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  Topology determines force distributions in one-dimensional random spring networks

Heidemann, K. M., Sageman-Furnas, A. O., Sharma, A., Rehfeldt, F., Schmidt, C. F., & Wardetzky, M. (2018). Topology determines force distributions in one-dimensional random spring networks. Physical Review E, 97(2): 022306. doi:10.1103/PhysRevE.97.022306.

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Heidemann, Knut M.1, Author              
Sageman-Furnas, Andrew O., Author
Sharma, Abhinav, Author
Rehfeldt, Florian, Author
Schmidt, Christoph F., Author
Wardetzky, Max, Author
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1Group Physics of social systems, Department of Dynamics of Complex Fluids, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_3171842              

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 Abstract: Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber-reinforced materials are also common in technology. An important characteristic of such materials is their resistance to failure under load. Rupture occurs when fibers break under excessive force and when that failure propagates. Therefore, it is crucial to understand force distributions. Force distributions within such networks are typically highly inhomogeneous and are not well understood. Here we construct a simple one-dimensional model system with periodic boundary conditions by randomly placing linear springs on a circle. We consider ensembles of such networks that consist of N nodes and have an average degree of connectivity z but vary in topology. Using a graph-theoretical approach that accounts for the full topology of each network in the ensemble, we show that, surprisingly, the force distributions can be fully characterized in terms of the parameters (N ,z). Despite the universal properties of such (N ,z) ensembles, our analysis further reveals that a classical mean-field approach fails to capture force distributions correctly. We demonstrate that network topology is a crucial determinant of force distributions in elastic spring networks.

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 Dates: 2018
 Publication Status: Published in print
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 Identifiers: DOI: 10.1103/PhysRevE.97.022306
BibTex Citekey: Heidemann2018b
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Title: Physical Review E
  Other : Phys. Rev. E
Source Genre: Journal
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Publ. Info: Melville, NY : American Physical Society
Pages: 11 Volume / Issue: 97 (2) Sequence Number: 022306 Start / End Page: - Identifier: ISSN: 1539-3755
CoNE: https://pure.mpg.de/cone/journals/resource/954925225012