighbors also being considered equal. More radical approaches to the problem have also been attempted, such as modeling the diffusion of the excitation under a constant force as a continuum process [79], or using the Eyring (membrane permeation) model to treat energy flux as diffusion in a potential with thermal barriers [80].…”

Section: Dendrimeric Materialsmentioning

confidence: 99%

Energy harvesting: a review of the interplay between structure and mechanism

Andrews

2008

J. Nanophoton

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Abstract. The science of energy harvesting has recently undergone radical change, with the advent of new materials exploiting mechanisms fundamentally different from those of traditional solar cells. Utilizing principles that are in many cases acquired from breakthroughs in molecular photobiology, the introduction of a range of new synthetic polymers, multichromophore arrays and nanoparticle-based materials heralds a marked resurgence of interest, a shift of focus and heightened expectations in the science of light-harvesting. The interplay between structure and mechanism significantly impinges upon issues extending from fundamental theory to the principles of energy-harvesting materials design. Understanding and exploiting the principles allows materials to be engineered that can harness absorbed energy with heightened efficiency. Two of the key areas of application are dendrimers and rare-earth doped solids.

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Energy transfer and trapping in regular hyperbranched macromolecules

Cited by 25 publications

References 14 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

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

Energy harvesting: a review of the interplay between structure and mechanism

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