DCF Seminar: Elastic networks: Continuum vs Network models
14:00 - 15:00
Dr. Knut Heidemann
Fraunhofer Institute for Intelligent Analysis and Information Systems, Sankt Augustin
Max-Planck-Institut für Dynamik und Selbstorganisation (MPIDS)
In this talk I study the mechanical properties of biopolymer networks. I discuss which of these properties can be described by continuum approaches and which features, on the contrary, require consideration of the discrete nature, or the topology, of the network. In part one, I study the elasticity of disordered networks of rigid filaments connected by flexible crosslinks [1,2]. I derive scaling relations for the differential shear modulus assuming affine deformations and infinite crosslink density, and compare these results with extensive 3D network simulations. In part two, I study the role topology plays for force distributions in a model system consisting of ensembles of random linear spring networks on a circle [3,4]. Combining graph-theoratical and probabilistic techniques, I derive mean and variance of the force supported by individual springs in terms of only two parameters: (i) average connectivity and (ii) number of nodes. The analysis shows that a classical mean-field approach fails to capture these characteristic quantities correctly. In contrast, I demonstrate that network topology is a crucial determinant of force distributions in an elastic spring network.
 K. M. Heidemann, A. Sharma, F. Rehfeldt, C. F. Schmidt & M. Wardetzky. Elasticity of 3D networks with rigid filaments and compliant crosslinks. Soft Matter 11, 343–354 (2015).
 A. Sharma, M. Sheinman, K. M. Heidemann & F. C. MacKintosh. Elastic response of filamentous networks with compliant crosslinks. Phys. Rev. E 88, 052705 (2013).
 K. M. Heidemann, A. O. Sageman-Furnas, A. Sharma, F. Rehfeldt, C. F. Schmidt & M. Wardetzky. Topology Counts: Force Distributions in Circular Spring Networks. Phys. Rev. Lett. 120, 068001 (2018).
 K. M. Heidemann, A. O. Sageman-Furnas, A. Sharma, F. Rehfeldt, C. F. Schmidt & M. Wardetzky. Topology determines force distributions in one-dimensional random spring networks. Phys. Rev. E 97, 022306 (2018).