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Exploring the applications of fractional calculus: Hierarchically built semiflexible polymers

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  • Fürstenberg, Florian
  • Dolgushev, Maxim
  • Blumen, Alexander

Abstract

In this article we study, through extensions of the generalized Gaussian scheme, the dynamics of semiflexible treelike polymers under the influence of external forces acting on particular (say, charged) monomers. Semiflexibility is introduced following our previous work (Dolgushev and Blumen, 2009 [15]), a procedure which allows one to study treelike structures with arbitrary stiffness and branching. Exemplarily, we illustrate the procedure using linear chains and hyperbranched polymers modeled through Vicsek fractals, and obtain in every case the monomer displacement averaged over the structure. Anomalous behavior manifests itself in the intermediate time region, where the different fractal architectures show distinct scaling behaviors. These behaviors are due to the power law behavior of the spectral density and lead, for arbitrary pulling forces, based on causality and the linear superposition principle, to fractional calculus expressions, in accordance to former phenomenological fractional laws in polymer physics.

Suggested Citation

  • Fürstenberg, Florian & Dolgushev, Maxim & Blumen, Alexander, 2015. "Exploring the applications of fractional calculus: Hierarchically built semiflexible polymers," Chaos, Solitons & Fractals, Elsevier, vol. 81(PB), pages 527-533.
    • Handle: RePEc:eee:chsofr:v:81:y:2015:i:pb:p:527-533
    DOI: 10.1016/j.chaos.2015.07.006
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    References listed on IDEAS

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    1. Pagnini, Gianni, 2014. "Short note on the emergence of fractional kinetics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 29-34.
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