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arXiv 0909.4324cond-mat.softcond-mat.dis-nn
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干扰III:通过被干扰物质的熵表征随机性

Jamming III: Characterizing Randomness via the Entropy of Jammed Matter

Christopher Briscoe, Chaoming Song, Ping Wang, Hernan A. Makse

摘要:

利用理论和模拟相同的球形颗粒的随机性的性质在无序堆积的摩擦和无摩擦的领域进行了研究。通过堵塞物质的力和体积系综来定义填充物的熵,并且难以解析地计算。一个介观系综的均衡状态,然后利用在努力预测的熵,通过依赖于配位数的体积函数的定义。得到了表征堵塞物不同状态的熵、体积分数和压实度的状态方程,阐明了堵塞颗粒物的相图。分析计算相比,使用体积波动分析和图形理论方法的数值模拟,具有合理的协议。堵塞系统的熵揭示了随机松散包装比随机紧密包装更无序,允许对这两个极限进行明确的解释。计算结果表明,在随机紧密堆积(RCP)的熵消失,而数值模拟表明,在RCP的微观状态,有限的熵仍然存在。负紧性的概念,探讨国家的体积分数低于现有的模拟协议,也探讨了扩大状态方程。我们讨论了可能的扩展到目前的介观方法描述包装从RLP RCP的状态方程的有序分支,以了解堵塞的物质在整个范围内的密度从RLP FCC的熵。

英文摘要:

The nature of randomness in disordered packings of frictional and frictionless spheres is investigated using theory and simulations of identical spherical grains. The entropy of the packings is defined through the force and volume ensemble of jammed matter and shown difficult to calculate analytically. A mesoscopic ensemble of isostatic states is then utilized in an effort to predict the entropy through the defnition of a volume function dependent on the coordination number. Equations of state are obtained relating entropy, volume fraction and compactivity characterizing the different states of jammed matter, and elucidating the phase diagram for jammed granular matter. Analytical calculations are compared to numerical simulations using volume fluctuation analysis and graph theoretical methods, with reasonable agreement. The entropy of the jammed system reveals that the random loose packings are more disordered than random close packings, allowing for an unambiguous interpretation of both limits. Ensemble calculations show that the entropy vanishes at random close packing (RCP), while numerical simulations show that a finite entropy remains in the microscopic states at RCP. The notion of a negative compactivity, that explores states with volume fractions below those achievable by existing simulation protocols, is also explored, expanding the equations of state. We discuss possible extensions to the present mesoscopic approach describing packings from RLP to RCP to the ordered branch of the equation of state in an effort to understand the entropy of jammed matter in the full range of densities from RLP to FCC.

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