Statistical Mechanics of a Cat's Cradle

Abstract

It is believed that, much like a cat's cradle, the cytoskeleton can be thought of as a network of strings under tension. We show that both regular and random bond-disordered networks having bonds that buckle upon compression exhibit a variety of phase transitions as a function of temperature and extension. The results of self-consistent phonon calculations for the regular networks agree very well with computer simulations at finite temperature. The analytic theory also yields a rigidity onset (mechanical percolation) and the fraction of extended bonds for random networks. There is very good agreement with the simulations by Delaney et al. (Europhys. Lett. 2005). The mean field theory reveals a nontranslationally invariant phase with self-generated heterogeneity of tautness, representing ``antiferroelasticity''.

4 pages, 4 figures

References in corpus (4)

• The structural glass transition and the entropy of the metastable states
• Thermodynamics of glasses: a first principle computation
• Microscopic theory of network glasses
• Stability and Dynamics of Crystals and Glasses of Motorized Particles

Cited by in corpus (8)

• Active contractility in actomyosin networks
• On the spontaneous collective motion of active matter
• Tensegrity and Motor-Driven Effective Interactions in a Model Cytoskeleton
• Stress-stabilized sub-isostatic fiber networks in a rope-like limit
• Motor-free Contractility in Active Gels
• The Interplay of Nonlinearity and Architecture in Equilibrium Cytoskeletal Mechanics
• Microscopic theory of the glassy dynamics of passive and active network materials
• Active patterning and asymmetric transport in a model actomyosin network