Optimal synchronization of Kuramoto oscillators: a dimensional reduction approach

A recently proposed dimensional reduction approach for studying synchronization in the Kuramoto model is employed to build optimal network topologies to favor or to suppress synchronization. The approach is based in the introduction of a collective coordinate for the time evolution of the phase locked oscillators, in the spirit of the Ott-Antonsen ansatz. We show that the optimal synchronization of a Kuramoto network demands the maximization of the quadratic function $\omega^T L \omega$, where $\omega$ stands for the vector of the natural frequencies of the oscillators, and $L$ for the network Laplacian matrix. Many recently obtained numerical results can be re-obtained analytically and in a simpler way from our maximization condition. A computationally efficient {hill climb} rewiring algorithm is proposed to generate networks with optimal synchronization properties. Our approach can be easily adapted to the case of the Kuramoto models with both attractive and repulsive interactions, and again many recent numerical results can be rederived in a simpler and clearer analytical manner.Comment: 6 pages, 6 figures, final version to appear in PR

Explosive synchronization with partial degree-frequency correlation

Networks of Kuramoto oscillators with a positive correlation between the oscillators frequencies and the degree of the their corresponding vertices exhibits the so-called explosive synchronization behavior, which is now under intensive investigation. Here, we study and report explosive synchronization in a situation that has not yet been considered, namely when only a part, typically small, of the vertices is subjected to a degree frequency correlation. Our results show that in order to have explosive synchronization, it suffices to have degree-frequency correlations only for the hubs, the vertices with the highest degrees. Moreover, we show that a partial degree-frequency correlation does not only promotes but also allows explosive synchronization to happen in networks for which a full degree-frequency correlation would not allow it. We perform exhaustive numerical experiments for synthetic networks and also for the undirected and unweighted version of the neural network of the worm Caenorhabditis elegans. The latter is an explicit example where partial degree-frequency correlation leads to explosive synchronization with hysteresis, in contrast with the fully correlated case, for which no explosive synchronization is observed.Comment: 10 pages, 6 figures, final version to appear in PR

Optimal global synchronization of partially forced Kuramoto oscillators

We consider the problem of global synchronization in a large random network of Kuramoto oscillators where some of them are subject to an external periodically driven force. We explore a recently proposed dimensional reduction approach and introduce an effective two-dimensional description for the problem. From the dimensionally reduced model, we obtain analytical predictions for some critical parameters necessary for the onset of a globally synchronized state in the system. Moreover, the low dimensional model also allows us to introduce an optimization scheme for the problem. Our main conclusion, which has been corroborated by exhaustive numerical simulations, is that for a given large random network of Kuramoto oscillators, with random natural frequencies $\omega_i$, such that a fraction of them is subject to an external periodic force with frequency $\Omega$, the best global synchronization properties correspond to the case where the fraction of the forced oscillators is chosen to be those ones such that $|\omega_i-\Omega|$ is maximal. Our results might shed some light on the structure and evolution of natural systems for which the presence or the absence of global synchronization are desired properties. Some properties of the optimal forced networks and its relation to recent results in the literature are also discussed.Comment: 8 pages, 3 figures. Final version accepted for publication in Chaos. After it is published, it will be found at https://publishing.aip.org/resources/librarians/products/journals

Regular rotating black holes and the weak energy condition

We revisit here a recent work on regular rotating black holes. We introduce a new mass function generalizing the commonly used Bardeen and Hayward mass functions and extend the recently proposed solutions in order to accommodate a cosmological constant $\Lambda$. We discuss some aspects of the causal structure (horizons) and the ergospheres of the new proposed solutions. We also show that, in contrast with the spherically symmetrical case, the black hole rotation will unavoidably lead to the violation of the weak energy condition for any physically reasonable choice of the mass function, reinforcing the idea the description of the interior region of a Kerr black hole is much more challenging than in the Schwarzschild case.Comment: 8 pages, 3 figure

Vertical stability of circular orbits in relativistic razor-thin disks

During the last few decades, there has been a growing interest in exact solutions of Einstein equations describing razor-thin disks. Despite the progress in the area, the analytical study of geodesic motion crossing the disk plane in these systems is not yet so developed. In the present work, we propose a definite vertical stability criterion for circular equatorial timelike geodesics in static, axially symmetric thin disks, possibly surrounded by other structures preserving axial symmetry. It turns out that the strong energy condition for the disk stress-energy content is sufficient for vertical stability of these orbits. Moreover, adiabatic invariance of the vertical action variable gives us an approximate third integral of motion for oblique orbits which deviate slightly from the equatorial plane. Such new approximate third integral certainly points to a better understanding of the analytical properties of these orbits. The results presented here, derived for static spacetimes, may be a starting point to study the motion around rotating, stationary razor-thin disks. Our results also allow us to conjecture that the strong energy condition should be sufficient to assure transversal stability of periodic orbits for any singular timelike hypersurface, provided it is invariant under the geodesic flow.Comment: 13 pages, 4 figures; Accepted for publication in Physical Review

The Axion and the Goldstone Higgs

We consider the renormalizable $SO(5)/SO(4)$ $\sigma$-model, in which the Higgs particle has a pseudo-Nambu-Goldstone boson character, and explore what the minimal field extension required to implement the Peccei-Quinn symmetry (PQ) is, within the partial compositeness scenario. It turns out that the minimal model does not require the enlargement of the exotic fermionic sector, but only the addition of a singlet scalar: it is sufficient that the exotic fermions involved in partial compositeness and the singlet scalar become charged under Peccei-Quinn transformations. We explore the phenomenological predictions for photonic signals in axion searches for all models discussed. Because of the constraints imposed on the exotic fermion sector by the Standard Model fermion masses, the expected range of allowed axion-photon couplings turns out to be generically narrowed with respect to that of standard invisible axion models, impacting the experimental quest.Comment: 31 pages, 2 Figures. Description improved, results unchange

Probing the Majorana neutrinos and their CP violation in decays of charged scalar mesons π,K,D,Ds,B,Bc\pi, K, D, D_s, B, B_c

Some of the outstanding questions of particle physics today concern the neutrino sector, in particular whether there are more neutrinos than those already known and whether they are Dirac or Majorana particles.There are different ways to explore these issues. In this article we describe neutrino-mediated decays of charged pseudoscalar mesons such as $\pi^{\pm}$, $K^{\pm}$ and $B^{\pm}$, in scenarios where extra neutrinos are heavy and can be on their mass shell. We discuss semileptonic and leptonic decays of such kinds. We investigate possible ways of using these decays in order to distinguish between the Dirac and Majorana character of neutrinos. Further, we argue that there are significant possibilities of detecting CP violation in such decays when there are at least two almost degenerate Majorana neutrinos involved. This latter type of scenario fits well into the known neutrino minimal standard model ($\nu$MSM) which could simultaneously explain the Dark Matter and Baryon Asymmetry of the Universe.Comment: v3: 37 pages, 14 figures; minor typographical errors corrected; published in Symmetr

On the renormalization of the electroweak chiral Lagrangian with a Higgs

We consider the scalar sector of the effective non-linear electroweak Lagrangian with a light "Higgs" particle, up to four derivatives in the chiral expansion. The complete off-shell renormalization procedure is implemented, including one loop corrections stemming from the leading two-derivative terms, for finite Higgs mass. This determines the complete set of independent chiral invariant scalar counterterms required for consistency; these include bosonic operators often disregarded. Furthermore, new counterterms involving the Higgs particle which are apparently chiral non-invariant are identified in the perturbative analysis. A novel general parametrization of the pseudoescalar field redefinitions is proposed, which reduces to the various usual ones for specific values of its parameter; the non-local field redefinitions reabsorbing all chiral non-invariant counterterms are then explicitly determined. The physical results translate into renormalization group equations which may be useful when comparing future Higgs data at different energies