Phantom Black Holes in Einstein-Maxwell-Dilaton Theory

We obtain the general static, spherically symmetric solution for the Einstein-Maxwell-dilaton system in four dimensions with a phantom coupling for the dilaton and/or the Maxwell field. This leads to new classes of black hole solutions, with single or multiple horizons. Using the geodesic equations, we analyse the corresponding Penrose diagrams revealing, in some cases, new causal structures.Comment: Latex file, 32 pages, 15 figures in eps format. Typo corrected in Eq. (3.18

Effect of assortative mixing in the second-order Kuramoto model

In this paper we analyze the second-order Kuramoto model presenting a positive correlation between the heterogeneity of the connections and the natural frequencies in scale-free networks. We numerically show that discontinuous transitions emerge not just in disassortative but also in assortative networks, in contrast with the first-order model. We also find that the effect of assortativity on network synchronization can be compensated by adjusting the phase damping. Our results show that it is possible to control collective behavior of damped Kuramoto oscillators by tuning the network structure or by adjusting the dissipation related to the phases movement.Comment: 7 pages, 6 figures. In press in Physical Review

Spectra of random networks in the weak clustering regime

The asymptotic behaviour of dynamical processes in networks can be expressed as a function of spectral properties of the corresponding adjacency and Laplacian matrices. Although many theoretical results are known for the spectra of traditional configuration models, networks generated through these models fail to describe many topological features of real-world networks, in particular non-null values of the clustering coefficient. Here we study effects of cycles of order three (triangles) in network spectra. By using recent advances in random matrix theory, we determine the spectral distribution of the network adjacency matrix as a function of the average number of triangles attached to each node for networks without modular structure and degree-degree correlations. Implications to network dynamics are discussed. Our findings can shed light in the study of how particular kinds of subgraphs influence network dynamics

Low-dimensional behavior of Kuramoto model with inertia in complex networks

Low-dimensional behavior of large systems of globally coupled oscillators has been intensively investigated since the introduction of the Ott-Antonsen ansatz. In this report, we generalize the Ott-Antonsen ansatz to second-order Kuramoto models in complex networks. With an additional inertia term, we find a low-dimensional behavior similar to the first-order Kuramoto model, derive a self-consistent equation and seek the time-dependent derivation of the order parameter. Numerical simulations are also conducted to verify our analytical results.Comment: 6 figure

Noise properties of two single electron transistors coupled by a nanomechanical resonator

We analyze the noise properties of two single electron transistors (SETs) coupled via a shared voltage gate consisting of a nanomechanical resonator. Working in the regime where the resonator can be treated as a classical system, we find that the SETs act on the resonator like two independent heat baths. The coupling to the resonator generates positive correlations in the currents flowing through each of the SETs as well as between the two currents. In the regime where the dynamics of the resonator is dominated by the back-action of the SETs, these positive correlations can lead to parametrically large enhancements of the low frequency current noise. These noise properties can be understood in terms of the effects on the SET currents of fluctuations in the state of a resonator in thermal equilibrium which persist for times of order the resonator damping time.Comment: Accepted for publication in Phys. Rev.

Cooperative behavior between oscillatory and excitable units: the peculiar role of positive coupling-frequency correlations

We study the collective dynamics of noise-driven excitable elements, so-called active rotators. Crucially here, the natural frequencies and the individual coupling strengths are drawn from some joint probability distribution. Combining a mean-field treatment with a Gaussian approximation allows us to find examples where the infinite-dimensional system is reduced to a few ordinary differential equations. Our focus lies in the cooperative behavior in a population consisting of two parts, where one is composed of excitable elements, while the other one contains only self-oscillatory units. Surprisingly, excitable behavior in the whole system sets in only if the excitable elements have a smaller coupling strength than the self-oscillating units. In this way positive local correlations between natural frequencies and couplings shape the global behavior of mixed populations of excitable and oscillatory elements.Comment: 10 pages, 6 figures, published in Eur. Phys. J.