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 analysed 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 scenario coincide, pointing towards universal behaviour. The qualitative difference in demixing scenarios is evidenced by distinct demixing behaviour: In the long range dominated cases demixing occurs in two stages. At first neighbouring 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 are 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.Comment: 12 pages, 10 figures, Phys. Rev. E, accepted for publication, http://journals.aps.org/pr

Instability onset and scaling laws of an autooscillating 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.Comment: 7 pages, 7 figure

Linear and nonlinear market correlations: characterizing financial crises and portfolio optimization

Pearson correlation and mutual information based complex networks of the day-to-day returns of US S&P500 stocks between 1985 and 2015 have been constructed in order to investigate the mutual dependencies of the stocks and their nature. We show that both networks detect qualitative differences especially during (recent) turbulent market periods thus indicating strongly fluctuating interconnections between the stocks of different companies in changing economic environments. A measure for the strength of nonlinear dependencies is derived using surrogate data and leads to interesting observations during periods of financial market crises. In contrast to the expectation that dependencies reduce mainly to linear correlations during crises we show that (at least in the 2008 crisis) nonlinear effects are significantly increasing. It turns out that the concept of centrality within a network could potentially be used as some kind of an early warning indicator for abnormal market behavior as we demonstrate with the example of the 2008 subprime mortgage crisis. Finally, we apply a Markowitz mean variance portfolio optimization and integrate the measure of nonlinear dependencies to scale the investment exposure. This leads to significant outperformance as compared to a fully invested portfolio.Comment: 12 pages, 11 figures, Phys. Rev. E, accepte

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

Efficient spatio-temporal event processing with STARK

For Big Data processing, Apache Spark has been widely accepted. However, when dealing with events or any other spatio-temporal data sets, Spark becomes very inefficient as it does not include any spatial or temporal data types and operators. In this paper we demonstrate our STARK project that adds the required data types and operators, such as spatio-temporal filter and join with various predicates to Spark. Additionally, it includes k nearest neighbor search and a density based clustering operator for data analysis tasks as well as spatial partitioning and indexing techniques for efficient processing. During the demo, programs can be created on real world event data sets using STARK's Scala API or our Pig Latin derivative Piglet in a web front end which also visualizes the results

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

Breaking Symmetries of the Reservoir Equations in Echo State Networks

Reservoir computing has repeatedly been shown to be extremely successful in the prediction of nonlinear time-series. However, there is no complete understanding of the proper design of a reservoir yet. We find that the simplest popular setup has a harmful symmetry, which leads to the prediction of what we call mirror-attractor. We prove this analytically. Similar problems can arise in a general context, and we use them to explain the success or failure of some designs. The symmetry is a direct consequence of the hyperbolic tangent activation function. Further, four ways to break the symmetry are compared numerically: A bias in the output, a shift in the input, a quadratic term in the readout, and a mixture of even and odd activation functions. Firstly, we test their susceptibility to the mirror-attractor. Secondly, we evaluate their performance on the task of predicting Lorenz data with the mean shifted to zero. The short-time prediction is measured with the forecast horizon while the largest Lyapunov exponent and the correlation dimension are used to represent the climate. Finally, the same analysis is repeated on a combined dataset of the Lorenz attractor and the Halvorsen attractor, which we designed to reveal potential problems with symmetry. We find that all methods except the output bias are able to fully break the symmetry with input shift and quadratic readout performing the best overall.Comment: 14 pages, 10 figures, accepted by chao

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

Controlling dynamical systems to complex target states using machine learning: next-generation vs. classical reservoir computing

Controlling nonlinear dynamical systems using machine learning allows to not only drive systems into simple behavior like periodicity but also to more complex arbitrary dynamics. For this, it is crucial that a machine learning system can be trained to reproduce the target dynamics sufficiently well. On the example of forcing a chaotic parametrization of the Lorenz system into intermittent dynamics, we show first that classical reservoir computing excels at this task. In a next step, we compare those results based on different amounts of training data to an alternative setup, where next-generation reservoir computing is used instead. It turns out that while delivering comparable performance for usual amounts of training data, next-generation RC significantly outperforms in situations where only very limited data is available. This opens even further practical control applications in real world problems where data is restricted.Comment: IJCNN 202

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)], 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.Comment: 7 pages, 4 figures, PRL (https://journals.aps.org/prl/), updated version with correct author affiliation