Topology Counts: Force Distributions in Circular Spring Networks

Physical Review Letters
Knut M HeidemannMax Wardetzky

Abstract

Filamentous polymer networks govern the mechanical properties of many biological materials. Force distributions within these networks are typically highly inhomogeneous, and, although the importance of force distributions for structural properties is well recognized, they are far from being understood quantitatively. Using a combination of probabilistic and graph-theoretical techniques, we derive force distributions in a model system consisting of ensembles of random linear spring networks on a circle. We show that characteristic quantities, such as the mean and variance of the force supported by individual springs, can be derived explicitly in terms of only two parameters: (i) average connectivity and (ii) number of nodes. Our analysis shows that a classical mean-field approach fails to capture these characteristic quantities correctly. In contrast, we demonstrate that network topology is a crucial determinant of force distributions in an elastic spring network. Our results for 1D linear spring networks readily generalize to arbitrary dimensions.

References

Jan 1, 1985·Physical Review. B, Condensed Matter·S FengE Garboczi
May 13, 2005·Nature·Cornelis StormPaul A Janmey
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Dec 18, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A SharmaF C MacKintosh
Nov 20, 2014·Soft Matter·Knut M HeidemannMax Wardetzky

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Citations

Dec 31, 2019·Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences·Kirsty Y WanWallace F Marshall
Mar 20, 2018·Physical Review. E·Knut M HeidemannMax Wardetzky
Dec 17, 2018·Progress in Biophysics and Molecular Biology·Susanne F SchlickFlorian Rehfeldt

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