Exploring the applications of fractional calculus: Hierarchically built semiflexible polymers |
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| Institution: | 1. Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran;2. Department of Mathematics and Statistics, Mississippi State University, Starkville, MS 39762, USA;1. School of Electronic and Information Engineering, Beihang University, Beijing 100191, PR China;2. Beijing Key Laboratory for Network-based Cooperative Air Traffic Management, Beijing 100191, PR China;3. Beijing Laboratory for General Aviation Technology, Beijing 100191, PR China;4. School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, PR China;1. Department of Financial Management, National Defense University, No. 70, Sec. 2, Zhongyang North Rd., Beitou, Taipei 112, Taiwan;2. Graduate Institute of Technology Management, National Taiwan University of Science and Technology, 43, Section 4, Keelung Road, Taipei 10607, Taiwan;3. Department of Accounting, College of Business Management and Accounting, Universiti Tenaga Nasional, Sultan Haji Ahmad Shah Campus, 26700 Muadzam Shah, Pahang, Malaysia;4. Department of Business Administration, National Central University, No. 300, Jung-Da Road, Jung-Li City, Tao-Yuan 320, Taiwan |
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| 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. |
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