Scale-Free Crystallization of two-dimensional Complex Plasmas: Domain Analysis using Minkowski Tensors

Experiments of the recrystallization processes in two-dimensional complex plasmas are analyzed in order 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 KTHNY 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 non-linear 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. Minkowski Tensor analysis turns out to be a powerful tool for investigations of crystallization processes. It is capable to reveal non-linear local topological properties, however, still provides easily interpretable results founded on a solid mathematical framework.Comment: 17 pages, 13 figures, 4 tables accepted for publication in PR

Synchronization of particle motion in compressed two-dimensional plasma crystals

The collective motion of dust particles during the mode-coupling induced melting of a two-dimensional plasma crystal is explored in molecular dynamics simulations. The crystal is compressed horizontally by an anisotropic confinement. This compression leads to an asymmetric triggering of the mode-coupling instability which is accompanied by alternating chains of in-phase and anti-phase oscillating particles. A new order parameter is proposed to quantify the synchronization with respect to different directions of the crystal. Depending on the orientation of the confinement anisotropy, mode-coupling instability and synchronized motion are observed in one or two directions. Notably, the synchronization is found to be direction-dependent. The good agreement with experiments suggests that the confinement anisotropy can be used to explain the observed synchronization process.Comment: 6 pages, 4 figure

Correlating Fourier phase information with real-space higher order statistics

We establish for the first time heuristic correlations between harmonic space phase information and higher order statistics. Using the spherical full-sky maps of the cosmic microwave background as an example we demonstrate that known phase correlations at large spatial scales can gradually be diminished when subtracting a suitable best-fit (Bianchi-) template map of given strength. The weaker phase correlations lead in turn to a vanishing signature of anisotropy when measuring the Minkowski functionals and scaling indices in real-space and comparing them with surrogate maps being free of phase correlations. Those investigations can open a new road to a better understanding of signatures of non-Gaussianities in complex spatial structures by elucidating the meaning of Fourier phase correlations and their influence on higher order statistics.Comment: 6 pages plus 1 supplemental page, 4 figures, submitte

Dim and bright void regimes in capacitively-coupled RF complex plasmas

We demonstrate experimentally that the void in capacitively-coupled RF complex plasmas can exist in two qualitative different regimes. The "bright" void is characterized by bright plasma emission associated with the void, whereas the "dim" void possesses no detectable emission feature. The transition from the dim to the bright regime occurs with an increase of the discharge power and has a discontinuous character. The discontinuity is manifested by a kink in the void size power dependencies. We reproduce the bright void (mechanically stabilized due to the balance of ion drag and electrostatic forces) by a simplified time-averaged 1D fluid model. To reproduce the dim void, we artificially include the radial ion diffusion into the continuity equation for ions, which allows to mechanically stabilize the void boundary due to very weak electrostatic forces. The electric field at the void boundary occurs to be so small that it, in accordance with the experimental observation, causes no void-related emission feature.Comment: 21 pages, 14 figure

Probing non-Gaussianities in the CMB on an incomplete sky using surrogates

We demonstrate the feasibility to generate surrogates by Fourier-based methods for an incomplete data set. This is performed for the case of a CMB analysis, where astrophysical foreground emission, mainly present in the Galactic plane, is a major challenge. The shuffling of the Fourier phases for generating surrogates is now enabled by transforming the spherical harmonics into a new set of basis functions that are orthonormal on the cut sky. The results show that non-Gaussianities and hemispherical asymmetries in the CMB as identified in several former investigations, can still be detected even when the complete Galactic plane (|b| < 30{\deg}) is removed. We conclude that the Galactic plane cannot be the dominant source for these anomalies. The results point towards a violation of statistical isotropy.Comment: 9 pages, 13 figures, accepted by Physical Review

Fluid demixing kinetics on spherical geometry: power spectrum and Minkowski functional analysis

Dynamic density functional theory calculations of fluid–fluid demixing on spherical geometries are characterized via their angular power spectrum as well as via the Minkowski functionals (MFs) of their binarized fluid density fields. MFs form a complete set of additive, motion invariant and continuous morphological measures sensitive to nonlinear (spatial) correlations. The temporal evolution of the fluid density fields is analyzed for different sphere sizes and mixing compositions. The demixing process in the stages of early spinodal decomposition and consecutive domain growth can be characterized by both methods and a power-law domain growth $L(t)\propto {t}^{\alpha }$ is evidenced for the MF measures. The average domain size obtained by the structure factor only responds to the late stage domain growth of the demixing process. MFs provide refined insights into the demixing process: they allow the detection of distinct stages in the early spinodal decomposition, provide a precise measure of the relative species composition of the mixture and, most importantly: after a proper rescaling, they allow the detection of a universal demixing behavior for a wide range of mixture fractions and for different sphere sizes

A Scaling Index Analysis of the WMAP three year data: Signatures of non-Gaussianities and Asymmetries in the CMB

Local scaling properties of the co-added foreground-cleaned three-year Wilkinson Microwave Anisotropy Probe (WMAP) data are estimated using weighted scaling indices. The scaling index method (SIM) is - for the first time - adapted and applied to the case of spherical symmetric spatial data. The results are compared with 1000 Monte Carlo simulations based on Gaussian fluctuations with a best fit $\Lambda$CDM power spectrum and WMAP-like beam and noise properties. Statistical quantities based on the scaling indices, namely the moments of the distribution and probability-based measures are determined. We find for most of the test statistics significant deviations from the Gaussian hypothesis. We find pronounced asymmetries, which can be interpreted as a global lack of structure in the northern hemisphere, which is consistent with previous findings. Furthermore, we detect a localized anomaly in the southern hemisphere, which gives rise to highly significant signature for non-Gaussianity in the spectrum of scaling indices. We identify this signature as the cold spot, which was also already detected in the first year WMAP data. Our results provide further evidence for both the presence of non-Gaussianities and asymmetries in the WMAP three-year data. More detailed bandand year-wise analyses are needed to elucidate the origin of the detected anomalies. In either case the scaling indices provide powerful nonlinear statistics to analyse CMB maps.Comment: submitted to MNRA

Dynamics of lane formation in driven binary complex plasmas

The dynamical onset of lane formation is studied in experiments with binary complex plasmas under microgravity conditions. Small microparticles are driven and penetrate into a cloud of big particles, revealing a strong tendency towards lane formation. The observed time-resolved lane formation process is in good agreement with computer simulations of a binary Yukawa model with Langevin dynamics. The laning is quantified in terms of the anisotropic scaling index, leading to a universal order parameter for driven systems.Comment: 4 pages, 3 figures, movies available at http://www.mpe.mpg.de/pke/lane-formation

On the Nature of X-ray Variability in Ark 564

We use data from a recent long ASCA observation of the Narrow Line Seyfert 1 Ark 564 to investigate in detail its timing properties. We show that a thorough analysis of the time series, employing techniques not generally applied to AGN light curves, can provide useful information to characterize the engines of these powerful sources.We searched for signs of non-stationarity in the data, but did not find strong evidences for it. We find that the process causing the variability is very likely nonlinear, suggesting that variability models based on many active regions, as the shot noise model, may not be applicable to Ark 564. The complex light curve can be viewed, for a limited range of time scales, as a fractal object with non-trivial fractal dimension and statistical self-similarity. Finally, using a nonlinear statistic based on the scaling index as a tool to discriminate time series, we demonstrate that the high and low count rate states, which are indistinguishable on the basis of their autocorrelation, structure and probability density functions, are intrinsically different, with the high state characterized by higher complexity.Comment: 13 pages, 13 figures, accepted for publication in A&

Automated 3D trabecular bone structure analysis of the proximal femur—prediction of biomechanical strength by CT and DXA

The standard diagnostic technique for assessing osteoporosis is dual X-ray absorptiometry (DXA) measuring bone mass parameters. In this study, a combination of DXA and trabecular structure parameters (acquired by computed tomography [CT]) most accurately predicted the biomechanical strength of the proximal femur and allowed for a better prediction than DXA alone. An automated 3D segmentation algorithm was applied to determine specific structure parameters of the trabecular bone in CT images of the proximal femur. This was done to evaluate the ability of these parameters for predicting biomechanical femoral bone strength in comparison with bone mineral content (BMC) and bone mineral density (BMD) acquired by DXA as standard diagnostic technique. One hundred eighty-seven proximal femur specimens were harvested from formalin-fixed human cadavers. BMC and BMD were determined by DXA. Structure parameters of the trabecular bone (i.e., morphometry, fuzzy logic, Minkowski functionals, and the scaling index method [SIM]) were computed from CT images. Absolute femoral bone strength was assessed with a biomechanical side-impact test measuring failure load (FL). Adjusted FL parameters for appraisal of relative bone strength were calculated by dividing FL by influencing variables such as body height, weight, or femoral head diameter. The best single parameter predicting FL and adjusted FL parameters was apparent trabecular separation (morphometry) or DXA-derived BMC or BMD with correlations up to r = 0.802. In combination with DXA, structure parameters (most notably the SIM and morphometry) added in linear regression models significant information in predicting FL and all adjusted FL parameters (up to R adj = 0.872) and allowed for a significant better prediction than DXA alone. A combination of bone mass (DXA) and structure parameters of the trabecular bone (linear and nonlinear, global and local) most accurately predicted absolute and relative femoral bone strength