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

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

Synchronization in systems with linear, yet nonreciprocal interactions

Synchronization of oscillatory subsystems is a widespread phenomenon in science. It is argued that the presence of nonlinearities is a necessary prerequisite for synchronization. Here, we study synchronization in complex plasmas consisting of microparticles in addition to the plasma. The particles can form 2D crystalline structures. They can melt via mode-coupling instability (MCI), which is a consequence of the effective nonreciprocal interactions. Synchronized particle motion during MCI-melting of 2D plasma crystal was reported in [1]. To disentangle the effects of nonlinearity and nonreciprocity on the emergence of synchronization, we solved numerically the nonlinear and the linearized system. Analyzing the synchronization with a new order parameter [2] reveals that a linearized version of the interaction model exhibits the same synchronization patterns as the full, nonlinear one. Further, theoretical considerations show that nonreciprocal interactions among particles generally provide a mechanism for the selection of dominant wave modes causing the system to show synchronized motion. Thus, we demonstrate numerically and analytically that also linear systems can synchronize and that the nonreciprocity of the interaction is the more decisive property for a n-body system to synchronize. [1] L. Couëdel et al., Phys. Rev. E, 89, 053108 (2014) [2] I. Laut et al., EPL, 110, 65001 (2015

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

Surrogate-assisted network analysis of nonlinear time series

The performance of recurrence networks and symbolic networks to detect weak nonlinearities in time series is compared to the nonlinear prediction error. For the synthetic data of the Lorenz system, the network measures show a comparable performance. In the case of relatively short and noisy real-world data from active galactic nuclei, the nonlinear prediction error yields more robust results than the network measures. The tests are based on surrogate data sets. The correlations in the Fourier phases of data sets from some surrogate generating algorithms are also examined. The phase correlations are shown to have an impact on the performance of the tests for nonlinearity.Comment: 9 pages, 5 figures, Chaos (http://scitation.aip.org/content/aip/journal/chaos), corrected typo

Network analysis of 3D 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.Comment: 9 pages, 9 figures; corrected Fig.4 and typo

Brownian-like motion of a single dust grain in a radio-frequency plasma discharge comparison of experiments and simulations

Bronwnian-like motion of a single dust-grain in a radio frequency plasma has been studied by different research groups. The rise of the particles temperature above “room temperature” is attributed to e.g. random fluctuations of the particle charge and fluctuations of the electrical field. Additional disturbance might occur due to gas density variations, temporal variation of the particles mass and particle interaction with the illuminating laser light. In addition, a nonoptimal frame rate of the optical diagnostic system and pixel locking can lead to an incorrect estimation of the particle kinetic temperature. Our experiments are conducted in a weakly ionized radio-frequency gas discharge at a low neutral gas pressure and power. A single micron sized spherical particle is trapped in a harmonic-like potential trap in the sheath of the lower driven electrode [1]. Its twodimensional planar motion is recorded with a long-distance microscope and a high-resolution camera. From the measured particle positions we derive the probability density function, the velocity autocorrelation function and the mean squared displacement. We obtain a particle kinetic temperature above 350 K, a neutral gas damping time of about 0.5 sec and a resonance frequency of 1-2 Hz. Anisotropic oscillation of the particle occurs, leading to angle dependent temperatures along the x and y direction in the plane of the recorded images, which can be explained by the presence of an asymmetric horizontal potential trap. Experimental observations are compared with our simulations using md simulations and the Ornstein-Uhlenbeck stochastic process