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 $R$-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 $\gamma$-ray Fermi/LAT and $R$-band SMARTS light curves. We found a good correlation between 7~mm and $R$-band light curves, with a delay of $170 \pm 30$ days in radio, but no correlation with the $\gamma$ rays. However, a group of several $\gamma$-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 $R$-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 $R$-band variability suggests that their origin is synchrotron radiation. The lack of correlation with $\gamma$-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

Dissipative chaotic scattering

We show that weak dissipation, typical in realistic situations, can have a metamorphic consequence on nonhyperbolic chaotic scattering in the sense that the physically important particle-decay law is altered, no matter how small the amount of dissipation. As a result, the previous conclusion about the unity of the fractal dimension of the set of singularities in scattering functions, a major claim about nonhyperbolic chaotic scattering, may not be observable.Comment: 4 pages, 2 figures, revte

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

Multistage Random Growing Small-World Networks with Power-law degree Distribution

In this paper, a simply rule that generates scale-free networks with very large clustering coefficient and very small average distance is presented. These networks are called {\bf Multistage Random Growing Networks}(MRGN) as the adding process of a new node to the network is composed of two stages. The analytic results of power-law exponent $\gamma=3$ and clustering coefficient $C=0.81$ are obtained, which agree with the simulation results approximately. In addition, the average distance of the networks increases logarithmical with the number of the network vertices is proved analytically. Since many real-life networks are both scale-free and small-world networks, MRGN may perform well in mimicking reality.Comment: 3 figures, 4 page

Ising model for distribution networks

An elementary Ising spin model is proposed for demonstrating cascading failures (break-downs, blackouts, collapses, avalanches, ...) that can occur in realistic networks for distribution and delivery by suppliers to consumers. A ferromagnetic Hamiltonian with quenched random fields results from policies that maximize the gap between demand and delivery. Such policies can arise in a competitive market where firms artificially create new demand, or in a solidary environment where too high a demand cannot reasonably be met. Network failure in the context of a policy of solidarity is possible when an initially active state becomes metastable and decays to a stable inactive state. We explore the characteristics of the demand and delivery, as well as the topological properties, which make the distribution network susceptible of failure. An effective temperature is defined, which governs the strength of the activity fluctuations which can induce a collapse. Numerical results, obtained by Monte Carlo simulations of the model on (mainly) scale-free networks, are supplemented with analytic mean-field approximations to the geometrical random field fluctuations and the thermal spin fluctuations. The role of hubs versus poorly connected nodes in initiating the breakdown of network activity is illustrated and related to model parameters

Homoclinic chaos in the dynamics of a general Bianchi IX model

The dynamics of a general Bianchi IX model with three scale factors is examined. The matter content of the model is assumed to be comoving dust plus a positive cosmological constant. The model presents a critical point of saddle-center-center type in the finite region of phase space. This critical point engenders in the phase space dynamics the topology of stable and unstable four dimensional tubes $R \times S^3$, where $R$ is a saddle direction and $S^3$ is the manifold of unstable periodic orbits in the center-center sector. A general characteristic of the dynamical flow is an oscillatory mode about orbits of an invariant plane of the dynamics which contains the critical point and a Friedmann-Robertson-Walker (FRW) singularity. We show that a pair of tubes (one stable, one unstable) emerging from the neighborhood of the critical point towards the FRW singularity have homoclinic transversal crossings. The homoclinic intersection manifold has topology $R \times S^2$ and is constituted of homoclinic orbits which are bi-asymptotic to the $S^3$ center-center manifold. This is an invariant signature of chaos in the model, and produces chaotic sets in phase space. The model also presents an asymptotic DeSitter attractor at infinity and initial conditions sets are shown to have fractal basin boundaries connected to the escape into the DeSitter configuration (escape into inflation), characterizing the critical point as a chaotic scatterer.Comment: 11 pages, 6 ps figures. Accepted for publication in Phys. Rev.