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arXiv 1510.03469cond-mat.soft
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干扰跃迁的标度理论

Scaling theory for the jamming transition

Carl P. Goodrich, Andrea J. Liu, James P. Sethna

摘要:

我们提出了一个标度分析系统的弹性能量附近的临界堵塞过渡的三个相关领域:压缩应变$Δϕ$相对于临界堵塞状态,剪切应变$ε$,和逆系统尺寸$1/N$。我们还使用$ΔZ$作为基础控制参数,$ΔZ$是相对于干扰时所需最小值的触点数量。我们的标度理论预测新的指数,指数等式和标度崩溃的能量,压力和剪切应力,我们验证与数值模拟的软球堵塞包装。它也产生了新的见解,为什么剪切模量和体积模量表现出不同的缩放;差异的出现,因为剪切应力消失为$1/\sqrt{N}$,而压力接近一个常数的热力学极限。标度分析的成功意味着干扰跃迁具有涌现标度不变性,并且应该有可能发展一种用于干扰的重整化群理论。

英文摘要:

We propose a scaling ansatz for the elastic energy of a system near the critical jamming transition in terms of three relevant fields: the compressive strain $Δϕ$ relative to the critical jammed state, the shear strain $ε$, and the inverse system size $1/N$. We also use $ΔZ$, the number of contacts relative to the minimum required at jamming, as an underlying control parameter. Our scaling theory predicts new exponents, exponent equalities and scaling collapses for energy, pressure and shear stress that we verify with numerical simulations of jammed packings of soft spheres. It also yields new insight into why the shear and bulk moduli exhibit different scalings; the difference arises because the shear stress vanishes as $1/\sqrt{N}$ while the pressure approaches a constant in the thermodynamic limit. The success of the scaling ansatz implies that the jamming transition exhibits an emergent scale invariance, and that it should be possible to develop a renormalization-group theory for jamming.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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