Flat bands and PT-symmetry in quasi-one-dimensional lattices

We examine the effect of adding PT-symmetric gain and loss terms to quasi 1D lattices (ribbons) that possess flat bands. We focus on three representative cases: (a) The Lieb ribbon, (b) The kagome ribbon, and (c) The stub Ribbon. In general we find that the effect on the flat band depends strongly on the geometrical details of the lattice being examined. One interesting and novel result that emerge from an analytical calculation of the band structure of the Lieb ribbon including gain and loss, is that its flat band survives the addition of PT-symmetry for any amount of gain and loss, while for the other two lattices, any presence of gain and loss destroys the flat bands. For all three ribbons, there are finite stability windows whose size decreases with the strength of the gain and loss parameter. For the Lieb and kagome cases, the size of this window converges to a finite value. The existence of finite stability windows, plus the constancy of the Lieb flat band are in marked contrast to the behavior of a pure one-dimensional lattice.Comment: 5 pages, 5 figure

The nonlinear magnetoinductive dimer

We examine a nonlinear magnetoinductive dimer and compute its linear and nonlinear symmetric, antisymmetric and asymmetric modes in closed-form, in the rotating-wave approximation. A linear stability analysis of these modes reveals that the asymmetric mode is always stable, for any allowed value of the coupling parameter and for both, hard and soft nonlinearity. A numerical computation of the dimer dynamics reveals a magnetic energy selftrapping whose threshold increases for increasing dimer coupling.Comment: 4 double-column pages, 6 figures, submitte

Central Bank and Price Stability: Is a Single Objetive Enough?

Current developments in monetary theory, coupled with the recent practical experience of many and diverse central banks, suggest a number of basic tenets that could be regarded as effective guideposts in the search for successful practices that could contribute to attain and to sustain macroeconomic stabilization. While common sense, the myriad of accompanying circumstances within which policies and institutions develop, tend to confound their significance and to blur their basic meaning and implications. The purpose of this paper is to review and revisit, in the light of prevailing experience, the state of the art regarding monetary and central banking policies and analyze, by outlining these experiences in the form of seven basic principles, their significance for the achievement and the maintenance of macroeconomic stabilization. While each of these principles can be reviewed independently, they are, of course closely linked. The paper first scrutinizes the manner in which the literature has dealt with these issues and, in light of recent experiences, attempts to integrate them into an unified framework and to draw a number of policy lessons and theoretical implications.

From age-sets to friendship networks in contemporary sociology : The continuity of soda among the Boorana of East Africa

This paper re-assesses a comparative sociology of kinship and friendship in East Africa with a particular focus on the Boorana Oromo of Kenya. It argues that the study of kinship dominated the developments of a comparative sociology during colonial times and that the post-colonial influences of war, the market and globalization have increased the role of the individual. As a result a comparative sociology of African kinship needs to be understood in relation to comparative sociological studies of friendship in East Africa, particularly associated with the sociology of education.Publisher PDFPeer reviewe

Self trapping transition for a nonlinear impurity within a linear chain

In the present work we revisit the issue of the self-trapping dynamical transition at a nonlinear impurity embedded in an otherwise linear lattice. For our Schr\"odinger chain example, we present rigorous arguments that establish necessary conditions and corresponding parametric bounds for the transition between linear decay and nonlinear persistence of a defect mode. The proofs combine a contraction mapping approach applied in the fully dynamical problem in the case of a 3D-lattice, together with variational arguments for the derivation of parametric bounds for the creation of stationary states associated with the expected fate of the self-trapping dynamical transition. The results are relevant for both power law nonlinearities and saturable ones. The analytical results are corroborated by numerical computations.Comment: 16 pages, 7 figures. To be published in Journal of Mathematical Physic

Interface solitons in quadratically nonlinear photonic lattices

We study the properties of two-color nonlinear localized modes which may exist at the interfaces separating two different periodic photonic lattices in quadratic media, focussing on the impact of phase mismatch of the photonic lattices on the properties, stability, and threshold power requirements for the generation of interface localized modes. We employ both an effective discrete model and continuum model with periodic potential and find good qualitative agreement between both models. Dynamics excitation of interface modes shows that, a two-color interface twisted mode splits into two beams with different escaping angles and carrying different energies when entering a uniform medium from the quadratic photonic lattice. The output position and energy contents of each two-color interface solitons can be controlled by judicious tuning ofComment: 6 pages, 8 figure

Qualitative analysis of the dynamics of the time delayed Chua's circuit

IEEE TRANS. CIRCUITS SYST.

Localized vortex beams in anisotropic Lieb lattices

We address the issue of nonlinear modes in a two-dimensional waveguide array, spatially distributed in the Lieb lattice geometry, and modeled by a saturable nonlinear Schr\"odinger equation. In particular, we analyze the existence and stability of vortex-type solutions finding localized patterns with symmetric and asymmetric profiles, ranging from topological charge S=1 to S=3. By taking into account the presence of anisotropy, which is inherent to experimental realization of waveguide arrays, we identify different stability behaviors according to their topological charge. Our findings might give insight on experimental feasibility to observe these kind of vortex states.Comment: 13 pages, 5 figure

Strong asymmetry for surface modes in nonlinear lattices with long-range coupling

We analyze the formation of localized surface modes on a nonlinear cubic waveguide array in the presence of exponentially-decreasing long-range interactions. We find that the long-range coupling induces a strong asymmetry between the focusing and defocusing cases for the topology of the surface modes and also for the minimum power needed to generate them. In particular, for the defocusing case, there is an upper power threshold for exciting staggered modes, which depends strongly on the long-range coupling strength. The power threshold for dynamical excitation of surface modes increase (decrease) with the strength of long-range coupling for the focusing (defocusing) cases. These effects seem to be generic for discrete lattices with long-range interactions.Comment: 4 pages, 5 figures, submitted for publicatio