805 research outputs found
Method for producing edge geometry superconducting tunnel junctions utilizing an NbN/MgO/NbN thin film structure
A method for fabricating an edge geometry superconducting tunnel junction device is discussed. The device is comprised of two niobium nitride superconducting electrodes and a magnesium oxide tunnel barrier sandwiched between the two electrodes. The NbN electrodes are preferably sputter-deposited, with the first NbN electrode deposited on an insulating substrate maintained at about 250 C to 500 C for improved quality of the electrode
Edge geometry superconducting tunnel junctions utilizing an NbN/MgO/NbN thin film structure
An edge defined geometry is used to produce very small area tunnel junctions in a structure with niobium nitride superconducting electrodes and a magnesium oxide tunnel barrier. The incorporation of an MgO tunnel barrier with two NbN electrodes results in improved current-voltage characteristics, and may lead to better junction noise characteristics. The NbN electrodes are preferably sputter-deposited, with the first NbN electrode deposited on an insulating substrate maintained at about 250 to 500 C for improved quality of the electrode
Synchronization in large directed networks of coupled phase oscillators
We extend recent theoretical approximations describing the transition to
synchronization in large undirected networks of coupled phase oscillators to
the case of directed networks. We also consider extensions to networks with
mixed positive/negative coupling strengths. We compare our theory with
numerical simulations and find good agreement
Approximating the largest eigenvalue of network adjacency matrices
The largest eigenvalue of the adjacency matrix of a network plays an
important role in several network processes (e.g., synchronization of
oscillators, percolation on directed networks, linear stability of equilibria
of network coupled systems, etc.). In this paper we develop approximations to
the largest eigenvalue of adjacency matrices and discuss the relationships
between these approximations. Numerical experiments on simulated networks are
used to test our results.Comment: 7 pages, 4 figure
Characterizing the dynamical importance of network nodes and links
The largest eigenvalue of the adjacency matrix of the networks is a key
quantity determining several important dynamical processes on complex networks.
Based on this fact, we present a quantitative, objective characterization of
the dynamical importance of network nodes and links in terms of their effect on
the largest eigenvalue. We show how our characterization of the dynamical
importance of nodes can be affected by degree-degree correlations and network
community structure. We discuss how our characterization can be used to
optimize techniques for controlling certain network dynamical processes and
apply our results to real networks.Comment: 4 pages, 4 figure
The onset of synchronization in large networks of coupled oscillators
We study the transition from incoherence to coherence in large networks of
coupled phase oscillators. We present various approximations that describe the
behavior of an appropriately defined order parameter past the transition, and
generalize recent results for the critical coupling strength. We find that,
under appropriate conditions, the coupling strength at which the transition
occurs is determined by the largest eigenvalue of the adjacency matrix. We show
how, with an additional assumption, a mean field approximation recently
proposed is recovered from our results. We test our theory with numerical
simulations, and find that it describes the transition when our assumptions are
satisfied. We find that our theory describes the transition well in situations
in which the mean field approximation fails. We study the finite size effects
caused by nodes with small degree and find that they cause the critical
coupling strength to increase.Comment: To appear in PRE; Added an Appendix, a reference, modified two
figures and improved the discussion of the range of validity of perturbative
approache
The emergence of coherence in complex networks of heterogeneous dynamical systems
We present a general theory for the onset of coherence in collections of
heterogeneous maps interacting via a complex connection network. Our method
allows the dynamics of the individual uncoupled systems to be either chaotic or
periodic, and applies generally to networks for which the number of connections
per node is large. We find that the critical coupling strength at which a
transition to synchrony takes place depends separately on the dynamics of the
individual uncoupled systems and on the largest eigenvalue of the adjacency
matrix of the coupling network. Our theory directly generalizes the Kuramoto
model of equal strength, all-to-all coupled phase oscillators to the case of
oscillators with more realistic dynamics coupled via a large heterogeneous
network.Comment: 4 pages, 1 figure. Published versio
Spatial patterns of desynchronization bursts in networks
We adapt a previous model and analysis method (the {\it master stability
function}), extensively used for studying the stability of the synchronous
state of networks of identical chaotic oscillators, to the case of oscillators
that are similar but not exactly identical. We find that bubbling induced
desynchronization bursts occur for some parameter values. These bursts have
spatial patterns, which can be predicted from the network connectivity matrix
and the unstable periodic orbits embedded in the attractor. We test the
analysis of bursts by comparison with numerical experiments. In the case that
no bursting occurs, we discuss the deviations from the exactly synchronous
state caused by the mismatch between oscillators
Characterizing the dynamical importance of network nodes and links
The largest eigenvalue of the adjacency matrix of networks is a key quantity determining several important dynamical processes on complex networks. Based on this fact, we present a quantitative, objective characterization of the dynamical importance of network nodes and links in terms of their effect on the largest eigenvalue. We show how our characterization of the dynamical importance of nodes can be affected by degree-degree correlations and network community structure. We discuss how our characterization can be used to optimize techniques for controlling certain network dynamical processes and apply our results to real networks
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