Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), Münchner Strasse 20, 82234 Weßling.
Phys Rev E. 2018 May;97(5-1):053201. doi: 10.1103/PhysRevE.97.053201.
Experiments of the recrystallization processes in two-dimensional complex plasmas are analyzed to rigorously test a recently developed scale-free phase transition theory. The "fractal-domain-structure" (FDS) theory is based on the kinetic theory of Frenkel. It assumes the formation of homogeneous domains, separated by defect lines, during crystallization and a fractal relationship between domain area and boundary length. For the defect number fraction and system energy a scale-free power-law relation is predicted. The long-range scaling behavior of the bond-order correlation function shows clearly that the complex plasma phase transitions are not of the Kosterlitz, Thouless, Halperin, Nelson, and Young type. Previous preliminary results obtained by counting the number of dislocations and applying a bond-order metric for structural analysis are reproduced. These findings are supplemented by extending the use of the bond-order metric to measure the defect number fraction and furthermore applying state-of-the-art analysis methods, allowing a systematic testing of the FDS theory with unprecedented scrutiny: A morphological analysis of lattice structure is performed via Minkowski tensor methods. Minkowski tensors form a complete family of additive, motion covariant and continuous morphological measures that are sensitive to nonlinear properties. The FDS theory is rigorously confirmed and predictions of the theory are reproduced extremely well. The predicted scale-free power-law relation between defect fraction number and system energy is verified for one more order of magnitude at high energies compared to the inherently discontinuous bond-order metric. It is found that the fractal relation between crystalline domain area and circumference is independent of the experiment, the particular Minkowski tensor method, and the particular choice of parameters. Thus, the fractal relationship seems to be inherent to two-dimensional phase transitions in complex plasmas. Minkowski tensor analysis turns out to be a powerful tool for investigations of crystallization processes. It is capable of revealing nonlinear local topological properties, however, still provides easily interpretable results founded on a solid mathematical framework.
对二维复杂等离子体中的再结晶过程进行了实验分析，以严格检验最近提出的无标度相变理论。该理论基于 Frenkel 的动理学理论，假设在结晶过程中形成均匀的畴，由缺陷线分隔，并在畴面积和边界长度之间存在分形关系。对于缺陷数分数和系统能量，预测出无标度幂律关系。键序相关函数的长程标度行为清楚地表明，复杂等离子体的相变不是 Kosterlitz、Thouless、Halperin、Nelson 和 Young 类型的相变。通过计数位错数和应用键序度量进行结构分析得到的先前初步结果得到了重现。这些发现通过将键序度量扩展到测量缺陷数分数，并进一步应用最先进的分析方法得到了补充，从而以前所未有的细致程度系统地检验了 FDS 理论：通过 Minkowski 张量方法对晶格结构进行形态分析。Minkowski 张量形成了一组完整的加性、运动协变和连续形态度量，对非线性性质敏感。FDS 理论得到了严格的确认，并且理论的预测得到了极好的重现。与键序度量的不连续性质相比，在更高的能量下，预测的缺陷分数与系统能量之间的无标度幂律关系得到了再验证，其数量级增加了一个。发现晶体畴面积与周长之间的分形关系与实验、特定的 Minkowski 张量方法和特定的参数选择无关。因此，这种分形关系似乎是复杂等离子体二维相变所固有的。Minkowski 张量分析被证明是研究结晶过程的有力工具。它能够揭示非线性局部拓扑性质，但仍然提供基于坚实数学框架的易于解释的结果。
