The identification of the different phases of a two-dimensional (2d) system, which might be in solid, hexatic, or liquid, requires the accurate determination of the correlation function of the translational and of the bond-orientational order parameters. According to the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory, in the solid phase the translational correlation function decays algebraically, as a consequence of the Mermin-Wagner long-wavelength fluctuations. Recent results have however reported an exponential-like decay. By revisiting different definitions of the translational correlation function commonly used in the literature, here we clarify that the observed exponential-like decay in the solid phase results from an inaccurate determination of the symmetry axis of the solid; the expected power-law behaviour is recovered when the symmetry axis is properly identified. We show that, contrary to the common assumption, the symmetry axis of a 2d solid is not fixed by the direction of its global bond-orientational parameter, and introduce an approach allowing to determine the symmetry axis from a real space analysis of the sample.
Shape-Determined Kinetic Pathways in 2D Solid-Solid Phase Transitions
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所北京凝聚态物理国家实验室）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
Theory of rigidity and numerical analysis of density of states of two-dimensional amorphous solids with dispersed frictional grains in the linear response regime
Single-run determination of the saturation vapor pressure and enthalpy of vaporization/sublimation of a substance undergoing successive solid-solid and solid-liquid phase transitions: the case of $N$-methyl acetamide
Creeping motion of a solid particle inside a spherical elastic cavity. II. Asymmetric motion
本文提出了一种计算小胶体颗粒在大弹性球腔内非对称运动的低雷诺数流体动力学流度函数的解析方法。结合第一部分[Daddi-Moussa-Ider，Löwen和Gekle，Eur. Phys. J. E 41，104（2018）]，其中研究了垂直于弹性腔表面的轴对称运动，可以解决任意力方向的一般运动。弹性流体动力学问题的制定和解决使用经典的图像方法，通过表示流体动力学流场作为一个多极展开涉及高阶导数的自由空间格林函数。在准稳定的限制，我们证明了粒子的自迁移率函数的粒子运动切线的表面的腔是大于预测内的刚性静止腔的大小相等。这种差异是合理的事实，即一个固定的刚性腔体引入额外的阻碍的平移运动的封装的颗粒，导致其流体动力学流动性的降低。此外，腔的运动进行了研究，揭示了平移对（复合）流动性，线性耦合的弹性腔的速度施加在固体颗粒上的力，是完全由膜剪切性能。我们的分析预测是有利的完全解决的计算机模拟的基础上完成的双层边界积分法相比。
