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A jammed state is a common phenomenon in complex granular systems, in which the relationship between the mechanical properties and the geometric structures is very complicated. The critical jammed state in a two-dimensional particle system is studied by numerical simulation. The system is composed of 2050 particles with two different radii, whose distribution is random. Initially the particles with a smaller radius are of a looser distribution in the given space. When the radius increases, a transition from the looser state to the jammed state happens. The particle dimension-radius ratio and the percentage of large particles kB play primary roles in this system, which are discussed in detail based on the statistical analysis of the average contact number, packing fraction, and contact type. By analyzing the relationship between pressure and packing fraction of the granular system, the critical jammed point for the applied pressure to the boundary can be found. Numerical simulation result shows that no obvious connection exists between the average contact number and the percentage of large particles for the case that the particle dimension-radius ratio is less than 1.4. The average contact number approximate to 4 when = 1.4, which is consistent with previous conclusions. The average contact number first decreases and then increases when the percentage of large particles become larger in the case 1.4. A minimum value C = 0.84 is obtained when kB = 0.5. When the percentage of large particles increases, the critical packing fraction decreases first and then increases in the case 1.8, but it almost keeps constant for 1.8. When the percentage of large particles is close to either 0% or 100%, the granular system is approximately mono-disperse. In this case, the average contact number and packing fraction become constant. When the percentage is close to 50%, the critical average contact number decreases all the time with larger particles-radius ratio, while the critical packing fraction decreases first and then increases. The percentage of large-small contact type is also discussed. The value varies following a quadratic function with the increase of the percentage of large particles, while the particles-radius ratio has slight impact on this variation. Specifically, we have calculated the percentage of large-small contact type based on probabilistic method, and the result agrees well with the simulation results. We give the reason why previous researchers studied the case of = 1.4 :1 and kB = 0.5 on the basis of results in this paper, and find that the values of and kB have no influence on the power-law relation around the critical jammed state.
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Keywords:
- jammed state /
- average contact number /
- packing fraction /
- contact type
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[1] Ouyang H W, Huang S C, Peng Z, Wang Q, Lin Z M 2008 Materials Science and Engineering of Powder Metallurgy 13 260 (in Chinese) [欧阳鸿武, 黄誓成, 彭政, 王琼, 刘卓民 2008 粉末冶金材料科学与工程 13 260]
[2] Liu A J, Nagel S R 1998 Nature 396 21
[3] O'Hern C, Langer S A, Liu A J, Nagel S R 2002 Phys. Rev. Lett. 88 075507
[4] O'Hern C, Silbert L E, Liu A J, Nagel S R 2003 Phys. Rev. E 68 011306
[5] Maimudar T S, Sperl M, Luding S, Behringger R P 2007 Phys. Rev. Lett. 98 058001
[6] Zhang G H, Sun Q C, Huang F F, Jing F 2011 Acta Phys. Sin. 60 124502 (in Chinese) [张国华, 孙其诚, 黄芳芳, 金峰 2011 60 124502]
[7] Bi D P, Zhang J, Behringger R P 2011 Nature 480 355
[8] Yang L, Hu L, Zhang X G 2015 Acta Phys. Sin. 64 134502 (in Chinese) [杨林, 胡林, 张兴刚 2015 64 134502]
[9] Liu H, Tong H, Xu N 2014 Chin. Phys. B 23 116105
[10] Hu M B, Jiang R, Wu Q S 2013 Chin. Phys. B 22 066301
[11] Eric l. Corwin, Heinrich M. Jaeger 2005 Nature 03698 1075
[12] Zhang X G, Hu L 2012 Chin. J. Comput. Phys. 29 627 (in Chinese) [张兴刚, 胡林 2012 计算物理 29 627]
[13] Feng X, Zhang G H, Sun Q C 2013 Acta Phys. Sin. 62 184501 (in Chinese) [冯旭, 张国华, 孙其诚 2013 62 184501]
[14] Zhang Z X, Xu N 2009 Nature 07998 230
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