1,737 research outputs found
Measurement of surface roughness slope
Instrument, consisting of isolator, differentiator, absolute value circuit, and integrator, uses output signal from surface texture analyzer profile-amplifier to calculate surface roughness slope. Calculations provide accurate, instantaneous value of the slope. Instrument is inexpensive and applicable to any commerical surface texture analyzer
Spatial network surrogates for disentangling complex system structure from spatial embedding of nodes
ACKNOWLEDGMENTS MW and RVD have been supported by the German Federal Ministry for Education and Research (BMBF) via the Young Investigators Group CoSy-CC2 (grant no. 01LN1306A). JFD thanks the Stordalen Foundation and BMBF (project GLUES) for financial support. JK acknowledges the IRTG 1740 funded by DFG and FAPESP. MT Gastner is acknowledged for providing his data on the airline, interstate, and Internet network. P Menck thankfully provided his data on the Scandinavian power grid. We thank S Willner on behalf of the entire zeean team for providing the data on the world trade network. All computations have been performed using the Python package pyunicorn [41] that is available at https://github.com/pik-copan/pyunicorn.Peer reviewedPreprin
Recurrence networks - A novel paradigm for nonlinear time series analysis
This paper presents a new approach for analysing structural properties of
time series from complex systems. Starting from the concept of recurrences in
phase space, the recurrence matrix of a time series is interpreted as the
adjacency matrix of an associated complex network which links different points
in time if the evolution of the considered states is very similar. A critical
comparison of these recurrence networks with similar existing techniques is
presented, revealing strong conceptual benefits of the new approach which can
be considered as a unifying framework for transforming time series into complex
networks that also includes other methods as special cases.
It is demonstrated that there are fundamental relationships between the
topological properties of recurrence networks and the statistical properties of
the phase space density of the underlying dynamical system. Hence, the network
description yields new quantitative characteristics of the dynamical complexity
of a time series, which substantially complement existing measures of
recurrence quantification analysis
Disentangling different types of El Ni\~no episodes by evolving climate network analysis
Complex network theory provides a powerful toolbox for studying the structure
of statistical interrelationships between multiple time series in various
scientific disciplines. In this work, we apply the recently proposed climate
network approach for characterizing the evolving correlation structure of the
Earth's climate system based on reanalysis data of surface air temperatures. We
provide a detailed study on the temporal variability of several global climate
network characteristics. Based on a simple conceptual view on red climate
networks (i.e., networks with a comparably low number of edges), we give a
thorough interpretation of our evolving climate network characteristics, which
allows a functional discrimination between recently recognized different types
of El Ni\~no episodes. Our analysis provides deep insights into the Earth's
climate system, particularly its global response to strong volcanic eruptions
and large-scale impacts of different phases of the El Ni\~no Southern
Oscillation (ENSO).Comment: 20 pages, 12 figure
Quasiperiodic graphs: structural design, scaling and entropic properties
A novel class of graphs, here named quasiperiodic, are constructed via
application of the Horizontal Visibility algorithm to the time series generated
along the quasiperiodic route to chaos. We show how the hierarchy of
mode-locked regions represented by the Farey tree is inherited by their
associated graphs. We are able to establish, via Renormalization Group (RG)
theory, the architecture of the quasiperiodic graphs produced by irrational
winding numbers with pure periodic continued fraction. And finally, we
demonstrate that the RG fixed-point degree distributions are recovered via
optimization of a suitably defined graph entropy
Fermi-Hubbard physics with atoms in an optical lattice
The Fermi-Hubbard model is a key concept in condensed matter physics and
provides crucial insights into electronic and magnetic properties of materials.
Yet, the intricate nature of Fermi systems poses a barrier to answer important
questions concerning d-wave superconductivity and quantum magnetism. Recently,
it has become possible to experimentally realize the Fermi-Hubbard model using
a fermionic quantum gas loaded into an optical lattice. In this atomic approach
to the Fermi-Hubbard model the Hamiltonian is a direct result of the optical
lattice potential created by interfering laser fields and short-ranged
ultracold collisions. It provides a route to simulate the physics of the
Hamiltonian and to address open questions and novel challenges of the
underlying many-body system. This review gives an overview of the current
efforts in understanding and realizing experiments with fermionic atoms in
optical lattices and discusses key experiments in the metallic,
band-insulating, superfluid and Mott-insulating regimes.Comment: Posted with permission from the Annual Review of of Condensed Matter
Physics Volume 1 \c{opyright} 2010 by Annual Reviews,
http://www.annualreviews.or
Ambiguities in recurrence-based complex network representations of time series
Recently, different approaches have been proposed for studying basic
properties of time series from a complex network perspective. In this work, the
corresponding potentials and limitations of networks based on recurrences in
phase space are investigated in some detail. We discuss the main requirements
that permit a feasible system-theoretic interpretation of network topology in
terms of dynamically invariant phase-space properties. Possible artifacts
induced by disregarding these requirements are pointed out and systematically
studied. Finally, a rigorous interpretation of the clustering coefficient and
the betweenness centrality in terms of invariant objects is proposed
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