Critical point of jamming transition in two-dimensional monodisperse systems
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THE EUROPEAN PHYSICAL JOURNAL E
Regular Article
Critical point of jamming transition in two-dimensional monodisperse systems Liping Deng1,2 , Cai Zhao1 , Zhenhuan Xu1 , and Wen Zheng1,2,3,a 1 2 3
Institute of Public Safety and Big Data, College of Data Science, Taiyuan University of Technology, Taiyuan 030060, China Key Laboratory of Impact and Safety Engineering, Ministry of Education, Ningbo University, Ningbo 315211, China Center for Healthy Big Data, Changzhi Medical College, Changzhi, Shanxi 046000, China Received 13 July 2020 / Received in final form 18 October 2020 / Accepted 2 November 2020 Published online: 3 December 2020 c EDP Sciences / Societ` a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. The existence of amorphous packings in two-dimensional monodisperse system is a classical unsolved problem. We get the energy minimum state by the energy minimization method of enthalpy under constant pressure conditions. Firstly, we find that there are two peaks in the experiment, which demonstrate the interesting features of the coexistence of crystals and amorphous crystals. And then, we confirm the critical point of jamming transition of the two-dimensional monodisperse is φc = 0.8418. Finally, we prove that the jamming scaling is still satisfied in two-dimensional monodispersed system: G/B ∼ p1/2 and vanishes as p → 0, and the boson peak shifts to lower frequencies for less compressed systems.
1 Introduction The jamming transition occurs when a system undergoes the transition from a liquid-like state to a rigid but disordered solid state, which is widely studied in dense disordered systems of colloids, emulsions, foams, and granular materials [1–5]. Amorphous packings of frictionless, spherical particles are isostatic at jamming onset, with the number of contacts equal to the number of degrees of freedom [6, 29]. In contrast, the existence of amorphous packings in two dimensions is a problem of debate in the literature: two-dimensional monodisperse systems are found to crystallize very easily, since disordered packings of disks are particularly unstable. In two-dimensional Euclidean space, the triangular lattice has the highest density of all possible ordered or √disordered packings with a packing fraction φhex = π/ 12 ≈ 0.9069 and each disk is surrounded by 6 neighbors [7]. Regarding amorphous packings, experiments find a maximum density of random close packing (RCP) of polydisperse disks at φrcp ≈ 0.84 [8], but various results exist from 0.82 to 0.89 of monodisperse disks [9]. In a recent research work, a special maximally random jammed state in the two-dimensional monodisperse disordered system with φM RJ = 0.826 was found
Contribution to the Topical Issue “Disordered, NonEquilibrium Systems: From Supercooled Liquids to Amorphous Solids” edited by Marco Baity Jesi, Yuliang Jin, Elijah Flenner, Marisa A. Frechero, Gustavo A. Appignanesi. a e-mail: [email protected]
in a small system (N < 200) through the Torquato-Jiao sequential linear programming algorith
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