Studying turbulence in a fluid with background damping

In this experimental paper, we demonstrate that turbulence can develop in a fluid system with background damping. For that purpose, we analyze dust acoustic waves, self-excited in a fluid complex plasma where the motion of individual microparticles was recorded with a high-speed video camera. We use the Wiener-Khinchin theorem to calculate the kinetic spectrum during different phases of the highly nonlinear periodic wave motion and show that a turbulent cascade develops at the phases of highest particle compression. We demonstrate that the energy cascade occurs despite the presence of a damping force due to the background neutral gas.

Heartbeat instability as auto-oscillation between dim and bright void regimes

We investigated the self-excited as well as optogalvanically stimulated heartbeat instability in RF discharge complex plasma. Three video cameras measured the motion of the microparticles, the plasma emission, and the laser-induced fluorescence simultaneously. Comprehensive studies of the optogalvanic control of the heartbeat instability revealed that the microparticle suspension can be stabilized by a continuous laser, whereas a modulated laser beam induces the void contraction either transiently or resonantly. The resonance occurred when the laser modulation frequency coincided with the frequency of small breathing oscillations of the microparticle suspension, which are known to be a prerequisite to the heartbeat instability. Based on the experimental results we suggest that the void contraction during the instability is caused by an abrupt void transition from the dim to the bright regime [Pikalev et al., Plasma Sources Sci. Technol. 30, 035014 (2021)PSTEEU0963-025210.1088/1361-6595/abe0a2]. In the bright regime, a time-averaged electric field at the void boundary heats the electrons causing bright plasma emission inside the void. The dim void has much lower electric field at the boundary and exhibits therefore no emission feature associated with it.

Calibrated reservoir computers

We observe the presence of infinitely fine-scaled alternations within the performance landscape of reservoir computers aimed for chaotic data forecasting. We investigate the emergence of the observed structures by means of variations of the transversal stability of the synchronization manifold relating the observational and internal dynamical states. Finally, we deduce a simple calibration method in order to attenuate the thus evidenced performance uncertainty.

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 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.

Instability onset and scaling laws of an auto-oscillating turbulent flow in a complex plasma

We study a complex plasma under microgravity conditions that is first stabilized with an oscillating electric field. Once the stabilization is stopped, the so-called heartbeat instability develops. We study how the kinetic energy spectrum changes during and after the onset of the instability and compare with the double cascade predicted by Kraichnan and Leith for two-dimensional turbulence. The onset of the instability manifests clearly in the ratio of the reduced rates of cascade of energy and enstrophy and in the power-law exponents of the energy spectra.

Wake-Mediated Propulsion of an Upstream Particle in Two-Dimensional Plasma Crystals

The wake-mediated propulsion of an "extra" particle in a channel of two neighboring rows of a two-dimensional plasma crystal, observed experimentally by Du et al. [Phys. Rev. E 89, 021101(R) (2014)PRESCM1539-375510.1103/PhysRevE.89.021101], is explained in simulations and theory. We use the simple model of a pointlike ion wake charge to reproduce this intriguing effect in simulations, allowing for a detailed investigation and a deeper understanding of the underlying dynamics. We show that the nonreciprocity of the particle interaction, owing to the wake charges, is responsible for a broken symmetry of the channel that enables a persistent self-propelled motion of the extra particle. We find good agreement of the terminal extra-particle velocity with our theoretical considerations and with experiments.

Kinetics of fluid demixing in complex plasmas: Domain growth analysis using Minkowski tensors

A molecular dynamics simulation of the demixing process of a binary complex plasma is analyzed and the role of distinct interaction potentials is discussed by using morphological Minkowski tensor analysis of the minority phase domain growth in a demixing simulated binary complex plasma. These Minkowski tensor methods are compared with previous results that utilized a power spectrum method based on the time-dependent average structure factor. It is shown that the Minkowski tensor methods are superior to the previously used power-spectrum method in the sense of higher sensitivity to changes in domain size. By analysis of the slope of the temporal evolution of Minkowski tensor measures, qualitative differences between the case of particle interaction with a single length scale compared to particle interactions with two different length scales (dominating long-range interaction) are revealed. After proper scaling the graphs for the two length scale scenarios coincide, pointing toward universal behavior. The qualitative difference in demixing scenarios is evidenced by distinct demixing behavior: in the long-range dominated cases demixing occurs in two stages. At first, neighboring particles agglomerate, then domains start to merge in cascades. However, in the case of only one interaction length scale only agglomeration but no merging of domains can be observed. Thus, Minkowski tensor analysis is likely to become a useful tool for further investigation of this (and other) demixing processes. It is capable to reveal (nonlinear) local topological properties, probing deeper than (linear) global power-spectrum analysis, however, still providing easily interpretable results founded on a solid mathematical framework.

Anisotropic confinement effects in a two-dimensional plasma crystal

The spectral asymmetry of the wave-energy distribution of dust particles during mode-coupling-induced melting, observed for the first time in plasma crystals by Couëdel et al. [Phys. Rev. E 89, 053108 (2014)PLEEE81539-375510.1103/PhysRevE.89.053108], is studied theoretically and by molecular-dynamics simulations. It is shown that an anisotropy of the well confining the microparticles selects the directions of preferred particle motion. The observed differences in intensity of waves of opposed directions are explained by a nonvanishing phonon flux. Anisotropic phonon scattering by defects and Umklapp scattering are proposed as possible reasons for the mean phonon flux.

Time series with tailored nonlinearities

It is demonstrated how to generate time series with tailored nonlinearities by inducing well-defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of nonlinearities are established and their origin is explained. By applying a set of simple constraints on the phases of an originally linear and uncorrelated Gaussian time series, the observed scaling behavior of the intensity distribution of empirical time series can be reproduced. The power law character of the intensity distributions being typical for, e.g., turbulence and financial data can thus be explained in terms of phase correlations.

Network analysis of three-dimensional complex plasma clusters in a rotating electric field

Network analysis was used to study the structure and time evolution of driven three-dimensional complex plasma clusters. The clusters were created by suspending micron-size particles in a glass box placed on top of the rf electrode in a capacitively coupled discharge. The particles were highly charged and manipulated by an external electric field that had a constant magnitude and uniformly rotated in the horizontal plane. Depending on the frequency of the applied electric field, the clusters rotated in the direction of the electric field or remained stationary. The positions of all particles were measured using stereoscopic digital in-line holography. The network analysis revealed the interplay between two competing symmetries in the cluster. The rotating cluster was shown to be more cylindrical than the nonrotating cluster. The emergence of vertical strings of particles was also confirmed.

Revisiting algorithms for generating surrogate time series

The method of surrogates is one of the key concepts of nonlinear data analysis. Here, we demonstrate that commonly used algorithms for generating surrogates often fail to generate truly linear time series. Rather, they create surrogate realizations with Fourier phase correlations leading to nondetections of nonlinearities. We argue that reliable surrogates can only be generated, if one tests separately for static and dynamic nonlinearities.

Complex plasmas in external fields: the role of non-hamiltonian interactions

Dedicated experiments with strongly coupled complex plasmas in external electric fields were carried out under microgravity conditions using the PK-4 dc discharge setup. The focus was put on the comparative analysis of the formation of stringlike anisotropic structures due to reciprocal (hamiltonian) and nonreciprocal (non-hamiltonian) interactions between microparticles (induced by ac and dc fields, respectively). The experiments complemented by numerical simulations demonstrate that the responses of complex plasmas in these two regimes are drastically different. It is suggested that the observed difference is a manifestation of intrinsic thermodynamic openness of driven strongly coupled systems.

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

SUMMARY

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.

INTRODUCTION

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.

METHODS

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.

RESULTS

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.

CONCLUSION

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.

Kinetics of fluid demixing in complex plasmas: role of two-scale interactions

Using experiments and combining theory and computer simulations, we show that binary complex plasmas are particularly good model systems to study the kinetics of fluid-fluid demixing at the "atomistic" (individual particle) level. The essential parameters of interparticle interactions in complex plasmas, such as the interaction range(s) and degree of nonadditivity, can be varied significantly, which allows systematic investigations of different demixing regimes. The critical role of competition between long-range and short-range interactions at the initial stage of the spinodal decomposition is discussed.

Model-independent test for scale-dependent non-Gaussianities in the cosmic microwave background

We present a model-independent method to test for scale-dependent non-Gaussianities in combination with scaling indices as test statistics. Therefore, surrogate data sets are generated, in which the power spectrum of the original data is preserved, while the higher order correlations are partly randomized by applying a scale-dependent shuffling procedure to the Fourier phases. We apply this method to the Wilkinson Microwave Anisotropy Probe data of the cosmic microwave background and find signatures for non-Gaussianities on large scales. Further tests are required to elucidate the origin of the detected anomalies.

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.

First observation of electrorheological plasmas

We report the experimental discovery of "electrorheological (ER) complex plasmas," where the control of the interparticle interaction by an externally applied electric field is due to distortion of the Debye spheres that surround microparticles (dust) in a plasma. We show that interactions in ER plasmas under weak ac fields are mathematically equivalent to those in conventional ER fluids. Microgravity experiments, as well as molecular dynamics simulations, show a phase transition from an isotropic to an anisotropic (string) plasma state as the electric field is increased.