Fig. 5: Distribution of the coordination number. | Nature Communications

Fig. 5: Distribution of the coordination number.

From: Jamming is a first-order transition with quenched disorder in amorphous materials sheared by cyclic quasistatic deformations

Fig. 5: Distribution of the coordination number.

a Probability distribution p(Z) at a few different φ for N = 1000. b p(Z) at φ = 0.843 for a few different N. For better visualization, we do not show the unjammed delta-peak at Z = 0 (see SI Fig. S1b for full distributions). c The fraction of jammed states FJ as a function of φ for a few different N. The intersection of curves gives \({\varphi }_{{{\rm{J}}}}^{\infty }=0.8432(2)\). d The data points of FJ with different N collapse as a function of \((\varphi -{\varphi }_{{{\rm{J}}}}^{\infty }){N}^{1/2}\). The solid line represents fitting to Eq. (4), with two fitting parameters u = 0.041(1) and σφ = 0.043(1). The average coordination number 〈Z〉 is plotted as a function of φ in e and of \((\varphi -{\varphi }_{{{\rm{J}}}}^{\infty }){N}^{1/2}\) in f. The solid line in f represents \(\langle Z\rangle={F}_{{{\rm{J}}}}{Z}_{{{\rm{J}}}}^{ * }\) using u = 0.041, σφ = 0.043 and \({Z}_{{{\rm{J}}}}^{ * }=4.1\). Symbols in b–f have the same meanings.

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