416 research outputs found
(Non)Invariance of dynamical quantities for orbit equivalent flows
We study how dynamical quantities such as Lyapunov exponents, metric entropy,
topological pressure, recurrence rates, and dimension-like characteristics
change under a time reparameterization of a dynamical system. These quantities
are shown to either remain invariant, transform according to a multiplicative
factor or transform through a convoluted dependence that may take the form of
an integral over the initial local values. We discuss the significance of these
results for the apparent non-invariance of chaos in general relativity and
explore applications to the synchronization of equilibrium states and the
elimination of expansions
Network synchronization: Optimal and Pessimal Scale-Free Topologies
By employing a recently introduced optimization algorithm we explicitely
design optimally synchronizable (unweighted) networks for any given scale-free
degree distribution. We explore how the optimization process affects
degree-degree correlations and observe a generic tendency towards
disassortativity. Still, we show that there is not a one-to-one correspondence
between synchronizability and disassortativity. On the other hand, we study the
nature of optimally un-synchronizable networks, that is, networks whose
topology minimizes the range of stability of the synchronous state. The
resulting ``pessimal networks'' turn out to have a highly assortative
string-like structure. We also derive a rigorous lower bound for the Laplacian
eigenvalue ratio controlling synchronizability, which helps understanding the
impact of degree correlations on network synchronizability.Comment: 11 pages, 4 figs, submitted to J. Phys. A (proceedings of Complex
Networks 2007
Multiwavelength analysis of brightness variations of 3C~279: Probing the relativistic jet structure and its evolution
We studied the correlation between brightness and polarization variations in
3C~279 at different wavelengths, over time intervals long enough to cover the
time lags due to opacity effects. We used these correlations together with VLBI
images to constrain the radio and high energy source position.We made 7 mm
radio continuum and -band polarimetric observations of 3C~279 between 2009
and 2014. The radio observations were performed at the Itapetinga Radio
Observatory, while the polarimetric data were obtained at Pico dos Dias
Observatory, both in Brazil. We compared our observations with the -ray
Fermi/LAT and -band SMARTS light curves. We found a good correlation between
7~mm and -band light curves, with a delay of days in radio, but
no correlation with the rays. However, a group of several -ray
flares in April 2011 could be associated with the start of the 7 mm strong
activity observed at the end of 2011.We also detected an increase in -band
polarization degree and rotation of the polarization angle simultaneous with
these flares. Contemporaneous VLBI images at the same radio frequency show two
new strong components close to the core, ejected in directions very different
from that of the jet.The good correlation between radio and -band
variability suggests that their origin is synchrotron radiation. The lack of
correlation with -rays produced by the Inverse Compton process on some
occasions could be due to the lack of low energy photons in the jet direction
or to absorption of the high energy photons by the broad line region clouds.
The variability of the polarization parameters during flares can be easily
explained by the combination of the jet polarization parameters and those of
newly formed jet components.Comment: 11 pages, 6 figures, 2 tables. Accepted by A&
Enhancing complex-network synchronization
Heterogeneity in the degree (connectivity) distribution has been shown to
suppress synchronization in networks of symmetrically coupled oscillators with
uniform coupling strength (unweighted coupling). Here we uncover a condition
for enhanced synchronization in directed networks with weighted coupling. We
show that, in the optimum regime, synchronizability is solely determined by the
average degree and does not depend on the system size and the details of the
degree distribution. In scale-free networks, where the average degree may
increase with heterogeneity, synchronizability is drastically enhanced and may
become positively correlated with heterogeneity, while the overall cost
involved in the network coupling is significantly reduced as compared to the
case of unweighted coupling.Comment: 4 pages, 3 figure
Network Synchronization, Diffusion, and the Paradox of Heterogeneity
Many complex networks display strong heterogeneity in the degree
(connectivity) distribution. Heterogeneity in the degree distribution often
reduces the average distance between nodes but, paradoxically, may suppress
synchronization in networks of oscillators coupled symmetrically with uniform
coupling strength. Here we offer a solution to this apparent paradox. Our
analysis is partially based on the identification of a diffusive process
underlying the communication between oscillators and reveals a striking
relation between this process and the condition for the linear stability of the
synchronized states. We show that, for a given degree distribution, the maximum
synchronizability is achieved when the network of couplings is weighted and
directed, and the overall cost involved in the couplings is minimum. This
enhanced synchronizability is solely determined by the mean degree and does not
depend on the degree distribution and system size. Numerical verification of
the main results is provided for representative classes of small-world and
scale-free networks.Comment: Synchronization in Weighted Network
Non-normality and non-monotonic dynamics in complex reaction networks
Complex chemical reaction networks, which underlie many industrial and
biological processes, often exhibit non-monotonic changes in chemical species
concentrations, typically described using nonlinear models. Such non-monotonic
dynamics are in principle possible even in linear models if the matrices
defining the models are non-normal, as characterized by a necessarily
non-orthogonal set of eigenvectors. However, the extent to which non-normality
is responsible for non-monotonic behavior remains an open question. Here, using
a master equation to model the reaction dynamics, we derive a general condition
for observing non-monotonic dynamics of individual species, establishing that
non-normality promotes non-monotonicity but is not a requirement for it. In
contrast, we show that non-normality is a requirement for non-monotonic
dynamics to be observed in the R\'enyi entropy. Using hydrogen combustion as an
example application, we demonstrate that non-monotonic dynamics under
experimental conditions are supported by a linear chain of connected
components, in contrast with the dominance of a single giant component observed
in typical random reaction networks. The exact linearity of the master equation
enables development of rigorous theory and simulations for dynamical networks
of unprecedented size (approaching dynamical variables, even for a
network of only 20 reactions and involving less than 100 atoms). Our
conclusions are expected to hold for other combustion processes, and the
general theory we develop is applicable to all chemical reaction networks,
including biological ones.Comment: Software implementing our methods is available as a Github repository
at https://github.com/znicolaou/ratematrix and an animated version of Fig. 1
is available at
https://northwestern.box.com/s/otn3m2cov9gi3enht3r8jh5kjo9qnv6
Signatures of small-world and scale-free properties in large computer programs
A large computer program is typically divided into many hundreds or even
thousands of smaller units, whose logical connections define a network in a
natural way. This network reflects the internal structure of the program, and
defines the ``information flow'' within the program. We show that, (1) due to
its growth in time this network displays a scale-free feature in that the
probability of the number of links at a node obeys a power-law distribution,
and (2) as a result of performance optimization of the program the network has
a small-world structure. We believe that these features are generic for large
computer programs. Our work extends the previous studies on growing networks,
which have mostly been for physical networks, to the domain of computer
software.Comment: 4 pages, 1 figure, to appear in Phys. Rev.
Distributed flow optimization and cascading effects in weighted complex networks
We investigate the effect of a specific edge weighting scheme on distributed flow efficiency and robustness to cascading
failures in scale-free networks. In particular, we analyze a simple, yet
fundamental distributed flow model: current flow in random resistor networks.
By the tuning of control parameter and by considering two general cases
of relative node processing capabilities as well as the effect of bandwidth, we
show the dependence of transport efficiency upon the correlations between the
topology and weights. By studying the severity of cascades for different
control parameter , we find that network resilience to cascading
overloads and network throughput is optimal for the same value of over
the range of node capacities and available bandwidth
On the Klein-Gordon equation and hyperbolic pseudoanalytic function theory
Elliptic pseudoanalytic function theory was considered independently by Bers
and Vekua decades ago. In this paper we develop a hyperbolic analogue of
pseudoanalytic function theory using the algebra of hyperbolic numbers. We
consider the Klein-Gordon equation with a potential. With the aid of one
particular solution we factorize the Klein-Gordon operator in terms of two
Vekua-type operators. We show that real parts of the solutions of one of these
Vekua-type operators are solutions of the considered Klein-Gordon equation.
Using hyperbolic pseudoanalytic function theory, we then obtain explicit
construction of infinite systems of solutions of the Klein-Gordon equation with
potential. Finally, we give some examples of application of the proposed
procedure
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