358 research outputs found
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
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