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Scale-free crystallization of two-dimensional complex plasmas: Domain analysis using Minkowski tensors

Böbel, Alexander and Knapek, Christina and Räth, Christoph (2018) Scale-free crystallization of two-dimensional complex plasmas: Domain analysis using Minkowski tensors. Physical Review E, 97, 053201. American Physical Society. DOI: 10.1103/PhysRevE.97.053201 ISSN 1539-3755

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Official URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.97.053201

Abstract

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.

Item URL in elib:https://elib.dlr.de/120709/
Document Type:Article
Title:Scale-free crystallization of two-dimensional complex plasmas: Domain analysis using Minkowski tensors
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Böbel, AlexanderAlexander.Boebel (at) dlr.deUNSPECIFIED
Knapek, ChristinaChristina.Knapek (at) dlr.deUNSPECIFIED
Räth, ChristophChristoph.Raeth (at) dlr.deUNSPECIFIED
Date:3 May 2018
Journal or Publication Title:Physical Review E
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In SCOPUS:Yes
In ISI Web of Science:No
Volume:97
DOI :10.1103/PhysRevE.97.053201
Page Range:053201
Publisher:American Physical Society
ISSN:1539-3755
Status:Published
Keywords:Crystallization, Phase Transition, Complex Plasmas, Minkowski Tensors, Data Analysis
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Research under Space Conditions
DLR - Research area:Raumfahrt
DLR - Program:R FR - Forschung unter Weltraumbedingungen
DLR - Research theme (Project):R - Komplexe Plasmen / Data analysis
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Materials Physics in Space > Research Group Complex Plasma
Deposited By: Böbel, Alexander
Deposited On:28 Jun 2018 13:02
Last Modified:31 Jul 2019 20:18

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