9,941 research outputs found
Topological Mixing with Ghost Rods
Topological chaos relies on the periodic motion of obstacles in a
two-dimensional flow in order to form nontrivial braids. This motion generates
exponential stretching of material lines, and hence efficient mixing. Boyland
et al. [P. L. Boyland, H. Aref, and M. A. Stremler, J. Fluid Mech. 403, 277
(2000)] have studied a specific periodic motion of rods that exhibits
topological chaos in a viscous fluid. We show that it is possible to extend
their work to cases where the motion of the stirring rods is topologically
trivial by considering the dynamics of special periodic points that we call
ghost rods, because they play a similar role to stirring rods. The ghost rods
framework provides a new technique for quantifying chaos and gives insight into
the mechanisms that produce chaos and mixing. Numerical simulations for Stokes
flow support our results.Comment: 13 pages, 11 figures. RevTeX4 format. (Final version
Recurrence-based time series analysis by means of complex network methods
Complex networks are an important paradigm of modern complex systems sciences
which allows quantitatively assessing the structural properties of systems
composed of different interacting entities. During the last years, intensive
efforts have been spent on applying network-based concepts also for the
analysis of dynamically relevant higher-order statistical properties of time
series. Notably, many corresponding approaches are closely related with the
concept of recurrence in phase space. In this paper, we review recent
methodological advances in time series analysis based on complex networks, with
a special emphasis on methods founded on recurrence plots. The potentials and
limitations of the individual methods are discussed and illustrated for
paradigmatic examples of dynamical systems as well as for real-world time
series. Complex network measures are shown to provide information about
structural features of dynamical systems that are complementary to those
characterized by other methods of time series analysis and, hence,
substantially enrich the knowledge gathered from other existing (linear as well
as nonlinear) approaches.Comment: To be published in International Journal of Bifurcation and Chaos
(2011
Topological properties and fractal analysis of recurrence network constructed from fractional Brownian motions
Many studies have shown that we can gain additional information on time
series by investigating their accompanying complex networks. In this work, we
investigate the fundamental topological and fractal properties of recurrence
networks constructed from fractional Brownian motions (FBMs). First, our
results indicate that the constructed recurrence networks have exponential
degree distributions; the relationship between and of recurrence networks decreases with the Hurst
index of the associated FBMs, and their dependence approximately satisfies
the linear formula . Moreover, our numerical results of
multifractal analysis show that the multifractality exists in these recurrence
networks, and the multifractality of these networks becomes stronger at first
and then weaker when the Hurst index of the associated time series becomes
larger from 0.4 to 0.95. In particular, the recurrence network with the Hurst
index possess the strongest multifractality. In addition, the
dependence relationships of the average information dimension on the Hurst index can also be
fitted well with linear functions. Our results strongly suggest that the
recurrence network inherits the basic characteristic and the fractal nature of
the associated FBM series.Comment: 25 pages, 1 table, 15 figures. accepted by Phys. Rev.
Characterization of complex networks: A survey of measurements
Each complex network (or class of networks) presents specific topological
features which characterize its connectivity and highly influence the dynamics
of processes executed on the network. The analysis, discrimination, and
synthesis of complex networks therefore rely on the use of measurements capable
of expressing the most relevant topological features. This article presents a
survey of such measurements. It includes general considerations about complex
network characterization, a brief review of the principal models, and the
presentation of the main existing measurements. Important related issues
covered in this work comprise the representation of the evolution of complex
networks in terms of trajectories in several measurement spaces, the analysis
of the correlations between some of the most traditional measurements,
perturbation analysis, as well as the use of multivariate statistics for
feature selection and network classification. Depending on the network and the
analysis task one has in mind, a specific set of features may be chosen. It is
hoped that the present survey will help the proper application and
interpretation of measurements.Comment: A working manuscript with 78 pages, 32 figures. Suggestions of
measurements for inclusion are welcomed by the author
Revealing intra-urban spatial structure through an exploratory analysis by combining road network abstraction model and taxi trajectory data
The unprecedented urbanization in China has dramatically changed the urban
spatial structure of cities. With the proliferation of individual-level
geospatial big data, previous studies have widely used the network abstraction
model to reveal the underlying urban spatial structure. However, the
construction of network abstraction models primarily focuses on the topology of
the road network without considering individual travel flows along with the
road networks. Individual travel flows reflect the urban dynamics, which can
further help understand the underlying spatial structure. This study therefore
aims to reveal the intra-urban spatial structure by integrating the road
network abstraction model and individual travel flows. To achieve this goal, we
1) quantify the spatial interaction relatedness of road segments based on the
Word2Vec model using large volumes of taxi trip data, then 2) characterize the
road abstraction network model according to the identified spatial interaction
relatedness, and 3) implement a community detection algorithm to reveal
sub-regions of a city. Our results reveal three levels of hierarchical spatial
structures in the Wuhan metropolitan area. This study provides a data-driven
approach to the investigation of urban spatial structure via identifying
traffic interaction patterns on the road network, offering insights to urban
planning practice and transportation management
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